Optimize automation-event process splitting
[ardour.git] / libs / ardour / tempo.cc
index ad894708f887eae755193aa2cc57a83501a12a80..ce2d311d391c475aa407395e29e27b119cd72c04 100644 (file)
 
 #include "pbd/enumwriter.h"
 #include "pbd/xml++.h"
-#include "evoral/Beats.hpp"
+
+#include "temporal/beats.h"
 
 #include "ardour/debug.h"
 #include "ardour/lmath.h"
 #include "ardour/tempo.h"
+#include "ardour/types_convert.h"
 
 #include "pbd/i18n.h"
 #include <locale.h>
@@ -45,24 +47,52 @@ 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, 4.0);
+Tempo    TempoMap::_default_tempo (120.0, 4.0, 120.0);
 
-framepos_t
-MetricSection::frame_at_minute (const double& time) const
+samplepos_t
+MetricSection::sample_at_minute (const double& time) const
 {
-       return (framepos_t) floor ((time * 60.0 * _sample_rate) + 0.5);
+       return (samplepos_t) floor ((time * 60.0 * _sample_rate) + 0.5);
 }
 
 double
-MetricSection::minute_at_frame (const framepos_t& frame) const
+MetricSection::minute_at_sample (const samplepos_t sample) const
+{
+       return (sample / (double) _sample_rate) / 60.0;
+}
+
+/***********************************************************************/
+
+bool
+ARDOUR::bbt_time_to_string (const BBT_Time& bbt, std::string& str)
+{
+       char buf[256];
+       int retval = snprintf (buf, sizeof(buf), "%" PRIu32 "|%" PRIu32 "|%" PRIu32, bbt.bars, bbt.beats,
+                              bbt.ticks);
+
+       if (retval <= 0 || retval >= (int)sizeof(buf)) {
+               return false;
+       }
+
+       str = buf;
+       return true;
+}
+
+bool
+ARDOUR::string_to_bbt_time (const std::string& str, BBT_Time& bbt)
 {
-       return (frame / (double) _sample_rate) / 60.0;
+       if (sscanf (str.c_str (), "%" PRIu32 "|%" PRIu32 "|%" PRIu32, &bbt.bars, &bbt.beats,
+                   &bbt.ticks) == 3) {
+               return true;
+       }
+       return false;
 }
 
+
 /***********************************************************************/
 
 double
-Meter::frames_per_grid (const Tempo& tempo, framecnt_t sr) const
+Meter::samples_per_grid (const Tempo& tempo, samplecnt_t sr) const
 {
        /* This is tempo- and meter-sensitive. The number it returns
           is based on the interval between any two lines in the
@@ -71,127 +101,138 @@ 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.note_types_per_minute() * (_note_type/tempo.note_type()));
+       return (60.0 * sr) / (tempo.note_types_per_minute() * (_note_type / tempo.note_type()));
 }
 
 double
-Meter::frames_per_bar (const Tempo& tempo, framecnt_t sr) const
+Meter::samples_per_bar (const Tempo& tempo, samplecnt_t sr) const
+{
+       return samples_per_grid (tempo, sr) * _divisions_per_bar;
+}
+
+/***********************************************************************/
+
+void
+MetricSection::add_state_to_node(XMLNode& node) const
+{
+       node.set_property ("pulse", _pulse);
+       node.set_property ("frame", sample());
+       node.set_property ("movable", !_initial);
+       node.set_property ("lock-style", _position_lock_style);
+}
+
+int
+MetricSection::set_state (const XMLNode& node, int /*version*/)
 {
-       return frames_per_grid (tempo, sr) * _divisions_per_bar;
+       node.get_property ("pulse", _pulse);
+
+       samplepos_t sample;
+       if (node.get_property ("frame", sample)) {
+               set_minute (minute_at_sample (sample));
+       }
+
+       bool tmp;
+       if (!node.get_property ("movable", tmp)) {
+               error << _("TempoSection XML node has no \"movable\" property") << endmsg;
+               throw failed_constructor();
+       }
+       _initial = !tmp;
+
+       if (!node.get_property ("lock-style", _position_lock_style)) {
+               if (!initial()) {
+                       _position_lock_style = MusicTime;
+               } else {
+                       _position_lock_style = AudioTime;
+               }
+       }
+       return 0;
 }
 
 /***********************************************************************/
 
 const string TempoSection::xml_state_node_name = "Tempo";
 
-TempoSection::TempoSection (const XMLNode& node, framecnt_t sample_rate)
+TempoSection::TempoSection (const XMLNode& node, samplecnt_t sample_rate)
        : MetricSection (0.0, 0, MusicTime, true, sample_rate)
        , Tempo (TempoMap::default_tempo())
-       , _c_func (0.0)
+       , _c (0.0)
        , _active (true)
        , _locked_to_meter (false)
+       , _clamped (false)
 {
-       XMLProperty const * prop;
-       LocaleGuard lg;
        BBT_Time bbt;
-       double pulse;
-       uint32_t frame;
-       bool had_beats_per_minute = false;
-
-       _legacy_bbt = BBT_Time (0, 0, 0);
-
-       if ((prop = node.property ("start")) != 0) {
-               if (sscanf (prop->value().c_str(), "%" PRIu32 "|%" PRIu32 "|%" PRIu32,
-                           &bbt.bars,
-                           &bbt.beats,
-                           &bbt.ticks) == 3) {
+       std::string start_bbt;
+       _legacy_bbt.bars = 0; // legacy session check compars .bars != 0; default BBT_Time c'tor uses 1.
+       if (node.get_property ("start", start_bbt)) {
+               if (string_to_bbt_time (start_bbt, bbt)) {
                        /* legacy session - start used to be in bbt*/
                        _legacy_bbt = bbt;
-                       pulse = -1.0;
+                       set_pulse(-1.0);
                        info << _("Legacy session detected. TempoSection XML node will be altered.") << endmsg;
                }
        }
 
-       if ((prop = node.property ("pulse")) != 0) {
-               if (sscanf (prop->value().c_str(), "%lf", &pulse) != 1) {
-                       error << _("TempoSection XML node has an illegal \"pulse\" value") << endmsg;
-               }
-       }
-
-       set_pulse (pulse);
-
-       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;
-               } else {
-                       set_minute (minute_at_frame (frame));
-               }
-       }
+       // Don't worry about return value, exception will be thrown on error
+       MetricSection::set_state (node, Stateful::loading_state_version);
 
-       /* replace old beats-per-minute with note-types-per-minute */
-       if ((prop = node.property ("beats-per-minute")) != 0) {
-               info << _("Renaming legacy \"beats-per-minute\" XML node to note-types-per-minute") << endmsg;
-               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;
+       if (node.get_property ("beats-per-minute", _note_types_per_minute)) {
+               if (_note_types_per_minute < 0.0) {
+                       error << _("TempoSection XML node has an illegal \"beats_per_minute\" value") << endmsg;
                        throw failed_constructor();
                }
-               had_beats_per_minute = true;
        }
 
-       if ((prop = node.property ("note-types-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 \"note-types-per-minute\" value") << endmsg;
+       if (node.get_property ("note-type", _note_type)) {
+               if (_note_type < 1.0) {
+                       error << _("TempoSection XML node has an illegal \"note-type\" value") << endmsg;
                        throw failed_constructor();
                }
-       } else if (!had_beats_per_minute) {
-               error << _("TempoSection XML node has no \"note-types-per-minute\" or \"beats-per-minute\" property") << endmsg;
-               throw failed_constructor();
-       }
-
-       if ((prop = node.property ("note-type")) == 0) {
+       } else {
                /* older session, make note type be quarter by default */
                _note_type = 4.0;
-       } else {
-               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 (!node.get_property ("clamped", _clamped)) {
+               _clamped = false;
        }
 
