Later code depends on prev_t not being NULL, use an assert()
[ardour.git] / libs / ardour / tempo.cc
index 97c468e1b6bdf1974437b9c09f9fe74e2c6e5ecc..d800eb6f6083fa029f44e989ae604a9c590a690d 100644 (file)
@@ -33,7 +33,7 @@
 #include "ardour/lmath.h"
 #include "ardour/tempo.h"
 
-#include "i18n.h"
+#include "pbd/i18n.h"
 #include <locale.h>
 
 using namespace std;
@@ -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);
+
+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
@@ -72,8 +84,8 @@ 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)
+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)
        , _active (true)
@@ -110,19 +122,18 @@ 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-minutee\" value") << endmsg;
+                       throw failed_constructor();
+               }
        }
 
        if ((prop = node.property ("note-type")) == 0) {
@@ -132,7 +143,7 @@ TempoSection::TempoSection (const XMLNode& node)
                if (sscanf (prop->value().c_str(), "%lf", &_note_type) != 1 || _note_type < 1.0) {
                        error << _("TempoSection XML node has an illegal \"note-type\" value") << endmsg;
                        throw failed_constructor();
-               }
+       }
        }
 
        if ((prop = node.property ("movable")) == 0) {
@@ -179,13 +190,13 @@ TempoSection::get_state() const
        char buf[256];
        LocaleGuard lg;
 
-       snprintf (buf, sizeof (buf), "%f", pulse());
+       snprintf (buf, sizeof (buf), "%lf", pulse());
        root->add_property ("pulse", buf);
        snprintf (buf, sizeof (buf), "%li", frame());
        root->add_property ("frame", buf);
-       snprintf (buf, sizeof (buf), "%f", _beats_per_minute);
+       snprintf (buf, sizeof (buf), "%lf", _note_types_per_minute);
        root->add_property ("beats-per-minute", buf);
-       snprintf (buf, sizeof (buf), "%f", _note_type);
+       snprintf (buf, sizeof (buf), "%lf", _note_type);
        root->add_property ("note-type", buf);
        snprintf (buf, sizeof (buf), "%s", movable()?"yes":"no");
        root->add_property ("movable", buf);
@@ -204,87 +215,125 @@ TempoSection::set_type (Type type)
        _type = type;
 }
 
-/** returns the tempo in whole pulses per minute at the zero-based (relative to session) frame.
+/** returns the Tempo at the session-relative minute.
 */
-double
-TempoSection::tempo_at_frame (const framepos_t& f, const framecnt_t& frame_rate) const
+Tempo
+TempoSection::tempo_at_minute (const double& m) const
 {
 
        if (_type == Constant || _c_func == 0.0) {
-               return pulses_per_minute();
+               return Tempo (note_types_per_minute(), note_type());
        }
 
-       return pulse_tempo_at_time (frame_to_minute (f - frame(), frame_rate));
+       return Tempo (_tempo_at_time (m - minute()), _note_type);
 }
 
-/** returns the zero-based frame (relative to session)
-   where the tempo in whole pulses per minute occurs in this section.
-   beat b is only used for constant tempos.
-   note that the tempo map may have multiple such values.
+/** 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.
+ *
 */
-framepos_t
-TempoSection::frame_at_tempo (const double& ppm, const double& b, const framecnt_t& frame_rate) const
+
+/** 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::minute_at_ntpm (const double& ntpm, const double& p) const
 {
        if (_type == Constant || _c_func == 0.0) {
-               return ((b - pulse())  * frames_per_pulse (frame_rate))  + frame();
+               return ((p - pulse()) / pulses_per_minute()) + minute();
        }
 
-       return minute_to_frame (time_at_pulse_tempo (ppm), frame_rate) + frame();
+       return _time_at_tempo (ntpm) + minute();
 }
-/** returns the tempo in pulses per minute at the zero-based (relative to session) beat.
-*/
-double
+
+/** 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 pulses_per_minute();
+               return Tempo (note_types_per_minute(), note_type());
+       }
+
+       return Tempo (_tempo_at_pulse (p - pulse()), _note_type);
+}
+
+/** 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::pulse_at_ntpm (const double& ntpm, const double& m) const
+{
+       if (_type == Constant || _c_func == 0.0) {
+               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;
+               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();
+               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
+{
+       if (_type == Constant || _c_func == 0.0) {
+               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();
+               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 +411,91 @@ 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_func_pulse (const double& end_npm, const double& end_pulse) const
 {
-       return c_func (end_bpm, frame_to_minute (end_frame - frame(), frame_rate));
-}
-
-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_func_minute (const double& end_npm, const double& end_minute) const
 {
-       return (frame / (double) frame_rate) / 60.0;
+       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_func) const
 {
-       return log (end_ppm / pulses_per_minute()) /  c_func;
+       return log (end_npm / note_types_per_minute()) / c_func;
 }
 
 /*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_func * 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_func;
 }
 
-/* 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_func) / _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_func) + 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_func * time) * (note_types_per_minute() / _c_func)) / _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_func * pulse * _note_type) / note_types_per_minute()) / _c_func;
 }
 
 /***********************************************************************/
 
 const string MeterSection::xml_state_node_name = "Meter";
 
-MeterSection::MeterSection (const XMLNode& node)
-       : MetricSection (0.0, 0, MusicTime), 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 +549,9 @@ 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));
                }
        }
 
@@ -569,12 +612,12 @@ MeterSection::get_state() const
        root->add_property ("bbt", buf);
        snprintf (buf, sizeof (buf), "%lf", beat());
        root->add_property ("beat", buf);
-       snprintf (buf, sizeof (buf), "%f", _note_type);
+       snprintf (buf, sizeof (buf), "%lf", _note_type);
        root->add_property ("note-type", buf);
        snprintf (buf, sizeof (buf), "%li", frame());
        root->add_property ("frame", buf);
        root->add_property ("lock-style", enum_2_string (position_lock_style()));
-       snprintf (buf, sizeof (buf), "%f", _divisions_per_bar);
+       snprintf (buf, sizeof (buf), "%lf", _divisions_per_bar);
        root->add_property ("divisions-per-bar", buf);
        snprintf (buf, sizeof (buf), "%s", movable()?"yes":"no");
        root->add_property ("movable", buf);
@@ -586,51 +629,83 @@ MeterSection::get_state() const
 /*
   Tempo Map Overview
 
-  Tempo is the rate of the musical pulse.
-  Meters divide the pulses into measures and beats.
-
-  Note that Tempo::beats_per_minute() has nothing to do with musical beats.
-  It should rather be thought of as tempo note divisions per minute.
-
-  TempoSections, which are nice to think of in whole pulses per minute,
-  and MeterSecions which divide tempo pulses into measures (via divisions_per_bar)
-  and beats (via note_divisor) are used to form a tempo map.
-  TempoSections and MeterSections may be locked to either audio or music (position lock style).
-  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 pulse/frame layout to find the beat & pulse or frame position of each meter (again depending on lock style).
+  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
 
-  Having done this, we can now find any one of tempo, beat, frame or pulse if a beat, frame, pulse or tempo is known.
+  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).
 
-  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.
+  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.
 
-  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.
+  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.
 
-  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())
+  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.
 
-  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.
+  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).
 
-  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.
-
-  A tempo locked to music is locked to musical pulses.
-  A meter locked to music is locked to beats.
-
-  Recomputing the tempo map is the process where the 'missing' position
-  (tempo pulse or meter pulse & beat in the case of AudioTime, frame for MusicTime) is calculated.
+  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,
   reordering is frequent. Care must be taken to keep _metrics in a solved state.
   Solved means ordered by frame or pulse with frame-accurate precision (see check_solved()).
+
+  Music and Audio
+
+  Music and audio-locked objects may seem interchangeable on the surface, but when translating
+  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.
+
+  You cannot use a frame measurement to determine beat distance except under special circumstances
+  (e.g. where the user has requested that a beat lie on a SMPTE frame or if the tempo is known to be constant over the duration).
+
+  This means is that a user operating on a musical grid must supply the desired beat position and/or current beat quantization in order for the
+  sample space the user is operating at to be translated correctly to the object.
+
+  The current approach is to interpret the supplied frame using the grid division the user has currently selected.
+  If the user has no musical grid set, they are actually operating in sample space (even SMPTE frames are rounded to audio frame), so
+  the supplied audio frame is interpreted as the desired musical location (beat_at_frame()).
+
+  tldr: Beat, being a function of time, has nothing to do with sample rate, but time quantization can get in the way of precision.
+
+  When frame_at_beat() is called, the position calculation is performed in pulses and minutes.
+  The result is rounded to audio frames.
+  When beat_at_frame() is called, the frame is converted to minutes, with no rounding performed on the result.
+
+  So :
+  frame_at_beat (beat_at_frame (frame)) == frame
+  but :
+  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.
+  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 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 {
     bool operator() (const MetricSection* a, const MetricSection* b) {
@@ -649,8 +724,8 @@ 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.note_types_per_minute(), _default_tempo.note_type(), TempoSection::Ramp, 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_movable (false);
        m->set_movable (false);
@@ -672,6 +747,18 @@ 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)
 {
@@ -733,13 +820,13 @@ TempoMap::remove_meter (const MeterSection& tempo, bool complete_operation)
 bool
 TempoMap::remove_meter_locked (const MeterSection& meter)
 {
-       Metrics::iterator i;
 
