harden TempoMap::next_tempo_section () a bit.
[ardour.git] / libs / ardour / tempo.cc
index 3a938c54d450340b44c5b8fac32700689e35ca59..3865fe3e197ba05575a8885c8a26c5ac12333a86 100644 (file)
@@ -45,7 +45,19 @@ using Timecode::BBT_Time;
 /* _default tempo is 4/4 qtr=120 */
 
 Meter    TempoMap::_default_meter (4.0, 4.0);
-Tempo    TempoMap::_default_tempo (120.0);
+Tempo    TempoMap::_default_tempo (120.0, 4.0, 120.0);
+
+framepos_t
+MetricSection::frame_at_minute (const double& time) const
+{
+       return (framepos_t) floor ((time * 60.0 * _sample_rate) + 0.5);
+}
+
+double
+MetricSection::minute_at_frame (const framepos_t& frame) const
+{
+       return (frame / (double) _sample_rate) / 60.0;
+}
 
 /***********************************************************************/
 
@@ -59,7 +71,7 @@ Meter::frames_per_grid (const Tempo& tempo, framecnt_t sr) const
           The return value IS NOT interpretable in terms of "beats".
        */
 
-       return (60.0 * sr) / (tempo.beats_per_minute() * (_note_type/tempo.note_type()));
+       return (60.0 * sr) / (tempo.note_types_per_minute() * (_note_type / tempo.note_type()));
 }
 
 double
@@ -72,12 +84,13 @@ Meter::frames_per_bar (const Tempo& tempo, framecnt_t sr) const
 
 const string TempoSection::xml_state_node_name = "Tempo";
 
-TempoSection::TempoSection (const XMLNode& node)
-       : MetricSection (0.0, 0, MusicTime, true)
+TempoSection::TempoSection (const XMLNode& node, framecnt_t sample_rate)
+       : MetricSection (0.0, 0, MusicTime, true, sample_rate)
        , Tempo (TempoMap::default_tempo())
-       , _c_func (0.0)
+       , _c (0.0)
        , _active (true)
        , _locked_to_meter (false)
+       , _legacy_end (false)
 {
        XMLProperty const * prop;
        LocaleGuard lg;
@@ -110,19 +123,18 @@ TempoSection::TempoSection (const XMLNode& node)
        if ((prop = node.property ("frame")) != 0) {
                if (sscanf (prop->value().c_str(), "%" PRIu32, &frame) != 1) {
                        error << _("TempoSection XML node has an illegal \"frame\" value") << endmsg;
+                       throw failed_constructor();
                } else {
-                       set_frame (frame);
+                       set_minute (minute_at_frame (frame));
                }
        }
 
-       if ((prop = node.property ("beats-per-minute")) == 0) {
-               error << _("TempoSection XML node has no \"beats-per-minute\" property") << endmsg;
-               throw failed_constructor();
-       }
-
-       if (sscanf (prop->value().c_str(), "%lf", &_beats_per_minute) != 1 || _beats_per_minute < 0.0) {
-               error << _("TempoSection XML node has an illegal \"beats_per_minute\" value") << endmsg;
-               throw failed_constructor();
+       /* XX replace old beats-per-minute name with note-types-per-minute */
+       if ((prop = node.property ("beats-per-minute")) != 0) {
+               if (sscanf (prop->value().c_str(), "%lf", &_note_types_per_minute) != 1 || _note_types_per_minute < 0.0) {
+                       error << _("TempoSection XML node has an illegal \"beats-per-minute\" value") << endmsg;
+                       throw failed_constructor();
+               }
        }
 
        if ((prop = node.property ("note-type")) == 0) {
@@ -135,12 +147,33 @@ TempoSection::TempoSection (const XMLNode& node)
                }
        }
 
+       /* XX replace old end-beats-per-minute name with note-types-per-minute */
+       if ((prop = node.property ("end-beats-per-minute")) != 0) {
+               if (sscanf (prop->value().c_str(), "%lf", &_end_note_types_per_minute) != 1 || _end_note_types_per_minute < 0.0) {
+                       info << _("TempoSection XML node has an illegal \"in-beats-per-minute\" value") << endmsg;
+                       //throw failed_constructor();
+                       _end_note_types_per_minute = _note_types_per_minute;
+                       _legacy_end = true;
+               }
+       } else {
+               _legacy_end = true;
+       }
+
+       if ((prop = node.property ("tempo-type")) != 0) {
+               TempoSection::Type old_type;
+
+               old_type = Type (string_2_enum (prop->value(), old_type));
+               if (old_type == TempoSection::Constant) {
+                       _end_note_types_per_minute = _note_types_per_minute;
+               }
+       }
+
        if ((prop = node.property ("movable")) == 0) {
                error << _("TempoSection XML node has no \"movable\" property") << endmsg;
                throw failed_constructor();
        }
 
-       set_movable (string_is_affirmative (prop->value()));
+       set_initial (!string_is_affirmative (prop->value()));
 
        if ((prop = node.property ("active")) == 0) {
                warning << _("TempoSection XML node has no \"active\" property") << endmsg;
@@ -149,14 +182,8 @@ TempoSection::TempoSection (const XMLNode& node)
                set_active (string_is_affirmative (prop->value()));
        }
 
-       if ((prop = node.property ("tempo-type")) == 0) {
-               _type = Constant;
-       } else {
-               _type = Type (string_2_enum (prop->value(), _type));
-       }
-
        if ((prop = node.property ("lock-style")) == 0) {
-               if (movable()) {
+               if (!initial()) {
                        set_position_lock_style (MusicTime);
                } else {
                        set_position_lock_style (AudioTime);
@@ -166,10 +193,19 @@ TempoSection::TempoSection (const XMLNode& node)
        }
 
        if ((prop = node.property ("locked-to-meter")) == 0) {
-               set_locked_to_meter (false);
+               if (initial()) {
+                       set_locked_to_meter (true);
+               } else {
+                       set_locked_to_meter (false);
+               }
        } else {
                set_locked_to_meter (string_is_affirmative (prop->value()));
        }
+
+       /* 5.5 marked initial tempo as not locked to meter. this should always be true anyway */
+       if (initial()) {
+               set_locked_to_meter (true);
+       }
 }
 
 XMLNode&
@@ -183,108 +219,148 @@ TempoSection::get_state() const
        root->add_property ("pulse", buf);
        snprintf (buf, sizeof (buf), "%li", frame());
        root->add_property ("frame", buf);
-       snprintf (buf, sizeof (buf), "%lf", _beats_per_minute);
+       snprintf (buf, sizeof (buf), "%lf", _note_types_per_minute);
        root->add_property ("beats-per-minute", buf);
        snprintf (buf, sizeof (buf), "%lf", _note_type);
        root->add_property ("note-type", buf);
-       snprintf (buf, sizeof (buf), "%s", movable()?"yes":"no");
+       snprintf (buf, sizeof (buf), "%lf", _end_note_types_per_minute);
+       root->add_property ("end-beats-per-minute", buf);
+       snprintf (buf, sizeof (buf), "%s", !initial()?"yes":"no");
        root->add_property ("movable", buf);
        snprintf (buf, sizeof (buf), "%s", active()?"yes":"no");
        root->add_property ("active", buf);
-       root->add_property ("tempo-type", enum_2_string (_type));
        root->add_property ("lock-style", enum_2_string (position_lock_style()));
        root->add_property ("locked-to-meter", locked_to_meter()?"yes":"no");
 
        return *root;
 }
 
-void
-TempoSection::set_type (Type type)
+/** returns the Tempo at the session-relative minute.
+*/
+Tempo
+TempoSection::tempo_at_minute (const double& m) const
 {
-       _type = type;
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && m < minute());
+       if (constant) {
+               return Tempo (note_types_per_minute(), note_type());
+       }
+
+       return Tempo (_tempo_at_time (m - minute()), _note_type, _end_note_types_per_minute);
 }
 
-/** returns the tempo in whole pulses per minute at the zero-based (relative to session) frame.
+/** returns the session relative minute where the supplied tempo in note types per minute occurs.
+ *  @param ntpm the tempo in mote types per minute used to calculate the returned minute
+ *  @param p the pulse used to calculate the returned minute for constant tempi
+ *  @return the minute at the supplied tempo
+ *
+ *  note that the note_type is currently ignored in this function. see below.
+ *
+*/
+
+/** if tempoA (120, 4.0) precedes tempoB (120, 8.0),
+ *  there should be no ramp between the two even if we are ramped.
+ *  in other words a ramp should only place a curve on note_types_per_minute.
+ *  we should be able to use Tempo note type here, but the above
+ *  complicates things a bit.
 */
 double
-TempoSection::tempo_at_frame (const framepos_t& f, const framecnt_t& frame_rate) const
+TempoSection::minute_at_ntpm (const double& ntpm, const double& p) const
 {
-
-       if (_type == Constant || _c_func == 0.0) {
-               return pulses_per_minute();
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && p < pulse());
+       if (constant) {
+               return ((p - pulse()) / pulses_per_minute()) + minute();
        }
 
-       return pulse_tempo_at_time (frame_to_minute (f - frame(), frame_rate));
+       return _time_at_tempo (ntpm) + minute();
 }
 
-/** returns the zero-based frame (relative to session)
-   where the tempo in whole pulses per minute occurs in this section.
-   pulse p is only used for constant tempos.
-   note that the tempo map may have multiple such values.
-*/
-framepos_t
-TempoSection::frame_at_tempo (const double& ppm, const double& p, const framecnt_t& frame_rate) const
+/** returns the Tempo at the supplied whole-note pulse.
+ */
+Tempo
+TempoSection::tempo_at_pulse (const double& p) const
 {
-       if (_type == Constant || _c_func == 0.0) {
-               return ((p - pulse()) * frames_per_pulse (frame_rate))  + frame();
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && p < pulse());
+
+       if (constant) {
+               return Tempo (note_types_per_minute(), note_type());
        }
 
-       return minute_to_frame (time_at_pulse_tempo (ppm), frame_rate) + frame();
+       return Tempo (_tempo_at_pulse (p - pulse()), _note_type, _end_note_types_per_minute);
 }
-/** returns the tempo in pulses per minute at the zero-based (relative to session) beat.
+
+/** returns the whole-note pulse where a tempo in note types per minute occurs.
+ *  constant tempi require minute m.
+ *  @param ntpm the note types per minute value used to calculate the returned pulse
+ *  @param m the minute used to calculate the returned pulse if the tempo is constant
+ *  @return the whole-note pulse at the supplied tempo
+ *
+ *  note that note_type is currently ignored in this function. see minute_at_tempo().
+ *
+ *  for constant tempi, this is anaologous to pulse_at_minute().
 */
 double
-TempoSection::tempo_at_pulse (const double& p) const
+TempoSection::pulse_at_ntpm (const double& ntpm, const double& m) const
 {
-
-       if (_type == Constant || _c_func == 0.0) {
-               return pulses_per_minute();
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && m < minute());
+       if (constant) {
+               return ((m - minute()) * pulses_per_minute()) + pulse();
        }
-       double const ppm = pulse_tempo_at_pulse (p - pulse());
-       return ppm;
+
+       return _pulse_at_tempo (ntpm) + pulse();
 }
 
-/** returns the zero-based beat (relative to session)
-   where the tempo in whole pulses per minute occurs given frame f. frame f is only used for constant tempos.
-   note that the session tempo map may have multiple beats at a given tempo.
+/** returns the whole-note pulse at the supplied session-relative minute.
 */
 double
-TempoSection::pulse_at_tempo (const double& ppm, const framepos_t& f, const framecnt_t& frame_rate) const
+TempoSection::pulse_at_minute (const double& m) const
 {
-       if (_type == Constant || _c_func == 0.0) {
-               double const pulses = ((f - frame()) / frames_per_pulse (frame_rate)) + pulse();
-               return  pulses;
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && m < minute());
+       if (constant) {
+               return ((m - minute()) * pulses_per_minute()) + pulse();
        }
-       return pulse_at_pulse_tempo (ppm) + pulse();
+
+       return _pulse_at_time (m - minute()) + pulse();
 }
 
-/** returns the zero-based pulse (relative to session origin)
-   where the zero-based frame (relative to session)
-   lies.
+/** returns the session-relative minute at the supplied whole-note pulse.
 */
 double
-TempoSection::pulse_at_frame (const framepos_t& f, const framecnt_t& frame_rate) const
+TempoSection::minute_at_pulse (const double& p) const
 {
-       if (_type == Constant || _c_func == 0.0) {
-               return ((f - frame()) / frames_per_pulse (frame_rate)) + pulse();
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && p < pulse());
+       if (constant) {
+               return ((p - pulse()) / pulses_per_minute()) + minute();
        }
 
-       return pulse_at_time (frame_to_minute (f - frame(), frame_rate)) + pulse();
+       return _time_at_pulse (p - pulse()) + minute();
 }
 
-/** returns the zero-based frame (relative to session start frame)
-   where the zero-based pulse (relative to session start)
-   falls.
+/** returns thw whole-note pulse at session frame position f.
+ *  @param f the frame position.
+ *  @return the position in whole-note pulses corresponding to f
+ *
+ *  for use with musical units whose granularity is coarser than frames (e.g. ticks)
 */
+double
+TempoSection::pulse_at_frame (const framepos_t& f) const
+{
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && f < frame());
+       if (constant) {
+               return (minute_at_frame (f - frame()) * pulses_per_minute()) + pulse();
+       }
+
+       return _pulse_at_time (minute_at_frame (f - frame())) + pulse();
+}
 
 framepos_t
-TempoSection::frame_at_pulse (const double& p, const framecnt_t& frame_rate) const
+TempoSection::frame_at_pulse (const double& p) const
 {
-       if (_type == Constant || _c_func == 0.0) {
-               return (framepos_t) floor ((p - pulse()) * frames_per_pulse (frame_rate)) + frame();
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && p < pulse());
+       if (constant) {
+               return frame_at_minute (((p - pulse()) / pulses_per_minute()) + minute());
        }
 
-       return minute_to_frame (time_at_pulse (p - pulse()), frame_rate) + frame();
+       return frame_at_minute (_time_at_pulse (p - pulse()) + minute());
 }
 
 /*
@@ -362,98 +438,99 @@ https://www.zhdk.ch/fileadmin/data_subsites/data_icst/Downloads/Timegrid/ICST_Te
 
 */
 
-/*
-  compute this ramp's function constant using the end tempo (in whole pulses per minute)
-  and duration (pulses into global start) of some later tempo section.
+/** compute this ramp's function constant from some tempo-pulse point
+ * @param end_npm end tempo (in note types per minute)
+ * @param end_pulse duration (pulses into global start) of some other position.
+ * @return the calculated function constant
 */
 double
-TempoSection::compute_c_func_pulse (const double& end_bpm, const double& end_pulse, const framecnt_t& frame_rate)
-{
-       double const log_tempo_ratio = log (end_bpm / pulses_per_minute());
-       return pulses_per_minute() *  (expm1 (log_tempo_ratio)) / (end_pulse - pulse());
-}
-
-/* compute the function constant from some later tempo section, given tempo (whole pulses/min.) and distance (in frames) from session origin */
-double
-TempoSection::compute_c_func_frame (const double& end_bpm, const framepos_t& end_frame, const framecnt_t& frame_rate) const
+TempoSection::compute_c_pulse (const double& end_npm, const double& end_pulse) const
 {
-       return c_func (end_bpm, frame_to_minute (end_frame - frame(), frame_rate));
-}
+       if (note_types_per_minute() == end_npm || type() == Constant) {
+               return 0.0;
+       }
 
-framepos_t
-TempoSection::minute_to_frame (const double& time, const framecnt_t& frame_rate) const
-{
-       return (framepos_t) floor ((time * 60.0 * frame_rate) + 0.5);
+       double const log_tempo_ratio = log (end_npm / note_types_per_minute());
+       return (note_types_per_minute() * expm1 (log_tempo_ratio)) / ((end_pulse - pulse()) * _note_type);
 }
 
+/** compute the function constant from some tempo-time point.
+ * @param end_npm tempo (note types/min.)
+ * @param end_minute distance (in minutes) from session origin
+ * @return the calculated function constant
+*/
 double
-TempoSection::frame_to_minute (const framepos_t& frame, const framecnt_t& frame_rate) const
+TempoSection::compute_c_minute (const double& end_npm, const double& end_minute) const
 {
-       return (frame / (double) frame_rate) / 60.0;
+       if (note_types_per_minute() == end_npm || type() == Constant) {
+               return 0.0;
+       }
+
+       return c_func (end_npm, end_minute - minute());
 }
 
 /* position function */
 double
-TempoSection::a_func (double end_ppm, double c_func) const
+TempoSection::a_func (double end_npm, double c) const
 {
-       return log (end_ppm / pulses_per_minute()) /  c_func;
+       return log (end_npm / note_types_per_minute()) / c;
 }
 
 /*function constant*/
 double
-TempoSection::c_func (double end_ppm, double end_time) const
+TempoSection::c_func (double end_npm, double end_time) const
 {
-       return log (end_ppm / pulses_per_minute()) /  end_time;
+       return log (end_npm / note_types_per_minute()) / end_time;
 }
 
-/* tempo in ppm at time in minutes */
+/* tempo in note types per minute at time in minutes */
 double
-TempoSection::pulse_tempo_at_time (const double& time) const
+TempoSection::_tempo_at_time (const double& time) const
 {
-       return exp (_c_func * time) * pulses_per_minute();
+       return exp (_c * time) * note_types_per_minute();
 }
 
-/* time in minutes at tempo in ppm */
+/* time in minutes at tempo in note types per minute */
 double
-TempoSection::time_at_pulse_tempo (const double& pulse_tempo) const
+TempoSection::_time_at_tempo (const double& npm) const
 {
-       return log (pulse_tempo / pulses_per_minute()) / _c_func;
+       return log (npm / note_types_per_minute()) / _c;
 }
 
-/* tick at tempo in ppm */
+/* pulse at tempo in note types per minute */
 double
-TempoSection::pulse_at_pulse_tempo (const double& pulse_tempo) const
+TempoSection::_pulse_at_tempo (const double& npm) const
 {
-       return (pulse_tempo - pulses_per_minute()) / _c_func;
+       return ((npm - note_types_per_minute()) / _c) / _note_type;
 }
 
-/* tempo in ppm at tick */
+/* tempo in note types per minute at pulse */
 double
-TempoSection::pulse_tempo_at_pulse (const double& pulse) const
+TempoSection::_tempo_at_pulse (const double& pulse) const
 {
-       return (pulse * _c_func) + pulses_per_minute();
+       return (pulse * _note_type * _c) + note_types_per_minute();
 }
 
 /* pulse at time in minutes */
 double
-TempoSection::pulse_at_time (const double& time) const
+TempoSection::_pulse_at_time (const double& time) const
 {
-       return expm1 (_c_func * time) * (pulses_per_minute() / _c_func);
+       return (expm1 (_c * time) * (note_types_per_minute() / _c)) / _note_type;
 }
 
 /* time in minutes at pulse */
 double
-TempoSection::time_at_pulse (const double& pulse) const
+TempoSection::_time_at_pulse (const double& pulse) const
 {
-       return log1p ((_c_func * pulse) / pulses_per_minute()) / _c_func;
+       return log1p ((_c * pulse * _note_type) / note_types_per_minute()) / _c;
 }
 
 /***********************************************************************/
 
 const string MeterSection::xml_state_node_name = "Meter";
 
-MeterSection::MeterSection (const XMLNode& node)
-       : MetricSection (0.0, 0, MusicTime, false), Meter (TempoMap::default_meter())
+MeterSection::MeterSection (const XMLNode& node, const framecnt_t sample_rate)
+       : MetricSection (0.0, 0, MusicTime, false, sample_rate), Meter (TempoMap::default_meter())
 {
        XMLProperty const * prop;
        LocaleGuard lg;
@@ -507,8 +584,9 @@ MeterSection::MeterSection (const XMLNode& node)
        if ((prop = node.property ("frame")) != 0) {
                if (sscanf (prop->value().c_str(), "%li", &frame) != 1) {
                        error << _("MeterSection XML node has an illegal \"frame\" value") << endmsg;
+                       throw failed_constructor();
                } else {
-                       set_frame (frame);
+                       set_minute (minute_at_frame (frame));
                }
        }
 
@@ -539,11 +617,11 @@ MeterSection::MeterSection (const XMLNode& node)
                throw failed_constructor();
        }
 
-       set_movable (string_is_affirmative (prop->value()));
+       set_initial (!string_is_affirmative (prop->value()));
 
        if ((prop = node.property ("lock-style")) == 0) {
                warning << _("MeterSection XML node has no \"lock-style\" property") << endmsg;
-               if (movable()) {
+               if (!initial()) {
                        set_position_lock_style (MusicTime);
                } else {
                        set_position_lock_style (AudioTime);
@@ -576,7 +654,7 @@ MeterSection::get_state() const
        root->add_property ("lock-style", enum_2_string (position_lock_style()));
        snprintf (buf, sizeof (buf), "%lf", _divisions_per_bar);
        root->add_property ("divisions-per-bar", buf);
-       snprintf (buf, sizeof (buf), "%s", movable()?"yes":"no");
+       snprintf (buf, sizeof (buf), "%s", !initial()?"yes":"no");
        root->add_property ("movable", buf);
 
        return *root;
@@ -586,48 +664,38 @@ MeterSection::get_state() const
 /*
   Tempo Map Overview
 
-  The Shaggs - Things I Wonder
-  https://www.youtube.com/watch?v=9wQK6zMJOoQ
-
-  Tempo is the rate of the musical pulse.
-  Meters divide the pulses into measures and beats.
-
-  TempoSections - provide pulses in the form of beats_per_minute() and note_type() where note_type is the division of a whole pulse,
-  and beats_per_minute is the number of note_types in one minute (unlike what its name suggests).
-  Note that Tempo::beats_per_minute() has nothing to do with musical beats. It has been left that way because
-  a shorter one hasn't been found yet (pulse_divisions_per_minute()?).
+  Tempo determines the rate of musical pulse determined by its components
+        note types per minute - the rate per minute of the whole note divisor _note_type
+       note type             - the division of whole notes (pulses) which occur at the rate of note types per minute.
+  Meter divides the musical pulse into measures and beats according to its components
+        divisions_per_bar
+       note_divisor
 
-  MeterSecions - divide pulses into measures (via divisions_per_bar) and beats (via note_divisor).
+  TempoSection - translates between time, musical pulse and tempo.
+        has a musical location in whole notes (pulses).
+       has a time location in minutes.
+       Note that 'beats' in Tempo::note_types_per_minute() are in fact note types per minute.
+       (In the rest of tempo map,'beat' usually refers to accumulated BBT beats (pulse and meter based).
 