-       if ((prop = node.property ("movable")) == 0) {
-               error << _("TempoSection XML node has no \"movable\" property") << endmsg;
-               throw failed_constructor();
+       if (node.get_property ("end-beats-per-minute", _end_note_types_per_minute)) {
+               if (_end_note_types_per_minute < 0.0) {
+                       info << _("TempoSection XML node has an illegal \"end-beats-per-minute\" value") << endmsg;
+                       throw failed_constructor();
+               }
        }
 
-       set_movable (string_is_affirmative (prop->value()));
+       TempoSection::Type old_type;
+       if (node.get_property ("tempo-type", old_type)) {
+               /* sessions with a tempo-type node contain no end-beats-per-minute.
+                  if the legacy node indicates a constant tempo, simply fill this in with the
+                  start tempo. otherwise we need the next neighbour to know what it will be.
+               */
 
-       if ((prop = node.property ("active")) == 0) {
-               warning << _("TempoSection XML node has no \"active\" property") << endmsg;
-               set_active(true);
-       } else {
-               set_active (string_is_affirmative (prop->value()));
+               if (old_type == TempoSection::Constant) {
+                       _end_note_types_per_minute = _note_types_per_minute;
+               } else {
+                       _end_note_types_per_minute = -1.0;
+               }
        }
 
-       if ((prop = node.property ("tempo-type")) == 0) {
-               _type = Constant;
-       } else {
-               _type = Type (string_2_enum (prop->value(), _type));
+       if (!node.get_property ("active", _active)) {
+               warning << _("TempoSection XML node has no \"active\" property") << endmsg;
+               _active = true;
        }
 
-       if ((prop = node.property ("lock-style")) == 0) {
-               if (movable()) {
-                       set_position_lock_style (MusicTime);
+       if (!node.get_property ("locked-to-meter", _locked_to_meter)) {
+               if (initial()) {
+                       set_locked_to_meter (true);
                } else {
-                       set_position_lock_style (AudioTime);
+                       set_locked_to_meter (false);
                }
-       } else {
-               set_position_lock_style (PositionLockStyle (string_2_enum (prop->value(), position_lock_style())));
        }
 
-       if ((prop = node.property ("locked-to-meter")) == 0) {
-               set_locked_to_meter (false);
-       } else {
-               set_locked_to_meter (string_is_affirmative (prop->value()));
+       /* 5.5 marked initial tempo as not locked to meter. this should always be true anyway */
+       if (initial()) {
+               set_locked_to_meter (true);
        }
 }
 
@@ -199,32 +240,17 @@ XMLNode&
 TempoSection::get_state() const
 {
        XMLNode *root = new XMLNode (xml_state_node_name);
-       char buf[256];
-       LocaleGuard lg;
-
-       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), "%lf", _note_types_per_minute);
-       root->add_property ("note-types-per-minute", buf);
-       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);
-       snprintf (buf, sizeof (buf), "%s", active()?"yes":"no");
-       root->add_property ("active", buf);
-       root->add_property ("tempo-type", enum_2_string (_type));
-       root->add_property ("lock-style", enum_2_string (position_lock_style()));
-       root->add_property ("locked-to-meter", locked_to_meter()?"yes":"no");
 
-       return *root;
-}
+       MetricSection::add_state_to_node (*root);
 
-void
-TempoSection::set_type (Type type)
-{
-       _type = type;
+       root->set_property ("beats-per-minute", _note_types_per_minute);
+       root->set_property ("note-type", _note_type);
+       root->set_property ("clamped", _clamped);
+       root->set_property ("end-beats-per-minute", _end_note_types_per_minute);
+       root->set_property ("active", _active);
+       root->set_property ("locked-to-meter", _locked_to_meter);
+
+       return *root;
 }
 
 /** returns the Tempo at the session-relative minute.
@@ -232,12 +258,12 @@ TempoSection::set_type (Type type)
 Tempo
 TempoSection::tempo_at_minute (const double& m) const
 {
-
-       if (_type == Constant || _c_func == 0.0) {
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && m < minute());
+       if (constant) {
                return Tempo (note_types_per_minute(), note_type());
        }
 
-       return Tempo (_tempo_at_time (m - minute()), _note_type);
+       return Tempo (_tempo_at_time (m - minute()), _note_type, _end_note_types_per_minute);
 }
 
 /** returns the session relative minute where the supplied tempo in note types per minute occurs.
@@ -249,17 +275,17 @@ TempoSection::tempo_at_minute (const double& m) const
  *
 */
 
-/** user feedback dictates that if tempoA (120, 4.0) precedes tempoB (120, 8.0),
- *  there will be no ramp between the two even if set to ramped.
+/** 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.
- *  we would ideally like to use arbitrary Tempo structs here.
 */
 double
 TempoSection::minute_at_ntpm (const double& ntpm, const double& p) const
 {
-       if (_type == Constant || _c_func == 0.0) {
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && p < pulse());
+       if (constant) {
                return ((p - pulse()) / pulses_per_minute()) + minute();
        }
 
@@ -271,12 +297,13 @@ TempoSection::minute_at_ntpm (const double& ntpm, const double& p) const
 Tempo
 TempoSection::tempo_at_pulse (const double& p) const
 {
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && p < pulse());
 
-       if (_type == Constant || _c_func == 0.0) {
+       if (constant) {
                return Tempo (note_types_per_minute(), note_type());
        }
 
-       return Tempo (_tempo_at_pulse (p - pulse()), _note_type);
+       return Tempo (_tempo_at_pulse (p - pulse()), _note_type, _end_note_types_per_minute);
 }
 
 /** returns the whole-note pulse where a tempo in note types per minute occurs.
@@ -292,7 +319,8 @@ TempoSection::tempo_at_pulse (const double& p) const
 double
 TempoSection::pulse_at_ntpm (const double& ntpm, const double& m) const
 {
-       if (_type == Constant || _c_func == 0.0) {
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && m < minute());
+       if (constant) {
                return ((m - minute()) * pulses_per_minute()) + pulse();
        }
 
@@ -304,7 +332,8 @@ TempoSection::pulse_at_ntpm (const double& ntpm, const double& m) const
 double
 TempoSection::pulse_at_minute (const double& m) const
 {
-       if (_type == Constant || _c_func == 0.0) {
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && m < minute());
+       if (constant) {
                return ((m - minute()) * pulses_per_minute()) + pulse();
        }
 
@@ -316,31 +345,40 @@ TempoSection::pulse_at_minute (const double& m) const
 double
 TempoSection::minute_at_pulse (const double& p) const
 {
-       if (_type == Constant || _c_func == 0.0) {
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && p < pulse());
+       if (constant) {
                return ((p - pulse()) / pulses_per_minute()) + minute();
        }
 
        return _time_at_pulse (p - pulse()) + minute();
 }
 
+/** returns thw whole-note pulse at session sample position f.
+ *  @param f the sample position.
+ *  @return the position in whole-note pulses corresponding to f
+ *
+ *  for use with musical units whose granularity is coarser than samples (e.g. ticks)
+*/
 double
-TempoSection::pulse_at_frame (const framepos_t& f) const
+TempoSection::pulse_at_sample (const samplepos_t f) const
 {
-       if (_type == Constant || _c_func == 0.0) {
-               return (minute_at_frame (f - frame()) * pulses_per_minute()) + pulse();
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && f < sample());
+       if (constant) {
+               return (minute_at_sample (f - sample()) * pulses_per_minute()) + pulse();
        }
 
-       return _pulse_at_time (minute_at_frame (f - frame())) + pulse();
+       return _pulse_at_time (minute_at_sample (f - sample())) + pulse();
 }
 
-framepos_t
-TempoSection::frame_at_pulse (const double& p) const
+samplepos_t
+TempoSection::sample_at_pulse (const double& p) const
 {
-       if (_type == Constant || _c_func == 0.0) {
-               return frame_at_minute (((p - pulse()) / pulses_per_minute()) + minute());
+       const bool constant = type() == Constant || _c == 0.0 || (initial() && p < pulse());
+       if (constant) {
+               return sample_at_minute (((p - pulse()) / pulses_per_minute()) + minute());
        }
 