-       for (i = _metrics.begin(); i != _metrics.end(); ++i) {
-               TempoSection* t = 0;
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
-                       if (meter.frame() == (*i)->frame()) {
-                               if (t->locked_to_meter()) {
+       if (meter.position_lock_style() == AudioTime) {
+               /* remove meter-locked tempo */
+               for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
+                       TempoSection* t = 0;
+                       if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
+                               if (t->locked_to_meter() && meter.frame() == (*i)->frame()) {
                                        delete (*i);
                                        _metrics.erase (i);
                                        break;
@@ -748,7 +835,7 @@ TempoMap::remove_meter_locked (const MeterSection& meter)
                }
        }
 
-       for (i = _metrics.begin(); i != _metrics.end(); ++i) {
+       for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
                if (dynamic_cast<MeterSection*> (*i) != 0) {
                        if (meter.frame() == (*i)->frame()) {
                                if ((*i)->movable()) {
@@ -892,14 +979,14 @@ TempoMap::do_insert (MetricSection* section)
                //dump (_metrics, 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)
 {
        TempoSection* ts = 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), type, pls, true);
        }
 
 
@@ -918,11 +1005,11 @@ TempoMap::replace_tempo (const TempoSection& ts, const Tempo& tempo, const doubl
                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);
+                       add_tempo_locked (tempo, pulse, minute_at_frame (frame), type, pls, true, locked_to_meter);
                } 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);
                        {
                                /* cannot move the first tempo section */
@@ -936,33 +1023,38 @@ TempoMap::replace_tempo (const TempoSection& ts, const Tempo& tempo, const doubl
 }
 
 TempoSection*
-TempoMap::add_tempo_locked (const Tempo& tempo, double pulse, framepos_t frame
+TempoMap::add_tempo_locked (const Tempo& tempo, double pulse, double minute
                            , TempoSection::Type type, 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.note_types_per_minute(), tempo.note_type(), type, pls, _frame_rate);
        t->set_locked_to_meter (locked_to_meter);
+       bool solved = false;
 
        do_insert (t);
 
        if (recompute) {
                if (pls == AudioTime) {
-                       solve_map_frame (_metrics, t, t->frame());
+                       solved = solve_map_minute (_metrics, t, t->minute());
                } else {
-                       solve_map_pulse (_metrics, t, t->pulse());
+                       solved = 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, PositionLockStyle pls)
 {
        MeterSection* m = 0;
        {
                Glib::Threads::RWLock::WriterLock lm (lock);
-               m = add_meter_locked (meter, beat, where, frame, pls, true);
+               m = add_meter_locked (meter, beat, where, pls, true);
        }
 
 
@@ -977,7 +1069,7 @@ 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, PositionLockStyle pls)
 {
        {
                Glib::Threads::RWLock::WriterLock lm (lock);
@@ -985,7 +1077,7 @@ TempoMap::replace_meter (const MeterSection& ms, const Meter& meter, const BBT_T
 
                if (ms.movable()) {
                        remove_meter_locked (ms);
-                       add_meter_locked (meter, beat, where, frame, pls, true);
+                       add_meter_locked (meter, beat, where, pls, true);
                } else {
                        MeterSection& first (first_meter());
                        TempoSection& first_t (first_tempo());
@@ -993,10 +1085,10 @@ 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_pulse (0.0);
                        first_t.set_position_lock_style (AudioTime);
                        recompute_map (_metrics);
@@ -1007,36 +1099,57 @@ TempoMap::replace_meter (const MeterSection& ms, const Meter& meter, const BBT_T
 }
 
 MeterSection*
-TempoMap::add_meter_locked (const Meter& meter, double beat, const Timecode::BBT_Time& where, framepos_t frame, PositionLockStyle pls, bool recompute)
+TempoMap::add_meter_locked (const Meter& meter, double beat, const BBT_Time& where, PositionLockStyle pls, bool recompute)
 {
-       const MeterSection& prev_m = meter_section_at_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 */
-               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,  time_minutes, TempoSection::Ramp, AudioTime, true, true);
+
+               if (!mlt) {
+                       return 0;
+               }
+
        }
 
-       MeterSection* new_meter = new MeterSection (pulse, frame, beat, where, meter.divisions_per_bar(), meter.note_divisor(), pls);
+       MeterSection* new_meter = new MeterSection (pulse, time_minutes, beat, where, meter.divisions_per_bar(), meter.note_divisor(), pls, _frame_rate);
+       bool solved = false;
 
        do_insert (new_meter);
 
        if (recompute) {
 
                if (pls == AudioTime) {
-                       solve_map_frame (_metrics, new_meter, frame);
+                       solved = solve_map_minute (_metrics, new_meter, time_minutes);
                } else {
-                       solve_map_bbt (_metrics, new_meter, where);
+                       solved = solve_map_bbt (_metrics, new_meter, where);
+                       /* required due to resetting the pulse of meter-locked tempi above.
+                          Arguably  solve_map_bbt() should use solve_map_pulse (_metrics, TempoSection) instead,
+                          but afaict this cannot cause the map to be left unsolved (these tempi are all audio locked).
+                       */
+                       recompute_map (_metrics);
                }
        }
 
+       if (!solved && recompute) {
+               /* if this has failed to solve, there is little we can do other than to ensure that
+                  the new map is recalculated.
+               */
+               warning << "Adding meter may have left the tempo map unsolved." << endmsg;
+               recompute_map (_metrics);
+       }
+
        return new_meter;
 }
 
 void
-TempoMap::change_initial_tempo (double beats_per_minute, double note_type)
+TempoMap::change_initial_tempo (double note_types_per_minute, double note_type)
 {
-       Tempo newtempo (beats_per_minute, note_type);
+       Tempo newtempo (note_types_per_minute, note_type);
        TempoSection* t;
 
        for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
@@ -1056,9 +1169,9 @@ 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)
 {
-       Tempo newtempo (beats_per_minute, note_type);
+       Tempo newtempo (note_types_per_minute, note_type);
 
        TempoSection* prev;
        TempoSection* first;
@@ -1185,14 +1298,15 @@ TempoMap::first_tempo ()
        return *t;
 }
 void
-TempoMap::recompute_tempos (Metrics& metrics)
+TempoMap::recompute_tempi (Metrics& metrics)
 {
        TempoSection* prev_t = 0;
 
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                TempoSection* t;
 
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
                        if (!t->active()) {
                                continue;
                        }
@@ -1205,20 +1319,21 @@ TempoMap::recompute_tempos (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_func (prev_t->compute_c_func_minute (t->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 (t->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_func (prev_t->compute_c_func_pulse (t->note_types_per_minute(), t->pulse()));
+                                       t->set_minute (prev_t->minute_at_ntpm (t->note_types_per_minute(), t->pulse()));
 
                                }
                        }
                        prev_t = t;
                }
        }
+       assert (prev_t);
        prev_t->set_c_func (0.0);
 }
 
@@ -1234,14 +1349,16 @@ TempoMap::recompute_meters (Metrics& metrics)
        MeterSection* prev_m = 0;
 
        for (Metrics::const_iterator mi = metrics.begin(); mi != metrics.end(); ++mi) {
-               if ((meter = dynamic_cast<MeterSection*> (*mi)) != 0) {
+               if (!(*mi)->is_tempo()) {
+                       meter = static_cast<MeterSection*> (*mi);
                        if (meter->position_lock_style() == AudioTime) {
                                double pulse = 0.0;
                                pair<double, BBT_Time> b_bbt;
                                TempoSection* meter_locked_tempo = 0;
                                for (Metrics::const_iterator ii = metrics.begin(); ii != metrics.end(); ++ii) {
                                        TempoSection* t;
-                                       if ((t = dynamic_cast<TempoSection*> (*ii)) != 0) {
+                                       if ((*ii)->is_tempo()) {
+                                               t = static_cast<TempoSection*> (*ii);
                                                if ((t->locked_to_meter() || !t->movable()) && t->frame() == meter->frame()) {
                                                        meter_locked_tempo = t;
                                                        break;
@@ -1292,7 +1409,7 @@ 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;
@@ -1305,15 +1422,6 @@ 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) {
@@ -1322,7 +1430,7 @@ TempoMap::recompute_map (Metrics& metrics, framepos_t end)
                return;
        }
 
-       recompute_tempos (metrics);
+       recompute_tempi (metrics);
        recompute_meters (metrics);
 }
 
@@ -1371,7 +1479,8 @@ TempoMap::metric_at (BBT_Time bbt) const
 
        for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
                MeterSection* mw;
-               if ((mw = dynamic_cast<MeterSection*> (*i)) != 0) {
+               if (!(*i)->is_tempo()) {
+                       mw = static_cast<MeterSection*> (*i);
                        BBT_Time section_start (mw->bbt());
 