-  Both tempos and meters have a pulse position and a frame position.
-  Meters also have a beat position, which is always 0.0 for the first meter.
-  TempoSections and MeterSections may be locked to either audio or music (position lock style).
-  The lock style determines the 'true' position of the section wich is used to calculate the other postion parameters of the section.
+  MeterSection - translates between BBT, meter-based beat and musical pulse.
+        has a musical location in whole notes (pulses)
+       has a musical location in meter-based beats
+       has a musical location in BBT time
+       has a time location expressed in minutes.
 
-  The first tempo and first meter are special. they must move together, and must be locked to audio.
-  Audio locked tempos which lie before the first meter are made inactive.
-  They will be re-activated if the first meter is again placed before them.
+  TempoSection and MeterSection may be locked to either audio or music (position lock style).
+  The lock style determines the location type to be kept as a reference when location is recalculated.
 
-  With tepo sections potentially being ramped, meters provide a way of mapping beats to whole pulses without
-  referring to the tempo function(s) involved as the distance in whole pulses between a meter and a subsequent beat is
-  sb->beat() - meter->beat() / meter->note_divisor().
-  Because every meter falls on a known pulse, (derived from its bar), the rest is easy as the duration in pulses between
-  two meters is of course
-  (meater_b->bar - meter_a->bar) * meter_a->divisions_per_bar / meter_a->note_divisor.
+  The first tempo and meter are special. they must move together, and are locked to audio.
+  Audio locked tempi which lie before the first meter are made inactive.
 
-  Below, beat calculations are based on meter sections and all pulse and tempo calculations are based on tempo sections.
-  Beat to frame conversion of course requires the use of meter and tempo.
+  Recomputing the map is the process where the 'missing' location types are calculated.
+        We construct the tempo map by first using the locked location type of each section
+       to determine non-locked location types (pulse or minute position).
+        We then use this map to find the pulse or minute position of each meter (again depending on lock style).
 
-  Remembering that ramped tempo sections interact, it is important to avoid referring to any other tempos when moving tempo sections,
-  Here, beats (meters) are used to determine the new pulse (see predict_tempo_position())
-
-  Recomputing the map is the process where the 'missing' position
-  (tempo pulse or meter pulse & beat in the case of AudioTime, frame for MusicTime) is calculated.
-  We construct the tempo map by first using the frame or pulse position (depending on position lock style) of each tempo.
-  We then use this tempo map (really just the tempos) to find the pulse or frame position of each meter (again depending on lock style).
-
-  Having done this, we can now find any musical duration by selecting the tempo and meter covering the position (or tempo) in question
-  and querying its appropriate meter/tempo.
+  Having done this, we can now traverse the Metrics list by pulse or minute
+  to query its relevant meter/tempo.
 
   It is important to keep the _metrics in an order that makes sense.
   Because ramped MusicTime and AudioTime tempos can interact with each other,
@@ -637,7 +705,7 @@ MeterSection::get_state() const
   Music and Audio
 
   Music and audio-locked objects may seem interchangeable on the surface, but when translating
-  between audio samples and beats, keep in mind that a sample is only a quantised approximation
+  between audio samples and beat, remember that a sample is only a quantised approximation
   of the actual time (in minutes) of a beat.
   Thus if a gui user points to the frame occupying the start of a music-locked object on 1|3|0, it does not
   mean that this frame is the actual location in time of 1|3|0.
@@ -664,11 +732,14 @@ MeterSection::get_state() const
   beat_at_frame (frame_at_beat (beat)) != beat due to the time quantization of frame_at_beat().
 
   Doing the second one will result in a beat distance error of up to 0.5 audio samples.
-  So instead work in pulses and/or beats and only use beat position to caclulate frame position (e.g. after tempo change).
-  For audio-locked objects, use frame position to calculate beat position.
+  frames_between_quarter_notes () eliminats this effect when determining time duration
+  from Beats distance, or instead work in quarter-notes and/or beats and convert to frames last.
 
-  The above pointless example would then do:
-  beat_at_pulse (pulse_at_beat (beat)) to avoid rounding.
+  The above pointless example could instead do:
+  beat_at_quarter_note (quarter_note_at_beat (beat)) to avoid rounding.
+
+  The Shaggs - Things I Wonder
+  https://www.youtube.com/watch?v=9wQK6zMJOoQ
 
 */
 struct MetricSectionSorter {
@@ -688,11 +759,13 @@ TempoMap::TempoMap (framecnt_t fr)
        _frame_rate = fr;
        BBT_Time start (1, 1, 0);
 
-       TempoSection *t = new TempoSection (0.0, 0, _default_tempo.beats_per_minute(), _default_tempo.note_type(), TempoSection::Ramp, AudioTime);
-       MeterSection *m = new MeterSection (0.0, 0, 0.0, start, _default_meter.divisions_per_bar(), _default_meter.note_divisor(), AudioTime);
+       TempoSection *t = new TempoSection (0.0, 0.0, _default_tempo, AudioTime, fr);
+       MeterSection *m = new MeterSection (0.0, 0.0, 0.0, start, _default_meter.divisions_per_bar(), _default_meter.note_divisor(), AudioTime, fr);
+
+       t->set_initial (true);
+       t->set_locked_to_meter (true);
 
-       t->set_movable (false);
-       m->set_movable (false);
+       m->set_initial (true);
 
        /* note: frame time is correct (zero) for both of these */
 
@@ -701,6 +774,55 @@ TempoMap::TempoMap (framecnt_t fr)
 
 }
 
+TempoMap::TempoMap (TempoMap const & other)
+{
+       _frame_rate = other._frame_rate;
+       for (Metrics::const_iterator m = other._metrics.begin(); m != other._metrics.end(); ++m) {
+               TempoSection* ts = dynamic_cast<TempoSection*> (*m);
+               MeterSection* ms = dynamic_cast<MeterSection*> (*m);
+
+               if (ts) {
+                       TempoSection* new_section = new TempoSection (*ts);
+                       _metrics.push_back (new_section);
+               } else {
+                       MeterSection* new_section = new MeterSection (*ms);
+                       _metrics.push_back (new_section);
+               }
+       }
+}
+
+TempoMap&
+TempoMap::operator= (TempoMap const & other)
+{
+       if (&other != this) {
+               _frame_rate = other._frame_rate;
+
+               Metrics::const_iterator d = _metrics.begin();
+               while (d != _metrics.end()) {
+                       delete (*d);
+                       ++d;
+               }
+               _metrics.clear();
+
+               for (Metrics::const_iterator m = other._metrics.begin(); m != other._metrics.end(); ++m) {
+                       TempoSection* ts = dynamic_cast<TempoSection*> (*m);
+                       MeterSection* ms = dynamic_cast<MeterSection*> (*m);
+
+                       if (ts) {
+                               TempoSection* new_section = new TempoSection (*ts);
+                               _metrics.push_back (new_section);
+                       } else {
+                               MeterSection* new_section = new MeterSection (*ms);
+                               _metrics.push_back (new_section);
+                       }
+               }
+       }
+
+       PropertyChanged (PropertyChange());
+
+       return *this;
+}
+
 TempoMap::~TempoMap ()
 {
        Metrics::const_iterator d = _metrics.begin();
@@ -711,6 +833,18 @@ TempoMap::~TempoMap ()
        _metrics.clear();
 }
 
+framepos_t
+TempoMap::frame_at_minute (const double time) const
+{
+       return (framepos_t) floor ((time * 60.0 * _frame_rate) + 0.5);
+}
+
+double
+TempoMap::minute_at_frame (const framepos_t frame) const
+{
+       return (frame / (double) _frame_rate) / 60.0;
+}
+
 void
 TempoMap::remove_tempo (const TempoSection& tempo, bool complete_operation)
 {
@@ -738,7 +872,7 @@ TempoMap::remove_tempo_locked (const TempoSection& tempo)
        for (i = _metrics.begin(); i != _metrics.end(); ++i) {
                if (dynamic_cast<TempoSection*> (*i) != 0) {
                        if (tempo.frame() == (*i)->frame()) {
-                               if ((*i)->movable()) {
+                               if (!(*i)->initial()) {
                                        delete (*i);
                                        _metrics.erase (i);
                                        return true;
@@ -790,7 +924,7 @@ TempoMap::remove_meter_locked (const MeterSection& meter)
        for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
                if (dynamic_cast<MeterSection*> (*i) != 0) {
                        if (meter.frame() == (*i)->frame()) {
-                               if ((*i)->movable()) {
+                               if (!(*i)->initial()) {
                                        delete (*i);
                                        _metrics.erase (i);
                                        return true;
@@ -844,7 +978,7 @@ TempoMap::do_insert (MetricSection* section)
                        bool const ipm = insert_tempo->position_lock_style() == MusicTime;
                        if ((ipm && tempo->pulse() == insert_tempo->pulse()) || (!ipm && tempo->frame() == insert_tempo->frame())) {
 
-                               if (!tempo->movable()) {
+                               if (tempo->initial()) {
 
                                        /* can't (re)move this section, so overwrite
                                         * its data content (but not its properties as
@@ -853,10 +987,6 @@ TempoMap::do_insert (MetricSection* section)
 
                                        *(dynamic_cast<Tempo*>(*i)) = *(dynamic_cast<Tempo*>(insert_tempo));
                                        (*i)->set_position_lock_style (AudioTime);
-                                       TempoSection* t;
-                                       if ((t = dynamic_cast<TempoSection*>(*i)) != 0) {
-                                               t->set_type (insert_tempo->type());
-                                       }
                                        need_add = false;
                                } else {
                                        delete (*i);
@@ -873,7 +1003,7 @@ TempoMap::do_insert (MetricSection* section)
 
                        if ((ipm && meter->beat() == insert_meter->beat()) || (!ipm && meter->frame() == insert_meter->frame())) {
 
-                               if (!meter->movable()) {
+                               if (meter->initial()) {
 
                                        /* can't (re)move this section, so overwrite
                                         * its data content (but not its properties as
@@ -903,15 +1033,24 @@ TempoMap::do_insert (MetricSection* section)
                MeterSection* const insert_meter = dynamic_cast<MeterSection*> (section);
                TempoSection* const insert_tempo = dynamic_cast<TempoSection*> (section);
                Metrics::iterator i;
+
                if (insert_meter) {
+                       TempoSection* prev_t = 0;
+
                        for (i = _metrics.begin(); i != _metrics.end(); ++i) {
                                MeterSection* const meter = dynamic_cast<MeterSection*> (*i);
+                               bool const ipm = insert_meter->position_lock_style() == MusicTime;
 
                                if (meter) {
-                                       bool const ipm = insert_meter->position_lock_style() == MusicTime;
                                        if ((ipm && meter->beat() > insert_meter->beat()) || (!ipm && meter->frame() > insert_meter->frame())) {
                                                break;
                                        }
+                               } else {
+                                       if (prev_t && prev_t->locked_to_meter() && (!ipm && prev_t->frame() == insert_meter->frame())) {
+                                               break;
+                                       }
+
+                                       prev_t = dynamic_cast<TempoSection*> (*i);
                                }
                        }
                } else if (insert_tempo) {
@@ -920,7 +1059,9 @@ TempoMap::do_insert (MetricSection* section)
 
                                if (tempo) {
                                        bool const ipm = insert_tempo->position_lock_style() == MusicTime;
-                                       if ((ipm && tempo->pulse() > insert_tempo->pulse()) || (!ipm && tempo->frame() > insert_tempo->frame())) {
+                                       const bool lm = insert_tempo->locked_to_meter();
+                                       if ((ipm && tempo->pulse() > insert_tempo->pulse()) || (!ipm && tempo->frame() > insert_tempo->frame())
+                                           || (lm && tempo->pulse() > insert_tempo->pulse())) {
                                                break;
                                        }
                                }
@@ -928,19 +1069,42 @@ TempoMap::do_insert (MetricSection* section)
                }
 
                _metrics.insert (i, section);
-               //dump (_metrics, std::cout);
+               //dump (std::cout);
        }
 }
-
+/* user supplies the exact pulse if pls == MusicTime */
 TempoSection*
-TempoMap::add_tempo (const Tempo& tempo, const double& pulse, const framepos_t& frame, ARDOUR::TempoSection::Type type, PositionLockStyle pls)
+TempoMap::add_tempo (const Tempo& tempo, const double& pulse, const framepos_t& frame, PositionLockStyle pls)
 {
+       if (tempo.note_types_per_minute() <= 0.0) {
+               warning << "Cannot add tempo. note types per minute must be greater than zero." << endmsg;
+               return 0;
+       }
+
        TempoSection* ts = 0;
+       TempoSection* prev_tempo = 0;
        {
                Glib::Threads::RWLock::WriterLock lm (lock);
-               ts = add_tempo_locked (tempo, pulse, frame, type, pls, true);
-       }
+               ts = add_tempo_locked (tempo, pulse, minute_at_frame (frame), pls, true);
+               for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
 
+                       if ((*i)->is_tempo()) {
+                               TempoSection* const this_t = static_cast<TempoSection*> (*i);
+
+                               bool const ipm = ts->position_lock_style() == MusicTime;
+                               bool const lm = ts->locked_to_meter();
+                               if ((ipm && this_t->pulse() == ts->pulse()) || (!ipm && this_t->frame() == ts->frame())
+                                   || (lm && this_t->pulse() == ts->pulse())) {
+                                       if (prev_tempo && prev_tempo->type() == TempoSection::Ramp) {
+                                               prev_tempo->set_end_note_types_per_minute (ts->note_types_per_minute());
+                                       }
+                                       break;
+                               }
+                               prev_tempo = this_t;
+                       }
+               }
+               recompute_map (_metrics);
+       }
 
        PropertyChanged (PropertyChange ());
 
@@ -948,60 +1112,90 @@ TempoMap::add_tempo (const Tempo& tempo, const double& pulse, const framepos_t&
 }
 
 void
-TempoMap::replace_tempo (const TempoSection& ts, const Tempo& tempo, const double& pulse, const framepos_t& frame, TempoSection::Type type, PositionLockStyle pls)
+TempoMap::replace_tempo (TempoSection& ts, const Tempo& tempo, const double& pulse, const framepos_t& frame, PositionLockStyle pls)
 {
+       if (tempo.note_types_per_minute() <= 0.0) {
+               warning << "Cannot replace tempo. note types per minute must be greater than zero." << endmsg;
+               return;
+       }
+
        const bool locked_to_meter = ts.locked_to_meter();
+       TempoSection* new_ts = 0;
 
        {
                Glib::Threads::RWLock::WriterLock lm (lock);
                TempoSection& first (first_tempo());
-               if (ts.frame() != first.frame()) {
-                       remove_tempo_locked (ts);
-                       add_tempo_locked (tempo, pulse, frame, type, pls, true, locked_to_meter);
+               if (!ts.initial()) {
+                       if (locked_to_meter) {
+                               {
+                                       /* cannot move a meter-locked tempo section */
+                                       *static_cast<Tempo*>(&ts) = tempo;
+                                       recompute_map (_metrics);
+                               }
+                       } else {
+                               remove_tempo_locked (ts);
+                               new_ts = add_tempo_locked (tempo, pulse, minute_at_frame (frame), pls, true, locked_to_meter);
+
+                               if (new_ts && new_ts->type() == TempoSection::Constant) {
+                                       new_ts->set_end_note_types_per_minute (new_ts->note_types_per_minute());
+                               } else {
+                                       for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
+
+                                               if ((*i)->is_tempo()) {
+                                                       TempoSection* const this_t = static_cast<TempoSection*> (*i);
+
+                                                       bool const ipm = new_ts->position_lock_style() == MusicTime;
+                                                       bool const lm = new_ts->locked_to_meter();
+                                                       if ((ipm && this_t->pulse() > new_ts->pulse()) || (!ipm && this_t->frame() > new_ts->frame())
+                                                           || (lm && this_t->pulse() > new_ts->pulse())) {
+                                                               new_ts->set_end_note_types_per_minute (tempo.end_note_types_per_minute());
+
+                                                               break;
+                                                       }
+                                               }
+                                       }
+                               }
+                       }
+
                } else {
-                       first.set_type (type);
                        first.set_pulse (0.0);
-                       first.set_frame (frame);
+                       first.set_minute (minute_at_frame (frame));
                        first.set_position_lock_style (AudioTime);
+                       first.set_locked_to_meter (true);
                        {
                                /* cannot move the first tempo section */
                                *static_cast<Tempo*>(&first) = tempo;
-                               recompute_map (_metrics);
                        }
                }
+               recompute_map (_metrics);
        }
 
        PropertyChanged (PropertyChange ());
 }
 
 TempoSection*
-TempoMap::add_tempo_locked (const Tempo& tempo, double pulse, framepos_t frame
-                           , TempoSection::Type type, PositionLockStyle pls, bool recompute, bool locked_to_meter)
+TempoMap::add_tempo_locked (const Tempo& tempo, double pulse, double minute
+                           , PositionLockStyle pls, bool recompute, bool locked_to_meter)
 {
-       TempoSection* t = new TempoSection (pulse, frame, tempo.beats_per_minute(), tempo.note_type(), type, pls);
+       TempoSection* t = new TempoSection (pulse, minute, tempo, pls, _frame_rate);
        t->set_locked_to_meter (locked_to_meter);
-       bool solved = false;
 
        do_insert (t);
 
        if (recompute) {
                if (pls == AudioTime) {
-                       solved = solve_map_frame (_metrics, t, t->frame());
+                       solve_map_minute (_metrics, t, t->minute());
                } else {
-                       solved = solve_map_pulse (_metrics, t, t->pulse());
+                       solve_map_pulse (_metrics, t, t->pulse());
                }
                recompute_meters (_metrics);
        }
 
-       if (!solved && recompute) {
-               recompute_map (_metrics);
-       }
-
        return t;
 }
 
 MeterSection*
-TempoMap::add_meter (const Meter& meter, const double& beat, const Timecode::BBT_Time& where, const framepos_t& frame, PositionLockStyle pls)
+TempoMap::add_meter (const Meter& meter, const double& beat, const Timecode::BBT_Time& where, framepos_t frame, PositionLockStyle pls)
 {
        MeterSection* m = 0;
        {
@@ -1012,7 +1206,7 @@ TempoMap::add_meter (const Meter& meter, const double& beat, const Timecode::BBT
 
 #ifndef NDEBUG
        if (DEBUG_ENABLED(DEBUG::TempoMap)) {
-               dump (_metrics, std::cerr);
+               dump (std::cerr);
        }
 #endif
 
@@ -1021,13 +1215,13 @@ TempoMap::add_meter (const Meter& meter, const double& beat, const Timecode::BBT
 }
 
 void
-TempoMap::replace_meter (const MeterSection& ms, const Meter& meter, const BBT_Time& where, const framepos_t& frame, PositionLockStyle pls)
+TempoMap::replace_meter (const MeterSection& ms, const Meter& meter, const BBT_Time& where, framepos_t frame, PositionLockStyle pls)
 {
        {
                Glib::Threads::RWLock::WriterLock lm (lock);
                const double beat = beat_at_bbt_locked (_metrics, where);
 
-               if (ms.movable()) {
+               if (!ms.initial()) {
                        remove_meter_locked (ms);
                        add_meter_locked (meter, beat, where, frame, pls, true);
                } else {
@@ -1037,10 +1231,11 @@ TempoMap::replace_meter (const MeterSection& ms, const Meter& meter, const BBT_T
                        *static_cast<Meter*>(&first) = meter;
                        first.set_position_lock_style (AudioTime);
                        first.set_pulse (0.0);
-                       first.set_frame (frame);
+                       first.set_minute (minute_at_frame (frame));
                        pair<double, BBT_Time> beat = make_pair (0.0, BBT_Time (1, 1, 0));
                        first.set_beat (beat);
-                       first_t.set_frame (first.frame());
+                       first_t.set_minute (first.minute());
+                       first_t.set_locked_to_meter (true);
                        first_t.set_pulse (0.0);
                        first_t.set_position_lock_style (AudioTime);
                        recompute_map (_metrics);
@@ -1053,13 +1248,14 @@ TempoMap::replace_meter (const MeterSection& ms, const Meter& meter, const BBT_T
 MeterSection*
 TempoMap::add_meter_locked (const Meter& meter, double beat, const BBT_Time& where, framepos_t frame, PositionLockStyle pls, bool recompute)
 {
-       const MeterSection& prev_m = meter_section_at_frame_locked  (_metrics, frame - 1);
+       const MeterSection& prev_m = meter_section_at_minute_locked  (_metrics, minute_at_beat_locked (_metrics, beat) - minute_at_frame (1));
        const double pulse = ((where.bars - prev_m.bbt().bars) * (prev_m.divisions_per_bar() / prev_m.note_divisor())) + prev_m.pulse();
+       const double time_minutes = minute_at_pulse_locked (_metrics, pulse);
        TempoSection* mlt = 0;
 
        if (pls == AudioTime) {
                /* add meter-locked tempo */
-               mlt = add_tempo_locked (tempo_at_frame_locked (_metrics, frame), pulse,  frame, TempoSection::Ramp, AudioTime, true, true);
+               mlt = add_tempo_locked (tempo_at_minute_locked (_metrics, time_minutes), pulse, minute_at_frame (frame), AudioTime, true, true);
 
                if (!mlt) {
                        return 0;
@@ -1067,7 +1263,8 @@ TempoMap::add_meter_locked (const Meter& meter, double beat, const BBT_Time& whe
 