-       return frame_at_minute (_time_at_pulse (p - pulse()) + minute());
+       return sample_at_minute (_time_at_pulse (p - pulse()) + minute());
 }
 
 /*
@@ -424,8 +462,12 @@ https://www.zhdk.ch/fileadmin/data_subsites/data_icst/Downloads/Timegrid/ICST_Te
  * @return the calculated function constant
 */
 double
-TempoSection::compute_c_func_pulse (const double& end_npm, const double& end_pulse) const
+TempoSection::compute_c_pulse (const double& end_npm, const double& end_pulse) const
 {
+       if (note_types_per_minute() == end_npm || type() == Constant) {
+               return 0.0;
+       }
+
        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);
 }
@@ -436,16 +478,20 @@ TempoSection::compute_c_func_pulse (const double& end_npm, const double& end_pul
  * @return the calculated function constant
 */
 double
-TempoSection::compute_c_func_minute (const double& end_npm, const double& end_minute) const
+TempoSection::compute_c_minute (const double& end_npm, const double& end_minute) const
 {
+       if (note_types_per_minute() == end_npm || type() == Constant) {
+               return 0.0;
+       }
+
        return c_func (end_npm, end_minute - minute());
 }
 
 /* position function */
 double
-TempoSection::a_func (double end_npm, double c_func) const
+TempoSection::a_func (double end_npm, double c) const
 {
-       return log (end_npm / note_types_per_minute()) / c_func;
+       return log (end_npm / note_types_per_minute()) / c;
 }
 
 /*function constant*/
@@ -459,174 +505,118 @@ TempoSection::c_func (double end_npm, double end_time) const
 double
 TempoSection::_tempo_at_time (const double& time) const
 {
-       return exp (_c_func * time) * note_types_per_minute();
+       return exp (_c * time) * note_types_per_minute();
 }
 
 /* time in minutes at tempo in note types per minute */
 double
 TempoSection::_time_at_tempo (const double& npm) const
 {
-       return log (npm / note_types_per_minute()) / _c_func;
+       return log (npm / note_types_per_minute()) / _c;
 }
 
 /* pulse at tempo in note types per minute */
 double
 TempoSection::_pulse_at_tempo (const double& npm) const
 {
-       return ((npm - note_types_per_minute()) / _c_func) / _note_type;
+       return ((npm - note_types_per_minute()) / _c) / _note_type;
 }
 
 /* tempo in note types per minute at pulse */
 double
 TempoSection::_tempo_at_pulse (const double& pulse) const
 {
-       return (pulse * _note_type * _c_func) + note_types_per_minute();
+       return (pulse * _note_type * _c) + note_types_per_minute();
 }
 
 /* pulse at time in minutes */
 double
 TempoSection::_pulse_at_time (const double& time) const
 {
-       return (expm1 (_c_func * time) * (note_types_per_minute() / _c_func)) / _note_type;
+       return (expm1 (_c * time) * (note_types_per_minute() / _c)) / _note_type;
 }
 
 /* time in minutes at pulse */
 double
 TempoSection::_time_at_pulse (const double& pulse) const
 {
-       return log1p ((_c_func * pulse * _note_type) / note_types_per_minute()) / _c_func;
+       return log1p ((_c * pulse * _note_type) / note_types_per_minute()) / _c;
 }
 
 /***********************************************************************/
 
 const string MeterSection::xml_state_node_name = "Meter";
 
-MeterSection::MeterSection (const XMLNode& node, const framecnt_t sample_rate)
+MeterSection::MeterSection (const XMLNode& node, const samplecnt_t sample_rate)
        : MetricSection (0.0, 0, MusicTime, false, sample_rate), Meter (TempoMap::default_meter())
 {
-       XMLProperty const * prop;
-       LocaleGuard lg;
-       BBT_Time bbt;
-       double pulse = 0.0;
-       double beat = 0.0;
-       framepos_t frame = 0;
        pair<double, BBT_Time> start;
+       start.first = 0.0;
 
-       if ((prop = node.property ("start")) != 0) {
-               if (sscanf (prop->value().c_str(), "%" PRIu32 "|%" PRIu32 "|%" PRIu32,
-                   &bbt.bars,
-                   &bbt.beats,
-                   &bbt.ticks) < 3) {
-                       error << _("MeterSection XML node has an illegal \"start\" value") << endmsg;
-               } else {
+       std::string bbt_str;
+       if (node.get_property ("start", bbt_str)) {
+               if (string_to_bbt_time (bbt_str, start.second)) {
                        /* legacy session - start used to be in bbt*/
                        info << _("Legacy session detected - MeterSection XML node will be altered.") << endmsg;
-                       pulse = -1.0;
-               }
-       }
-
-       if ((prop = node.property ("pulse")) != 0) {
-               if (sscanf (prop->value().c_str(), "%lf", &pulse) != 1) {
-                       error << _("MeterSection XML node has an illegal \"pulse\" value") << endmsg;
+                       set_pulse (-1.0);
+               } else {
+                       error << _("MeterSection XML node has an illegal \"start\" value") << endmsg;
                }
        }
-       set_pulse (pulse);
 
-       if ((prop = node.property ("beat")) != 0) {
-               if (sscanf (prop->value().c_str(), "%lf", &beat) != 1) {
-                       error << _("MeterSection XML node has an illegal \"beat\" value") << endmsg;
-               }
-       }
+       MetricSection::set_state (node, Stateful::loading_state_version);
 
-       start.first = beat;
+       node.get_property ("beat", start.first);
 
-       if ((prop = node.property ("bbt")) == 0) {
+       if (node.get_property ("bbt", bbt_str)) {
+               if (!string_to_bbt_time (bbt_str, start.second)) {
+                       error << _("MeterSection XML node has an illegal \"bbt\" value") << endmsg;
+                       throw failed_constructor();
+               }
+       } else {
                warning << _("MeterSection XML node has no \"bbt\" property") << endmsg;
-       } else if (sscanf (prop->value().c_str(), "%" PRIu32 "|%" PRIu32 "|%" PRIu32,
-                   &bbt.bars,
-                   &bbt.beats,
-                   &bbt.ticks) < 3) {
-               error << _("MeterSection XML node has an illegal \"bbt\" value") << endmsg;
-               throw failed_constructor();
        }
 
-       start.second = bbt;
        set_beat (start);
 
-       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;
-               } else {
-                       set_minute (minute_at_frame (frame));
-               }
-       }
-
        /* beats-per-bar is old; divisions-per-bar is new */
 
-       if ((prop = node.property ("divisions-per-bar")) == 0) {
-               if ((prop = node.property ("beats-per-bar")) == 0) {
+       if (!node.get_property ("divisions-per-bar", _divisions_per_bar)) {
+               if (!node.get_property ("beats-per-bar", _divisions_per_bar)) {
                        error << _("MeterSection XML node has no \"beats-per-bar\" or \"divisions-per-bar\" property") << endmsg;
                        throw failed_constructor();
                }
        }
-       if (sscanf (prop->value().c_str(), "%lf", &_divisions_per_bar) != 1 || _divisions_per_bar < 0.0) {
+
+       if (_divisions_per_bar < 0.0) {
                error << _("MeterSection XML node has an illegal \"divisions-per-bar\" value") << endmsg;
                throw failed_constructor();
        }
 
-       if ((prop = node.property ("note-type")) == 0) {
+       if (!node.get_property ("note-type", _note_type)) {
                error << _("MeterSection XML node has no \"note-type\" property") << endmsg;
                throw failed_constructor();
        }
-       if (sscanf (prop->value().c_str(), "%lf", &_note_type) != 1 || _note_type < 0.0) {
-               error << _("MeterSection XML node has an illegal \"note-type\" value") << endmsg;
-               throw failed_constructor();
-       }
 