                        if (section_start.bars > bbt.bars || (section_start.bars == bbt.bars && section_start.beats > bbt.beats)) {
@@ -1385,36 +1494,44 @@ TempoMap::metric_at (BBT_Time bbt) const
        return m;
 }
 
+/** 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).
+ *
+ * This function uses both tempo and meter.
+ */
 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));
 }
 
-/* meter / tempo section based */
+/* 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_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) {
-               MeterSection* m;
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
-                       if (prev_m && m->frame() > frame) {
-                               next_m = m;
+               if (!(*i)->is_tempo()) {
+                       if (prev_m && (*i)->minute() > minute) {
+                               next_m = static_cast<MeterSection*> (*i);
                                break;
                        }
-                       prev_m = m;
+                       prev_m = static_cast<MeterSection*> (*i);
                }
        }
-       if (frame < prev_m->frame()) {
-               return 0.0;
-       }
-       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) {
                return next_m->beat();
        }
@@ -1422,222 +1539,370 @@ TempoMap::beat_at_frame_locked (const Metrics& metrics, const framecnt_t& frame)
        return beat;
 }
 
-framecnt_t
+/** 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 section based */
-framecnt_t
-TempoMap::frame_at_beat_locked (const Metrics& metrics, const double& beat) const
+/* meter & tempo section based */
+double
+TempoMap::minute_at_beat_locked (const Metrics& metrics, const double& beat) const
 {
-       const TempoSection& prev_t = tempo_section_at_beat_locked (metrics, beat);
        MeterSection* prev_m = 0;
+       TempoSection* prev_t = 0;
+
+       MeterSection* m;
 
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
-               MeterSection* m;
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection*> (*i);
                        if (prev_m && m->beat() > beat) {
                                break;
                        }
                        prev_m = m;
                }
        }
+       assert (prev_m);
 
-       return prev_t.frame_at_pulse (((beat - prev_m->beat()) / prev_m->note_divisor()) + prev_m->pulse(), _frame_rate);
-}
-
-double
-TempoMap::pulse_at_beat (const double& beat) const
-{
-       Glib::Threads::RWLock::ReaderLock lm (lock);
-       return pulse_at_beat_locked (_metrics, beat);
-}
-
-double
-TempoMap::pulse_at_beat_locked (const Metrics& metrics, const double& beat) const
-{
-       MeterSection* prev_m = 0;
+       TempoSection* t;
 
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
-               MeterSection* m;
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
-                       if (prev_m && m->beat() > beat) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
+                       if (prev_t && ((t->pulse() - prev_m->pulse()) * prev_m->note_divisor()) + prev_m->beat() > beat) {
                                break;
                        }
-                       prev_m = m;
+                       prev_t = t;
                }
 
        }
-       double const ret = prev_m->pulse() + ((beat - prev_m->beat()) / prev_m->note_divisor());
-       return ret;
+       assert (prev_t);
+
+       return prev_t->minute_at_pulse (((beat - prev_m->beat()) / prev_m->note_divisor()) + prev_m->pulse());
 }
 
-double
-TempoMap::beat_at_pulse (const double& pulse) const
+/** 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 beat_at_pulse_locked (_metrics, pulse);
+
+       return tempo_at_minute_locked (_metrics, minute_at_frame (frame));
 }
 
-double
-TempoMap::beat_at_pulse_locked (const Metrics& metrics, const double& pulse) const
+Tempo
+TempoMap::tempo_at_minute_locked (const Metrics& metrics, const double& minute) const
 {
-       MeterSection* prev_m = 0;
+       TempoSection* prev_t = 0;
+
+       TempoSection* t;
 
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
-               MeterSection* m;
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
-                       if (prev_m && m->pulse() > pulse) {
-                               if (((pulse - prev_m->pulse()) * prev_m->note_divisor()) + prev_m->beat() > m->beat()) {
-                                       break;
-                               }
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
+                       if (!t->active()) {
+                               continue;
                        }
-                       prev_m = m;
+                       if ((prev_t) && t->minute() > minute) {
+                               /* t is the section past frame */
+                               return prev_t->tempo_at_minute (minute);
+                       }
+                       prev_t = t;
                }
        }
 
-       double const ret = ((pulse - prev_m->pulse()) * prev_m->note_divisor()) + prev_m->beat();
-       return ret;
+       return Tempo (prev_t->note_types_per_minute(), prev_t->note_type());
 }
 
-double
-TempoMap::pulse_at_frame (const framecnt_t& frame) const
+/** returns the frame at which the supplied tempo occurs, or
+ *  the frame of the last tempo section (search exhausted)
+ *  only the position of the first occurence will be returned
+ *  (extend me)
+*/
+framepos_t
+TempoMap::frame_at_tempo (const Tempo& tempo) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       return pulse_at_frame_locked (_metrics, frame);
+
+       return frame_at_minute (minute_at_tempo_locked (_metrics, tempo));
 }
 
-/* tempo section based */
 double
-TempoMap::pulse_at_frame_locked (const Metrics& metrics, const framecnt_t& frame) const
+TempoMap::minute_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) const
 {
-       /* HOLD (at least) THE READER LOCK */
        TempoSection* prev_t = 0;
+       const double tempo_bpm = tempo.note_types_per_minute();
 
-       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
+       Metrics::const_iterator i;
+
+       for (i = metrics.begin(); i != metrics.end(); ++i) {
                TempoSection* t;
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
+
                        if (!t->active()) {
                                continue;
                        }
-                       if (prev_t && t->frame() > frame) {
-                               /*the previous ts is the one containing the frame */
-                               const double ret = prev_t->pulse_at_frame (frame, _frame_rate);
-                               return ret;
+
+                       const double t_bpm = t->note_types_per_minute();
+
+                       if (t_bpm == tempo_bpm) {
+                               return t->minute();
+                       }
+
+                       if (prev_t) {
+                               const double prev_t_bpm = prev_t->note_types_per_minute();
+
+                               if ((t_bpm > tempo_bpm && prev_t_bpm < tempo_bpm) || (t_bpm < tempo_bpm && prev_t_bpm > tempo_bpm)) {
+                                       return prev_t->minute_at_ntpm (prev_t->note_types_per_minute(), prev_t->pulse());
+                               }
                        }
                        prev_t = t;
                }
        }
 
-       /* treated as constant for this ts */
-       const double pulses_in_section = (frame - prev_t->frame()) / prev_t->frames_per_pulse (_frame_rate);
-
-       return pulses_in_section + prev_t->pulse();
-}
-
-framecnt_t
-TempoMap::frame_at_pulse (const double& pulse) const
-{
-       Glib::Threads::RWLock::ReaderLock lm (lock);
-       return frame_at_pulse_locked (_metrics, pulse);
+       return prev_t->minute();
 }
 
-/* tempo section based */
-framecnt_t
-TempoMap::frame_at_pulse_locked (const Metrics& metrics, const double& pulse) const
+Tempo
+TempoMap::tempo_at_pulse_locked (const Metrics& metrics, const double& pulse) const
 {
-       /* HOLD THE READER LOCK */
+       TempoSection* prev_t = 0;
 
-       const TempoSection* prev_t = 0;
+       TempoSection* t;
 
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
-               TempoSection* t;
-
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
                        if (!t->active()) {
                                continue;
                        }
-                       if (prev_t && t->pulse() > pulse) {
-                               return prev_t->frame_at_pulse (pulse, _frame_rate);
+                       if ((prev_t) && t->pulse() > pulse) {
+                               /* t is the section past frame */
+                               return prev_t->tempo_at_pulse (pulse);
                        }
-
                        prev_t = t;
                }
        }
-       /* must be treated as constant, irrespective of _type */
-       double const pulses_in_section = pulse - prev_t->pulse();
-       double const dtime = pulses_in_section * prev_t->frames_per_pulse (_frame_rate);
-
-       framecnt_t const ret = (framecnt_t) floor (dtime) + prev_t->frame();
 
-       return ret;
-}
-
-const 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 (prev_t->note_types_per_minute(), prev_t->note_type());
 }
 
-const Tempo
-TempoMap::tempo_at_frame_locked (const Metrics& metrics, const framepos_t& frame) const
+double
+TempoMap::pulse_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) const
 {
        TempoSection* prev_t = 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 ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
+
                        if (!t->active()) {
                                continue;
                        }
-                       if ((prev_t) && t->frame() > frame) {
-                               /* t is the section past frame */
-                               const double ret_bpm = prev_t->tempo_at_frame (frame, _frame_rate) * prev_t->note_type();
-                               const Tempo ret_tempo (ret_bpm, prev_t->note_type());
-                               return ret_tempo;
+
+                       const double t_bpm = t->note_types_per_minute();
+
+                       if (t_bpm == tempo_bpm) {
+                               return t->pulse();
+                       }
+
+                       if (prev_t) {
+                               const double prev_t_bpm = prev_t->note_types_per_minute();
+
+                               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;
                }
        }
 