        }
 
-       MeterSection* new_meter = new MeterSection (pulse, frame, beat, where, meter.divisions_per_bar(), meter.note_divisor(), pls);
+       MeterSection* new_meter = new MeterSection (pulse, minute_at_frame (frame), beat, where, meter.divisions_per_bar(), meter.note_divisor(), pls, _frame_rate);
+
        bool solved = false;
 
        do_insert (new_meter);
@@ -1075,7 +1272,13 @@ TempoMap::add_meter_locked (const Meter& meter, double beat, const BBT_Time& whe
        if (recompute) {
 
                if (pls == AudioTime) {
-                       solved = solve_map_frame (_metrics, new_meter, frame);
+                       solved = solve_map_minute (_metrics, new_meter, minute_at_frame (frame));
+                       /* we failed, most likely due to some impossible frame requirement wrt audio-locked tempi.
+                          fudge frame so that the meter ends up at its BBT position instead.
+                       */
+                       if (!solved) {
+                               solved = solve_map_minute (_metrics, new_meter, minute_at_frame (prev_m.frame() + 1));
+                       }
                } else {
                        solved = solve_map_bbt (_metrics, new_meter, where);
                        /* required due to resetting the pulse of meter-locked tempi above.
@@ -1098,9 +1301,9 @@ TempoMap::add_meter_locked (const Meter& meter, double beat, const BBT_Time& whe
 }
 
 void
-TempoMap::change_initial_tempo (double beats_per_minute, double note_type)
+TempoMap::change_initial_tempo (double note_types_per_minute, double note_type, double end_note_types_per_minute)
 {
-       Tempo newtempo (beats_per_minute, note_type);
+       Tempo newtempo (note_types_per_minute, note_type, end_note_types_per_minute);
        TempoSection* t;
 
        for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
@@ -1120,9 +1323,9 @@ TempoMap::change_initial_tempo (double beats_per_minute, double note_type)
 }
 
 void
-TempoMap::change_existing_tempo_at (framepos_t where, double beats_per_minute, double note_type)
+TempoMap::change_existing_tempo_at (framepos_t where, double note_types_per_minute, double note_type, double end_ntpm)
 {
-       Tempo newtempo (beats_per_minute, note_type);
+       Tempo newtempo (note_types_per_minute, note_type, end_ntpm);
 
        TempoSection* prev;
        TempoSection* first;
@@ -1217,7 +1420,7 @@ TempoMap::first_tempo () const
                        if (!t->active()) {
                                continue;
                        }
-                       if (!t->movable()) {
+                       if (t->initial()) {
                                return *t;
                        }
                }
@@ -1238,7 +1441,7 @@ TempoMap::first_tempo ()
                        if (!t->active()) {
                                continue;
                        }
-                       if (!t->movable()) {
+                       if (t->initial()) {
                                return *t;
                        }
                }
@@ -1261,7 +1464,7 @@ TempoMap::recompute_tempi (Metrics& metrics)
                        if (!t->active()) {
                                continue;
                        }
-                       if (!t->movable()) {
+                       if (t->initial()) {
                                if (!prev_t) {
                                        t->set_pulse (0.0);
                                        prev_t = t;
@@ -1270,21 +1473,22 @@ TempoMap::recompute_tempi (Metrics& metrics)
                        }
                        if (prev_t) {
                                if (t->position_lock_style() == AudioTime) {
-                                       prev_t->set_c_func (prev_t->compute_c_func_frame (t->pulses_per_minute(), t->frame(), _frame_rate));
+                                       prev_t->set_c (prev_t->compute_c_minute (prev_t->end_note_types_per_minute(), t->minute()));
                                        if (!t->locked_to_meter()) {
-                                               t->set_pulse (prev_t->pulse_at_tempo (t->pulses_per_minute(), t->frame(), _frame_rate));
+                                               t->set_pulse (prev_t->pulse_at_ntpm (prev_t->end_note_types_per_minute(), t->minute()));
                                        }
 
                                } else {
-                                       prev_t->set_c_func (prev_t->compute_c_func_pulse (t->pulses_per_minute(), t->pulse(), _frame_rate));
-                                       t->set_frame (prev_t->frame_at_tempo (t->pulses_per_minute(), t->pulse(), _frame_rate));
+                                       prev_t->set_c (prev_t->compute_c_pulse (prev_t->end_note_types_per_minute(), t->pulse()));
+                                       t->set_minute (prev_t->minute_at_ntpm (prev_t->end_note_types_per_minute(), t->pulse()));
 
                                }
                        }
                        prev_t = t;
                }
        }
-       prev_t->set_c_func (0.0);
+       assert (prev_t);
+       prev_t->set_c (0.0);
 }
 
 /* tempos must be positioned correctly.
@@ -1309,7 +1513,7 @@ TempoMap::recompute_meters (Metrics& metrics)
                                        TempoSection* t;
                                        if ((*ii)->is_tempo()) {
                                                t = static_cast<TempoSection*> (*ii);
-                                               if ((t->locked_to_meter() || !t->movable()) && t->frame() == meter->frame()) {
+                                               if (t->locked_to_meter() && t->frame() == meter->frame()) {
                                                        meter_locked_tempo = t;
                                                        break;
                                                }
@@ -1317,14 +1521,16 @@ TempoMap::recompute_meters (Metrics& metrics)
                                }
 
                                if (prev_m) {
-                                       const double beats = (meter->bbt().bars - prev_m->bbt().bars) * prev_m->divisions_per_bar();
+                                       double beats = (meter->bbt().bars - prev_m->bbt().bars) * prev_m->divisions_per_bar();
                                        if (beats + prev_m->beat() != meter->beat()) {
                                                /* reordering caused a bbt change */
+
+                                               beats = meter->beat() - prev_m->beat();
                                                b_bbt = make_pair (beats + prev_m->beat()
                                                                   , BBT_Time ((beats / prev_m->divisions_per_bar()) + prev_m->bbt().bars, 1, 0));
                                                pulse = prev_m->pulse() + (beats / prev_m->note_divisor());
 
-                                       } else if (meter->movable()) {
+                                       } else if (!meter->initial()) {
                                                b_bbt = make_pair (meter->beat(), meter->bbt());
                                                pulse = prev_m->pulse() + (beats / prev_m->note_divisor());
                                        }
@@ -1359,7 +1565,7 @@ TempoMap::recompute_meters (Metrics& metrics)
 
                                meter->set_beat (b_bbt);
                                meter->set_pulse (pulse);
-                               meter->set_frame (frame_at_pulse_locked (metrics, pulse));
+                               meter->set_minute (minute_at_pulse_locked (metrics, pulse));
                        }
 
                        prev_m = meter;
@@ -1372,15 +1578,6 @@ TempoMap::recompute_map (Metrics& metrics, framepos_t end)
 {
        /* CALLER MUST HOLD WRITE LOCK */
 
-       if (end < 0) {
-
-               /* we will actually stop once we hit
-                  the last metric.
-               */
-               end = max_framepos;
-
-       }
-
        DEBUG_TRACE (DEBUG::TempoMath, string_compose ("recomputing tempo map, zero to %1\n", end));
 
        if (end == 0) {
@@ -1453,9 +1650,10 @@ TempoMap::metric_at (BBT_Time bbt) const
        return m;
 }
 
-/** Returns the beat duration corresponding to the supplied frame, possibly returning a negative value.
+/** Returns the BBT (meter-based) beat corresponding to the supplied frame, possibly returning a negative value.
  * @param frame The session frame position.
  * @return The beat duration according to the tempo map at the supplied frame.
+ *
  * If the supplied frame lies before the first meter, the returned beat duration will be negative.
  * The returned beat is obtained using the first meter and the continuation of the tempo curve (backwards).
  *
@@ -1465,20 +1663,21 @@ double
 TempoMap::beat_at_frame (const framecnt_t& frame) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       return beat_at_frame_locked (_metrics, frame);
+
+       return beat_at_minute_locked (_metrics, minute_at_frame (frame));
 }
 
 /* This function uses both tempo and meter.*/
 double
-TempoMap::beat_at_frame_locked (const Metrics& metrics, const framecnt_t& frame) const
+TempoMap::beat_at_minute_locked (const Metrics& metrics, const double& minute) const
 {
-       const TempoSection& ts = tempo_section_at_frame_locked (metrics, frame);
+       const TempoSection& ts = tempo_section_at_minute_locked (metrics, minute);
        MeterSection* prev_m = 0;
        MeterSection* next_m = 0;
 
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                if (!(*i)->is_tempo()) {
-                       if (prev_m && (*i)->frame() > frame) {
+                       if (prev_m && (*i)->minute() > minute) {
                                next_m = static_cast<MeterSection*> (*i);
                                break;
                        }
@@ -1486,7 +1685,7 @@ TempoMap::beat_at_frame_locked (const Metrics& metrics, const framecnt_t& frame)
                }
        }
 
-       const double beat = prev_m->beat() + (ts.pulse_at_frame (frame, _frame_rate) - prev_m->pulse()) * prev_m->note_divisor();
+       const double beat = prev_m->beat() + (ts.pulse_at_minute (minute) - prev_m->pulse()) * prev_m->note_divisor();
 
        /* audio locked meters fake their beat */
        if (next_m && next_m->beat() < beat) {
@@ -1496,16 +1695,23 @@ TempoMap::beat_at_frame_locked (const Metrics& metrics, const framecnt_t& frame)
        return beat;
 }
 
+/** Returns the frame corresponding to the supplied BBT (meter-based) beat.
+ * @param beat The BBT (meter-based) beat.
+ * @return The frame duration according to the tempo map at the supplied BBT (meter-based) beat.
+ *
+ * This function uses both tempo and meter.
+ */
 framepos_t
 TempoMap::frame_at_beat (const double& beat) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       return frame_at_beat_locked (_metrics, beat);
+
+       return frame_at_minute (minute_at_beat_locked (_metrics, beat));
 }
 
 /* meter & tempo section based */
-framepos_t
-TempoMap::frame_at_beat_locked (const Metrics& metrics, const double& beat) const
+double
+TempoMap::minute_at_beat_locked (const Metrics& metrics, const double& beat) const
 {
        MeterSection* prev_m = 0;
        TempoSection* prev_t = 0;
@@ -1521,12 +1727,18 @@ TempoMap::frame_at_beat_locked (const Metrics& metrics, const double& beat) cons
                        prev_m = m;
                }
        }
+       assert (prev_m);
 
        TempoSection* t;
 
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                if ((*i)->is_tempo()) {
                        t = static_cast<TempoSection*> (*i);
+
+                       if (!t->active()) {
+                               continue;
+                       }
+
                        if (prev_t && ((t->pulse() - prev_m->pulse()) * prev_m->note_divisor()) + prev_m->beat() > beat) {
                                break;
                        }
@@ -1534,44 +1746,46 @@ TempoMap::frame_at_beat_locked (const Metrics& metrics, const double& beat) cons
                }
 
        }
+       assert (prev_t);
 
-       return prev_t->frame_at_pulse (((beat - prev_m->beat()) / prev_m->note_divisor()) + prev_m->pulse(), _frame_rate);
+       return prev_t->minute_at_pulse (((beat - prev_m->beat()) / prev_m->note_divisor()) + prev_m->pulse());
 }
 
+/** Returns a Tempo corresponding to the supplied frame position.
+ * @param frame The audio frame.
+ * @return a Tempo according to the tempo map at the supplied frame.
+ *
+ */
 Tempo
 TempoMap::tempo_at_frame (const framepos_t& frame) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       return tempo_at_frame_locked (_metrics, frame);
+
+       return tempo_at_minute_locked (_metrics, minute_at_frame (frame));
 }
 
 Tempo
-TempoMap::tempo_at_frame_locked (const Metrics& metrics, const framepos_t& frame) const
+TempoMap::tempo_at_minute_locked (const Metrics& metrics, const double& minute) const
 {
        TempoSection* prev_t = 0;
 
        TempoSection* t;
 
-       for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
+       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                if ((*i)->is_tempo()) {
                        t = static_cast<TempoSection*> (*i);
                        if (!t->active()) {
                                continue;
                        }
-                       if ((prev_t) && t->frame() > frame) {
+                       if ((prev_t) && t->minute() > minute) {
                                /* t is the section past frame */
-                               const double ret_bpm = prev_t->tempo_at_frame (frame, _frame_rate) * 4.0;
-                               const Tempo ret_tempo (ret_bpm, prev_t->note_type());
-                               return ret_tempo;
+                               return prev_t->tempo_at_minute (minute);
                        }
                        prev_t = t;
                }
        }
 
-       const double ret = prev_t->beats_per_minute();
-       const Tempo ret_tempo (ret, prev_t->note_type ());
-
-       return ret_tempo;
+       return Tempo (prev_t->note_types_per_minute(), prev_t->note_type(), prev_t->end_note_types_per_minute());
 }
 
 /** returns the frame at which the supplied tempo occurs, or
@@ -1583,19 +1797,83 @@ framepos_t
 TempoMap::frame_at_tempo (const Tempo& tempo) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       return frame_at_tempo_locked (_metrics, tempo);
+
+       return frame_at_minute (minute_at_tempo_locked (_metrics, tempo));
 }
 
+double
+TempoMap::minute_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) const
+{
+       TempoSection* prev_t = 0;
+       const double tempo_bpm = tempo.note_types_per_minute();
 
-framepos_t
-TempoMap::frame_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) const
+       Metrics::const_iterator i;
+
+       for (i = metrics.begin(); i != metrics.end(); ++i) {
+               TempoSection* t;
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
+
+                       if (!t->active()) {
+                               continue;
+                       }
+
+
+
+                       if (t->note_types_per_minute() == tempo_bpm) {
+                               return t->minute();
+                       }
+
+                       if (prev_t) {
+                               const double prev_t_bpm = prev_t->note_types_per_minute();
+                               const double prev_t_end_bpm = prev_t->end_note_types_per_minute();
+                               if ((prev_t_bpm > tempo_bpm && prev_t_end_bpm < tempo_bpm)
+                                   || (prev_t_bpm < tempo_bpm && prev_t_end_bpm > tempo_bpm)
+                                   || (prev_t_end_bpm == tempo_bpm)) {
+
+                                       return prev_t->minute_at_ntpm (tempo_bpm, t->pulse());
+                               }
+                       }
+                       prev_t = t;
+               }
+       }
+
+       return prev_t->minute();
+}
+
+Tempo
+TempoMap::tempo_at_pulse_locked (const Metrics& metrics, const double& pulse) const
+{
+       TempoSection* prev_t = 0;
+
+       TempoSection* t;
+
+       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
+                       if (!t->active()) {
+                               continue;
+                       }
+                       if ((prev_t) && t->pulse() > pulse) {
+                               /* t is the section past frame */
+                               return prev_t->tempo_at_pulse (pulse);
+                       }
+                       prev_t = t;
+               }
+       }
+
+       return Tempo (prev_t->note_types_per_minute(), prev_t->note_type(), prev_t->end_note_types_per_minute());
+}
+
+double
+TempoMap::pulse_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) const
 {
        TempoSection* prev_t = 0;
-       const double tempo_ppm = tempo.beats_per_minute() / 4.0;
+       const double tempo_bpm = tempo.note_types_per_minute();
 
        Metrics::const_iterator i;
 
-       for (i = _metrics.begin(); i != _metrics.end(); ++i) {
+       for (i = metrics.begin(); i != metrics.end(); ++i) {
                TempoSection* t;
                if ((*i)->is_tempo()) {
                        t = static_cast<TempoSection*> (*i);
@@ -1604,47 +1882,60 @@ TempoMap::frame_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) con
                                continue;
                        }
 
-                       const double t_ppm = t->beats_per_minute() / 4.0;
+                       const double t_bpm = t->note_types_per_minute();
 
-                       if (t_ppm == tempo_ppm) {
-                               return t->frame();
+                       if (t_bpm == tempo_bpm) {
+                               return t->pulse();
                        }
 
                        if (prev_t) {
-                               const double prev_t_ppm = prev_t->beats_per_minute() / 4.0;
+                               const double prev_t_bpm = prev_t->note_types_per_minute();
 
-                               if ((t_ppm > tempo_ppm && prev_t_ppm < tempo_ppm) || (t_ppm < tempo_ppm && prev_t_ppm > tempo_ppm)) {
-                                       return prev_t->frame_at_tempo (tempo_ppm, prev_t->pulse(), _frame_rate);
+                               if ((t_bpm > tempo_bpm && prev_t_bpm < tempo_bpm) || (t_bpm < tempo_bpm && prev_t_bpm > tempo_bpm)) {
+                                       return prev_t->pulse_at_ntpm (prev_t->note_types_per_minute(), prev_t->minute());
                                }
                        }
                        prev_t = t;
                }
        }
 
-       return prev_t->frame();
+       return prev_t->pulse();
 }
 
-/** more precise than doing tempo_at_frame (frame_at_beat (b)),
- *  as there is no intermediate frame rounding.
+/** Returns a Tempo corresponding to the supplied position in quarter-note beats.
+ * @param qn the position in quarter note beats.
+ * @return the Tempo at the supplied quarter-note.
  */
 Tempo
-TempoMap::tempo_at_beat (const double& beat) const
+TempoMap::tempo_at_quarter_note (const double& qn) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       const MeterSection* prev_m = &meter_section_at_beat_locked (_metrics, beat);
-       const TempoSection* prev_t = &tempo_section_at_beat_locked (_metrics, beat);
-       const double note_type = prev_t->note_type();
 
-       return Tempo (prev_t->tempo_at_pulse (((beat - prev_m->beat()) / prev_m->note_divisor()) + prev_m->pulse()) * 4.0, note_type);
+       return tempo_at_pulse_locked (_metrics, qn / 4.0);
 }
 
+/** Returns the position in quarter-note beats corresponding to the supplied Tempo.
+ * @param tempo the tempo.
+ * @return the position in quarter-note beats where the map bpm
+ * is equal to that of the Tempo. currently ignores note_type.
+ */
 double
-TempoMap::pulse_at_beat (const double& beat) const
+TempoMap::quarter_note_at_tempo (const Tempo& tempo) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       return pulse_at_beat_locked (_metrics, beat);
+
+       return pulse_at_tempo_locked (_metrics, tempo) * 4.0;;
 }
 
+/** Returns the whole-note pulse corresponding to the supplied  BBT (meter-based) beat.
+ * @param metrics the list of metric sections used to calculate the pulse.
+ * @param beat The BBT (meter-based) beat.
+ * @return the whole-note pulse at the supplied BBT (meter-based) beat.
+ *
+ * a pulse or whole note is the base musical position of a MetricSection.
+ * it is equivalent to four quarter notes.
+ *
+ */
 double
 TempoMap::pulse_at_beat_locked (const Metrics& metrics, const double& beat) const
 {
@@ -1653,13 +1944,14 @@ TempoMap::pulse_at_beat_locked (const Metrics& metrics, const double& beat) cons
        return prev_m->pulse() + ((beat - prev_m->beat()) / prev_m->note_divisor());
 }
 
-double
-TempoMap::beat_at_pulse (const double& pulse) const
-{
-       Glib::Threads::RWLock::ReaderLock lm (lock);
-       return beat_at_pulse_locked (_metrics, pulse);
-}
-
+/** Returns the BBT (meter-based) beat corresponding to the supplied whole-note pulse .
+ * @param metrics the list of metric sections used to calculate the beat.
+ * @param pulse the whole-note pulse.
+ * @return the meter-based beat at the supplied whole-note pulse.
+ *
+ * a pulse or whole note is the base musical position of a MetricSection.
+ * it is equivalent to four quarter notes.
+ */
 double
 TempoMap::beat_at_pulse_locked (const Metrics& metrics, const double& pulse) const
 {
@@ -1670,28 +1962,20 @@ TempoMap::beat_at_pulse_locked (const Metrics& metrics, const double& pulse) con
                if (!(*i)->is_tempo()) {
                        m = static_cast<MeterSection*> (*i);
                        if (prev_m && m->pulse() > pulse) {
-                               if (((pulse - prev_m->pulse()) * prev_m->note_divisor()) + prev_m->beat() > m->beat()) {
-                                       break;
-                               }
+                               break;
                        }
                        prev_m = m;
                }
        }
+       assert (prev_m);
 
        double const ret = ((pulse - prev_m->pulse()) * prev_m->note_divisor()) + prev_m->beat();
        return ret;
 }
 
+/* tempo section based */
 double
-TempoMap::pulse_at_frame (const framepos_t& frame) const
-{
-       Glib::Threads::RWLock::ReaderLock lm (lock);
-       return pulse_at_frame_locked (_metrics, frame);
-}
-
-/* tempo section based */
-double
-TempoMap::pulse_at_frame_locked (const Metrics& metrics, const framepos_t& frame) const
+TempoMap::pulse_at_minute_locked (const Metrics& metrics, const double& minute) const
 {
        /* HOLD (at least) THE READER LOCK */
        TempoSection* prev_t = 0;
@@ -1703,9 +1987,9 @@ TempoMap::pulse_at_frame_locked (const Metrics& metrics, const framepos_t& frame
                        if (!t->active()) {
                                continue;
                        }
-                       if (prev_t && t->frame() > frame) {
+                       if (prev_t && t->minute() > minute) {
                                /*the previous ts is the one containing the frame */
-                               const double ret = prev_t->pulse_at_frame (frame, _frame_rate);
+                               const double ret = prev_t->pulse_at_minute (minute);
                                /* audio locked section in new meter*/
                                if (t->pulse() < ret) {
                                        return t->pulse();
@@ -1717,21 +2001,14 @@ TempoMap::pulse_at_frame_locked (const Metrics& metrics, const framepos_t& frame
        }
 
        /* treated as constant for this ts */
-       const double pulses_in_section = (frame - prev_t->frame()) / prev_t->frames_per_pulse (_frame_rate);
+       const double pulses_in_section = ((minute - prev_t->minute()) * prev_t->note_types_per_minute()) / prev_t->note_type();
 
        return pulses_in_section + prev_t->pulse();
 }
 
-framepos_t
-TempoMap::frame_at_pulse (const double& pulse) const
-{
-       Glib::Threads::RWLock::ReaderLock lm (lock);
-       return frame_at_pulse_locked (_metrics, pulse);
-}
-
 /* tempo section based */
-framepos_t
-TempoMap::frame_at_pulse_locked (const Metrics& metrics, const double& pulse) const
+double
+TempoMap::minute_at_pulse_locked (const Metrics& metrics, const double& pulse) const
 {
        /* HOLD THE READER LOCK */
 