-       if ((prop = node.property ("movable")) == 0) {
-               error << _("MeterSection XML node has no \"movable\" property") << endmsg;
+       if (_note_type < 0.0) {
+               error << _("MeterSection XML node has an illegal \"note-type\" value") << endmsg;
                throw failed_constructor();
        }
-
-       set_movable (string_is_affirmative (prop->value()));
-
-       if ((prop = node.property ("lock-style")) == 0) {
-               warning << _("MeterSection XML node has no \"lock-style\" property") << endmsg;
-               if (movable()) {
-                       set_position_lock_style (MusicTime);
-               } else {
-                       set_position_lock_style (AudioTime);
-               }
-       } else {
-               set_position_lock_style (PositionLockStyle (string_2_enum (prop->value(), position_lock_style())));
-       }
 }
 
 XMLNode&
 MeterSection::get_state() const
 {
        XMLNode *root = new XMLNode (xml_state_node_name);
-       char buf[256];
-       LocaleGuard lg;
-
-       snprintf (buf, sizeof (buf), "%lf", pulse());
-       root->add_property ("pulse", buf);
-       snprintf (buf, sizeof (buf), "%" PRIu32 "|%" PRIu32 "|%" PRIu32,
-                 bbt().bars,
-                 bbt().beats,
-                 bbt().ticks);
-       root->add_property ("bbt", buf);
-       snprintf (buf, sizeof (buf), "%lf", beat());
-       root->add_property ("beat", buf);
-       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), "%lf", _divisions_per_bar);
-       root->add_property ("divisions-per-bar", buf);
-       snprintf (buf, sizeof (buf), "%s", movable()?"yes":"no");
-       root->add_property ("movable", buf);
+
+       MetricSection::add_state_to_node (*root);
+
+       std::string bbt_str;
+       bbt_time_to_string (_bbt, bbt_str);
+       root->set_property ("bbt", bbt_str);
+       root->set_property ("beat", beat());
+       root->set_property ("note-type", _note_type);
+       root->set_property ("divisions-per-bar", _divisions_per_bar);
 
        return *root;
 }
@@ -671,40 +661,40 @@ MeterSection::get_state() const
   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()).
+  Solved means ordered by sample or pulse with sample-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.
+  Thus if a gui user points to the sample occupying the start of a music-locked object on 1|3|0, it does not
+  mean that this sample 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).
+  You cannot use a sample measurement to determine beat distance except under special circumstances
+  (e.g. where the user has requested that a beat lie on a SMPTE sample 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()).
+  The current approach is to interpret the supplied sample 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 samples are rounded to audio sample), so
+  the supplied audio sample is interpreted as the desired musical location (beat_at_sample()).
 
   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.
+  When sample_at_beat() is called, the position calculation is performed in pulses and minutes.
+  The result is rounded to audio samples.
+  When beat_at_sample() is called, the sample is converted to minutes, with no rounding performed on the result.
 
   So :
-  frame_at_beat (beat_at_frame (frame)) == frame
+  sample_at_beat (beat_at_sample (sample)) == sample
   but :
-  beat_at_frame (frame_at_beat (beat)) != beat due to the time quantization of frame_at_beat().
+  beat_at_sample (sample_at_beat (beat)) != beat due to the time quantization of sample_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.
+  samples_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 samples last.
 
   The above pointless example could instead do:
   beat_at_quarter_note (quarter_note_at_beat (beat)) to avoid rounding.
@@ -721,28 +711,64 @@ struct MetricSectionSorter {
 
 struct MetricSectionFrameSorter {
     bool operator() (const MetricSection* a, const MetricSection* b) {
-           return a->frame() < b->frame();
+           return a->sample() < b->sample();
     }
 };
 
-TempoMap::TempoMap (framecnt_t fr)
+TempoMap::TempoMap (samplecnt_t fr)
 {
-       _frame_rate = fr;
+       _sample_rate = fr;
        BBT_Time start (1, 1, 0);
 
-       TempoSection *t = new TempoSection (0.0, 0.0, _default_tempo.note_types_per_minute(), _default_tempo.note_type(), TempoSection::Ramp, AudioTime, fr);
+       TempoSection *t = new TempoSection (0.0, 0.0, _default_tempo, AudioTime, fr);
        MeterSection *m = new MeterSection (0.0, 0.0, 0.0, start, _default_meter.divisions_per_bar(), _default_meter.note_divisor(), AudioTime, fr);
 
-       t->set_movable (false);
-       m->set_movable (false);
+       t->set_initial (true);
+       t->set_locked_to_meter (true);
+
+       m->set_initial (true);
 
-       /* note: frame time is correct (zero) for both of these */
+       /* note: sample time is correct (zero) for both of these */
 
        _metrics.push_back (t);
        _metrics.push_back (m);
 
 }
 
+TempoMap&
+TempoMap::operator= (TempoMap const & other)
+{
+       if (&other != this) {
+               Glib::Threads::RWLock::ReaderLock lr (other.lock);
+               Glib::Threads::RWLock::WriterLock lm (lock);
+               _sample_rate = other._sample_rate;
+
+               Metrics::const_iterator d = _metrics.begin();
+               while (d != _metrics.end()) {
+                       delete (*d);
+                       ++d;
+               }
+               _metrics.clear();
+
+               for (Metrics::const_iterator m = other._metrics.begin(); m != other._metrics.end(); ++m) {
+                       TempoSection const * const ts = dynamic_cast<TempoSection const * const> (*m);
+                       MeterSection const * const ms = dynamic_cast<MeterSection const * const> (*m);
+
+                       if (ts) {
+                               TempoSection* new_section = new TempoSection (*ts);
+                               _metrics.push_back (new_section);
+                       } else {
+                               MeterSection* new_section = new MeterSection (*ms);
+                               _metrics.push_back (new_section);
+                       }
+               }
+       }
+
+       PropertyChanged (PropertyChange());
+
+       return *this;
+}
+
 TempoMap::~TempoMap ()
 {
        Metrics::const_iterator d = _metrics.begin();
@@ -753,16 +779,16 @@ TempoMap::~TempoMap ()
        _metrics.clear();
 }
 
-framepos_t
-TempoMap::frame_at_minute (const double time) const
+samplepos_t
+TempoMap::sample_at_minute (const double time) const
 {
-       return (framepos_t) floor ((time * 60.0 * _frame_rate) + 0.5);
+       return (samplepos_t) floor ((time * 60.0 * _sample_rate) + 0.5);
 }
 
 double
-TempoMap::minute_at_frame (const framepos_t frame) const
+TempoMap::minute_at_sample (const samplepos_t sample) const
 {
-       return (frame / (double) _frame_rate) / 60.0;
+       return (sample / (double) _sample_rate) / 60.0;
 }
 
 void
@@ -791,8 +817,8 @@ TempoMap::remove_tempo_locked (const TempoSection& tempo)
 
        for (i = _metrics.begin(); i != _metrics.end(); ++i) {
                if (dynamic_cast<TempoSection*> (*i) != 0) {
-                       if (tempo.frame() == (*i)->frame()) {
-                               if ((*i)->movable()) {
+                       if (tempo.sample() == (*i)->sample()) {
+                               if (!(*i)->initial()) {
                                        delete (*i);
                                        _metrics.erase (i);
                                        return true;
@@ -832,7 +858,7 @@ TempoMap::remove_meter_locked (const MeterSection& meter)
                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()) {
+                               if (t->locked_to_meter() && meter.sample() == (*i)->sample()) {
                                        delete (*i);
                                        _metrics.erase (i);
                                        break;
@@ -843,8 +869,8 @@ TempoMap::remove_meter_locked (const MeterSection& meter)
 
        for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
                if (dynamic_cast<MeterSection*> (*i) != 0) {
-                       if (meter.frame() == (*i)->frame()) {
-                               if ((*i)->movable()) {
+                       if (meter.sample() == (*i)->sample()) {
+                               if (!(*i)->initial()) {
                                        delete (*i);
                                        _metrics.erase (i);
                                        return true;
@@ -896,9 +922,9 @@ TempoMap::do_insert (MetricSection* section)
 