-       const double ret = prev_t->beats_per_minute();
-       const Tempo ret_tempo (ret, prev_t->note_type ());
-
-       return ret_tempo;
+       return prev_t->pulse();
 }
 
+/** 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_quarter_note (const double& qn) const
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       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::beat_at_bbt (const Timecode::BBT_Time& bbt)
+TempoMap::quarter_note_at_tempo (const Tempo& tempo) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       return beat_at_bbt_locked (_metrics, bbt);
-}
 
+       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::beat_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time& bbt) const
+TempoMap::pulse_at_beat_locked (const Metrics& metrics, const double& beat) const
 {
-       /* CALLER HOLDS READ LOCK */
+       const MeterSection* prev_m = &meter_section_at_beat_locked (metrics, beat);
+
+       return prev_m->pulse() + ((beat - prev_m->beat()) / prev_m->note_divisor());
+}
 
+/** 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
+{
        MeterSection* prev_m = 0;
 
-       /* because audio-locked meters have 'fake' integral beats,
-          there is no pulse offset here.
-       */
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                MeterSection* m;
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
-                       if (prev_m) {
-                               const double bars_to_m = (m->beat() - prev_m->beat()) / prev_m->divisions_per_bar();
-                               if ((bars_to_m + (prev_m->bbt().bars - 1)) > (bbt.bars - 1)) {
-                                       break;
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection*> (*i);
+                       if (prev_m && m->pulse() > pulse) {
+                               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_minute_locked (const Metrics& metrics, const double& minute) const
+{
+       /* HOLD (at least) THE READER LOCK */
+       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->minute() > minute) {
+                               /*the previous ts is the one containing the frame */
+                               const double ret = prev_t->pulse_at_minute (minute);
+                               /* audio locked section in new meter*/
+                               if (t->pulse() < ret) {
+                                       return t->pulse();
+                               }
+                               return ret;
+                       }
+                       prev_t = t;
+               }
+       }
+
+       /* treated as constant for this ts */
+       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();
+}
+
+/* tempo section based */
+double
+TempoMap::minute_at_pulse_locked (const Metrics& metrics, const double& pulse) const
+{
+       /* HOLD THE READER LOCK */
+
+       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->pulse() > pulse) {
+                               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->note_type()) / prev_t->note_types_per_minute();
+
+       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)
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+       return beat_at_bbt_locked (_metrics, bbt);
+}
+
+
+double
+TempoMap::beat_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time& bbt) const
+{
+       /* CALLER HOLDS READ LOCK */
+
+       MeterSection* prev_m = 0;
+
+       /* because audio-locked meters have 'fake' integral beats,
+          there is no pulse offset here.
+       */
+       MeterSection* m;
+
+       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection*> (*i);
+                       if (prev_m) {
+                               const double bars_to_m = (m->beat() - prev_m->beat()) / prev_m->divisions_per_bar();
+                               if ((bars_to_m + (prev_m->bbt().bars - 1)) > (bbt.bars - 1)) {
+                                       break;
                                }
                        }
                        prev_m = m;
@@ -1651,11 +1916,16 @@ 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
@@ -1665,10 +1935,11 @@ TempoMap::bbt_at_beat_locked (const Metrics& metrics, const double& b) const
        MeterSection* prev_m = 0;
        const double beats = max (0.0, b);
 
-       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
-               MeterSection* m = 0;
+       MeterSection* m = 0;
 
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
+       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection*> (*i);
                        if (prev_m) {
                                if (m->beat() > beats) {
                                        /* this is the meter after the one our beat is on*/
@@ -1679,6 +1950,7 @@ 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());
@@ -1709,12 +1981,32 @@ 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::quarter_note_at_bbt_rt (const Timecode::BBT_Time& bbt)
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock, Glib::Threads::TRY_LOCK);
+
+       if (!lm.locked()) {
+               throw std::logic_error ("TempoMap::quarter_note_at_bbt_rt() could not lock tempo map");
+       }
+
+       return pulse_at_bbt_locked (_metrics, bbt) * 4.0;
 }
 
 double
@@ -1727,9 +2019,11 @@ TempoMap::pulse_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time&
        /* because audio-locked meters have 'fake' integral beats,
           there is no pulse offset here.
        */
+       MeterSection* m;
+
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
-               MeterSection* m;
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection*> (*i);
                        if (prev_m) {
                                if (m->bbt().bars > bbt.bars) {
                                        break;
@@ -1746,23 +2040,41 @@ 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
 {
        MeterSection* prev_m = 0;
 
+       MeterSection* m = 0;
+
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
-               MeterSection* m = 0;
 
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection*> (*i);
 
                        if (prev_m) {
                                double const pulses_to_m = m->pulse() - prev_m->pulse();
@@ -1776,6 +2088,8 @@ 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);
@@ -1805,7 +2119,12 @@ TempoMap::bbt_at_pulse_locked (const Metrics& metrics, const double& pulse) cons
        return ret;
 }
 
-const BBT_Time
+/** 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)
 {
        if (frame < 0) {
@@ -1813,31 +2132,102 @@ 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;
+               warning << string_compose (_("tempo map was asked for BBT time at frame %1\n"), frame) << endmsg;
                return bbt;
        }
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return bbt_at_frame_locked (_metrics, frame);
+       return bbt_at_minute_locked (_metrics, minute_at_frame (frame));
+}
+
+BBT_Time
+TempoMap::bbt_at_frame_rt (framepos_t 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_minute_locked (_metrics, minute_at_frame (frame));
 }
 
 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;
                bbt.ticks = 0;
-               warning << string_compose (_("tempo map asked for BBT time at frame %1\n"), frame) << endmsg;
                return bbt;
        }
-       const double beat = beat_at_frame_locked (metrics, frame);
 
-       return bbt_at_beat_locked (metrics, beat);
+       const TempoSection& ts = tempo_section_at_minute_locked (metrics, minute);
+       MeterSection* prev_m = 0;
+       MeterSection* next_m = 0;
+
+       MeterSection* m;
+
+       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection*> (*i);
+                       if (prev_m && m->minute() > minute) {
+                               next_m = m;
+                               break;
+                       }
+                       prev_m = m;
+               }
+       }
+
+       double beat = prev_m->beat() + (ts.pulse_at_minute (minute) - prev_m->pulse()) * prev_m->note_divisor();
+
+       /* handle frame before first meter */
+       if (minute < prev_m->minute()) {
+               beat = 0.0;
+       }
+       /* audio locked meters fake their beat */
+       if (next_m && next_m->beat() < beat) {
+               beat = next_m->beat();
+       }
+
+       beat = max (0.0, beat);
+
+       const double beats_in_ms = beat - prev_m->beat();
+       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);
+       const double remaining_beats = beats_in_ms - (bars_in_ms * prev_m->divisions_per_bar());
+       const double remaining_ticks = (remaining_beats - floor (remaining_beats)) * BBT_Time::ticks_per_beat;
+
+       BBT_Time ret;
+
+       ret.ticks = (uint32_t) floor (remaining_ticks + 0.5);
+       ret.beats = (uint32_t) floor (remaining_beats);
+       ret.bars = total_bars;
+
+       /* 0 0 0 to 1 1 0 - based mapping*/
+       ++ret.bars;
+       ++ret.beats;
+
+       if (ret.ticks >= BBT_Time::ticks_per_beat) {
+               ++ret.beats;
+               ret.ticks -= BBT_Time::ticks_per_beat;
+       }
+
+       if (ret.beats >= prev_m->divisions_per_bar() + 1) {
+               ++ret.bars;
+               ret.beats = 1;
+       }
+
+       return ret;
 }
 
-const framepos_t
+/** 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) {
@@ -1850,19 +2240,207 @@ TempoMap::frame_at_bbt (const BBT_Time& bbt)
        }
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return frame_at_bbt_locked (_metrics, bbt);
+       return frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
 }
 
 /* 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 quarter-note beat position corresponding to the supplied frame.
+ *
+ * @param frame the position in frames.
+ * @return The quarter-note position of the supplied frame. Ignores meter.
+ *
+*/
+double
+TempoMap::quarter_note_at_frame (const framepos_t frame) const
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       const double ret = quarter_note_at_minute_locked (_metrics, minute_at_frame (frame));
+
+       return ret;
+}
+
+double
+TempoMap::quarter_note_at_minute_locked (const Metrics& metrics, const double minute) const
+{
+       const double ret = pulse_at_minute_locked (metrics, minute) * 4.0;
+
+       return ret;
+}
+
+double
+TempoMap::quarter_note_at_frame_rt (const framepos_t frame) const
+{
+       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_minute_locked (_metrics, minute_at_frame (frame)) * 4.0;
+
        return ret;
 }
 