@@ -1746,18 +2023,23 @@ TempoMap::frame_at_pulse_locked (const Metrics& metrics, const double& pulse) co
                                continue;
                        }
                        if (prev_t && t->pulse() > pulse) {
-                               return prev_t->frame_at_pulse (pulse, _frame_rate);
+                               return prev_t->minute_at_pulse (pulse);
                        }
 
                        prev_t = t;
                }
        }
        /* must be treated as constant, irrespective of _type */
-       double const dtime = (pulse - prev_t->pulse()) * prev_t->frames_per_pulse (_frame_rate);
+       double const dtime = ((pulse - prev_t->pulse()) * prev_t->note_type()) / prev_t->note_types_per_minute();
 
-       return (framecnt_t) floor (dtime) + prev_t->frame();
+       return dtime + prev_t->minute();
 }
 
+/** Returns the BBT (meter-based) beat corresponding to the supplied BBT time.
+ * @param bbt The BBT time (meter-based).
+ * @return bbt The BBT beat (meter-based) at the supplied BBT time.
+ *
+ */
 double
 TempoMap::beat_at_bbt (const Timecode::BBT_Time& bbt)
 {
@@ -1798,11 +2080,16 @@ TempoMap::beat_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time&
        return ret;
 }
 
+/** Returns the BBT time corresponding to the supplied BBT (meter-based) beat.
+ * @param beat The BBT (meter-based) beat.
+ * @return The BBT time (meter-based) at the supplied meter-based beat.
+ *
+ */
 Timecode::BBT_Time
-TempoMap::bbt_at_beat (const double& beats)
+TempoMap::bbt_at_beat (const double& beat)
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       return bbt_at_beat_locked (_metrics, beats);
+       return bbt_at_beat_locked (_metrics, beat);
 }
 
 Timecode::BBT_Time
@@ -1827,6 +2114,7 @@ TempoMap::bbt_at_beat_locked (const Metrics& metrics, const double& b) const
                        prev_m = m;
                }
        }
+       assert (prev_m);
 
        const double beats_in_ms = beats - prev_m->beat();
        const uint32_t bars_in_ms = (uint32_t) floor (beats_in_ms / prev_m->divisions_per_bar());
@@ -1857,24 +2145,32 @@ TempoMap::bbt_at_beat_locked (const Metrics& metrics, const double& b) const
        return ret;
 }
 
+/** Returns the quarter-note beat corresponding to the supplied BBT time (meter-based).
+ * @param bbt The BBT time (meter-based).
+ * @return the quarter note beat at the supplied BBT time
+ *
+ * quarter-notes ignore meter and are based on pulse (the musical unit of MetricSection).
+ *
+ * while the input uses meter, the output does not.
+ */
 double
-TempoMap::pulse_at_bbt (const Timecode::BBT_Time& bbt)
+TempoMap::quarter_note_at_bbt (const Timecode::BBT_Time& bbt)
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return pulse_at_bbt_locked (_metrics, bbt);
+       return pulse_at_bbt_locked (_metrics, bbt) * 4.0;
 }
 
 double
-TempoMap::pulse_at_bbt_rt (const Timecode::BBT_Time& bbt)
+TempoMap::quarter_note_at_bbt_rt (const Timecode::BBT_Time& bbt)
 {
-       Glib::Threads::RWLock::ReaderLock lm (lock);
+       Glib::Threads::RWLock::ReaderLock lm (lock, Glib::Threads::TRY_LOCK);
 
        if (!lm.locked()) {
-               throw std::logic_error ("TempoMap::pulse_at_bbt_rt() could not lock tempo map");
+               throw std::logic_error ("TempoMap::quarter_note_at_bbt_rt() could not lock tempo map");
        }
 
-       return pulse_at_bbt_locked (_metrics, bbt);
+       return pulse_at_bbt_locked (_metrics, bbt) * 4.0;
 }
 
 double
@@ -1908,14 +2204,30 @@ TempoMap::pulse_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time&
        return ret;
 }
 
+/** Returns the BBT time corresponding to the supplied quarter-note beat.
+ * @param qn the quarter-note beat.
+ * @return The BBT time (meter-based) at the supplied meter-based beat.
+ *
+ * quarter-notes ignore meter and are based on pulse (the musical unit of MetricSection).
+ *
+ */
 Timecode::BBT_Time
-TempoMap::bbt_at_pulse (const double& pulse)
+TempoMap::bbt_at_quarter_note (const double& qn)
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return bbt_at_pulse_locked (_metrics, pulse);
+       return bbt_at_pulse_locked (_metrics, qn / 4.0);
 }
 
+/** Returns the BBT time (meter-based) corresponding to the supplied whole-note pulse position.
+ * @param metrics The list of metric sections used to determine the result.
+ * @param pulse The whole-note pulse.
+ * @return The BBT time at the supplied whole-note pulse.
+ *
+ * a pulse or whole note is the basic musical position of a MetricSection.
+ * it is equivalent to four quarter notes.
+ * while the output uses meter, the input does not.
+ */
 Timecode::BBT_Time
 TempoMap::bbt_at_pulse_locked (const Metrics& metrics, const double& pulse) const
 {
@@ -1940,6 +2252,8 @@ TempoMap::bbt_at_pulse_locked (const Metrics& metrics, const double& pulse) cons
                }
        }
 
+       assert (prev_m);
+
        const double beats_in_ms = (pulse - prev_m->pulse()) * prev_m->note_divisor();
        const uint32_t bars_in_ms = (uint32_t) floor (beats_in_ms / prev_m->divisions_per_bar());
        const uint32_t total_bars = bars_in_ms + (prev_m->bbt().bars - 1);
@@ -1969,6 +2283,11 @@ TempoMap::bbt_at_pulse_locked (const Metrics& metrics, const double& pulse) cons
        return ret;
 }
 
+/** Returns the BBT time corresponding to the supplied frame position.
+ * @param frame the position in audio samples.
+ * @return the BBT time at the frame position .
+ *
+ */
 BBT_Time
 TempoMap::bbt_at_frame (framepos_t frame)
 {
@@ -1977,30 +2296,37 @@ TempoMap::bbt_at_frame (framepos_t frame)
                bbt.bars = 1;
                bbt.beats = 1;
                bbt.ticks = 0;
-               warning << string_compose (_("tempo map asked for BBT time at frame %1\n"), frame) << endmsg;
+#ifndef NDEBUG
+               warning << string_compose (_("tempo map was asked for BBT time at frame %1\n"), frame) << endmsg;
+#endif
                return bbt;
        }
+
+       const double minute =  minute_at_frame (frame);
+
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return bbt_at_frame_locked (_metrics, frame);
+       return bbt_at_minute_locked (_metrics, minute);
 }
 
 BBT_Time
 TempoMap::bbt_at_frame_rt (framepos_t frame)
 {
+       const double minute =  minute_at_frame (frame);
+
        Glib::Threads::RWLock::ReaderLock lm (lock, Glib::Threads::TRY_LOCK);
 
        if (!lm.locked()) {
                throw std::logic_error ("TempoMap::bbt_at_frame_rt() could not lock tempo map");
        }
 
-       return bbt_at_frame_locked (_metrics, frame);
+       return bbt_at_minute_locked (_metrics, minute);
 }
 
 Timecode::BBT_Time
-TempoMap::bbt_at_frame_locked (const Metrics& metrics, const framepos_t& frame) const
+TempoMap::bbt_at_minute_locked (const Metrics& metrics, const double& minute) const
 {
-       if (frame < 0) {
+       if (minute < 0) {
                BBT_Time bbt;
                bbt.bars = 1;
                bbt.beats = 1;
@@ -2008,7 +2334,7 @@ TempoMap::bbt_at_frame_locked (const Metrics& metrics, const framepos_t& frame)
                return bbt;
        }
 
-       const TempoSection& ts = tempo_section_at_frame_locked (metrics, frame);
+       const TempoSection& ts = tempo_section_at_minute_locked (metrics, minute);
        MeterSection* prev_m = 0;
        MeterSection* next_m = 0;
 
@@ -2017,7 +2343,7 @@ TempoMap::bbt_at_frame_locked (const Metrics& metrics, const framepos_t& frame)
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                if (!(*i)->is_tempo()) {
                        m = static_cast<MeterSection*> (*i);
-                       if (prev_m && m->frame() > frame) {
+                       if (prev_m && m->minute() > minute) {
                                next_m = m;
                                break;
                        }
@@ -2025,10 +2351,10 @@ TempoMap::bbt_at_frame_locked (const Metrics& metrics, const framepos_t& frame)
                }
        }
 
-       double beat = prev_m->beat() + (ts.pulse_at_frame (frame, _frame_rate) - prev_m->pulse()) * prev_m->note_divisor();
+       double beat = prev_m->beat() + (ts.pulse_at_minute (minute) - prev_m->pulse()) * prev_m->note_divisor();
 
        /* handle frame before first meter */
-       if (frame < prev_m->frame()) {
+       if (minute < prev_m->minute()) {
                beat = 0.0;
        }
        /* audio locked meters fake their beat */
@@ -2067,120 +2393,203 @@ TempoMap::bbt_at_frame_locked (const Metrics& metrics, const framepos_t& frame)
        return ret;
 }
 
+/** Returns the frame position corresponding to the supplied BBT time.
+ * @param bbt the position in BBT time.
+ * @return the frame position at bbt.
+ *
+ */
 framepos_t
 TempoMap::frame_at_bbt (const BBT_Time& bbt)
 {
        if (bbt.bars < 1) {
+#ifndef NDEBUG
                warning << string_compose (_("tempo map asked for frame time at bar < 1  (%1)\n"), bbt) << endmsg;
+#endif
                return 0;
        }
 
        if (bbt.beats < 1) {
                throw std::logic_error ("beats are counted from one");
        }
-       Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return frame_at_bbt_locked (_metrics, bbt);
+       double minute;
+       {
+               Glib::Threads::RWLock::ReaderLock lm (lock);
+               minute = minute_at_bbt_locked (_metrics, bbt);
+       }
+
+       return frame_at_minute (minute);
 }
 
 /* meter & tempo section based */
-framepos_t
-TempoMap::frame_at_bbt_locked (const Metrics& metrics, const BBT_Time& bbt) const
+double
+TempoMap::minute_at_bbt_locked (const Metrics& metrics, const BBT_Time& bbt) const
 {
        /* HOLD THE READER LOCK */
 
-       const framepos_t ret = frame_at_beat_locked (metrics, beat_at_bbt_locked (metrics, bbt));
+       const double ret = minute_at_beat_locked (metrics, beat_at_bbt_locked (metrics, bbt));
        return ret;
 }
 
 /**
- * Returns the distance from 0 in quarter pulses at the supplied frame.
+ * Returns the quarter-note beat position corresponding to the supplied frame.
  *
- * Plugin APIs don't count ticks in the same way PROGRAM_NAME does.
- * We use ticks per beat whereas the rest of the world uses ticks per quarter note.
- * This is more or less the VST's ppqPos (a scalar you use to obtain tick position
- * in whatever ppqn you're using).
+ * @param frame the position in frames.
+ * @return The quarter-note position of the supplied frame. Ignores meter.
  *
- * @param frame The distance in frames relative to session 0 whose quarter note distance you would like.
- * @return The quarter note (quarter pulse) distance from session 0 to the supplied frame. Ignores meter.
 */
-
 double
-TempoMap::quarter_note_at_frame (const framepos_t frame)
+TempoMap::quarter_note_at_frame (const framepos_t frame) const
 {
-       Glib::Threads::RWLock::ReaderLock lm (lock, Glib::Threads::TRY_LOCK);
+       const double minute =  minute_at_frame (frame);
 
-       const double ret = quarter_note_at_frame_locked (_metrics, frame);
+       Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return ret;
+       return pulse_at_minute_locked (_metrics, minute) * 4.0;
 }
 
 double
-TempoMap::quarter_note_at_frame_locked (const Metrics& metrics, const framepos_t frame) const
+TempoMap::quarter_note_at_frame_rt (const framepos_t frame) const
 {
-       const double ret = pulse_at_frame_locked (metrics, frame) * 4.0;
-
-       return ret;
-}
+       const double minute =  minute_at_frame (frame);
 
-double
-TempoMap::quarter_note_at_frame_rt (const framepos_t frame)
-{
        Glib::Threads::RWLock::ReaderLock lm (lock, Glib::Threads::TRY_LOCK);
 
        if (!lm.locked()) {
                throw std::logic_error ("TempoMap::quarter_note_at_frame_rt() could not lock tempo map");
        }
 
-       const double ret = pulse_at_frame_locked (_metrics, frame) * 4.0;
-
-       return ret;
+       return pulse_at_minute_locked (_metrics, minute) * 4.0;
 }
 
+/**
+ * Returns the frame position corresponding to the supplied quarter-note beat.
+ *
+ * @param quarter_note the quarter-note position.
+ * @return the frame position of the supplied quarter-note. Ignores meter.
+ *
+ *
+*/
 framepos_t
-TempoMap::frame_at_quarter_note (const double quarter_note)
+TempoMap::frame_at_quarter_note (const double quarter_note) const
 {
-       Glib::Threads::RWLock::ReaderLock lm (lock, Glib::Threads::TRY_LOCK);
+       double minute;
+       {
+               Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       const framepos_t ret = frame_at_quarter_note_locked (_metrics, quarter_note);
+               minute = minute_at_pulse_locked (_metrics, quarter_note / 4.0);
+       }
 
-       return ret;
+       return frame_at_minute (minute);
 }
 
-framepos_t
-TempoMap::frame_at_quarter_note_locked (const Metrics& metrics, const double quarter_note) const
+/** Returns the quarter-note beats corresponding to the supplied BBT (meter-based) beat.
+ * @param beat The BBT (meter-based) beat.
+ * @return The quarter-note position of the supplied BBT (meter-based) beat.
+ *
+ * a quarter-note may be compared with and assigned to Evoral::Beats.
+ *
+ */
+double
+TempoMap::quarter_note_at_beat (const double beat) const
 {
-       const framepos_t ret = frame_at_pulse_locked (metrics, quarter_note / 4.0);
+       Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return ret;
+       return pulse_at_beat_locked (_metrics, beat) * 4.0;
 }
 
+/** Returns the BBT (meter-based) beat position corresponding to the supplied quarter-note beats.
+ * @param quarter_note The position in quarter-note beats.
+ * @return the BBT (meter-based) beat position of the supplied quarter-note beats.
+ *
+ * a quarter-note is the musical unit of Evoral::Beats.
+ *
+ */
 double
-TempoMap::quarter_note_at_beat (const double beat)
+TempoMap::beat_at_quarter_note (const double quarter_note) const
 {
-       Glib::Threads::RWLock::ReaderLock lm (lock, Glib::Threads::TRY_LOCK);
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       return beat_at_pulse_locked (_metrics, quarter_note / 4.0);
+}
 
-       const double ret = quarter_note_at_beat_locked (_metrics, beat);
+/** Returns the duration in frames between two supplied quarter-note beat positions.
+ * @param start the first position in quarter-note beats.
+ * @param end the end position in quarter-note beats.
+ * @return the frame distance ober the quarter-note beats duration.
+ *
+ * use this rather than e.g.
+ * frame_at-quarter_note (end_beats) - frame_at_quarter_note (start_beats).
+ * frames_between_quarter_notes() doesn't round to audio frames as an intermediate step,
+ *
+ */
+framecnt_t
+TempoMap::frames_between_quarter_notes (const double start, const double end) const
+{
+       double minutes;
 
-       return ret;
+       {
+               Glib::Threads::RWLock::ReaderLock lm (lock);
+               minutes = minutes_between_quarter_notes_locked (_metrics, start, end);
+       }
+
+       return frame_at_minute (minutes);
 }
 
 double
-TempoMap::quarter_note_at_beat_locked (const Metrics& metrics, const double beat) const
+TempoMap::minutes_between_quarter_notes_locked (const Metrics& metrics, const double start, const double end) const
 {
-       const double ret = pulse_at_beat_locked (metrics, beat) * 4.0;
 
-       return ret;
+       return minute_at_pulse_locked (metrics, end / 4.0) - minute_at_pulse_locked (metrics, start / 4.0);
 }
 
 double
-TempoMap::beat_at_quarter_note (const double quarter_note)
+TempoMap::quarter_notes_between_frames (const framecnt_t start, const framecnt_t end) const
 {
-       Glib::Threads::RWLock::ReaderLock lm (lock, Glib::Threads::TRY_LOCK);
+       Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       const double ret = beat_at_pulse_locked (_metrics, quarter_note / 4.0);
+       return quarter_notes_between_frames_locked (_metrics, start, end);
+}
 
-       return ret;
+double
+TempoMap::quarter_notes_between_frames_locked (const Metrics& metrics, const framecnt_t start, const framecnt_t end) const
+{
+       const TempoSection* prev_t = 0;
+
+       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
+               TempoSection* t;
+
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
+                       if (!t->active()) {
+                               continue;
+                       }
+                       if (prev_t && t->frame() > start) {
+                               break;
+                       }
+                       prev_t = t;
+               }
+       }
+       assert (prev_t);
+       const double start_qn = prev_t->pulse_at_frame (start);
+
+       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
+               TempoSection* t;
+
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
+                       if (!t->active()) {
+                               continue;
+                       }
+                       if (prev_t && t->frame() > end) {
+                               break;
+                       }
+                       prev_t = t;
+               }
+       }
+       const double end_qn = prev_t->pulse_at_frame (end);
+
+       return (end_qn - start_qn) * 4.0;
 }
 
 bool
@@ -2199,12 +2608,12 @@ TempoMap::check_solved (const Metrics& metrics) const
                        }
                        if (prev_t) {
                                /* check ordering */
-                               if ((t->frame() <= prev_t->frame()) || (t->pulse() <= prev_t->pulse())) {
+                               if ((t->minute() <= prev_t->minute()) || (t->pulse() <= prev_t->pulse())) {
                                        return false;
                                }
 
                                /* precision check ensures tempo and frames align.*/
-                               if (t->frame() != prev_t->frame_at_tempo (t->pulses_per_minute(), t->pulse(), _frame_rate)) {
+                               if (t->frame() != frame_at_minute (prev_t->minute_at_ntpm (prev_t->end_note_types_per_minute(), t->pulse()))) {
                                        if (!t->locked_to_meter()) {
                                                return false;
                                        }
@@ -2213,8 +2622,8 @@ TempoMap::check_solved (const Metrics& metrics) const
                                /* gradient limit - who knows what it should be?
                                   things are also ok (if a little chaotic) without this
                                */
-                               if (fabs (prev_t->c_func()) > 1000.0) {
-                                       //std::cout << "c : " << prev_t->c_func() << std::endl;
+                               if (fabs (prev_t->c()) > 1000.0) {
+                                       //std::cout << "c : " << prev_t->c() << std::endl;
                                        return false;
                                }
                        }
@@ -2224,18 +2633,11 @@ TempoMap::check_solved (const Metrics& metrics) const
                if (!(*i)->is_tempo()) {
                        m = static_cast<MeterSection*> (*i);
                        if (prev_m && m->position_lock_style() == AudioTime) {
-                               const TempoSection* t = &tempo_section_at_frame_locked (metrics, m->frame() - 1);
-                               const framepos_t nascent_m_frame = t->frame_at_pulse (m->pulse(), _frame_rate);
+                               const TempoSection* t = &tempo_section_at_minute_locked (metrics, minute_at_frame (m->frame() - 1));
+                               const framepos_t nascent_m_frame = frame_at_minute (t->minute_at_pulse (m->pulse()));
                                /* Here we check that a preceding section of music doesn't overlap a subsequent one.
-                                  It is complicated by the fact that audio locked meters represent a discontinuity in the pulse
-                                  (they place an exact pulse at a particular time expressed only in frames).
-                                  This has the effect of shifting the calculated frame at the meter pulse (wrt the previous section of music)
-                                  away from its actual frame (which is now the frame location of the exact pulse).
-                                  This can result in the calculated frame (from the previous musical section)
-                                  differing from the exact frame by one sample.
-                                  Allow for that.
                                */
-                               if (t && (nascent_m_frame > m->frame() + 1 || nascent_m_frame < 0)) {
+                               if (t && (nascent_m_frame > m->frame() || nascent_m_frame < 0)) {
                                        return false;
                                }
                        }
@@ -2249,23 +2651,23 @@ TempoMap::check_solved (const Metrics& metrics) const
 }
 
 bool
-TempoMap::set_active_tempos (const Metrics& metrics, const framepos_t& frame)
+TempoMap::set_active_tempi (const Metrics& metrics, const framepos_t& frame)
 {
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                TempoSection* t;
                if ((*i)->is_tempo()) {
                        t = static_cast<TempoSection*> (*i);
-                       if (!t->movable()) {
+                       if (t->locked_to_meter()) {
                                t->set_active (true);
-                               continue;
-                       }
-                       if (t->movable() && t->active () && t->position_lock_style() == AudioTime && t->frame() < frame) {
-                               t->set_active (false);
-                               t->set_pulse (0.0);
-                       } else if (t->movable() && t->position_lock_style() == AudioTime && t->frame() > frame) {
-                               t->set_active (true);
-                       } else if (t->movable() && t->position_lock_style() == AudioTime && t->frame() == frame) {
-                               return false;
+                       } else if (t->position_lock_style() == AudioTime) {
+                               if (t->frame() < frame) {
+                                       t->set_active (false);
+                                       t->set_pulse (-1.0);
+                               } else if (t->frame() > frame) {
+                                       t->set_active (true);
+                               } else if (t->frame() == frame) {
+                                       return false;
+                               }
                        }
                }
        }
@@ -2273,29 +2675,30 @@ TempoMap::set_active_tempos (const Metrics& metrics, const framepos_t& frame)
 }
 
 bool
-TempoMap::solve_map_frame (Metrics& imaginary, TempoSection* section, const framepos_t& frame)
+TempoMap::solve_map_minute (Metrics& imaginary, TempoSection* section, const double& minute)
 {
        TempoSection* prev_t = 0;
        TempoSection* section_prev = 0;
-       framepos_t first_m_frame = 0;
+       double first_m_minute = 0.0;
+       const bool sml = section->locked_to_meter();
 