                        /* Tempo sections */
                        bool const ipm = insert_tempo->position_lock_style() == MusicTime;
-                       if ((ipm && tempo->pulse() == insert_tempo->pulse()) || (!ipm && tempo->frame() == insert_tempo->frame())) {
+                       if ((ipm && tempo->pulse() == insert_tempo->pulse()) || (!ipm && tempo->sample() == insert_tempo->sample())) {
 
-                               if (!tempo->movable()) {
+                               if (tempo->initial()) {
 
                                        /* can't (re)move this section, so overwrite
                                         * its data content (but not its properties as
@@ -907,10 +933,6 @@ TempoMap::do_insert (MetricSection* section)
 
                                        *(dynamic_cast<Tempo*>(*i)) = *(dynamic_cast<Tempo*>(insert_tempo));
                                        (*i)->set_position_lock_style (AudioTime);
-                                       TempoSection* t;
-                                       if ((t = dynamic_cast<TempoSection*>(*i)) != 0) {
-                                               t->set_type (insert_tempo->type());
-                                       }
                                        need_add = false;
                                } else {
                                        delete (*i);
@@ -925,9 +947,9 @@ TempoMap::do_insert (MetricSection* section)
 
                        bool const ipm = insert_meter->position_lock_style() == MusicTime;
 
-                       if ((ipm && meter->beat() == insert_meter->beat()) || (!ipm && meter->frame() == insert_meter->frame())) {
+                       if ((ipm && meter->beat() == insert_meter->beat()) || (!ipm && meter->sample() == insert_meter->sample())) {
 
-                               if (!meter->movable()) {
+                               if (meter->initial()) {
 
                                        /* can't (re)move this section, so overwrite
                                         * its data content (but not its properties as
@@ -957,15 +979,24 @@ TempoMap::do_insert (MetricSection* section)
                MeterSection* const insert_meter = dynamic_cast<MeterSection*> (section);
                TempoSection* const insert_tempo = dynamic_cast<TempoSection*> (section);
                Metrics::iterator i;
+
                if (insert_meter) {
+                       TempoSection* prev_t = 0;
+
                        for (i = _metrics.begin(); i != _metrics.end(); ++i) {
                                MeterSection* const meter = dynamic_cast<MeterSection*> (*i);
+                               bool const ipm = insert_meter->position_lock_style() == MusicTime;
 
                                if (meter) {
-                                       bool const ipm = insert_meter->position_lock_style() == MusicTime;
-                                       if ((ipm && meter->beat() > insert_meter->beat()) || (!ipm && meter->frame() > insert_meter->frame())) {
+                                       if ((ipm && meter->beat() > insert_meter->beat()) || (!ipm && meter->sample() > insert_meter->sample())) {
+                                               break;
+                                       }
+                               } else {
+                                       if (prev_t && prev_t->locked_to_meter() && (!ipm && prev_t->sample() == insert_meter->sample())) {
                                                break;
                                        }
+
+                                       prev_t = dynamic_cast<TempoSection*> (*i);
                                }
                        }
                } else if (insert_tempo) {
@@ -974,7 +1005,9 @@ TempoMap::do_insert (MetricSection* section)
 
                                if (tempo) {
                                        bool const ipm = insert_tempo->position_lock_style() == MusicTime;
-                                       if ((ipm && tempo->pulse() > insert_tempo->pulse()) || (!ipm && tempo->frame() > insert_tempo->frame())) {
+                                       const bool lm = insert_tempo->locked_to_meter();
+                                       if ((ipm && tempo->pulse() > insert_tempo->pulse()) || (!ipm && tempo->sample() > insert_tempo->sample())
+                                           || (lm && tempo->pulse() > insert_tempo->pulse())) {
                                                break;
                                        }
                                }
@@ -982,19 +1015,26 @@ TempoMap::do_insert (MetricSection* section)
                }
 
                _metrics.insert (i, section);
-               //dump (_metrics, std::cout);
+               //dump (std::cout);
        }
 }
 /* user supplies the exact pulse if pls == MusicTime */
 TempoSection*
-TempoMap::add_tempo (const Tempo& tempo, const double& pulse, const framepos_t& frame, ARDOUR::TempoSection::Type type, PositionLockStyle pls)
+TempoMap::add_tempo (const Tempo& tempo, const double& pulse, const samplepos_t sample, PositionLockStyle pls)
 {
+       if (tempo.note_types_per_minute() <= 0.0) {
+               warning << "Cannot add tempo. note types per minute must be greater than zero." << endmsg;
+               return 0;
+       }
+
        TempoSection* ts = 0;
        {
                Glib::Threads::RWLock::WriterLock lm (lock);
-               ts = add_tempo_locked (tempo, pulse, minute_at_frame (frame), type, pls, true);
-       }
+               /* here we default to not clamped for a new tempo section. preference? */
+               ts = add_tempo_locked (tempo, pulse, minute_at_sample (sample), pls, true, false, false);
 
+               recompute_map (_metrics);
+       }
 
        PropertyChanged (PropertyChange ());
 
@@ -1002,27 +1042,49 @@ TempoMap::add_tempo (const Tempo& tempo, const double& pulse, const framepos_t&
 }
 
 void
-TempoMap::replace_tempo (const TempoSection& ts, const Tempo& tempo, const double& pulse, const framepos_t& frame, TempoSection::Type type, PositionLockStyle pls)
+TempoMap::replace_tempo (TempoSection& ts, const Tempo& tempo, const double& pulse, const samplepos_t sample, PositionLockStyle pls)
 {
-       const bool locked_to_meter = ts.locked_to_meter();
+       if (tempo.note_types_per_minute() <= 0.0) {
+               warning << "Cannot replace tempo. note types per minute must be greater than zero." << endmsg;
+               return;
+       }
+
+       bool const locked_to_meter = ts.locked_to_meter();
+       bool const ts_clamped = ts.clamped();
+       TempoSection* new_ts = 0;
 
        {
                Glib::Threads::RWLock::WriterLock lm (lock);
                TempoSection& first (first_tempo());
-               if (ts.frame() != first.frame()) {
-                       remove_tempo_locked (ts);
-                       add_tempo_locked (tempo, pulse, minute_at_frame (frame), type, pls, true, locked_to_meter);
+               if (!ts.initial()) {
+                       if (locked_to_meter) {
+                               {
+                                       /* cannot move a meter-locked tempo section */
+                                       *static_cast<Tempo*>(&ts) = tempo;
+                                       recompute_map (_metrics);
+                               }
+                       } else {
+                               remove_tempo_locked (ts);
+                               new_ts = add_tempo_locked (tempo, pulse, minute_at_sample (sample), pls, true, locked_to_meter, ts_clamped);
+                               /* enforce clampedness of next tempo section */
+                               TempoSection* next_t = next_tempo_section_locked (_metrics, new_ts);
+                               if (next_t && next_t->clamped()) {
+                                       next_t->set_note_types_per_minute (new_ts->end_note_types_per_minute());
+                               }
+                       }
+
                } else {
-                       first.set_type (type);
                        first.set_pulse (0.0);
-                       first.set_minute (minute_at_frame (frame));
+                       first.set_minute (minute_at_sample (sample));
                        first.set_position_lock_style (AudioTime);
+                       first.set_locked_to_meter (true);
+                       first.set_clamped (ts_clamped);
                        {
                                /* cannot move the first tempo section */
                                *static_cast<Tempo*>(&first) = tempo;
-                               recompute_map (_metrics);
                        }
                }
+               recompute_map (_metrics);
        }
 
        PropertyChanged (PropertyChange ());
@@ -1030,43 +1092,53 @@ TempoMap::replace_tempo (const TempoSection& ts, const Tempo& tempo, const doubl
 
 TempoSection*
 TempoMap::add_tempo_locked (const Tempo& tempo, double pulse, double minute
-                           , TempoSection::Type type, PositionLockStyle pls, bool recompute, bool locked_to_meter)
+                           , PositionLockStyle pls, bool recompute, bool locked_to_meter, bool clamped)
 {
-       TempoSection* t = new TempoSection (pulse, minute, tempo.note_types_per_minute(), tempo.note_type(), type, pls, _frame_rate);
+       TempoSection* t = new TempoSection (pulse, minute, tempo, pls, _sample_rate);
        t->set_locked_to_meter (locked_to_meter);
-       bool solved = false;
+       t->set_clamped (clamped);
 
        do_insert (t);
 