+/**
+ * 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) const
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       const framepos_t ret = frame_at_minute (minute_at_quarter_note_locked (_metrics, quarter_note));
+
+       return ret;
+}
+
+double
+TempoMap::minute_at_quarter_note_locked (const Metrics& metrics, const double quarter_note) const
+{
+       const double ret = minute_at_pulse_locked (metrics, quarter_note / 4.0);
+
+       return ret;
+}
+
+/** 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)
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       const double ret = quarter_note_at_beat_locked (_metrics, beat);
+
+       return ret;
+}
+
+double
+TempoMap::quarter_note_at_beat_locked (const Metrics& metrics, const double beat) const
+{
+       const double ret = pulse_at_beat_locked (metrics, beat) * 4.0;
+
+       return ret;
+}
+
+/** 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::beat_at_quarter_note (const double quarter_note)
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       const double ret = beat_at_quarter_note_locked (_metrics, quarter_note);
+
+       return ret;
+}
+
+double
+TempoMap::beat_at_quarter_note_locked (const Metrics& metrics, const double quarter_note) const
+{
+
+       return beat_at_pulse_locked (metrics, quarter_note / 4.0);
+}
+
+/** 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
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       return frame_at_minute (minutes_between_quarter_notes_locked (_metrics, start, end));
+}
+
+double
+TempoMap::minutes_between_quarter_notes_locked (const Metrics& metrics, const double start, const double end) const
+{
+
+       return minute_at_pulse_locked (metrics, end / 4.0) - minute_at_pulse_locked (metrics, start / 4.0);
+}
+
+double
+TempoMap::quarter_notes_between_frames (const framecnt_t start, const framecnt_t end) const
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       return quarter_notes_between_frames_locked (_metrics, start, end);
+}
+
+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
 TempoMap::check_solved (const Metrics& metrics) const
 {
@@ -1872,32 +2450,43 @@ TempoMap::check_solved (const Metrics& metrics) const
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                TempoSection* t;
                MeterSection* m;
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
                        if (!t->active()) {
                                continue;
                        }
                        if (prev_t) {
-                               if ((t->frame() <= prev_t->frame()) || (t->pulse() <= prev_t->pulse())) {
+                               /* check ordering */
+                               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 (t->note_types_per_minute(), t->pulse()))) {
                                        if (!t->locked_to_meter()) {
                                                return false;
                                        }
                                }
+
+                               /* 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;
+                                       return false;
+                               }
                        }
                        prev_t = t;
                }
 
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection*> (*i);
                        if (prev_m && m->position_lock_style() == AudioTime) {
-                               TempoSection* t = const_cast<TempoSection*>(&tempo_section_at_locked (metrics, m->frame() - 1));
-                               const double nascent_m_pulse = ((m->beat() - prev_m->beat()) / prev_m->note_divisor()) + prev_m->pulse();
-                               const framepos_t nascent_m_frame = t->frame_at_pulse (nascent_m_pulse, _frame_rate);
-
-                               if (t && (nascent_m_frame > m->frame() || nascent_m_frame < 0)) {
+                               const TempoSection* t = &tempo_section_at_minute_locked (metrics, minute_at_frame (m->frame() - 1));
+                               const double nascent_m_minute = t->minute_at_pulse (m->pulse());
+                               /* Here we check that a preceding section of music doesn't overlap a subsequent one.
+                               */
+                               if (t && (nascent_m_minute > m->minute() || nascent_m_minute < 0.0)) {
                                        return false;
                                }
                        }
@@ -1915,7 +2504,8 @@ TempoMap::set_active_tempos (const Metrics& metrics, const framepos_t& frame)
 {
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                TempoSection* t;
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
                        if (!t->movable()) {
                                t->set_active (true);
                                continue;
@@ -1934,31 +2524,34 @@ 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;
 
+       /* can't move a tempo before the first meter */
        for (Metrics::iterator i = imaginary.begin(); i != imaginary.end(); ++i) {
                MeterSection* m;
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection*> (*i);
                        if (!m->movable()) {
-                               first_m_frame = m->frame();
+                               first_m_minute = m->minute();
                                break;
                        }
                }
        }
-       if (section->movable() && frame <= first_m_frame) {
+       if (section->movable() && 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;
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
 
                        if (!t->active()) {
                                continue;
@@ -1966,15 +2559,18 @@ TempoMap::solve_map_frame (Metrics& imaginary, TempoSection* section, const fram
                        if (prev_t) {
                                if (t == section) {
                                        section_prev = prev_t;
+                                       if (t->locked_to_meter()) {
+                                               prev_t = 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_func (prev_t->compute_c_func_pulse (t->note_types_per_minute(), t->pulse()));
+                                       t->set_minute (prev_t->minute_at_ntpm (t->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_func (prev_t->compute_c_func_minute (t->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 (t->note_types_per_minute(), t->minute()));
                                        }
                                }
                        }
@@ -1983,22 +2579,26 @@ 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));
+               section_prev->set_c_func (section_prev->compute_c_func_minute (section->note_types_per_minute(), minute));
                if (!section->locked_to_meter()) {
-                       section->set_pulse (section_prev->pulse_at_frame (frame, _frame_rate));
+                       section->set_pulse (section_prev->pulse_at_ntpm (section->note_types_per_minute(), minute));
                }
        }
 
-       recompute_tempos (imaginary);
+#if (0)
+       recompute_tempi (imaginary);
 
        if (check_solved (imaginary)) {
                return true;
+       } else {
+               dunp (imaginary, std::cout);
        }
+#endif
 
        MetricSectionFrameSorter fcmp;
        imaginary.sort (fcmp);
 
-       recompute_tempos (imaginary);
+       recompute_tempi (imaginary);
 
        if (check_solved (imaginary)) {
                return true;
@@ -2017,7 +2617,8 @@ TempoMap::solve_map_pulse (Metrics& imaginary, TempoSection* section, const doub
 
        for (Metrics::iterator i = imaginary.begin(); i != imaginary.end(); ++i) {
                TempoSection* t;
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
                        if (!t->active()) {
                                continue;
                        }
@@ -2032,12 +2633,12 @@ TempoMap::solve_map_pulse (Metrics& imaginary, TempoSection* section, const doub
                                        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_func (prev_t->compute_c_func_pulse (t->note_types_per_minute(), t->pulse()));
+                                       t->set_minute (prev_t->minute_at_ntpm (t->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_func (prev_t->compute_c_func_minute (t->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 (t->note_types_per_minute(), t->minute()));
                                        }
                                }
                        }
@@ -2046,20 +2647,24 @@ 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_func (section_prev->compute_c_func_pulse (section->note_types_per_minute(), pulse));
+               section->set_minute (section_prev->minute_at_ntpm (section->note_types_per_minute(), pulse));
        }
 
-       recompute_tempos (imaginary);
+#if (0)
+       recompute_tempi (imaginary);
 
        if (check_solved (imaginary)) {
                return true;
+       } else {
+               dunp (imaginary, std::cout);
        }
+#endif
 
        MetricSectionSorter cmp;
        imaginary.sort (cmp);
 
-       recompute_tempos (imaginary);
+       recompute_tempi (imaginary);
        /* Reordering
         * XX need a restriction here, but only for this case,
         * as audio locked tempos don't interact in the same way.
@@ -2078,29 +2683,28 @@ 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_locked (imaginary, frame);
-       if ((!section->movable() && other->movable()) || (!other->movable() && section->movable() && other->frame() >= frame)) {
+       const MeterSection* other =  &meter_section_at_minute_locked (imaginary, minute);
+       if ((!section->movable() && other->movable()) || (!other->movable() && section->movable() && other->minute() >= minute)) {
                return false;
        }
 
        if (!section->movable()) {
                /* lock the first tempo to our first meter */
-               if (!set_active_tempos (imaginary, frame)) {
+               if (!set_active_tempos (imaginary, section->frame_at_minute (minute))) {
                        return false;
                }
        }
 
-       /* it would make sense to bail out if there is no audio-locked meter,
-          however it may be desirable to move a music-locked meter by frame at some point.
-       */
        TempoSection* meter_locked_tempo = 0;
+
        for (Metrics::const_iterator ii = imaginary.begin(); ii != imaginary.end(); ++ii) {
                TempoSection* t;
-               if ((t = dynamic_cast<TempoSection*> (*ii)) != 0) {
-                       if ((t->locked_to_meter() || !t->movable()) && t->frame() == section->frame()) {
+               if ((*ii)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*ii);
+                       if ((t->locked_to_meter() || !t->movable()) && t->minute() == section->minute()) {
                                meter_locked_tempo = t;
                                break;
                        }
@@ -2118,24 +2722,28 @@ TempoMap::solve_map_frame (Metrics& imaginary, MeterSection* section, const fram
 
        for (Metrics::iterator i = imaginary.begin(); i != imaginary.end(); ++i) {
                MeterSection* m;
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
+               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();
+                                       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;
                                                }
@@ -2150,15 +2758,20 @@ TempoMap::solve_map_frame (Metrics& imaginary, MeterSection* section, const fram
                                                        return false;
                                                }
                                        } else {
-                                               /* all is ok. set section's tempo */
-                                               MeterSection* meter_copy = const_cast<MeterSection*> (&meter_section_at_locked (future_map, section->frame()));
-                                               meter_copy->set_frame (frame);
+                                               /* all is ok. set section's locked tempo if allowed.
+                                                  possibly disallowed 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_minute_locked (future_map, section->minute()));
+
+                                               meter_copy->set_minute (minute);
 