        /* can't move a tempo before the first meter */
        for (Metrics::iterator i = imaginary.begin(); i != imaginary.end(); ++i) {
                MeterSection* m;
                if (!(*i)->is_tempo()) {
                        m = static_cast<MeterSection*> (*i);
-                       if (!m->movable()) {
-                               first_m_frame = m->frame();
+                       if (m->initial()) {
+                               first_m_minute = m->minute();
                                break;
                        }
                }
        }
-       if (section->movable() && frame <= first_m_frame) {
+       if (!section->initial() && minute <= first_m_minute) {
                return false;
        }
 
        section->set_active (true);
-       section->set_frame (frame);
+       section->set_minute (minute);
 
        for (Metrics::iterator i = imaginary.begin(); i != imaginary.end(); ++i) {
                TempoSection* t;
@@ -2305,21 +2708,36 @@ TempoMap::solve_map_frame (Metrics& imaginary, TempoSection* section, const fram
                        if (!t->active()) {
                                continue;
                        }
+
                        if (prev_t) {
+
                                if (t == section) {
+                                       continue;
+                               }
+
+                               if (t->frame() == frame_at_minute (minute)) {
+                                       return false;
+                               }
+
+                               const bool tlm = t->position_lock_style() == MusicTime;
+
+                               if (prev_t && !section_prev && ((sml && tlm && t->pulse() > section->pulse()) || (!tlm && t->minute() > minute))) {
                                        section_prev = prev_t;
-                                       if (t->locked_to_meter()) {
-                                               prev_t = t;
+
+                                       section_prev->set_c (section_prev->compute_c_minute (section_prev->end_note_types_per_minute(), minute));
+                                       if (!section->locked_to_meter()) {
+                                               section->set_pulse (section_prev->pulse_at_ntpm (section_prev->end_note_types_per_minute(), minute));
                                        }
-                                       continue;
+                                       prev_t = section;
                                }
+
                                if (t->position_lock_style() == MusicTime) {
-                                       prev_t->set_c_func (prev_t->compute_c_func_pulse (t->pulses_per_minute(), t->pulse(), _frame_rate));
-                                       t->set_frame (prev_t->frame_at_pulse (t->pulse(), _frame_rate));
+                                       prev_t->set_c (prev_t->compute_c_pulse (prev_t->end_note_types_per_minute(), t->pulse()));
+                                       t->set_minute (prev_t->minute_at_ntpm (prev_t->end_note_types_per_minute(), t->pulse()));
                                } else {
-                                       prev_t->set_c_func (prev_t->compute_c_func_frame (t->pulses_per_minute(), t->frame(), _frame_rate));
+                                       prev_t->set_c (prev_t->compute_c_minute (prev_t->end_note_types_per_minute(), t->minute()));
                                        if (!t->locked_to_meter()) {
-                                               t->set_pulse (prev_t->pulse_at_frame (t->frame(), _frame_rate));
+                                               t->set_pulse (prev_t->pulse_at_ntpm (prev_t->end_note_types_per_minute(), t->minute()));
                                        }
                                }
                        }
@@ -2327,13 +2745,6 @@ TempoMap::solve_map_frame (Metrics& imaginary, TempoSection* section, const fram
                }
        }
 
-       if (section_prev) {
-               section_prev->set_c_func (section_prev->compute_c_func_frame (section->pulses_per_minute(), frame, _frame_rate));
-               if (!section->locked_to_meter()) {
-                       section->set_pulse (section_prev->pulse_at_frame (frame, _frame_rate));
-               }
-       }
-
 #if (0)
        recompute_tempi (imaginary);
 
@@ -2371,7 +2782,7 @@ TempoMap::solve_map_pulse (Metrics& imaginary, TempoSection* section, const doub
                        if (!t->active()) {
                                continue;
                        }
-                       if (!t->movable()) {
+                       if (t->initial()) {
                                t->set_pulse (0.0);
                                prev_t = t;
                                continue;
@@ -2381,13 +2792,14 @@ TempoMap::solve_map_pulse (Metrics& imaginary, TempoSection* section, const doub
                                        section_prev = prev_t;
                                        continue;
                                }
+
                                if (t->position_lock_style() == MusicTime) {
-                                       prev_t->set_c_func (prev_t->compute_c_func_pulse (t->pulses_per_minute(), t->pulse(), _frame_rate));
-                                       t->set_frame (prev_t->frame_at_pulse (t->pulse(), _frame_rate));
+                                       prev_t->set_c (prev_t->compute_c_pulse (prev_t->end_note_types_per_minute(), t->pulse()));
+                                       t->set_minute (prev_t->minute_at_ntpm (prev_t->end_note_types_per_minute(), t->pulse()));
                                } else {
-                                       prev_t->set_c_func (prev_t->compute_c_func_frame (t->pulses_per_minute(), t->frame(), _frame_rate));
+                                       prev_t->set_c (prev_t->compute_c_minute (prev_t->end_note_types_per_minute(), t->minute()));
                                        if (!t->locked_to_meter()) {
-                                               t->set_pulse (prev_t->pulse_at_frame (t->frame(), _frame_rate));
+                                               t->set_pulse (prev_t->pulse_at_ntpm (prev_t->end_note_types_per_minute(), t->minute()));
                                        }
                                }
                        }
@@ -2396,8 +2808,8 @@ TempoMap::solve_map_pulse (Metrics& imaginary, TempoSection* section, const doub
        }
 
        if (section_prev) {
-               section_prev->set_c_func (section_prev->compute_c_func_pulse (section->pulses_per_minute(), pulse, _frame_rate));
-               section->set_frame (section_prev->frame_at_pulse (pulse, _frame_rate));
+               section_prev->set_c (section_prev->compute_c_pulse (section_prev->end_note_types_per_minute(), pulse));
+               section->set_minute (section_prev->minute_at_ntpm (section_prev->end_note_types_per_minute(), pulse));
        }
 
 #if (0)
@@ -2432,17 +2844,17 @@ TempoMap::solve_map_pulse (Metrics& imaginary, TempoSection* section, const doub
 }
 
 bool
-TempoMap::solve_map_frame (Metrics& imaginary, MeterSection* section, const framepos_t& frame)
+TempoMap::solve_map_minute (Metrics& imaginary, MeterSection* section, const double& minute)
 {
-       /* disallow moving first meter past any subsequent one, and any movable meter before the first one */
-       const MeterSection* other =  &meter_section_at_frame_locked (imaginary, frame);
-       if ((!section->movable() && other->movable()) || (!other->movable() && section->movable() && other->frame() >= frame)) {
+       /* disallow moving first meter past any subsequent one, and any initial meter before the first one */
+       const MeterSection* other =  &meter_section_at_minute_locked (imaginary, minute);
+       if ((section->initial() && !other->initial()) || (other->initial() && !section->initial() && other->minute() >= minute)) {
                return false;
        }
 
-       if (!section->movable()) {
+       if (section->initial()) {
                /* lock the first tempo to our first meter */
-               if (!set_active_tempos (imaginary, frame)) {
+               if (!set_active_tempi (imaginary, frame_at_minute (minute))) {
                        return false;
                }
        }
@@ -2453,7 +2865,7 @@ TempoMap::solve_map_frame (Metrics& imaginary, MeterSection* section, const fram
                TempoSection* t;
                if ((*ii)->is_tempo()) {
                        t = static_cast<TempoSection*> (*ii);
-                       if ((t->locked_to_meter() || !t->movable()) && t->frame() == section->frame()) {
+                       if (t->locked_to_meter() && t->frame() == section->frame()) {
                                meter_locked_tempo = t;
                                break;
                        }
@@ -2474,22 +2886,25 @@ TempoMap::solve_map_frame (Metrics& imaginary, MeterSection* section, const fram
                if (!(*i)->is_tempo()) {
                        m = static_cast<MeterSection*> (*i);
                        if (m == section){
-                               if (prev_m && section->movable()) {
-                                       const double beats = (pulse_at_frame_locked (imaginary, frame) - prev_m->pulse()) * prev_m->note_divisor();
+                               if (prev_m && !section->initial()) {
+                                       const double beats = (pulse_at_minute_locked (imaginary, minute) - prev_m->pulse()) * prev_m->note_divisor();
                                        if (beats + prev_m->beat() < section->beat()) {
-                                               /* set the frame/pulse corresponding to its musical position,
+                                               /* set the section pulse according to its musical position,
                                                 * as an earlier time than this has been requested.
                                                */
                                                const double new_pulse = ((section->beat() - prev_m->beat())
                                                                          / prev_m->note_divisor()) + prev_m->pulse();
 
-                                               const framepos_t smallest_frame = frame_at_pulse_locked (future_map, new_pulse);
-
-                                               if ((solved = solve_map_frame (future_map, tempo_copy, smallest_frame))) {
-                                                       meter_locked_tempo->set_pulse (new_pulse);
-                                                       solve_map_frame (imaginary, meter_locked_tempo, smallest_frame);
-                                                       section->set_frame (smallest_frame);
+                                               tempo_copy->set_position_lock_style (MusicTime);
+                                               if ((solved = solve_map_pulse (future_map, tempo_copy, new_pulse))) {
+                                                       meter_locked_tempo->set_position_lock_style (MusicTime);
+                                                       section->set_position_lock_style (MusicTime);
                                                        section->set_pulse (new_pulse);
+                                                       solve_map_pulse (imaginary, meter_locked_tempo, new_pulse);
+                                                       meter_locked_tempo->set_position_lock_style (AudioTime);
+                                                       section->set_position_lock_style (AudioTime);
+                                                       section->set_minute (meter_locked_tempo->minute());
+
                                                } else {
                                                        solved = false;
                                                }
@@ -2505,17 +2920,19 @@ TempoMap::solve_map_frame (Metrics& imaginary, MeterSection* section, const fram
                                                }
                                        } else {
                                                /* all is ok. set section's locked tempo if allowed.
-                                                  possibly disallowed if there is an adjacent audio-locked tempo.
+                                                  possibly disallow if there is an adjacent audio-locked tempo.
                                                   XX this check could possibly go. its never actually happened here.
                                                */
-                                               MeterSection* meter_copy = const_cast<MeterSection*> (&meter_section_at_frame_locked (future_map, section->frame()));
-                                               meter_copy->set_frame (frame);
+                                               MeterSection* meter_copy = const_cast<MeterSection*>
+                                                       (&meter_section_at_minute_locked (future_map, section->minute()));
 
-                                               if ((solved = solve_map_frame (future_map, tempo_copy, frame))) {
-                                                       section->set_frame (frame);
+                                               meter_copy->set_minute (minute);
+
+                                               if ((solved = solve_map_minute (future_map, tempo_copy, minute))) {
+                                                       section->set_minute (minute);
                                                        meter_locked_tempo->set_pulse (((section->beat() - prev_m->beat())
                                                                                                / prev_m->note_divisor()) + prev_m->pulse());
-                                                       solve_map_frame (imaginary, meter_locked_tempo, frame);
+                                                       solve_map_minute (imaginary, meter_locked_tempo, minute);
                                                } else {
                                                        solved = false;
                                                }
@@ -2531,16 +2948,16 @@ TempoMap::solve_map_frame (Metrics& imaginary, MeterSection* section, const fram
                                                }
                                        }
                                } else {
-                                       /* not movable (first meter atm) */
+                                       /* initial (first meter atm) */
 
-                                       tempo_copy->set_frame (frame);
+                                       tempo_copy->set_minute (minute);
                                        tempo_copy->set_pulse (0.0);
 
-                                       if ((solved = solve_map_frame (future_map, tempo_copy, frame))) {
-                                               section->set_frame (frame);
-                                               meter_locked_tempo->set_frame (frame);
+                                       if ((solved = solve_map_minute (future_map, tempo_copy, minute))) {
+                                               section->set_minute (minute);
+                                               meter_locked_tempo->set_minute (minute);
                                                meter_locked_tempo->set_pulse (0.0);
-                                               solve_map_frame (imaginary, meter_locked_tempo, frame);
+                                               solve_map_minute (imaginary, meter_locked_tempo, minute);
                                        } else {
                                                solved = false;
                                        }
@@ -2596,20 +3013,25 @@ TempoMap::solve_map_bbt (Metrics& imaginary, MeterSection* section, const BBT_Ti
                MeterSection* m;
                if (!(*i)->is_tempo()) {
                        m = static_cast<MeterSection*> (*i);
+
+                       if (m == section) {
+                               continue;
+                       }
+
                        pair<double, BBT_Time> b_bbt;
                        double new_pulse = 0.0;
 
                        if (prev_m && m->bbt().bars > when.bars && !section_prev){
                                section_prev = prev_m;
+
                                const double beats = (when.bars - section_prev->bbt().bars) * section_prev->divisions_per_bar();
                                const double pulse = (beats / section_prev->note_divisor()) + section_prev->pulse();
                                pair<double, BBT_Time> b_bbt = make_pair (beats + section_prev->beat(), when);
 
                                section->set_beat (b_bbt);
                                section->set_pulse (pulse);
-                               section->set_frame (frame_at_pulse_locked (imaginary, pulse));
+                               section->set_minute (minute_at_pulse_locked (imaginary, pulse));
                                prev_m = section;
-                               continue;
                        }
 
                        if (m->position_lock_style() == AudioTime) {
@@ -2619,7 +3041,7 @@ TempoMap::solve_map_bbt (Metrics& imaginary, MeterSection* section, const BBT_Ti
                                        TempoSection* t;
                                        if ((*ii)->is_tempo()) {
                                                t = static_cast<TempoSection*> (*ii);
-                                               if ((t->locked_to_meter() || !t->movable()) && t->frame() == m->frame()) {
+                                               if (t->locked_to_meter() && t->frame() == m->frame()) {
                                                        meter_locked_tempo = t;
                                                        break;
                                                }
@@ -2631,14 +3053,21 @@ TempoMap::solve_map_bbt (Metrics& imaginary, MeterSection* section, const BBT_Ti
                                }
 
                                if (prev_m) {
-                                       const double beats = ((m->bbt().bars - prev_m->bbt().bars) * prev_m->divisions_per_bar());
+                                       double beats = ((m->bbt().bars - prev_m->bbt().bars) * prev_m->divisions_per_bar());
 
                                        if (beats + prev_m->beat() != m->beat()) {
                                                /* tempo/ meter change caused a change in beat (bar). */
+
+                                               /* the user has requested that the previous section of music overlaps this one.
+                                                  we have no choice but to change the bar number here, as being locked to audio means
+                                                  we must stay where we are on the timeline.
+                                               */
+                                               beats = m->beat() - prev_m->beat();
                                                b_bbt = make_pair (beats + prev_m->beat()
                                                                   , BBT_Time ((beats / prev_m->divisions_per_bar()) + prev_m->bbt().bars, 1, 0));
                                                new_pulse = prev_m->pulse() + (beats / prev_m->note_divisor());
-                                       } else if (m->movable()) {
+
+                                       } else if (!m->initial()) {
                                                b_bbt = make_pair (m->beat(), m->bbt());
                                                new_pulse = prev_m->pulse() + (beats / prev_m->note_divisor());
                                        }
@@ -2664,7 +3093,7 @@ TempoMap::solve_map_bbt (Metrics& imaginary, MeterSection* section, const BBT_Ti
                                new_pulse = (beats / prev_m->note_divisor()) + prev_m->pulse();
                                m->set_beat (b_bbt);
                                m->set_pulse (new_pulse);
-                               m->set_frame (frame_at_pulse_locked (imaginary, new_pulse));
+                               m->set_minute (minute_at_pulse_locked (imaginary, new_pulse));
                        }
 
                        prev_m = m;
@@ -2679,7 +3108,7 @@ TempoMap::solve_map_bbt (Metrics& imaginary, MeterSection* section, const BBT_Ti
 
                section->set_beat (b_bbt);
                section->set_pulse (pulse);
-               section->set_frame (frame_at_pulse_locked (imaginary, pulse));
+               section->set_minute (minute_at_pulse_locked (imaginary, pulse));
        }
 
        MetricSectionSorter cmp;
@@ -2754,7 +3183,7 @@ TempoMap::copy_metrics_and_point (const Metrics& metrics, Metrics& copy, MeterSe
 /** answers the question "is this a valid beat position for this tempo section?".
  *  it returns true if the tempo section can be moved to the requested bbt position,
  *  leaving the tempo map in a solved state.
- * @param section the tempo section to be moved
+ * @param ts the tempo section to be moved
  * @param bbt the requested new position for the tempo section
  * @return true if the tempo section can be moved to the position, otherwise false.
  */
@@ -2787,7 +3216,7 @@ TempoMap::can_solve_bbt (TempoSection* ts, const BBT_Time& bbt)
 * This is for a gui that needs to know the pulse or frame of a tempo section if it were to be moved to some bbt time,
 * taking any possible reordering as a consequence of this into account.
 * @param section - the section to be altered
-* @param bbt - the bbt where the altered tempo will fall
+* @param bbt - the BBT time  where the altered tempo will fall
 * @return returns - the position in pulses and frames (as a pair) where the new tempo section will lie.
 */
 pair<double, framepos_t>
@@ -2802,6 +3231,10 @@ TempoMap::predict_tempo_position (TempoSection* section, const BBT_Time& bbt)
 
        const double beat = beat_at_bbt_locked (future_map, bbt);
 
+       if (section->position_lock_style() == AudioTime) {
+               tempo_copy->set_position_lock_style (MusicTime);
+       }
+
        if (solve_map_pulse (future_map, tempo_copy, pulse_at_beat_locked (future_map, beat))) {
                ret.first = tempo_copy->pulse();
                ret.second = tempo_copy->frame();
@@ -2818,8 +3251,24 @@ TempoMap::predict_tempo_position (TempoSection* section, const BBT_Time& bbt)
        return ret;
 }
 
+/** moves a TempoSection to a specified position.
+ * @param ts - the section to be moved
+ * @param frame - the new position in frames for the tempo
+ * @param sub_num - the snap division to use if using musical time.
+ *
+ * if sub_num is non-zero, the frame position is used to calculate an exact
+ * musical position.
+ * sub_num   | effect
+ * -1        | snap to bars (meter-based)
+ *  0        | no snap - use audio frame for musical position
+ *  1        | snap to meter-based (BBT) beat
+ * >1        | snap to quarter-note subdivision (i.e. 4 will snap to sixteenth notes)
+ *
+ * this follows the snap convention in the gui.
+ * if sub_num is zero, the musical position will be taken from the supplied frame.
+ */
 void
-TempoMap::gui_move_tempo (TempoSection* ts, const framepos_t& frame, const int& sub_num)
+TempoMap::gui_set_tempo_position (TempoSection* ts, const framepos_t& frame, const int& sub_num)
 {
        Metrics future_map;
 
@@ -2831,7 +3280,7 @@ TempoMap::gui_move_tempo (TempoSection* ts, const framepos_t& frame, const int&
 
                        tempo_copy->set_position_lock_style (AudioTime);
 
-                       if (solve_map_frame (future_map, tempo_copy, frame)) {
+                       if (solve_map_minute (future_map, tempo_copy, minute_at_frame (frame))) {
                                const double beat = exact_beat_at_frame_locked (future_map, frame, sub_num);
                                const double pulse = pulse_at_beat_locked (future_map, beat);
 
@@ -2848,30 +3297,26 @@ TempoMap::gui_move_tempo (TempoSection* ts, const framepos_t& frame, const int&
                        Glib::Threads::RWLock::WriterLock lm (lock);
                        TempoSection* tempo_copy = copy_metrics_and_point (_metrics, future_map, ts);
 
-                       if (solve_map_frame (future_map, tempo_copy, frame)) {
+                       if (solve_map_minute (future_map, tempo_copy, minute_at_frame (frame))) {
                                if (sub_num != 0) {
                                        /* We're moving the object that defines the grid while snapping to it...
                                         * Placing the ts at the beat corresponding to the requested frame may shift the
                                         * grid in such a way that the mouse is left hovering over a completerly different division,
                                         * causing jittering when the mouse next moves (esp. large tempo deltas).
-                                        * To avoid this, place the ts at the requested frame in a dummy map
-                                        * then find the closest beat subdivision to that frame in the dummy.
+                                        *
                                         * This alters the snap behaviour slightly in that we snap to beat divisions
                                         * in the future map rather than the existing one.
                                         */
-                                       const double beat = exact_beat_at_frame_locked (future_map, frame, sub_num);
-                                       const double pulse = pulse_at_beat_locked (future_map, beat);
-
-                                       if (solve_map_pulse (future_map, tempo_copy, pulse)) {
-                                               /* snapping to a grid. force MusicTime temporarily. */
-                                               ts->set_position_lock_style (MusicTime);
-                                               solve_map_pulse (_metrics, ts, pulse);
-                                               ts->set_position_lock_style (AudioTime);
+                                       const double qn = exact_qn_at_frame_locked (future_map, frame, sub_num);
+                                       const framepos_t snapped_frame = frame_at_minute (minute_at_pulse_locked (future_map, qn / 4.0));
 
+                                       if (solve_map_minute (future_map, tempo_copy, minute_at_frame (snapped_frame))) {
+                                               solve_map_minute (_metrics, ts, minute_at_frame (snapped_frame));
+                                               ts->set_pulse (qn / 4.0);
                                                recompute_meters (_metrics);
                                        }
                                } else {
-                                       solve_map_frame (_metrics, ts, frame);
+                                       solve_map_minute (_metrics, ts, minute_at_frame (frame));
                                        recompute_meters (_metrics);
                                }
                        }
@@ -2884,11 +3329,19 @@ TempoMap::gui_move_tempo (TempoSection* ts, const framepos_t& frame, const int&
                ++d;
        }
 
-       MetricPositionChanged (); // Emit Signal
+       MetricPositionChanged (PropertyChange ()); // Emit Signal
 }
 
+/** moves a MeterSection to a specified position.
+ * @param ms - the section to be moved
+ * @param frame - the new position in frames for the meter
+ *
+ * as a meter cannot snap to anything but bars,
+ * the supplied frame is rounded to the nearest bar, possibly
+ * leaving the meter position unchanged.
+ */
 void
-TempoMap::gui_move_meter (MeterSection* ms, const framepos_t& frame)
+TempoMap::gui_set_meter_position (MeterSection* ms, const framepos_t& frame)
 {
        Metrics future_map;
 