+       TempoSection* prev_tempo = 0;
+       for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
+               TempoSection* const this_t = dynamic_cast<TempoSection*>(*i);
+               if (this_t) {
+                       if (this_t == t) {
+                               if (prev_tempo && prev_tempo->type() == TempoSection::Ramp) {
+                                       prev_tempo->set_end_note_types_per_minute (t->note_types_per_minute());
+                               }
+                               break;
+                       }
+                       prev_tempo = this_t;
+               }
+       }
+
        if (recompute) {
                if (pls == AudioTime) {
-                       solved = solve_map_minute (_metrics, t, t->minute());
+                       solve_map_minute (_metrics, t, t->minute());
                } else {
-                       solved = solve_map_pulse (_metrics, t, t->pulse());
+                       solve_map_pulse (_metrics, t, t->pulse());
                }
                recompute_meters (_metrics);
        }
 
-       if (!solved && recompute) {
-               recompute_map (_metrics);
-       }
-
        return t;
 }
 
 MeterSection*
-TempoMap::add_meter (const Meter& meter, const double& beat, const Timecode::BBT_Time& where, PositionLockStyle pls)
+TempoMap::add_meter (const Meter& meter, const Timecode::BBT_Time& where, samplepos_t sample, PositionLockStyle pls)
 {
        MeterSection* m = 0;
        {
                Glib::Threads::RWLock::WriterLock lm (lock);
-               m = add_meter_locked (meter, beat, where, pls, true);
+               m = add_meter_locked (meter, where, sample, pls, true);
        }
 
 
 #ifndef NDEBUG
        if (DEBUG_ENABLED(DEBUG::TempoMap)) {
-               dump (_metrics, std::cerr);
+               dump (std::cerr);
        }
 #endif
 
@@ -1075,15 +1147,14 @@ 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, PositionLockStyle pls)
+TempoMap::replace_meter (const MeterSection& ms, const Meter& meter, const BBT_Time& where, samplepos_t sample, PositionLockStyle pls)
 {
        {
                Glib::Threads::RWLock::WriterLock lm (lock);
-               const double beat = beat_at_bbt_locked (_metrics, where);
 
-               if (ms.movable()) {
+               if (!ms.initial()) {
                        remove_meter_locked (ms);
-                       add_meter_locked (meter, beat, where, pls, true);
+                       add_meter_locked (meter, where, sample, pls, true);
                } else {
                        MeterSection& first (first_meter());
                        TempoSection& first_t (first_tempo());
@@ -1091,10 +1162,11 @@ TempoMap::replace_meter (const MeterSection& ms, const Meter& meter, const BBT_T
                        *static_cast<Meter*>(&first) = meter;
                        first.set_position_lock_style (AudioTime);
                        first.set_pulse (0.0);
-                       //first.set_minute (minute_at_frame (frame));
+                       first.set_minute (minute_at_sample (sample));
                        pair<double, BBT_Time> beat = make_pair (0.0, BBT_Time (1, 1, 0));
                        first.set_beat (beat);
                        first_t.set_minute (first.minute());
+                       first_t.set_locked_to_meter (true);
                        first_t.set_pulse (0.0);
                        first_t.set_position_lock_style (AudioTime);
                        recompute_map (_metrics);
@@ -1105,24 +1177,26 @@ TempoMap::replace_meter (const MeterSection& ms, const Meter& meter, const BBT_T
 }
 
 MeterSection*
-TempoMap::add_meter_locked (const Meter& meter, double beat, const BBT_Time& where, PositionLockStyle pls, bool recompute)
+TempoMap::add_meter_locked (const Meter& meter, const BBT_Time& bbt, samplepos_t sample, PositionLockStyle pls, bool recompute)
 {
-       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;
+       double const minute_at_bbt = minute_at_bbt_locked (_metrics, bbt);
+       const MeterSection& prev_m = meter_section_at_minute_locked  (_metrics, minute_at_bbt - minute_at_sample (1));
+       double const pulse = ((bbt.bars - prev_m.bbt().bars) * (prev_m.divisions_per_bar() / prev_m.note_divisor())) + prev_m.pulse();
+       /* the natural time of the BBT position */
+       double const time_minutes = minute_at_pulse_locked (_metrics, pulse);
 
        if (pls == AudioTime) {
-               /* add meter-locked tempo */
-               mlt = add_tempo_locked (tempo_at_minute_locked (_metrics, time_minutes), pulse,  time_minutes, TempoSection::Ramp, AudioTime, true, true);
+               /* add meter-locked tempo at the natural time in the current map (sample may differ). */
+               Tempo const tempo_at_time = tempo_at_minute_locked (_metrics, time_minutes);
+               TempoSection* mlt = add_tempo_locked (tempo_at_time, pulse, time_minutes, AudioTime, true, true, false);
 
                if (!mlt) {
                        return 0;
                }
-
        }
+       /* still using natural time for the position, ignoring lock style. */
+       MeterSection* new_meter = new MeterSection (pulse, time_minutes, beat_at_bbt_locked (_metrics, bbt), bbt, meter.divisions_per_bar(), meter.note_divisor(), pls, _sample_rate);
 
-       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);
@@ -1130,9 +1204,16 @@ TempoMap::add_meter_locked (const Meter& meter, double beat, const BBT_Time& whe
        if (recompute) {
 
                if (pls == AudioTime) {
-                       solved = solve_map_minute (_metrics, new_meter, time_minutes);
+                       /* now set the audio locked meter's position to sample */
+                       solved = solve_map_minute (_metrics, new_meter, minute_at_sample (sample));
+                       /* we failed, most likely due to some impossible sample requirement wrt audio-locked tempi.
+                          fudge sample so that the meter ends up at its BBT position instead.
+                       */
+                       if (!solved) {
+                               solved = solve_map_minute (_metrics, new_meter, minute_at_sample (prev_m.sample() + 1));
+                       }
                } else {
-                       solved = solve_map_bbt (_metrics, new_meter, where);
+                       solved = solve_map_bbt (_metrics, new_meter, bbt);
                        /* 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).
@@ -1153,9 +1234,9 @@ TempoMap::add_meter_locked (const Meter& meter, double beat, const BBT_Time& whe
 }
 
 void
-TempoMap::change_initial_tempo (double note_types_per_minute, double note_type)
+TempoMap::change_initial_tempo (double note_types_per_minute, double note_type, double end_note_types_per_minute)
 {
-       Tempo newtempo (note_types_per_minute, note_type);
+       Tempo newtempo (note_types_per_minute, note_type, end_note_types_per_minute);
        TempoSection* t;
 
        for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
@@ -1175,9 +1256,9 @@ TempoMap::change_initial_tempo (double note_types_per_minute, double note_type)
 }
 
 void
-TempoMap::change_existing_tempo_at (framepos_t where, double note_types_per_minute, double note_type)
+TempoMap::change_existing_tempo_at (samplepos_t where, double note_types_per_minute, double note_type, double end_ntpm)
 {
-       Tempo newtempo (note_types_per_minute, note_type);
+       Tempo newtempo (note_types_per_minute, note_type, end_ntpm);
 
        TempoSection* prev;
        TempoSection* first;
@@ -1188,7 +1269,7 @@ TempoMap::change_existing_tempo_at (framepos_t where, double note_types_per_minu
 
        for (first = 0, i = _metrics.begin(), prev = 0; i != _metrics.end(); ++i) {
 
-               if ((*i)->frame() > where) {
+               if ((*i)->sample() > where) {
                        break;
                }
 