-                                               if ((solved = solve_map_frame (future_map, tempo_copy, frame))) {
-                                                       section->set_frame (frame);
+                                               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;
                                                }
@@ -2176,14 +2789,14 @@ TempoMap::solve_map_frame (Metrics& imaginary, MeterSection* section, const fram
                                } else {
                                        /* not movable (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;
                                        }
@@ -2224,7 +2837,8 @@ TempoMap::solve_map_bbt (Metrics& imaginary, MeterSection* section, const BBT_Ti
        /* disallow setting section to an existing meter's bbt */
        for (Metrics::iterator i = imaginary.begin(); i != imaginary.end(); ++i) {
                MeterSection* m;
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection*> (*i);
                        if (m != section && m->bbt().bars == when.bars) {
                                return false;
                        }
@@ -2236,7 +2850,8 @@ TempoMap::solve_map_bbt (Metrics& imaginary, MeterSection* section, const BBT_Ti
 
        for (Metrics::iterator i = imaginary.begin(); i != imaginary.end(); ++i) {
                MeterSection* m;
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection*> (*i);
                        pair<double, BBT_Time> b_bbt;
                        double new_pulse = 0.0;
 
@@ -2248,7 +2863,7 @@ 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));
                                prev_m = section;
                                continue;
                        }
@@ -2258,7 +2873,8 @@ TempoMap::solve_map_bbt (Metrics& imaginary, MeterSection* section, const BBT_Ti
 
                                for (Metrics::const_iterator ii = imaginary.begin(); ii != imaginary.end(); ++ii) {
                                        TempoSection* t;
-                                       if ((t = dynamic_cast<TempoSection*> (*ii)) != 0) {
+                                       if ((*ii)->is_tempo()) {
+                                               t = static_cast<TempoSection*> (*ii);
                                                if ((t->locked_to_meter() || !t->movable()) && t->frame() == m->frame()) {
                                                        meter_locked_tempo = t;
                                                        break;
@@ -2304,7 +2920,7 @@ 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;
@@ -2319,7 +2935,7 @@ 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;
@@ -2341,7 +2957,8 @@ TempoMap::copy_metrics_and_point (const Metrics& metrics, Metrics& copy, TempoSe
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                TempoSection* t;
                MeterSection* m;
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
                        if (t == section) {
                                ret = new TempoSection (*t);
                                copy.push_back (ret);
@@ -2351,7 +2968,8 @@ TempoMap::copy_metrics_and_point (const Metrics& metrics, Metrics& copy, TempoSe
                        TempoSection* cp = new TempoSection (*t);
                        copy.push_back (cp);
                }
-               if ((m = dynamic_cast<MeterSection *> (*i)) != 0) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection *> (*i);
                        MeterSection* cp = new MeterSection (*m);
                        copy.push_back (cp);
                }
@@ -2368,12 +2986,14 @@ TempoMap::copy_metrics_and_point (const Metrics& metrics, Metrics& copy, MeterSe
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                TempoSection* t;
                MeterSection* m;
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
                        TempoSection* cp = new TempoSection (*t);
                        copy.push_back (cp);
                }
 
-               if ((m = dynamic_cast<MeterSection *> (*i)) != 0) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection *> (*i);
                        if (m == section) {
                                ret = new MeterSection (*m);
                                copy.push_back (ret);
@@ -2390,7 +3010,7 @@ 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.
  */
@@ -2423,7 +3043,7 @@ 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>
@@ -2454,19 +3074,43 @@ 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)
+TempoMap::gui_move_tempo (TempoSection* ts, const framepos_t& frame, const int& sub_num)
 {
        Metrics future_map;
 
        if (ts->position_lock_style() == MusicTime) {
                {
+                       /* if we're snapping to a musical grid, set the pulse exactly instead of via the supplied frame. */
                        Glib::Threads::RWLock::WriterLock lm (lock);
                        TempoSection* tempo_copy = copy_metrics_and_point (_metrics, future_map, ts);
-                       const double pulse = pulse_at_frame_locked (future_map, frame);
-                       if (solve_map_pulse (future_map, tempo_copy, pulse)) {
-                               solve_map_pulse (_metrics, ts, pulse);
-                               recompute_meters (_metrics);
+
+                       tempo_copy->set_position_lock_style (AudioTime);
+
+                       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);
+
+                               if (solve_map_pulse (future_map, tempo_copy, pulse)) {
+                                       solve_map_pulse (_metrics, ts, pulse);
+                                       recompute_meters (_metrics);
+                               }
                        }
                }
 
@@ -2475,9 +3119,33 @@ TempoMap::gui_move_tempo (TempoSection* ts, const framepos_t& frame)
                {
                        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)) {
-                               solve_map_frame (_metrics, ts, frame);
-                               recompute_meters (_metrics);
+
+                       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);
+
+                                               recompute_meters (_metrics);
+                                       }
+                               } else {
+                                       solve_map_minute (_metrics, ts, minute_at_frame (frame));
+                                       recompute_meters (_metrics);
+                               }
                        }
                }
        }
@@ -2491,6 +3159,14 @@ TempoMap::gui_move_tempo (TempoSection* ts, const framepos_t& frame)
        MetricPositionChanged (); // 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)
 {
@@ -2502,9 +3178,9 @@ 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);
-                               recompute_tempos (_metrics);
+                       if (solve_map_minute (future_map, copy, minute_at_frame (frame))) {
+                               solve_map_minute (_metrics, ms, minute_at_frame (frame));
+                               recompute_tempi (_metrics);
                        }
                }
        } else {
@@ -2512,12 +3188,12 @@ 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)) {
                                solve_map_bbt (_metrics, ms, bbt);
-                               recompute_tempos (_metrics);
+                               recompute_tempi (_metrics);
                        }
                }
        }
@@ -2539,11 +3215,11 @@ TempoMap::gui_change_tempo (TempoSection* ts, const Tempo& bpm)
        {
                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());
-               recompute_tempos (future_map);
+               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());
+                       ts->set_note_types_per_minute (bpm.note_types_per_minute());
                        recompute_map (_metrics);
                        can_solve = true;
                }
@@ -2561,14 +3237,14 @@ TempoMap::gui_change_tempo (TempoSection* ts, const Tempo& bpm)
 }
 
 void
-TempoMap::gui_dilate_tempo (TempoSection* ts, const framepos_t& frame, const framepos_t& end_frame, const double& pulse)
+TempoMap::gui_dilate_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;
@@ -2584,92 +3260,119 @@ TempoMap::gui_dilate_tempo (TempoSection* ts, const framepos_t& frame, const fra
                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_locked (future_map, prev_t->frame() - 1));
+               assert (prev_t);
+
+               if (prev_t->pulse() > 0.0) {
+                       prev_to_prev_t = const_cast<TempoSection*>(&tempo_section_at_minute_locked (future_map, minute_at_frame (prev_t->frame() - 1)));
                }
 
                TempoSection* next_t = 0;
                for (Metrics::iterator i = future_map.begin(); i != future_map.end(); ++i) {
                        TempoSection* t = 0;
-                       if ((t = dynamic_cast<TempoSection*> (*i)) != 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;
-               double start_pulse = prev_t->pulse_at_frame (frame, _frame_rate);
 
                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());
                }
 
-               frameoffset_t prev_t_frame_contribution = fr_off - (contribution * (double) fr_off);
-               double end_pulse = prev_t->pulse_at_frame (end_frame, _frame_rate);
+               const frameoffset_t prev_t_frame_contribution = fr_off - (contribution * (double) fr_off);
+
+               const double start_pulse = prev_t->pulse_at_minute (minute_at_frame (frame));
+               const double end_pulse = prev_t->pulse_at_minute (minute_at_frame (end_frame));
+
                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()));
-
+                                               new_bpm = prev_t->note_types_per_minute() * ((frame - prev_to_prev_t->frame())
+                                                                                       / (double) ((frame + prev_t_frame_contribution) - prev_to_prev_t->frame()));
+                                       } else {
+                                               new_bpm = prev_t->note_types_per_minute();
+                                       }
                                } else {
                                        /* prev to prev is irrelevant */
 