@@ -2898,8 +3351,8 @@ TempoMap::gui_move_meter (MeterSection* ms, const framepos_t& frame)
                        Glib::Threads::RWLock::WriterLock lm (lock);
                        MeterSection* copy = copy_metrics_and_point (_metrics, future_map, ms);
 
-                       if (solve_map_frame (future_map, copy, frame)) {
-                               solve_map_frame (_metrics, ms, frame);
+                       if (solve_map_minute (future_map, copy, minute_at_frame (frame))) {
+                               solve_map_minute (_metrics, ms, minute_at_frame (frame));
                                recompute_tempi (_metrics);
                        }
                }
@@ -2908,7 +3361,7 @@ TempoMap::gui_move_meter (MeterSection* ms, const framepos_t& frame)
                        Glib::Threads::RWLock::WriterLock lm (lock);
                        MeterSection* copy = copy_metrics_and_point (_metrics, future_map, ms);
 
-                       const double beat = beat_at_frame_locked (_metrics, frame);
+                       const double beat = beat_at_minute_locked (_metrics, minute_at_frame (frame));
                        const Timecode::BBT_Time bbt = bbt_at_beat_locked (_metrics, beat);
 
                        if (solve_map_bbt (future_map, copy, bbt)) {
@@ -2924,22 +3377,39 @@ TempoMap::gui_move_meter (MeterSection* ms, const framepos_t& frame)
                ++d;
        }
 
-       MetricPositionChanged (); // Emit Signal
+       MetricPositionChanged (PropertyChange ()); // Emit Signal
 }
 
 bool
-TempoMap::gui_change_tempo (TempoSection* ts, const Tempo& bpm)
+TempoMap::gui_change_tempo (TempoSection* ts, const Tempo& bpm, bool change_end)
 {
        Metrics future_map;
        bool can_solve = false;
        {
                Glib::Threads::RWLock::WriterLock lm (lock);
                TempoSection* tempo_copy = copy_metrics_and_point (_metrics, future_map, ts);
-               tempo_copy->set_beats_per_minute (bpm.beats_per_minute());
+
+               if (change_end && tempo_copy->type() == TempoSection::Constant) {
+                       tempo_copy->set_end_note_types_per_minute (bpm.note_types_per_minute());
+                       tempo_copy->set_note_types_per_minute (bpm.note_types_per_minute());
+               } else if (change_end) {
+                       tempo_copy->set_end_note_types_per_minute (bpm.note_types_per_minute());
+               } else {
+                       tempo_copy->set_note_types_per_minute (bpm.note_types_per_minute());
+               }
+
                recompute_tempi (future_map);
 
                if (check_solved (future_map)) {
-                       ts->set_beats_per_minute (bpm.beats_per_minute());
+                       if (change_end && ts->type() == TempoSection::Constant) {
+                               ts->set_end_note_types_per_minute (bpm.note_types_per_minute());
+                               ts->set_note_types_per_minute (bpm.note_types_per_minute());
+                       } else if (change_end) {
+                               ts->set_end_note_types_per_minute (bpm.note_types_per_minute());
+                       } else {
+                               ts->set_note_types_per_minute (bpm.note_types_per_minute());
+                       }
+
                        recompute_map (_metrics);
                        can_solve = true;
                }
@@ -2951,20 +3421,21 @@ TempoMap::gui_change_tempo (TempoSection* ts, const Tempo& bpm)
                ++d;
        }
        if (can_solve) {
-               MetricPositionChanged (); // Emit Signal
+               MetricPositionChanged (PropertyChange ()); // Emit Signal
        }
+
        return can_solve;
 }
 
 void
-TempoMap::gui_dilate_tempo (TempoSection* ts, const framepos_t& frame, const framepos_t& end_frame, const double& pulse)
+TempoMap::gui_stretch_tempo (TempoSection* ts, const framepos_t frame, const framepos_t end_frame)
 {
        /*
          Ts (future prev_t)   Tnext
          |                    |
          |     [drag^]        |
          |----------|----------
-               e_f  pulse(frame)
+               e_f  qn_beats(frame)
        */
 
        Metrics future_map;
@@ -2977,181 +3448,394 @@ TempoMap::gui_dilate_tempo (TempoSection* ts, const framepos_t& frame, const fra
                }
 
                TempoSection* prev_t = copy_metrics_and_point (_metrics, future_map, ts);
-               TempoSection* prev_to_prev_t = 0;
-               const frameoffset_t fr_off = end_frame - frame;
 
-               if (prev_t && prev_t->pulse() > 0.0) {
-                       prev_to_prev_t = const_cast<TempoSection*>(&tempo_section_at_frame_locked (future_map, prev_t->frame() - 1));
+               if (!prev_t) {
+                       return;
                }
 
-               TempoSection* next_t = 0;
-               for (Metrics::iterator i = future_map.begin(); i != future_map.end(); ++i) {
-                       TempoSection* t = 0;
-                       if ((*i)->is_tempo()) {
-                               t = static_cast<TempoSection*> (*i);
-                               if (t->frame() > ts->frame()) {
-                                       next_t = t;
-                                       break;
-                               }
-                       }
-               }
                /* minimum allowed measurement distance in frames */
-               const framepos_t min_dframe = 2;
-
-               /* the change in frames is the result of changing the slope of at most 2 previous tempo sections.
-                  constant to constant is straightforward, as the tempo prev to prev_t has constant slope.
-               */
-               double contribution = 0.0;
-
-               if (next_t && prev_to_prev_t && prev_to_prev_t->type() == TempoSection::Ramp) {
-                       contribution = (prev_t->frame() - prev_to_prev_t->frame()) / (double) (next_t->frame() - prev_to_prev_t->frame());
-               }
-
-               const frameoffset_t prev_t_frame_contribution = fr_off - (contribution * (double) fr_off);
-
-               const double start_pulse = prev_t->pulse_at_frame (frame, _frame_rate);
-               const double end_pulse = prev_t->pulse_at_frame (end_frame, _frame_rate);
+               framepos_t const min_dframe = 2;
 
                double new_bpm;
 
-               if (prev_t->type() == TempoSection::Constant || prev_t->c_func() == 0.0) {
-
-                       if (prev_t->position_lock_style() == MusicTime) {
-                               if (prev_to_prev_t && prev_to_prev_t->type() == TempoSection::Ramp) {
-                                       if (frame > prev_to_prev_t->frame() + min_dframe && (frame + prev_t_frame_contribution) > prev_to_prev_t->frame() + min_dframe) {
-
-                                               new_bpm = prev_t->beats_per_minute() * ((frame - prev_to_prev_t->frame())
-                                                                                       / (double) ((frame + prev_t_frame_contribution) - prev_to_prev_t->frame()));
-                                       } else {
-                                               new_bpm = prev_t->beats_per_minute();
-                                       }
-                               } else {
-                                       /* prev to prev is irrelevant */
-
-                                       if (start_pulse > prev_t->pulse() && end_pulse > prev_t->pulse()) {
-                                               new_bpm = prev_t->beats_per_minute() * ((start_pulse - prev_t->pulse()) / (end_pulse - prev_t->pulse()));
-                                       } else {
-                                               new_bpm = prev_t->beats_per_minute();
-                                       }
-                               }
-                       } else {
-                               /* AudioTime */
-                               if (prev_to_prev_t && prev_to_prev_t->type() == TempoSection::Ramp) {
-                                       if (frame > prev_to_prev_t->frame() + min_dframe && end_frame > prev_to_prev_t->frame() + min_dframe) {
-
-                                               new_bpm = prev_t->beats_per_minute() * ((frame - prev_to_prev_t->frame())
-                                                                                       / (double) ((end_frame) - prev_to_prev_t->frame()));
-                                       } else {
-                                               new_bpm = prev_t->beats_per_minute();
-                                       }
-                               } else {
-                                       /* prev_to_prev_t is irrelevant */
+               if (frame > prev_t->frame() + min_dframe && end_frame > prev_t->frame() + min_dframe) {
 
-                                       if (frame > prev_t->frame() + min_dframe && end_frame > prev_t->frame() + min_dframe) {
-                                               new_bpm = prev_t->beats_per_minute() * ((frame - prev_t->frame()) / (double) (end_frame - prev_t->frame()));
-                                       } else {
-                                               new_bpm = prev_t->beats_per_minute();
-                                       }
-                               }
-                       }
+                       new_bpm = prev_t->note_types_per_minute() * ((frame - prev_t->frame())
+                                                                                  / (double) (end_frame - prev_t->frame()));
                } else {
-
-                       double frame_ratio = 1.0;
-                       double pulse_ratio = 1.0;
-                       const framepos_t pulse_pos = prev_t->frame_at_pulse (pulse, _frame_rate);
-
-                       if (prev_to_prev_t) {
-                               if (pulse_pos > prev_to_prev_t->frame() + min_dframe && (pulse_pos - fr_off) > prev_to_prev_t->frame() + min_dframe) {
-                                       frame_ratio = (((pulse_pos - fr_off) - prev_to_prev_t->frame()) / (double) ((pulse_pos) - prev_to_prev_t->frame()));
-                               }
-                               if (end_pulse > prev_to_prev_t->pulse() && start_pulse > prev_to_prev_t->pulse()) {
-                                       pulse_ratio = ((start_pulse - prev_to_prev_t->pulse()) / (end_pulse - prev_to_prev_t->pulse()));
-                               }
-                       } else {
-                               if (pulse_pos > prev_t->frame() + min_dframe && (pulse_pos - fr_off) > prev_t->frame() + min_dframe) {
-                                       frame_ratio = (((pulse_pos - fr_off) - prev_t->frame()) / (double) ((pulse_pos) - prev_t->frame()));
-                               }
-                               pulse_ratio = (start_pulse / end_pulse);
-                       }
-                       new_bpm = prev_t->beats_per_minute() * (pulse_ratio * frame_ratio);
+                       new_bpm = prev_t->note_types_per_minute();
                }
 
+               std::cout << "new bpm : " << new_bpm << std::endl;
+               new_bpm = min (new_bpm, (double) 1000.0);
+
                /* don't clamp and proceed here.
                   testing has revealed that this can go negative,
                   which is an entirely different thing to just being too low.
                */
+
                if (new_bpm < 0.5) {
-                       return;
+                       goto out;
                }
-               new_bpm = min (new_bpm, (double) 1000.0);
-               prev_t->set_beats_per_minute (new_bpm);
+
+               if (prev_t && prev_t->type() == TempoSection::Ramp) {
+                       prev_t->set_note_types_per_minute (new_bpm);
+               } else {
+                       prev_t->set_end_note_types_per_minute (new_bpm);
+                       prev_t->set_note_types_per_minute (new_bpm);
+               }
+
                recompute_tempi (future_map);
                recompute_meters (future_map);
 
                if (check_solved (future_map)) {
-                       ts->set_beats_per_minute (new_bpm);
+                       if (prev_t && prev_t->type() == TempoSection::Ramp) {
+                               ts->set_note_types_per_minute (new_bpm);
+                       } else {
+                               ts->set_end_note_types_per_minute (new_bpm);
+                               ts->set_note_types_per_minute (new_bpm);
+                       }
                        recompute_tempi (_metrics);
                        recompute_meters (_metrics);
                }
        }
 
+       MetricPositionChanged (PropertyChange ()); // Emit Signal
+
+out:
        Metrics::const_iterator d = future_map.begin();
        while (d != future_map.end()) {
                delete (*d);
                ++d;
        }
 
-       MetricPositionChanged (); // Emit Signal
 }
-
-/** Returns the exact beat subdivision closest to the supplied frame, possibly returning a negative value.
- * @param frame  The session frame position.
- * @param sub_num The requested beat subdivision to use when rounding the frame position.
- * @return The beat position of the supplied frame.
- * If the supplied frame lies before the first meter, the return will be negative.
- * The returned beat is obtained using the first meter and the continuation of the tempo curve (backwards).
- *
- * This function uses both tempo and meter.
- */
-double
-TempoMap::exact_beat_at_frame (const framepos_t& frame, const int32_t sub_num)
+void
+TempoMap::gui_stretch_tempo_end (TempoSection* ts, const framepos_t frame, const framepos_t end_frame)
 {
-       Glib::Threads::RWLock::ReaderLock lm (lock);
+       /*
+         Ts (future prev_t)   Tnext
+         |                    |
+         |     [drag^]        |
+         |----------|----------
+               e_f  qn_beats(frame)
+       */
 
-       return exact_beat_at_frame_locked (_metrics, frame, sub_num);
-}
+       Metrics future_map;
 
-double
-TempoMap::exact_beat_at_frame_locked (const Metrics& metrics, const framepos_t& frame, const int32_t sub_num)
-{
-       double beat = beat_at_frame_locked (metrics, frame);
+       {
+               Glib::Threads::RWLock::WriterLock lm (lock);
 
-       if (sub_num > 1) {
-               beat = floor (beat) + (floor (((beat - floor (beat)) * (double) sub_num) + 0.5) / sub_num);
-       } else if (sub_num == 1) {
-               /* snap to beat */
-               beat = floor (beat + 0.5);
-       } else if (sub_num == -1) {
-               /* snap to  bar */
-               Timecode::BBT_Time bbt = bbt_at_beat_locked (metrics, beat);
-               bbt.beats = 1;
-               bbt.ticks = 0;
+               if (!ts) {
+                       return;
+               }
 
-               const double prev_b = beat_at_bbt_locked (_metrics, bbt);
-               ++bbt.bars;
-               const double next_b = beat_at_bbt_locked (_metrics, bbt);
+               TempoSection* prev_t = copy_metrics_and_point (_metrics, future_map, ts);
 
-               if ((beat - prev_b) > (next_b - prev_b) / 2.0) {
-                       beat = next_b;
+/*
+               TempoSection* next_t = 0;
+               for (Metrics::const_iterator i = future_map.begin(); i != future_map.end(); ++i) {
+                       if ((*i)->is_tempo() && (*i)->minute() >  prev_t->minute()) {
+                               next_t = static_cast<TempoSection*> (*i);
+                               break;
+                       }
+               }
+
+               if (!next_t) {
+                       return;
+               }
+*/
+               if (!prev_t) {
+                       return;
+               }
+
+
+               /* minimum allowed measurement distance in frames */
+               framepos_t const min_dframe = 2;
+               double new_bpm;
+
+               if (frame > prev_t->frame() + min_dframe && end_frame > prev_t->frame() + min_dframe) {
+                       new_bpm = prev_t->end_note_types_per_minute() * ((frame - prev_t->frame())
+                                                                                / (double) (end_frame - prev_t->frame()));
                } else {
-                       beat = prev_b;
+                       new_bpm = prev_t->end_note_types_per_minute();
+               }
+
+               new_bpm = min (new_bpm, (double) 1000.0);
+
+               if (new_bpm < 0.5) {
+                       goto out;
+               }
+
+               prev_t->set_end_note_types_per_minute (new_bpm);
+
+               recompute_tempi (future_map);
+               recompute_meters (future_map);
+
+               if (check_solved (future_map)) {
+                       ts->set_end_note_types_per_minute (new_bpm);
+
+                       recompute_tempi (_metrics);
+                       recompute_meters (_metrics);
                }
        }
 
-       return beat;
+       MetricPositionChanged (PropertyChange ()); // Emit Signal
+
+out:
+       Metrics::const_iterator d = future_map.begin();
+       while (d != future_map.end()) {
+               delete (*d);
+               ++d;
+       }
+
 }
+bool
+TempoMap::gui_twist_tempi (TempoSection* ts, const Tempo& bpm, const framepos_t frame, const framepos_t end_frame)
+{
+       TempoSection* next_t = 0;
+       TempoSection* next_to_next_t = 0;
+       Metrics future_map;
+       bool can_solve = false;
+
+       /* minimum allowed measurement distance in frames */
+       framepos_t const min_dframe = 2;
+
+       {
+               Glib::Threads::RWLock::WriterLock lm (lock);
+               if (!ts) {
+                       return false;
+               }
+
+               TempoSection* tempo_copy = copy_metrics_and_point (_metrics, future_map, ts);
+               TempoSection* prev_to_prev_t = 0;
+               const frameoffset_t fr_off = end_frame - frame;
+
+               if (!tempo_copy) {
+                       return false;
+               }
+
+               if (tempo_copy->pulse() > 0.0) {
+                       prev_to_prev_t = const_cast<TempoSection*>(&tempo_section_at_minute_locked (future_map, minute_at_frame (tempo_copy->frame() - 1)));
+               }
+
+               for (Metrics::const_iterator i = future_map.begin(); i != future_map.end(); ++i) {
+                       if ((*i)->is_tempo() && (*i)->minute() >  tempo_copy->minute()) {
+                               next_t = static_cast<TempoSection*> (*i);
+                               break;
+                       }
+               }
+
+               if (!next_t) {
+                       return false;
+               }
+
+               for (Metrics::const_iterator i = future_map.begin(); i != future_map.end(); ++i) {
+                       if ((*i)->is_tempo() && (*i)->minute() >  next_t->minute()) {
+                               next_to_next_t = static_cast<TempoSection*> (*i);
+                               break;
+                       }
+               }
+
+               if (!next_to_next_t) {
+                       std::cout << "no next to next t" << std::endl;
+                       return false;
+               }
+
+               double prev_contribution = 0.0;
+
+               if (next_t && prev_to_prev_t && prev_to_prev_t->type() == TempoSection::Ramp) {
+                       prev_contribution = (tempo_copy->frame() - prev_to_prev_t->frame()) / (double) (next_t->frame() - prev_to_prev_t->frame());
+               }
+
+               const frameoffset_t tempo_copy_frame_contribution = fr_off - (prev_contribution * (double) fr_off);
+
+
+               framepos_t old_tc_pos = tempo_copy->frame();
+               framepos_t old_next_pos = next_t->frame();
+               double old_next_minute = next_t->minute();
+               framepos_t old_next_to_next_pos = next_to_next_t->frame();
+               double old_next_to_next_minute = next_to_next_t->minute();
+
+               double new_bpm;
+               double new_next_bpm;
+               double new_copy_end_bpm;
+
+               if (frame > prev_to_prev_t->frame() + min_dframe && (frame + tempo_copy_frame_contribution) > prev_to_prev_t->frame() + min_dframe) {
+                       new_bpm = tempo_copy->note_types_per_minute() * ((frame - tempo_copy->frame())
+                                                                                      / (double) (end_frame - tempo_copy->frame()));
+               } else {
+                       new_bpm = tempo_copy->note_types_per_minute();
+               }
+
+               /* don't clamp and proceed here.
+                  testing has revealed that this can go negative,
+                  which is an entirely different thing to just being too low.
+               */
+               if (new_bpm < 0.5) {
+                       return false;
+               }
+
+               new_bpm = min (new_bpm, (double) 1000.0);
+
+               tempo_copy->set_note_types_per_minute (new_bpm);
+               if (tempo_copy->type() == TempoSection::Constant) {
+                       tempo_copy->set_end_note_types_per_minute (new_bpm);
+               }
+               recompute_tempi (future_map);
+
+               if (check_solved (future_map)) {
+
+                       if (!next_t) {
+                               return false;
+                       }
+                       ts->set_note_types_per_minute (new_bpm);
+                       if (ts->type() == TempoSection::Constant) {
+                               ts->set_end_note_types_per_minute (new_bpm);
+                       }
+                       recompute_map (_metrics);
+                       can_solve = true;
+               }
+
+               if (next_t->type() == TempoSection::Constant || next_t->c() == 0.0) {
+                       if (frame > prev_to_prev_t->frame() + min_dframe && end_frame > prev_to_prev_t->frame() + min_dframe) {
+
+                               new_next_bpm = next_t->note_types_per_minute() * ((next_to_next_t->minute() - old_next_minute)
+                                                                                       / (double) ((old_next_to_next_minute) - old_next_minute));
+
+                       } else {
+                               new_next_bpm = next_t->note_types_per_minute();
+                       }
+
+                       next_t->set_note_types_per_minute (new_next_bpm);
+                       recompute_tempi (future_map);
+
+                       if (check_solved (future_map)) {
+                               for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
+                                       if ((*i)->is_tempo() && (*i)->minute() >  ts->minute()) {
+                                               next_t = static_cast<TempoSection*> (*i);
+                                               break;
+                                       }
+                               }
+
+                               if (!next_t) {
+                                       return false;
+                               }
+                               next_t->set_note_types_per_minute (new_next_bpm);
+                               recompute_map (_metrics);
+                               can_solve = true;
+                       }
+               } else {
+                       double next_frame_ratio = 1.0;
+                       double copy_frame_ratio = 1.0;
+
+                       if (next_to_next_t) {
+                               next_frame_ratio =  (next_to_next_t->frame() - old_next_pos) / (double) (old_next_to_next_pos -  old_next_pos);
+
+                               copy_frame_ratio =   ((old_tc_pos - next_t->frame()) / (double) (old_tc_pos - old_next_pos));
+
+                       } else {
+                               //next_frame_ratio = (((next_to_next_pos - fr_off) - next_t->frame()) / (double) ((next_to_next_pos) - next_t->frame()));
+                               //next_pulse_ratio = (start_pulse / end_pulse);
+                       }
+
+                       new_next_bpm = next_t->note_types_per_minute() * next_frame_ratio;
+                       new_copy_end_bpm =  tempo_copy->end_note_types_per_minute() * copy_frame_ratio;
+
+                       next_t->set_note_types_per_minute (new_next_bpm);
+                       tempo_copy->set_end_note_types_per_minute (new_copy_end_bpm);
+                       recompute_tempi (future_map);
+
+                       if (check_solved (future_map)) {
+                               for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
+                                       if ((*i)->is_tempo() && (*i)->minute() >  ts->minute()) {
+                                               next_t = static_cast<TempoSection*> (*i);
+                                               break;
+                                       }
+                               }
+
+                               if (!next_t) {
+                                       return false;
+                               }
+                               next_t->set_note_types_per_minute (new_next_bpm);
+                               ts->set_end_note_types_per_minute (new_copy_end_bpm);
+                               recompute_map (_metrics);
+                               can_solve = true;
+                       }
+               }
+       }
+
+       Metrics::const_iterator d = future_map.begin();
+       while (d != future_map.end()) {
+               delete (*d);
+               ++d;
+       }
+       if (can_solve) {
+               MetricPositionChanged (PropertyChange ()); // Emit Signal
+       }
+
+       return can_solve;
+}
+/** Returns the exact bbt-based beat corresponding to the bar, beat or quarter note subdivision nearest to
+ * the supplied frame, possibly returning a negative value.
+ *
+ * @param frame  The session frame position.
+ * @param sub_num The subdivision to use when rounding the beat.
+ *                A value of -1 indicates rounding to BBT bar. 1 indicates rounding to BBT beats.
+ *                Positive integers indicate quarter note (non BBT) divisions.
+ *                0 indicates that the returned beat should not be rounded (equivalent to quarter_note_at_frame()).
+ * @return The beat position of the supplied frame.
+ *
+ * when working to a musical grid, the use of sub_nom indicates that
+ * the position should be interpreted musically.
+ *
+ * it effectively snaps to meter bars, meter beats or quarter note divisions
+ * (as per current gui convention) and returns a musical position independent of frame rate.
+ *
+ * If the supplied frame lies before the first meter, the return will be negative,
+ * in which case the returned beat uses the first meter (for BBT subdivisions) and
+ * the continuation of the tempo curve (backwards).
+ *
+ * This function is sensitive to tempo and meter.
+ */
 double
-TempoMap::exact_qn_at_frame (const framepos_t& frame, const int32_t sub_num)
+TempoMap::exact_beat_at_frame (const framepos_t& frame, const int32_t sub_num) const
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       return exact_beat_at_frame_locked (_metrics, frame, sub_num);
+}
+
+double
+TempoMap::exact_beat_at_frame_locked (const Metrics& metrics, const framepos_t& frame, const int32_t divisions) const
+{
+       return beat_at_pulse_locked (_metrics, exact_qn_at_frame_locked (metrics, frame, divisions) / 4.0);
+}
+
+/** Returns the exact quarter note corresponding to the bar, beat or quarter note subdivision nearest to
+ * the supplied frame, possibly returning a negative value.
+ *
+ * @param frame  The session frame position.
+ * @param sub_num The subdivision to use when rounding the quarter note.
+ *                A value of -1 indicates rounding to BBT bar. 1 indicates rounding to BBT beats.
+ *                Positive integers indicate quarter note (non BBT) divisions.
+ *                0 indicates that the returned quarter note should not be rounded (equivalent to quarter_note_at_frame()).
+ * @return The quarter note position of the supplied frame.
+ *
+ * When working to a musical grid, the use of sub_nom indicates that
+ * the frame position should be interpreted musically.
+ *
+ * it effectively snaps to meter bars, meter beats or quarter note divisions
+ * (as per current gui convention) and returns a musical position independent of frame rate.
+ *
+ * If the supplied frame lies before the first meter, the return will be negative,
+ * in which case the returned quarter note uses the first meter (for BBT subdivisions) and
+ * the continuation of the tempo curve (backwards).
+ *
+ * This function is tempo-sensitive.
+ */
+double
+TempoMap::exact_qn_at_frame (const framepos_t& frame, const int32_t sub_num) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
@@ -3159,24 +3843,24 @@ TempoMap::exact_qn_at_frame (const framepos_t& frame, const int32_t sub_num)
 }
 