@@ -1272,7 +1353,7 @@ TempoMap::first_tempo () const
                        if (!t->active()) {
                                continue;
                        }
-                       if (!t->movable()) {
+                       if (t->initial()) {
                                return *t;
                        }
                }
@@ -1293,7 +1374,7 @@ TempoMap::first_tempo ()
                        if (!t->active()) {
                                continue;
                        }
-                       if (!t->movable()) {
+                       if (t->initial()) {
                                return *t;
                        }
                }
@@ -1316,36 +1397,38 @@ TempoMap::recompute_tempi (Metrics& metrics)
                        if (!t->active()) {
                                continue;
                        }
-                       if (!t->movable()) {
+                       if (t->initial()) {
                                if (!prev_t) {
                                        t->set_pulse (0.0);
                                        prev_t = t;
                                        continue;
                                }
                        }
+
                        if (prev_t) {
                                if (t->position_lock_style() == AudioTime) {
-                                       prev_t->set_c_func (prev_t->compute_c_func_minute (t->note_types_per_minute(), t->minute()));
+                                       prev_t->set_c (prev_t->compute_c_minute (prev_t->end_note_types_per_minute(), t->minute()));
                                        if (!t->locked_to_meter()) {
-                                               t->set_pulse (prev_t->pulse_at_ntpm (t->note_types_per_minute(), t->minute()));
+                                               t->set_pulse (prev_t->pulse_at_ntpm (prev_t->end_note_types_per_minute(), t->minute()));
                                        }
 
                                } else {
-                                       prev_t->set_c_func (prev_t->compute_c_func_pulse (t->note_types_per_minute(), t->pulse()));
-                                       t->set_minute (prev_t->minute_at_ntpm (t->note_types_per_minute(), t->pulse()));
+                                       prev_t->set_c (prev_t->compute_c_pulse (prev_t->end_note_types_per_minute(), t->pulse()));
+                                       t->set_minute (prev_t->minute_at_ntpm (prev_t->end_note_types_per_minute(), t->pulse()));
 
                                }
                        }
                        prev_t = t;
                }
        }
-       prev_t->set_c_func (0.0);
+       assert (prev_t);
+       prev_t->set_c (0.0);
 }
 
 /* tempos must be positioned correctly.
    the current approach is to use a meter's bbt time as its base position unit.
    an audio-locked meter requires a recomputation of pulse and beat (but not bbt),
-   while a music-locked meter requires recomputations of frame pulse and beat (but not bbt)
+   while a music-locked meter requires recomputations of sample pulse and beat (but not bbt)
 */
 void
 TempoMap::recompute_meters (Metrics& metrics)
@@ -1364,7 +1447,7 @@ TempoMap::recompute_meters (Metrics& metrics)
                                        TempoSection* t;
                                        if ((*ii)->is_tempo()) {
                                                t = static_cast<TempoSection*> (*ii);
-                                               if ((t->locked_to_meter() || !t->movable()) && t->frame() == meter->frame()) {
+                                               if (t->locked_to_meter() && t->sample() == meter->sample()) {
                                                        meter_locked_tempo = t;
                                                        break;
                                                }
@@ -1372,14 +1455,16 @@ TempoMap::recompute_meters (Metrics& metrics)
                                }
 
                                if (prev_m) {
-                                       const double beats = (meter->bbt().bars - prev_m->bbt().bars) * prev_m->divisions_per_bar();
+                                       double beats = (meter->bbt().bars - prev_m->bbt().bars) * prev_m->divisions_per_bar();
                                        if (beats + prev_m->beat() != meter->beat()) {
                                                /* reordering caused a bbt change */
+
+                                               beats = meter->beat() - prev_m->beat();
                                                b_bbt = make_pair (beats + prev_m->beat()
                                                                   , BBT_Time ((beats / prev_m->divisions_per_bar()) + prev_m->bbt().bars, 1, 0));
                                                pulse = prev_m->pulse() + (beats / prev_m->note_divisor());
 
-                                       } else if (meter->movable()) {
+                                       } else if (!meter->initial()) {
                                                b_bbt = make_pair (meter->beat(), meter->bbt());
                                                pulse = prev_m->pulse() + (beats / prev_m->note_divisor());
                                        }
@@ -1423,7 +1508,7 @@ TempoMap::recompute_meters (Metrics& metrics)
 }
 
 void
-TempoMap::recompute_map (Metrics& metrics, framepos_t end)
+TempoMap::recompute_map (Metrics& metrics, samplepos_t end)
 {
        /* CALLER MUST HOLD WRITE LOCK */
 
@@ -1440,11 +1525,15 @@ TempoMap::recompute_map (Metrics& metrics, framepos_t end)
 }
 
 TempoMetric
-TempoMap::metric_at (framepos_t frame, Metrics::const_iterator* last) const
+TempoMap::metric_at (samplepos_t sample, Metrics::const_iterator* last) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
        TempoMetric m (first_meter(), first_tempo());
 
+       if (last) {
+               *last = ++_metrics.begin();
+       }
+
        /* at this point, we are *guaranteed* to have m.meter and m.tempo pointing
           at something, because we insert the default tempo and meter during
           TempoMap construction.
@@ -1454,7 +1543,7 @@ TempoMap::metric_at (framepos_t frame, Metrics::const_iterator* last) const
 
        for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
 
-               if ((*i)->frame() > frame) {
+               if ((*i)->sample() > sample) {
                        break;
                }
 
@@ -1499,21 +1588,21 @@ 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.
+/** Returns the BBT (meter-based) beat corresponding to the supplied sample, possibly returning a negative value.
+ * @param sample The session sample position.
+ * @return The beat duration according to the tempo map at the supplied sample.
  *
- * If the supplied frame lies before the first meter, the returned beat duration will be negative.
+ * If the supplied sample 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
+TempoMap::beat_at_sample (const samplecnt_t sample) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return beat_at_minute_locked (_metrics, minute_at_frame (frame));
+       return beat_at_minute_locked (_metrics, minute_at_sample (sample));
 }
 
 /* This function uses both tempo and meter.*/
@@ -1544,18 +1633,18 @@ TempoMap::beat_at_minute_locked (const Metrics& metrics, const double& minute) c
        return beat;
 }
 
-/** Returns the frame corresponding to the supplied BBT (meter-based) beat.
+/** Returns the sample 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.
+ * @return The sample 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
+samplepos_t
+TempoMap::sample_at_beat (const double& beat) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return frame_at_minute (minute_at_beat_locked (_metrics, beat));
+       return sample_at_minute (minute_at_beat_locked (_metrics, beat));
 }
 
 /* meter & tempo section based */
@@ -1576,12 +1665,18 @@ TempoMap::minute_at_beat_locked (const Metrics& metrics, const double& beat) con
                        prev_m = m;
                }
        }
+       assert (prev_m);
 
        TempoSection* t;
 
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                if ((*i)->is_tempo()) {
                        t = static_cast<TempoSection*> (*i);
+
+                       if (!t->active()) {
+                               continue;
+                       }
+
                        if (prev_t && ((t->pulse() - prev_m->pulse()) * prev_m->note_divisor()) + prev_m->beat() > beat) {
                                break;
                        }
@@ -1589,21 +1684,22 @@ TempoMap::minute_at_beat_locked (const Metrics& metrics, const double& beat) con
                }
 
        }
+       assert (prev_t);
 
        return prev_t->minute_at_pulse (((beat - prev_m->beat()) / prev_m->note_divisor()) + prev_m->pulse());
 }
 
-/** Returns a Tempo corresponding to the supplied frame position.
- * @param frame The audio frame.
- * @return a Tempo according to the tempo map at the supplied frame.
+/** Returns a Tempo corresponding to the supplied sample position.
+ * @param sample The audio sample.
+ * @return a Tempo according to the tempo map at the supplied sample.
  *
  */
 Tempo
-TempoMap::tempo_at_frame (const framepos_t& frame) const
+TempoMap::tempo_at_sample (const samplepos_t sample) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return tempo_at_minute_locked (_metrics, minute_at_frame (frame));
+       return tempo_at_minute_locked (_metrics, minute_at_sample (sample));
 }
 