-                                       if (start_pulse != prev_t->pulse()) {
-                                               new_bpm = prev_t->beats_per_minute() * ((start_pulse - prev_t->pulse()) / (end_pulse - prev_t->pulse()));
+                                       if (start_pulse > prev_t->pulse() && end_pulse > prev_t->pulse()) {
+                                               new_bpm = prev_t->note_types_per_minute() * ((start_pulse - prev_t->pulse()) / (end_pulse - prev_t->pulse()));
                                        } else {
-                                               new_bpm = prev_t->beats_per_minute();
+                                               new_bpm = prev_t->note_types_per_minute();
                                        }
                                }
                        } else {
                                /* AudioTime */
                                if (prev_to_prev_t && prev_to_prev_t->type() == TempoSection::Ramp) {
-                                       new_bpm = prev_t->beats_per_minute() * ((frame - prev_t->frame())
-                                                                               / (double) ((frame + prev_t_frame_contribution) - prev_t->frame()));
+                                       if (frame > prev_to_prev_t->frame() + min_dframe && end_frame > prev_to_prev_t->frame() + min_dframe) {
+
+                                               new_bpm = prev_t->note_types_per_minute() * ((frame - prev_to_prev_t->frame())
+                                                                                       / (double) ((end_frame) - prev_to_prev_t->frame()));
+                                       } else {
+                                               new_bpm = prev_t->note_types_per_minute();
+                                       }
                                } else {
                                        /* prev_to_prev_t is irrelevant */
 
-                                       if (end_frame != prev_t->frame()) {
-                                               new_bpm = prev_t->beats_per_minute() * ((frame - prev_t->frame()) / (double) (end_frame - prev_t->frame()));
+                                       if (frame > prev_t->frame() + min_dframe && end_frame > prev_t->frame() + min_dframe) {
+                                               new_bpm = prev_t->note_types_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();
                                        }
                                }
                        }
                } else {
 
-                       double frame_ratio;
-                       double pulse_ratio;
-                       const framepos_t pulse_pos = prev_t->frame_at_pulse (pulse, _frame_rate);
+                       double frame_ratio = 1.0;
+                       double pulse_ratio = 1.0;
+                       const double pulse_pos = frame;
 
                        if (prev_to_prev_t) {
-
-                               frame_ratio = (((pulse_pos - fr_off) - prev_to_prev_t->frame()) / (double) ((pulse_pos) - prev_to_prev_t->frame()));
-                               pulse_ratio = ((start_pulse - prev_to_prev_t->pulse()) / (end_pulse - prev_to_prev_t->pulse()));
+                               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 {
-
-                               frame_ratio = (((pulse_pos - fr_off) - prev_t->frame()) / (double) ((pulse_pos) - prev_t->frame()));
+                               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() * (pulse_ratio * frame_ratio);
                }
 
-               prev_t->set_beats_per_minute (new_bpm);
-               recompute_tempos (future_map);
+               /* 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;
+               }
+               new_bpm = min (new_bpm, (double) 1000.0);
+               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);
-                       recompute_tempos (_metrics);
+                       ts->set_note_types_per_minute (new_bpm);
+                       recompute_tempi (_metrics);
                        recompute_meters (_metrics);
                }
        }
@@ -2683,16 +3386,159 @@ TempoMap::gui_dilate_tempo (TempoSection* ts, const framepos_t& frame, const fra
        MetricPositionChanged (); // Emit Signal
 }
 
+/** 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_beat_at_frame (const framepos_t& frame, const int32_t sub_num)
+{
+       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)
+{
+       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)
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       return exact_qn_at_frame_locked (_metrics, frame, sub_num);
+}
+
+double
+TempoMap::exact_qn_at_frame_locked (const Metrics& metrics, const framepos_t& frame, const int32_t sub_num)
+{
+       double qn = quarter_note_at_minute_locked (metrics, minute_at_frame (frame));
+
+       if (sub_num > 1) {
+               qn = floor (qn) + (floor (((qn - floor (qn)) * (double) sub_num) + 0.5) / sub_num);
+       } else if (sub_num == 1) {
+               /* the gui requested exact musical (BBT) beat */
+               qn = quarter_note_at_beat_locked (metrics, floor (beat_at_minute_locked (metrics, minute_at_frame (frame)) + 0.5));
+       } 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;
+               ++bbt.bars;
+               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;
+               } else {
+                       qn = prev_b;
+               }
+       }
+
+       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 = 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;
+       BBT_Time pos_bbt = bbt_at_minute_locked (_metrics, minute_at_frame (pos));
+       const framecnt_t offset = frame_at_minute (minute_at_bbt_locked (_metrics, pos_bbt));
+       const double divisions = meter_section_at_minute_locked (_metrics, minute_at_frame (pos)).divisions_per_bar();
+
+       if (dir > 0) {
+               pos_bbt.bars += bbt.bars;
+
+               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;
+               }
+
+               pos_bbt.beats += bbt.beats;
+               if ((double) pos_bbt.beats > divisions) {
+                       pos_bbt.bars += 1;
+                       pos_bbt.beats -= divisions;
+               }
+
+               return frame_at_minute (minute_at_bbt_locked (_metrics, pos_bbt)) - offset;
+       } else {
+               pos_bbt.bars -= bbt.bars;
+
+               if (pos_bbt.ticks < bbt.ticks) {
+                       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.ticks -= bbt.ticks;
+               }
+
+               if (pos_bbt.beats <= bbt.beats) {
+                       pos_bbt.bars--;
+                       pos_bbt.beats = divisions - (bbt.beats - pos_bbt.beats);
+               } else {
+                       pos_bbt.beats -= bbt.beats;
+               }
+
+               return offset - frame_at_minute (minute_at_bbt_locked (_metrics, pos_bbt));
+       }
 
-       return frame_at_beat_locked (_metrics, total_beats);
+       return 0;
 }
 
 framepos_t
@@ -2711,7 +3557,103 @@ 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 (beat_at_frame_locked (_metrics, fr) * BBT_Time::ticks_per_beat);
+       uint32_t ticks = (uint32_t) floor (max (0.0, beat_at_minute_locked (_metrics, minute_at_frame (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;
+
+       if (dir > 0) {
+               /* round to next (or same iff dir == RoundUpMaybe) */
+
+               uint32_t mod = ticks % ticks_one_subdivisions_worth;
+
+               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;
+               }
+
+               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) */
+
+               uint32_t difference = ticks % ticks_one_subdivisions_worth;
+
+               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;
+               }
+
+               if (ticks < difference) {
+                       ticks = BBT_Time::ticks_per_beat - ticks;
+               } else {
+                       ticks -= difference;
+               }
+
+       } 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));
+                       }
+
+               } 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));
+                       } else {
+                               ticks = lrint (ticks - rem);
+                               DEBUG_TRACE (DEBUG::SnapBBT, string_compose ("moved backward to %1\n", ticks));
+                       }
+               } else {
+                       /* on the subdivision, do nothing */
+               }
+       }
+
+       const framepos_t ret_frame = frame_at_minute (minute_at_beat_locked (_metrics, beats + (ticks / BBT_Time::ticks_per_beat)));
+
+       return ret_frame;
+}
+
+framepos_t
+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_minute_locked (_metrics, minute_at_frame (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;
 
@@ -2798,7 +3740,7 @@ TempoMap::round_to_beat_subdivision (framepos_t fr, int sub_num, RoundMode dir)
                }
        }
 
-       const framepos_t ret_frame = frame_at_beat_locked (_metrics, beats + (ticks / BBT_Time::ticks_per_beat));
+       const framepos_t ret_frame = frame_at_minute (minute_at_quarter_note_locked (_metrics, beats + (ticks / BBT_Time::ticks_per_beat)));
 
        return ret_frame;
 }
@@ -2808,7 +3750,7 @@ TempoMap::round_to_type (framepos_t frame, RoundMode dir, BBTPointType type)
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       const double beat_at_framepos = beat_at_frame_locked (_metrics, frame);
+       const double beat_at_framepos = max (0.0, beat_at_minute_locked (_metrics, minute_at_frame (frame)));
        BBT_Time bbt (bbt_at_beat_locked (_metrics, beat_at_framepos));
 
        switch (type) {
@@ -2817,22 +3759,22 @@ TempoMap::round_to_type (framepos_t frame, RoundMode dir, BBTPointType type)
                        /* find bar previous to 'frame' */
                        bbt.beats = 1;
                        bbt.ticks = 0;
-                       return frame_at_bbt_locked (_metrics, bbt);
+                       return frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
 
                } else if (dir > 0) {
                        /* find bar following 'frame' */
                        ++bbt.bars;
                        bbt.beats = 1;
                        bbt.ticks = 0;
-                       return frame_at_bbt_locked (_metrics, bbt);
+                       return frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
                } 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) { 
                                return next_ft;
@@ -2845,11 +3787,11 @@ TempoMap::round_to_type (framepos_t frame, RoundMode dir, BBTPointType type)
 
        case Beat:
                if (dir < 0) {
-                       return frame_at_beat_locked (_metrics, floor (beat_at_framepos));
+                       return frame_at_minute (minute_at_beat_locked (_metrics, floor (beat_at_framepos)));
                } else if (dir > 0) {
-                       return frame_at_beat_locked (_metrics, ceil (beat_at_framepos));
+                       return frame_at_minute (minute_at_beat_locked (_metrics, ceil (beat_at_framepos)));
                } else {
-                       return frame_at_beat_locked (_metrics, floor (beat_at_framepos + 0.5));
+                       return frame_at_minute (minute_at_beat_locked (_metrics, floor (beat_at_framepos + 0.5)));
                }
                break;
        }
@@ -2859,46 +3801,71 @@ TempoMap::round_to_type (framepos_t frame, RoundMode dir, BBTPointType type)
 