 double
-TempoMap::exact_qn_at_frame_locked (const Metrics& metrics, const framepos_t& frame, const int32_t sub_num)
+TempoMap::exact_qn_at_frame_locked (const Metrics& metrics, const framepos_t& frame, const int32_t sub_num) const
 {
-       double qn = quarter_note_at_frame_locked (metrics, frame);
+       double qn = pulse_at_minute_locked (metrics, minute_at_frame (frame)) * 4.0;
 
        if (sub_num > 1) {
                qn = floor (qn) + (floor (((qn - floor (qn)) * (double) sub_num) + 0.5) / sub_num);
        } else if (sub_num == 1) {
-               /* snap to quarter note */
-               qn = floor (qn + 0.5);
+               /* the gui requested exact musical (BBT) beat */
+               qn = pulse_at_beat_locked (metrics, (floor (beat_at_minute_locked (metrics, minute_at_frame (frame)) + 0.5))) * 4.0;
        } else if (sub_num == -1) {
                /* snap to  bar */
                Timecode::BBT_Time bbt = bbt_at_pulse_locked (metrics, qn / 4.0);
                bbt.beats = 1;
                bbt.ticks = 0;
 
-               const double prev_b = pulse_at_bbt_locked (_metrics, bbt) * 4.0;
+               const double prev_b = pulse_at_bbt_locked (metrics, bbt) * 4.0;
                ++bbt.bars;
-               const double next_b = pulse_at_bbt_locked (_metrics, bbt) * 4.0;
+               const double next_b = pulse_at_bbt_locked (metrics, bbt) * 4.0;
 
                if ((qn - prev_b) > (next_b - prev_b) / 2.0) {
                        qn = next_b;
@@ -3188,131 +3872,98 @@ TempoMap::exact_qn_at_frame_locked (const Metrics& metrics, const framepos_t& fr
        return qn;
 }
 
+/** returns the frame duration of the supplied BBT time at a specified frame position in the tempo map.
+ * @param pos the frame position in the tempo map.
+ * @param bbt the distance in BBT time from pos to calculate.
+ * @param dir the rounding direction..
+ * @return the duration in frames between pos and bbt
+*/
 framecnt_t
 TempoMap::bbt_duration_at (framepos_t pos, const BBT_Time& bbt, int dir)
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       const double tick_at_time = max (0.0, beat_at_frame_locked (_metrics, pos)) * BBT_Time::ticks_per_beat;
-       const double bbt_ticks = bbt.ticks + (bbt.beats * BBT_Time::ticks_per_beat);
-       const double total_beats = (tick_at_time + bbt_ticks) / BBT_Time::ticks_per_beat;
-
-       return frame_at_beat_locked (_metrics, total_beats);
-}
+       BBT_Time pos_bbt = bbt_at_minute_locked (_metrics, minute_at_frame (pos));
 
-framepos_t
-TempoMap::round_to_bar (framepos_t fr, RoundMode dir)
-{
-       return round_to_type (fr, dir, Bar);
-}
-
-framepos_t
-TempoMap::round_to_beat (framepos_t fr, RoundMode dir)
-{
-       return round_to_type (fr, dir, Beat);
-}
-
-framepos_t
-TempoMap::round_to_beat_subdivision (framepos_t fr, int sub_num, RoundMode dir)
-{
-       Glib::Threads::RWLock::ReaderLock lm (lock);
-       uint32_t ticks = (uint32_t) floor (max (0.0, beat_at_frame_locked (_metrics, fr)) * BBT_Time::ticks_per_beat);
-       uint32_t beats = (uint32_t) floor (ticks / BBT_Time::ticks_per_beat);
-       uint32_t ticks_one_subdivisions_worth = (uint32_t) BBT_Time::ticks_per_beat / sub_num;
-
-       ticks -= beats * BBT_Time::ticks_per_beat;
+       const double divisions = meter_section_at_minute_locked (_metrics, minute_at_frame (pos)).divisions_per_bar();
 
        if (dir > 0) {
-               /* round to next (or same iff dir == RoundUpMaybe) */
-
-               uint32_t mod = ticks % ticks_one_subdivisions_worth;
+               pos_bbt.bars += bbt.bars;
 
-               if (mod == 0 && dir == RoundUpMaybe) {
-                       /* right on the subdivision, which is fine, so do nothing */
-
-               } else if (mod == 0) {
-                       /* right on the subdivision, so the difference is just the subdivision ticks */
-                       ticks += ticks_one_subdivisions_worth;
-
-               } else {
-                       /* not on subdivision, compute distance to next subdivision */
-
-                       ticks += ticks_one_subdivisions_worth - mod;
+               pos_bbt.ticks += bbt.ticks;
+               if ((double) pos_bbt.ticks > BBT_Time::ticks_per_beat) {
+                       pos_bbt.beats += 1;
+                       pos_bbt.ticks -= BBT_Time::ticks_per_beat;
                }
 
-               if (ticks >= BBT_Time::ticks_per_beat) {
-                       ticks -= BBT_Time::ticks_per_beat;
+               pos_bbt.beats += bbt.beats;
+               if ((double) pos_bbt.beats > divisions) {
+                       pos_bbt.bars += 1;
+                       pos_bbt.beats -= divisions;
                }
-       } else if (dir < 0) {
+               const framecnt_t pos_bbt_frame = frame_at_minute (minute_at_bbt_locked (_metrics, pos_bbt));
 
-               /* round to previous (or same iff dir == RoundDownMaybe) */
-
-               uint32_t difference = ticks % ticks_one_subdivisions_worth;
+               return pos_bbt_frame - pos;
 
-               if (difference == 0 && dir == RoundDownAlways) {
-                       /* right on the subdivision, but force-rounding down,
-                          so the difference is just the subdivision ticks */
-                       difference = ticks_one_subdivisions_worth;
-               }
+       } else {
 
-               if (ticks < difference) {
-                       ticks = BBT_Time::ticks_per_beat - ticks;
+               if (pos_bbt.bars <= bbt.bars) {
+                       pos_bbt.bars = 1;
                } else {
-                       ticks -= difference;
+                       pos_bbt.bars -= bbt.bars;
                }
 
-       } else {
-               /* round to nearest */
-               double rem;
-
-               /* compute the distance to the previous and next subdivision */
-
-               if ((rem = fmod ((double) ticks, (double) ticks_one_subdivisions_worth)) > ticks_one_subdivisions_worth/2.0) {
-
-                       /* closer to the next subdivision, so shift forward */
-
-                       ticks = lrint (ticks + (ticks_one_subdivisions_worth - rem));
-
-                       DEBUG_TRACE (DEBUG::SnapBBT, string_compose ("moved forward to %1\n", ticks));
-
-                       if (ticks > BBT_Time::ticks_per_beat) {
-                               ++beats;
-                               ticks -= BBT_Time::ticks_per_beat;
-                               DEBUG_TRACE (DEBUG::SnapBBT, string_compose ("fold beat to %1\n", beats));
+               if (pos_bbt.ticks < bbt.ticks) {
+                       if (pos_bbt.bars > 1) {
+                               if (pos_bbt.beats == 1) {
+                                       pos_bbt.bars--;
+                                       pos_bbt.beats = divisions;
+                               } else {
+                                       pos_bbt.beats--;
+                               }
+                               pos_bbt.ticks = BBT_Time::ticks_per_beat - (bbt.ticks - pos_bbt.ticks);
+                       } else {
+                               pos_bbt.beats = 1;
+                               pos_bbt.ticks = 0;
                        }
+               } else {
+                       pos_bbt.ticks -= bbt.ticks;
+               }
 
-               } else if (rem > 0) {
-
-                       /* closer to previous subdivision, so shift backward */
-
-                       if (rem > ticks) {
-                               if (beats == 0) {
-                                       /* can't go backwards past zero, so ... */
-                                       return 0;
-                               }
-                               /* step back to previous beat */
-                               --beats;
-                               ticks = lrint (BBT_Time::ticks_per_beat - rem);
-                               DEBUG_TRACE (DEBUG::SnapBBT, string_compose ("step back beat to %1\n", beats));
+               if (pos_bbt.beats <= bbt.beats) {
+                       if (pos_bbt.bars > 1) {
+                               pos_bbt.bars--;
+                               pos_bbt.beats = divisions - (bbt.beats - pos_bbt.beats);
                        } else {
-                               ticks = lrint (ticks - rem);
-                               DEBUG_TRACE (DEBUG::SnapBBT, string_compose ("moved backward to %1\n", ticks));
+                               pos_bbt.beats = 1;
                        }
                } else {
-                       /* on the subdivision, do nothing */
+                       pos_bbt.beats -= bbt.beats;
                }
+
+               return pos - frame_at_minute (minute_at_bbt_locked (_metrics, pos_bbt));
        }
 
-       const framepos_t ret_frame = frame_at_beat_locked (_metrics, beats + (ticks / BBT_Time::ticks_per_beat));
+       return 0;
+}
 
-       return ret_frame;
+MusicFrame
+TempoMap::round_to_bar (framepos_t fr, RoundMode dir)
+{
+       return round_to_type (fr, dir, Bar);
 }
 
-framepos_t
+MusicFrame
+TempoMap::round_to_beat (framepos_t fr, RoundMode dir)
+{
+       return round_to_type (fr, dir, Beat);
+}
+
+MusicFrame
 TempoMap::round_to_quarter_note_subdivision (framepos_t fr, int sub_num, RoundMode dir)
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       uint32_t ticks = (uint32_t) floor (max (0.0, quarter_note_at_frame_locked (_metrics, fr)) * BBT_Time::ticks_per_beat);
+       uint32_t ticks = (uint32_t) floor (max (0.0, pulse_at_minute_locked (_metrics, minute_at_frame (fr))) * BBT_Time::ticks_per_beat * 4.0);
        uint32_t beats = (uint32_t) floor (ticks / BBT_Time::ticks_per_beat);
        uint32_t ticks_one_subdivisions_worth = (uint32_t) BBT_Time::ticks_per_beat / sub_num;
 
@@ -3336,9 +3987,14 @@ TempoMap::round_to_quarter_note_subdivision (framepos_t fr, int sub_num, RoundMo
                        ticks += ticks_one_subdivisions_worth - mod;
                }
 
-               if (ticks >= BBT_Time::ticks_per_beat) {
-                       ticks -= BBT_Time::ticks_per_beat;
-               }
+//NOTE:  this code intentionally limits the rounding so we don't advance to the next beat.
+//  For the purposes of "jump-to-next-subdivision", we DO want to advance to the next beat.
+//     And since the "prev" direction DOES move beats, I assume this code is unintended.
+//  But I'm keeping it around, until we determine there are no terrible consequences.
+//             if (ticks >= BBT_Time::ticks_per_beat) {
+//                     ticks -= BBT_Time::ticks_per_beat;
+//             }
+
        } else if (dir < 0) {
 
                /* round to previous (or same iff dir == RoundDownMaybe) */
@@ -3384,7 +4040,7 @@ TempoMap::round_to_quarter_note_subdivision (framepos_t fr, int sub_num, RoundMo
                        if (rem > ticks) {
                                if (beats == 0) {
                                        /* can't go backwards past zero, so ... */
-                                       return 0;
+                                       return MusicFrame (0, 0);
                                }
                                /* step back to previous beat */
                                --beats;
@@ -3399,88 +4055,133 @@ TempoMap::round_to_quarter_note_subdivision (framepos_t fr, int sub_num, RoundMo
                }
        }
 
-       const framepos_t ret_frame = frame_at_quarter_note_locked (_metrics, beats + (ticks / BBT_Time::ticks_per_beat));
+       MusicFrame ret (0, 0);
+       ret.frame = frame_at_minute (minute_at_pulse_locked (_metrics, (beats + (ticks / BBT_Time::ticks_per_beat)) / 4.0));
+       ret.division = sub_num;
 
-       return ret_frame;
+       return ret;
 }
 
-framepos_t
+MusicFrame
 TempoMap::round_to_type (framepos_t frame, RoundMode dir, BBTPointType type)
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-
-       const double beat_at_framepos = max (0.0, beat_at_frame_locked (_metrics, frame));
+       const double minute = minute_at_frame (frame);
+       const double beat_at_framepos = max (0.0, beat_at_minute_locked (_metrics, minute));
        BBT_Time bbt (bbt_at_beat_locked (_metrics, beat_at_framepos));
+       MusicFrame ret (0, 0);
 
        switch (type) {
        case Bar:
+               ret.division = -1;
+
                if (dir < 0) {
                        /* find bar previous to 'frame' */
+                       if (bbt.bars > 0)
+                               --bbt.bars;
                        bbt.beats = 1;
                        bbt.ticks = 0;
-                       return frame_at_bbt_locked (_metrics, bbt);
+
+                       ret.frame = frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
+
+                       return ret;
 
                } else if (dir > 0) {
                        /* find bar following 'frame' */
                        ++bbt.bars;
                        bbt.beats = 1;
                        bbt.ticks = 0;
-                       return frame_at_bbt_locked (_metrics, bbt);
+
+                       ret.frame = frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
+
+                       return ret;
                } else {
                        /* true rounding: find nearest bar */
-                       framepos_t raw_ft = frame_at_bbt_locked (_metrics, bbt);
+                       framepos_t raw_ft = frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
                        bbt.beats = 1;
                        bbt.ticks = 0;
-                       framepos_t prev_ft = frame_at_bbt_locked (_metrics, bbt);
+                       framepos_t prev_ft = frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
                        ++bbt.bars;
-                       framepos_t next_ft = frame_at_bbt_locked (_metrics, bbt);
+                       framepos_t next_ft = frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
+
+                       if ((raw_ft - prev_ft) > (next_ft - prev_ft) / 2) {
+                               ret.frame = next_ft;
 
-                       if ((raw_ft - prev_ft) > (next_ft - prev_ft) / 2) { 
-                               return next_ft;
+                               return ret;
                        } else {
-                               return prev_ft;
+                               --bbt.bars;
+                               ret.frame = prev_ft;
+
+                               return ret;
                        }
                }
 
                break;
 
        case Beat:
+               ret.division = 1;
+
                if (dir < 0) {
-                       return frame_at_beat_locked (_metrics, floor (beat_at_framepos));
+                       ret.frame = frame_at_minute (minute_at_beat_locked (_metrics, floor (beat_at_framepos)));
+
+                       return ret;
                } else if (dir > 0) {
-                       return frame_at_beat_locked (_metrics, ceil (beat_at_framepos));
+                       ret.frame = frame_at_minute (minute_at_beat_locked (_metrics, ceil (beat_at_framepos)));
+
+                       return ret;
                } else {
-                       return frame_at_beat_locked (_metrics, floor (beat_at_framepos + 0.5));
+                       ret.frame = frame_at_minute (minute_at_beat_locked (_metrics, floor (beat_at_framepos + 0.5)));
+
+                       return ret;
                }
                break;
        }
 
-       return 0;
+       return MusicFrame (0, 0);
 }
 
 void
 TempoMap::get_grid (vector<TempoMap::BBTPoint>& points,
-                   framepos_t lower, framepos_t upper)
+                   framepos_t lower, framepos_t upper, uint32_t bar_mod)
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       int32_t cnt = ceil (beat_at_frame_locked (_metrics, lower));
+       int32_t cnt = ceil (beat_at_minute_locked (_metrics, minute_at_frame (lower)));
        framecnt_t pos = 0;
        /* although the map handles negative beats, bbt doesn't. */
        if (cnt < 0.0) {
                cnt = 0.0;
        }
 
-       if (frame_at_beat_locked (_metrics, cnt) >= upper) {
+       if (minute_at_beat_locked (_metrics, cnt) >= minute_at_frame (upper)) {
                return;
        }
+       if (bar_mod == 0) {
+               while (pos >= 0 && pos < upper) {
+                       pos = frame_at_minute (minute_at_beat_locked (_metrics, cnt));
+                       const TempoSection tempo = tempo_section_at_minute_locked (_metrics, minute_at_frame (pos));
+                       const MeterSection meter = meter_section_at_minute_locked (_metrics, minute_at_frame (pos));
+                       const BBT_Time bbt = bbt_at_beat_locked (_metrics, cnt);
+
+                       points.push_back (BBTPoint (meter, tempo_at_minute_locked (_metrics, minute_at_frame (pos)), pos, bbt.bars, bbt.beats, tempo.c()));
+                       ++cnt;
+               }
+       } else {
+               BBT_Time bbt = bbt_at_minute_locked (_metrics, minute_at_frame (lower));
+               bbt.beats = 1;
+               bbt.ticks = 0;
+
+               if (bar_mod != 1) {
+                       bbt.bars -= bbt.bars % bar_mod;
+                       ++bbt.bars;
+               }
 
-       while (pos < upper) {
-               pos = frame_at_beat_locked (_metrics, cnt);
-               const TempoSection tempo = tempo_section_at_frame_locked (_metrics, pos);
-               const MeterSection meter = meter_section_at_frame_locked (_metrics, pos);
-               const BBT_Time bbt = bbt_at_beat_locked (_metrics, cnt);
-               points.push_back (BBTPoint (meter, tempo_at_frame_locked (_metrics, pos), pos, bbt.bars, bbt.beats, tempo.c_func()));
-               ++cnt;
+               while (pos >= 0 && pos < upper) {
+                       pos = frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
+                       const TempoSection tempo = tempo_section_at_minute_locked (_metrics, minute_at_frame (pos));
+                       const MeterSection meter = meter_section_at_minute_locked (_metrics, minute_at_frame (pos));
+                       points.push_back (BBTPoint (meter, tempo_at_minute_locked (_metrics, minute_at_frame (pos)), pos, bbt.bars, bbt.beats, tempo.c()));
+                       bbt.bars += bar_mod;
+               }
        }
 }
 
@@ -3488,11 +4189,20 @@ const TempoSection&
 TempoMap::tempo_section_at_frame (framepos_t frame) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       return tempo_section_at_frame_locked (_metrics, frame);
+
+       return tempo_section_at_minute_locked (_metrics, minute_at_frame (frame));
+}
+
+TempoSection&
+TempoMap::tempo_section_at_frame (framepos_t frame)
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       return tempo_section_at_minute_locked (_metrics, minute_at_frame (frame));
 }
 
 const TempoSection&
-TempoMap::tempo_section_at_frame_locked (const Metrics& metrics, framepos_t frame) const
+TempoMap::tempo_section_at_minute_locked (const Metrics& metrics, double minute) const
 {
        TempoSection* prev = 0;
 
@@ -3505,7 +4215,7 @@ TempoMap::tempo_section_at_frame_locked (const Metrics& metrics, framepos_t fram
                        if (!t->active()) {
                                continue;
                        }
-                       if (prev && t->frame() > frame) {
+                       if (prev && t->minute() > minute) {
                                break;
                        }
 