 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;
        }
-       while (pos < upper) {
-               pos = frame_at_beat_locked (_metrics, cnt);
-               const TempoSection tempo = tempo_section_at_locked (_metrics, pos);
-               const MeterSection meter = meter_section_at_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;
+
+       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_func()));
+                       ++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 >= 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_func()));
+                       bbt.bars += bar_mod;
+               }
        }
 }
 
 const TempoSection&
-TempoMap::tempo_section_at (framepos_t frame) const
+TempoMap::tempo_section_at_frame (framepos_t frame) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       return tempo_section_at_locked (_metrics, frame);
+
+       return tempo_section_at_minute_locked (_metrics, minute_at_frame (frame));
 }
 
 const TempoSection&
-TempoMap::tempo_section_at_locked (const Metrics& metrics, framepos_t frame) const
+TempoMap::tempo_section_at_minute_locked (const Metrics& metrics, double minute) const
 {
-       Metrics::const_iterator i;
        TempoSection* prev = 0;
 
-       for (i = metrics.begin(); i != metrics.end(); ++i) {
-               TempoSection* t;
+       TempoSection* t;
 
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
+       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->frame() > frame) {
+                       if (prev && t->minute() > minute) {
                                break;
                        }
 
@@ -2920,28 +3887,12 @@ TempoMap::tempo_section_at_beat_locked (const Metrics& metrics, const double& be
        TempoSection* prev_t = 0;
        const MeterSection* prev_m = &meter_section_at_beat_locked (metrics, beat);
 
-       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
-               TempoSection* t;
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
-                       if (prev_t && ((t->pulse() - prev_m->pulse()) * prev_m->note_divisor()) + prev_m->beat() > beat) {
-                               break;
-                       }
-                       prev_t = t;
-               }
-
-       }
-       return *prev_t;
-}
-
-const TempoSection&
-TempoMap::tempo_section_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) {
-               TempoSection* t;
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
-                       if (prev_t && t->pulse() > pulse) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
+                       if (prev_t && ((t->pulse() - prev_m->pulse()) * prev_m->note_divisor()) + prev_m->beat() > beat) {
                                break;
                        }
                        prev_t = t;
@@ -2955,47 +3906,59 @@ TempoMap::tempo_section_at_pulse_locked (const Metrics& metrics, const double& p
    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);
 
-       const TempoSection* ts_at = &tempo_section_at_locked (_metrics, frame);
+       const TempoSection* ts_at = 0;
        const TempoSection* ts_after = 0;
        Metrics::const_iterator i;
+       TempoSection* t;
 
        for (i = _metrics.begin(); i != _metrics.end(); ++i) {
-               TempoSection* t;
 
-               if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
                        if (!t->active()) {
                                continue;
                        }
-                       if ((*i)->frame() > frame) {
+                       if (ts_at && (*i)->frame() > frame) {
                                ts_after = t;
                                break;
                        }
+                       ts_at = t;
                }
        }
+       assert (ts_at);
 
        if (ts_after) {
-               return  (60.0 * _frame_rate) / (ts_at->tempo_at_frame (frame, _frame_rate));
+               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_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;
 
+       MeterSection* m;
+
        for (i = metrics.begin(); i != metrics.end(); ++i) {
-               MeterSection* m;
 
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection*> (*i);
 
-                       if (prev && (*i)->frame() > frame) {
+                       if (prev && (*i)->minute() > minute) {
                                break;
                        }
 
@@ -3011,14 +3974,6 @@ TempoMap::meter_section_at_locked (const Metrics& metrics, framepos_t frame) con
        return *prev;
 }
 
-
-const MeterSection&
-TempoMap::meter_section_at (framepos_t frame) const
-{
-       Glib::Threads::RWLock::ReaderLock lm (lock);
-       return meter_section_at_locked (_metrics, frame);
-}
-
 const MeterSection&
 TempoMap::meter_section_at_beat_locked (const Metrics& metrics, const double& beat) const
 {
@@ -3026,7 +3981,8 @@ TempoMap::meter_section_at_beat_locked (const Metrics& metrics, const double& be
 
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                MeterSection* m;
-               if ((m = dynamic_cast<MeterSection*> (*i)) != 0) {
+               if (!(*i)->is_tempo()) {
+                       m = static_cast<MeterSection*> (*i);
                        if (prev_m && m->beat() > beat) {
                                break;
                        }
@@ -3066,7 +4022,7 @@ TempoMap::fix_legacy_session ()
                                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;
@@ -3091,7 +4047,7 @@ TempoMap::fix_legacy_session ()
 
                        if (!t->movable()) {
                                t->set_pulse (0.0);
-                               t->set_frame (0);
+                               t->set_minute (0.0);
                                t->set_position_lock_style (AudioTime);
                                prev_t = t;
                                continue;
@@ -3148,26 +4104,28 @@ 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);
                                }
 
                                catch (failed_constructor& err){
                                        error << _("Tempo map: could not set new state, restoring old one.") << endmsg;
                                        _metrics = old_metrics;
+                                       old_metrics.clear();
                                        break;
                                }
 
                        } 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);
                                }
 
                                catch (failed_constructor& err) {
                                        error << _("Tempo map: could not set new state, restoring old one.") << endmsg;
                                        _metrics = old_metrics;
+                                       old_metrics.clear();
                                        break;
                                }
                        }
@@ -3219,6 +4177,13 @@ TempoMap::set_state (const XMLNode& node, int /*version*/)
                }
 
                recompute_map (_metrics);
+
+               Metrics::const_iterator d = old_metrics.begin();
+               while (d != old_metrics.end()) {
+                       delete (*d);
+                       ++d;
+               }
+               old_metrics.clear ();
        }
 
        PropertyChanged (PropertyChange ());
@@ -3237,17 +4202,25 @@ TempoMap::dump (const Metrics& metrics, std::ostream& o) const
        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 << t->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() << " (movable? " << t->movable() << ')'
+                         << " 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 << std::setprecision (17) << "  current      : " << t->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 (t->note_types_per_minute(), t->minute())
+                                 << " | " << frame_at_minute (prev_t->minute_at_ntpm (t->note_types_per_minute(), t->pulse()))
+                                 << " | " << prev_t->minute_at_ntpm (t->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()) << " (movable? " << m->movable() << ')' << endl;
                }
        }
        o << "------" << std::endl;
@@ -3260,7 +4233,7 @@ TempoMap::n_tempos() const
        int cnt = 0;
 
        for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
-               if (dynamic_cast<const TempoSection*>(*i) != 0) {
+               if ((*i)->is_tempo()) {
                        cnt++;
                }
        }
@@ -3275,7 +4248,7 @@ TempoMap::n_meters() const
        int cnt = 0;
 
        for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
-               if (dynamic_cast<const MeterSection*>(*i) != 0) {
+               if (!(*i)->is_tempo()) {
                        cnt++;
                }
        }
@@ -3286,129 +4259,24 @@ 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 ();
-
-               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());
+       for (Metrics::reverse_iterator i = _metrics.rbegin(); i != _metrics.rend(); ++i) {
+               if ((*i)->frame() >= where && (*i)->movable ()) {
+                       MeterSection* ms;
+                       TempoSection* ts;
 
-                               }
-                               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_move_meter (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 (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_move_tempo (ts, (*i)->frame() + amount, 0);
                        }
-
-                       prev = (*i);
                }
-
-               recompute_map (_metrics);
        }
 
-
        PropertyChanged (PropertyChange ());
 }
+
 bool
 TempoMap::remove_time (framepos_t where, framecnt_t amount)
 {
@@ -3434,7 +4302,7 @@ 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);
@@ -3447,12 +4315,12 @@ 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;
                }
 
@@ -3470,29 +4338,24 @@ 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 pos, Evoral::Beats beats) const
+TempoMap::framepos_plus_qn (framepos_t frame, Evoral::Beats beats) const
 {
-       return frame_at_beat (beat_at_frame (pos) + beats.to_double());
-}
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+       const double frame_qn = quarter_notes_between_frames_locked (_metrics, 0, frame);
 
-/** 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
-{
-       return frame_at_beat (beat_at_frame (pos) - beats.to_double());
+       return frame_at_minute (minute_at_quarter_note_locked (_metrics, frame_qn + beats.to_double()));
 }
 
-/** 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;
@@ -3508,16 +4371,18 @@ 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
+TempoMap::framewalk_to_qn (framepos_t pos, framecnt_t distance) const
 {
-       return Evoral::Beats (beat_at_frame (pos + distance) - beat_at_frame (pos));
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       return Evoral::Beats (quarter_notes_between_frames_locked (_metrics, pos, pos + distance));
 }
 
 struct bbtcmp {
@@ -3533,7 +4398,7 @@ 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&