@@ -3520,7 +4230,35 @@ TempoMap::tempo_section_at_frame_locked (const Metrics& metrics, framepos_t fram
 
        return *prev;
 }
+TempoSection&
+TempoMap::tempo_section_at_minute_locked (const Metrics& metrics, double minute)
+{
+       TempoSection* prev = 0;
+
+       TempoSection* t;
+
+       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
 
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
+                       if (!t->active()) {
+                               continue;
+                       }
+                       if (prev && t->minute() > minute) {
+                               break;
+                       }
+
+                       prev = t;
+               }
+       }
+
+       if (prev == 0) {
+               fatal << endmsg;
+               abort(); /*NOTREACHED*/
+       }
+
+       return *prev;
+}
 const TempoSection&
 TempoMap::tempo_section_at_beat_locked (const Metrics& metrics, const double& beat) const
 {
@@ -3532,6 +4270,11 @@ TempoMap::tempo_section_at_beat_locked (const Metrics& metrics, const double& be
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                if ((*i)->is_tempo()) {
                        t = static_cast<TempoSection*> (*i);
+
+                       if (!t->active()) {
+                               continue;
+                       }
+
                        if (prev_t && ((t->pulse() - prev_m->pulse()) * prev_m->note_divisor()) + prev_m->beat() > beat) {
                                break;
                        }
@@ -3542,11 +4285,47 @@ TempoMap::tempo_section_at_beat_locked (const Metrics& metrics, const double& be
        return *prev_t;
 }
 
+TempoSection*
+TempoMap::next_tempo_section (TempoSection* ts) const
+{
+       if (!ts) {
+               return 0;
+       }
+
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       TempoSection* prev = 0;
+
+       for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
+
+               if ((*i)->is_tempo()) {
+                       TempoSection* t = static_cast<TempoSection*> (*i);
+
+                       if (!t->active()) {
+                               continue;
+                       }
+
+                       if (prev && prev == ts) {
+
+                               return t;
+                       }
+
+                       prev = t;
+               }
+       }
+
+       if (prev == 0) {
+               fatal << endmsg;
+               abort(); /*NOTREACHED*/
+       }
+
+       return 0;
+}
 /* don't use this to calculate length (the tempo is only correct for this frame).
    do that stuff based on the beat_at_frame and frame_at_beat api
 */
 double
-TempoMap::frames_per_beat_at (const framepos_t& frame, const framecnt_t& sr) const
+TempoMap::frames_per_quarter_note_at (const framepos_t& frame, const framecnt_t& sr) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
@@ -3569,16 +4348,24 @@ TempoMap::frames_per_beat_at (const framepos_t& frame, const framecnt_t& sr) con
                        ts_at = t;
                }
        }
+       assert (ts_at);
 
        if (ts_after) {
-               return  (60.0 * _frame_rate) / (ts_at->tempo_at_frame (frame, _frame_rate) * 4.0);
+               return  (60.0 * _frame_rate) / ts_at->tempo_at_minute (minute_at_frame (frame)).quarter_notes_per_minute();
        }
        /* must be treated as constant tempo */
-       return ts_at->frames_per_beat (_frame_rate);
+       return ts_at->frames_per_quarter_note (_frame_rate);
+}
+
+const MeterSection&
+TempoMap::meter_section_at_frame (framepos_t frame) const
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+       return meter_section_at_minute_locked (_metrics, minute_at_frame (frame));
 }
 
 const MeterSection&
-TempoMap::meter_section_at_frame_locked (const Metrics& metrics, framepos_t frame) const
+TempoMap::meter_section_at_minute_locked (const Metrics& metrics, double minute) const
 {
        Metrics::const_iterator i;
        MeterSection* prev = 0;
@@ -3590,7 +4377,7 @@ TempoMap::meter_section_at_frame_locked (const Metrics& metrics, framepos_t fram
                if (!(*i)->is_tempo()) {
                        m = static_cast<MeterSection*> (*i);
 
-                       if (prev && (*i)->frame() > frame) {
+                       if (prev && (*i)->minute() > minute) {
                                break;
                        }
 
@@ -3606,14 +4393,6 @@ TempoMap::meter_section_at_frame_locked (const Metrics& metrics, framepos_t fram
        return *prev;
 }
 
-
-const MeterSection&
-TempoMap::meter_section_at_frame (framepos_t frame) const
-{
-       Glib::Threads::RWLock::ReaderLock lm (lock);
-       return meter_section_at_frame_locked (_metrics, frame);
-}
-
 const MeterSection&
 TempoMap::meter_section_at_beat_locked (const Metrics& metrics, const double& beat) const
 {
@@ -3652,17 +4431,18 @@ TempoMap::fix_legacy_session ()
 {
        MeterSection* prev_m = 0;
        TempoSection* prev_t = 0;
+       bool have_initial_t = false;
 
        for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
                MeterSection* m;
                TempoSection* t;
 
                if ((m = dynamic_cast<MeterSection*>(*i)) != 0) {
-                       if (!m->movable()) {
+                       if (m->initial()) {
                                pair<double, BBT_Time> bbt = make_pair (0.0, BBT_Time (1, 1, 0));
                                m->set_beat (bbt);
                                m->set_pulse (0.0);
-                               m->set_frame (0);
+                               m->set_minute (0.0);
                                m->set_position_lock_style (AudioTime);
                                prev_m = m;
                                continue;
@@ -3685,15 +4465,26 @@ TempoMap::fix_legacy_session ()
                                continue;
                        }
 
-                       if (!t->movable()) {
+                       if (t->initial()) {
                                t->set_pulse (0.0);
-                               t->set_frame (0);
+                               t->set_minute (0.0);
                                t->set_position_lock_style (AudioTime);
                                prev_t = t;
+                               have_initial_t = true;
                                continue;
                        }
 
                        if (prev_t) {
+                               /* some 4.x sessions have no initial (non-movable) tempo. */
+                               if (!have_initial_t) {
+                                       prev_t->set_pulse (0.0);
+                                       prev_t->set_minute (0.0);
+                                       prev_t->set_position_lock_style (AudioTime);
+                                       prev_t->set_initial (true);
+                                       prev_t->set_locked_to_meter (true);
+                                       have_initial_t = true;
+                               }
+
                                const double beat = ((t->legacy_bbt().bars - 1) * ((prev_m) ? prev_m->note_divisor() : 4.0))
                                        + (t->legacy_bbt().beats - 1)
                                        + (t->legacy_bbt().ticks / BBT_Time::ticks_per_beat);
@@ -3708,6 +4499,30 @@ TempoMap::fix_legacy_session ()
                }
        }
 }
+void
+TempoMap::fix_legacy_end_session ()
+{
+       TempoSection* prev_t = 0;
+
+       for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
+               TempoSection* t;
+
+               if ((t = dynamic_cast<TempoSection*>(*i)) != 0) {
+
+                       if (!t->active()) {
+                               continue;
+                       }
+
+                       if (prev_t) {
+                               if (prev_t->type() != TempoSection::Constant) {
+                                       prev_t->set_end_note_types_per_minute (t->note_types_per_minute());
+                               }
+                       }
+
+                       prev_t = t;
+               }
+       }
+}
 
 XMLNode&
 TempoMap::get_state ()
@@ -3744,7 +4559,7 @@ TempoMap::set_state (const XMLNode& node, int /*version*/)
                        if (child->name() == TempoSection::xml_state_node_name) {
 
                                try {
-                                       TempoSection* ts = new TempoSection (*child);
+                                       TempoSection* ts = new TempoSection (*child, _frame_rate);
                                        _metrics.push_back (ts);
                                }
 
@@ -3758,7 +4573,7 @@ TempoMap::set_state (const XMLNode& node, int /*version*/)
                        } else if (child->name() == MeterSection::xml_state_node_name) {
 
                                try {
-                                       MeterSection* ms = new MeterSection (*child);
+                                       MeterSection* ms = new MeterSection (*child, _frame_rate);
                                        _metrics.push_back (ms);
                                }
 
@@ -3784,6 +4599,12 @@ TempoMap::set_state (const XMLNode& node, int /*version*/)
                                        fix_legacy_session();
                                        break;
                                }
+
+                               if (t->legacy_end()) {
+                                       fix_legacy_end_session();
+                                       break;
+                               }
+
                                break;
                        }
                }
@@ -3832,27 +4653,36 @@ TempoMap::set_state (const XMLNode& node, int /*version*/)
 }
 
 void
-TempoMap::dump (const Metrics& metrics, std::ostream& o) const
+TempoMap::dump (std::ostream& o) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock, Glib::Threads::TRY_LOCK);
        const MeterSection* m;
        const TempoSection* t;
        const TempoSection* prev_t = 0;
 
-       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
+       for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
 
                if ((t = dynamic_cast<const TempoSection*>(*i)) != 0) {
-                       o << "Tempo @ " << *i << t->beats_per_minute() << " BPM (pulse = 1/" << t->note_type() << ") at " << t->pulse() << " frame= " << t->frame() << " (movable? "
-                         << t->movable() << ')' << " pos lock: " << enum_2_string (t->position_lock_style()) << std::endl;
-                       o << "current      : " << t->beats_per_minute() << " | " << t->pulse() << " | " << t->frame() << std::endl;
+                       o << "Tempo @ " << *i << " start : " << t->note_types_per_minute() << " end : " << t->end_note_types_per_minute() << " BPM (pulse = 1/" << t->note_type()
+                         << " type= " << enum_2_string (t->type()) << ") "  << " at pulse= " << t->pulse()
+                         << " minute= " << t->minute() << " frame= " << t->frame() << " (initial? " << t->initial() << ')'
+                         << " pos lock: " << enum_2_string (t->position_lock_style()) << std::endl;
                        if (prev_t) {
-                               o << "previous     : " << prev_t->beats_per_minute() << " | " << prev_t->pulse() << " | " << prev_t->frame() << std::endl;
-                               o << "calculated   : " << prev_t->tempo_at_pulse (t->pulse()) *  prev_t->note_type() << " | " << prev_t->pulse_at_tempo (t->pulses_per_minute(), t->frame(), _frame_rate) <<  " | " << prev_t->frame_at_tempo (t->pulses_per_minute(), t->pulse(), _frame_rate) << std::endl;
+                               o <<  "  current start  : " << t->note_types_per_minute()
+                                 <<  "  current end  : " << t->end_note_types_per_minute()
+                                 << " | " << t->pulse() << " | " << t->frame() << " | " << t->minute() << std::endl;
+                               o << "  previous     : " << prev_t->note_types_per_minute()
+                                 << " | " << prev_t->pulse() << " | " << prev_t->frame() << " | " << prev_t->minute() << std::endl;
+                               o << "  calculated   : " << prev_t->tempo_at_pulse (t->pulse())
+                                 << " | " << prev_t->pulse_at_ntpm (prev_t->end_note_types_per_minute(), t->minute())
+                                 << " | " << frame_at_minute (prev_t->minute_at_ntpm (prev_t->end_note_types_per_minute(), t->pulse()))
+                                 << " | " << prev_t->minute_at_ntpm (prev_t->end_note_types_per_minute(), t->pulse()) << std::endl;
                        }
                        prev_t = t;
                } else if ((m = dynamic_cast<const MeterSection*>(*i)) != 0) {
-                       o << "Meter @ " << *i << ' ' << m->divisions_per_bar() << '/' << m->note_divisor() << " at " << m->bbt() << " frame= " << m->frame()
-                         << " pulse: " << m->pulse() <<  " beat : " << m->beat() << " pos lock: " << enum_2_string (m->position_lock_style()) << " (movable? " << m->movable() << ')' << endl;
+                       o << "Meter @ " << *i << ' ' << m->divisions_per_bar() << '/' << m->note_divisor() << " at " << m->bbt()
+                         << " frame= " << m->frame() << " pulse: " << m->pulse() <<  " beat : " << m->beat()
+                         << " pos lock: " << enum_2_string (m->position_lock_style()) << " (initial? " << m->initial() << ')' << endl;
                }
        }
        o << "------" << std::endl;
@@ -3891,129 +4721,24 @@ TempoMap::n_meters() const
 void
 TempoMap::insert_time (framepos_t where, framecnt_t amount)
 {
-       {
-               Glib::Threads::RWLock::WriterLock lm (lock);
-               for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
-                       if ((*i)->frame() >= where && (*i)->movable ()) {
-                               (*i)->set_frame ((*i)->frame() + amount);
-                       }
-               }
-
-               /* now reset the BBT time of all metrics, based on their new
-                * audio time. This is the only place where we do this reverse
-                * timestamp.
-                */
-
-               Metrics::iterator i;
-               const MeterSection* meter;
-               const TempoSection* tempo;
-               MeterSection *m;
-               TempoSection *t;
-
-               meter = &first_meter ();
-               tempo = &first_tempo ();
+       for (Metrics::reverse_iterator i = _metrics.rbegin(); i != _metrics.rend(); ++i) {
+               if ((*i)->frame() >= where && !(*i)->initial ()) {
+                       MeterSection* ms;
+                       TempoSection* ts;
 
-               BBT_Time start;
-               BBT_Time end;
-
-               // cerr << "\n###################### TIMESTAMP via AUDIO ##############\n" << endl;
-
-               bool first = true;
-               MetricSection* prev = 0;
-
-               for (i = _metrics.begin(); i != _metrics.end(); ++i) {
-
-                       BBT_Time bbt;
-                       //TempoMetric metric (*meter, *tempo);
-                       MeterSection* ms = const_cast<MeterSection*>(meter);
-                       TempoSection* ts = const_cast<TempoSection*>(tempo);
-                       if (prev) {
-                               if (ts){
-                                       if ((t = dynamic_cast<TempoSection*>(prev)) != 0) {
-                                               if (!t->active()) {
-                                                       continue;
-                                               }
-                                               ts->set_pulse (t->pulse());
-                                       }
-                                       if ((m = dynamic_cast<MeterSection*>(prev)) != 0) {
-                                               ts->set_pulse (m->pulse());
-                                       }
-                                       ts->set_frame (prev->frame());
-
-                               }
-                               if (ms) {
-                                       if ((m = dynamic_cast<MeterSection*>(prev)) != 0) {
-                                               pair<double, BBT_Time> start = make_pair (m->beat(), m->bbt());
-                                               ms->set_beat (start);
-                                               ms->set_pulse (m->pulse());
-                                       }
-                                       if ((t = dynamic_cast<TempoSection*>(prev)) != 0) {
-                                               if (!t->active()) {
-                                                       continue;
-                                               }
-                                               const double beat = beat_at_pulse_locked (_metrics, t->pulse());
-                                               pair<double, BBT_Time> start = make_pair (beat, bbt_at_beat_locked (_metrics, beat));
-                                               ms->set_beat (start);
-                                               ms->set_pulse (t->pulse());
-                                       }
-                                       ms->set_frame (prev->frame());
-                               }
-
-                       } else {
-                               // metric will be at frames=0 bbt=1|1|0 by default
-                               // which is correct for our purpose
+                       if ((ms = dynamic_cast <MeterSection*>(*i)) != 0) {
+                               gui_set_meter_position (ms, (*i)->frame() + amount);
                        }
 
-                       // cerr << bbt << endl;
-
-                       if ((t = dynamic_cast<TempoSection*>(*i)) != 0) {
-                               if (!t->active()) {
-                                       continue;
-                               }
-                               t->set_pulse (pulse_at_frame_locked (_metrics, m->frame()));
-                               tempo = t;
-                               // cerr << "NEW TEMPO, frame = " << (*i)->frame() << " beat = " << (*i)->pulse() <<endl;
-                       } else if ((m = dynamic_cast<MeterSection*>(*i)) != 0) {
-                               bbt = bbt_at_frame_locked (_metrics, m->frame());
-
-                               // cerr << "timestamp @ " << (*i)->frame() << " with " << bbt.bars << "|" << bbt.beats << "|" << bbt.ticks << " => ";
-
-                               if (first) {
-                                       first = false;
-                               } else {
-
-                                       if (bbt.ticks > BBT_Time::ticks_per_beat/2) {
-                                               /* round up to next beat */
-                                               bbt.beats += 1;
-                                       }
-
-                                       bbt.ticks = 0;
-
-                                       if (bbt.beats != 1) {
-                                               /* round up to next bar */
-                                               bbt.bars += 1;
-                                               bbt.beats = 1;
-                                       }
-                               }
-                               pair<double, BBT_Time> start = make_pair (max (0.0, beat_at_frame_locked (_metrics, m->frame())), bbt);
-                               m->set_beat (start);
-                               m->set_pulse (pulse_at_frame_locked (_metrics, m->frame()));
-                               meter = m;
-                               // cerr << "NEW METER, frame = " << (*i)->frame() << " beat = " << (*i)->pulse() <<endl;
-                       } else {
-                               fatal << _("programming error: unhandled MetricSection type") << endmsg;
-                               abort(); /*NOTREACHED*/
+                       if ((ts = dynamic_cast <TempoSection*>(*i)) != 0) {
+                               gui_set_tempo_position (ts, (*i)->frame() + amount, 0);
                        }
-
-                       prev = (*i);
                }
-
-               recompute_map (_metrics);
        }
 
-
        PropertyChanged (PropertyChange ());
 }
+
 bool
 TempoMap::remove_time (framepos_t where, framecnt_t amount)
 {
@@ -4039,7 +4764,7 @@ TempoMap::remove_time (framepos_t where, framecnt_t amount)
                        }
                        else if ((*i)->frame() >= where) {
                                // TODO: make sure that moved tempo/meter markers are rounded to beat/bar boundaries
-                               (*i)->set_frame ((*i)->frame() - amount);
+                               (*i)->set_minute ((*i)->minute() - minute_at_frame (amount));
                                if ((*i)->frame() == where) {
                                        // marker was immediately after end of range
                                        tempo_after = dynamic_cast<TempoSection*> (*i);
@@ -4052,12 +4777,12 @@ TempoMap::remove_time (framepos_t where, framecnt_t amount)
                //find the last TEMPO and METER metric (if any) and move it to the cut point so future stuff is correct
                if (last_tempo && !tempo_after) {
                        metric_kill_list.remove(last_tempo);
-                       last_tempo->set_frame(where);
+                       last_tempo->set_minute (minute_at_frame (where));
                        moved = true;
                }
                if (last_meter && !meter_after) {
                        metric_kill_list.remove(last_meter);
-                       last_meter->set_frame(where);
+                       last_meter->set_minute (minute_at_frame (where));
                        moved = true;
                }
 
@@ -4075,40 +4800,24 @@ TempoMap::remove_time (framepos_t where, framecnt_t amount)
        return moved;
 }
 
-/** Add some (fractional) beats to a session frame position, and return the result in frames.
+/** Add some (fractional) Beats to a session frame position, and return the result in frames.
  *  pos can be -ve, if required.
  */
 framepos_t
-TempoMap::framepos_plus_beats (framepos_t frame, Evoral::Beats beats) const
-{
-       Glib::Threads::RWLock::ReaderLock lm (lock);
-
-       return frame_at_beat_locked (_metrics, beat_at_frame_locked (_metrics, frame) + beats.to_double());
-}
-framepos_t
-TempoMap::framepos_plus_qn (framepos_t frame, Evoral::Beats quarter_note) const
-{
-       Glib::Threads::RWLock::ReaderLock lm (lock);
-
-       return frame_at_quarter_note_locked (_metrics, quarter_note_at_frame_locked (_metrics, frame) + quarter_note.to_double());
-}
-
-/** Subtract some (fractional) beats from a frame position, and return the result in frames */
-framepos_t
-TempoMap::framepos_minus_beats (framepos_t pos, Evoral::Beats beats) const
+TempoMap::framepos_plus_qn (framepos_t frame, Evoral::Beats beats) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
+       const double frame_qn = pulse_at_minute_locked (_metrics, minute_at_frame (frame)) * 4.0;
 
-       return frame_at_beat_locked (_metrics, beat_at_frame_locked (_metrics, pos) - beats.to_double());
+       return frame_at_minute (minute_at_pulse_locked (_metrics, (frame_qn + beats.to_double()) / 4.0));
 }
 
-/** Add the BBT interval op to pos and return the result */
 framepos_t
 TempoMap::framepos_plus_bbt (framepos_t pos, BBT_Time op) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       BBT_Time pos_bbt = bbt_at_beat_locked (_metrics, beat_at_frame_locked (_metrics, pos));
+       BBT_Time pos_bbt = bbt_at_beat_locked (_metrics, beat_at_minute_locked (_metrics, minute_at_frame (pos)));
        pos_bbt.ticks += op.ticks;
        if (pos_bbt.ticks >= BBT_Time::ticks_per_beat) {
                ++pos_bbt.beats;
@@ -4124,27 +4833,20 @@ TempoMap::framepos_plus_bbt (framepos_t pos, BBT_Time op) const
        }
        pos_bbt.bars += op.bars;
 
-       return frame_at_bbt_locked (_metrics, pos_bbt);
+       return frame_at_minute (minute_at_bbt_locked (_metrics, pos_bbt));
 }
 
 /** Count the number of beats that are equivalent to distance when going forward,
     starting at pos.
 */
-Evoral::Beats
-TempoMap::framewalk_to_beats (framepos_t pos, framecnt_t distance) const
-{
-       Glib::Threads::RWLock::ReaderLock lm (lock);
-
-       return Evoral::Beats (beat_at_frame_locked (_metrics, pos + distance) - beat_at_frame_locked (_metrics, pos));
-}
-
 Evoral::Beats
 TempoMap::framewalk_to_qn (framepos_t pos, framecnt_t distance) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return Evoral::Beats (quarter_note_at_frame_locked (_metrics, pos + distance) - quarter_note_at_frame_locked (_metrics, pos));
+       return Evoral::Beats (quarter_notes_between_frames_locked (_metrics, pos, pos + distance));
 }
+
 struct bbtcmp {
     bool operator() (const BBT_Time& a, const BBT_Time& b) {
            return a < b;
@@ -4158,7 +4860,7 @@ operator<< (std::ostream& o, const Meter& m) {
 
 std::ostream&
 operator<< (std::ostream& o, const Tempo& t) {
-       return o << t.beats_per_minute() << " 1/" << t.note_type() << "'s per minute";
+       return o << t.note_types_per_minute() << " 1/" << t.note_type() << "'s per minute";
 }
 
 std::ostream&