 Tempo
@@ -1620,27 +1716,27 @@ TempoMap::tempo_at_minute_locked (const Metrics& metrics, const double& minute)
                                continue;
                        }
                        if ((prev_t) && t->minute() > minute) {
-                               /* t is the section past frame */
+                               /* t is the section past sample */
                                return prev_t->tempo_at_minute (minute);
                        }
                        prev_t = t;
                }
        }
 
-       return Tempo (prev_t->note_types_per_minute(), prev_t->note_type());
+       return Tempo (prev_t->note_types_per_minute(), prev_t->note_type(), prev_t->end_note_types_per_minute());
 }
 
-/** returns the frame at which the supplied tempo occurs, or
- *  the frame of the last tempo section (search exhausted)
+/** returns the sample at which the supplied tempo occurs, or
+ *  the sample 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
+samplepos_t
+TempoMap::sample_at_tempo (const Tempo& tempo) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return frame_at_minute (minute_at_tempo_locked (_metrics, tempo));
+       return sample_at_minute (minute_at_tempo_locked (_metrics, tempo));
 }
 
 double
@@ -1660,17 +1756,20 @@ TempoMap::minute_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) co
                                continue;
                        }
 
-                       const double t_bpm = t->note_types_per_minute();
 
-                       if (t_bpm == tempo_bpm) {
+
+                       if (t->note_types_per_minute() == tempo_bpm) {
                                return t->minute();
                        }
 
                        if (prev_t) {
                                const double prev_t_bpm = prev_t->note_types_per_minute();
+                               const double prev_t_end_bpm = prev_t->end_note_types_per_minute();
+                               if ((prev_t_bpm > tempo_bpm && prev_t_end_bpm < tempo_bpm)
+                                   || (prev_t_bpm < tempo_bpm && prev_t_end_bpm > tempo_bpm)
+                                   || (prev_t_end_bpm == tempo_bpm)) {
 
-                               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());
+                                       return prev_t->minute_at_ntpm (tempo_bpm, t->pulse());
                                }
                        }
                        prev_t = t;
@@ -1694,14 +1793,14 @@ TempoMap::tempo_at_pulse_locked (const Metrics& metrics, const double& pulse) co
                                continue;
                        }
                        if ((prev_t) && t->pulse() > pulse) {
-                               /* t is the section past frame */
+                               /* t is the section past sample */
                                return prev_t->tempo_at_pulse (pulse);
                        }
                        prev_t = t;
                }
        }
 
-       return Tempo (prev_t->note_types_per_minute(), prev_t->note_type());
+       return Tempo (prev_t->note_types_per_minute(), prev_t->note_type(), prev_t->end_note_types_per_minute());
 }
 
 double
@@ -1763,7 +1862,7 @@ TempoMap::quarter_note_at_tempo (const Tempo& tempo) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return pulse_at_tempo_locked (_metrics, tempo) * 4.0;;
+       return pulse_at_tempo_locked (_metrics, tempo) * 4.0;
 }
 
 /** Returns the whole-note pulse corresponding to the supplied  BBT (meter-based) beat.
@@ -1806,6 +1905,7 @@ TempoMap::beat_at_pulse_locked (const Metrics& metrics, const double& pulse) con
                        prev_m = m;
                }
        }
+       assert (prev_m);
 
        double const ret = ((pulse - prev_m->pulse()) * prev_m->note_divisor()) + prev_m->beat();
        return ret;
@@ -1826,7 +1926,7 @@ TempoMap::pulse_at_minute_locked (const Metrics& metrics, const double& minute)
                                continue;
                        }
                        if (prev_t && t->minute() > minute) {
-                               /*the previous ts is the one containing the frame */
+                               /*the previous ts is the one containing the sample */
                                const double ret = prev_t->pulse_at_minute (minute);
                                /* audio locked section in new meter*/
                                if (t->pulse() < ret) {
@@ -1952,6 +2052,7 @@ 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());
@@ -2089,6 +2190,8 @@ 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);
@@ -2118,37 +2221,44 @@ TempoMap::bbt_at_pulse_locked (const Metrics& metrics, const double& pulse) cons
        return ret;
 }
 
-/** Returns the BBT time corresponding to the supplied frame position.
- * @param frame the position in audio samples.
- * @return the BBT time at the frame position .
+/** Returns the BBT time corresponding to the supplied sample position.
+ * @param sample the position in audio samples.
+ * @return the BBT time at the sample position .
  *
  */
 BBT_Time
-TempoMap::bbt_at_frame (framepos_t frame)
+TempoMap::bbt_at_sample (samplepos_t sample)
 {
-       if (frame < 0) {
+       if (sample < 0) {
                BBT_Time bbt;
                bbt.bars = 1;
                bbt.beats = 1;
                bbt.ticks = 0;
-               warning << string_compose (_("tempo map was asked for BBT time at frame %1\n"), frame) << endmsg;
+#ifndef NDEBUG
+               warning << string_compose (_("tempo map was asked for BBT time at sample %1\n"), sample) << endmsg;
+#endif
                return bbt;
        }
+
+       const double minute =  minute_at_sample (sample);
+
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return bbt_at_minute_locked (_metrics, minute_at_frame (frame));
+       return bbt_at_minute_locked (_metrics, minute);
 }
 
 BBT_Time
-TempoMap::bbt_at_frame_rt (framepos_t frame)
+TempoMap::bbt_at_sample_rt (samplepos_t sample)
 {
+       const double minute =  minute_at_sample (sample);
+
        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");
+               throw std::logic_error ("TempoMap::bbt_at_sample_rt() could not lock tempo map");
        }
 
-       return bbt_at_minute_locked (_metrics, minute_at_frame (frame));
+       return bbt_at_minute_locked (_metrics, minute);
 }
 
 Timecode::BBT_Time
@@ -2181,7 +2291,7 @@ TempoMap::bbt_at_minute_locked (const Metrics& metrics, const double& minute) co
 
        double beat = prev_m->beat() + (ts.pulse_at_minute (minute) - prev_m->pulse()) * prev_m->note_divisor();
 
-       /* handle frame before first meter */
+       /* handle sample before first meter */
        if (minute < prev_m->minute()) {
                beat = 0.0;
        }
@@ -2221,25 +2331,32 @@ TempoMap::bbt_at_minute_locked (const Metrics& metrics, const double& minute) co
        return ret;
 }
 
-/** Returns the frame position corresponding to the supplied BBT time.
+/** Returns the sample position corresponding to the supplied BBT time.
  * @param bbt the position in BBT time.
- * @return the frame position at bbt.
+ * @return the sample position at bbt.
  *
  */
-framepos_t
-TempoMap::frame_at_bbt (const BBT_Time& bbt)
+samplepos_t
+TempoMap::sample_at_bbt (const BBT_Time& bbt)
 {
        if (bbt.bars < 1) {
-               warning << string_compose (_("tempo map asked for frame time at bar < 1  (%1)\n"), bbt) << endmsg;
+#ifndef NDEBUG
+               warning << string_compose (_("tempo map asked for sample time at bar < 1  (%1)\n"), bbt) << endmsg;
+#endif
                return 0;
        }
 
        if (bbt.beats < 1) {
                throw std::logic_error ("beats are counted from one");
        }
-       Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
+       double minute;
+       {
+               Glib::Threads::RWLock::ReaderLock lm (lock);
+               minute = minute_at_bbt_locked (_metrics, bbt);
+       }
+
+       return sample_at_minute (minute);
 }
 
 /* meter & tempo section based */
@@ -2253,135 +2370,108 @@ TempoMap::minute_at_bbt_locked (const Metrics& metrics, const BBT_Time& bbt) con
 }
 
 /**
- * Returns the quarter-note beat position corresponding to the supplied frame.
+ * Returns the quarter-note beat position corresponding to the supplied sample.
  *
- * @param frame the position in frames.
- * @return The quarter-note position of the supplied frame. Ignores meter.
+ * @param sample the position in samples.
+ * @return The quarter-note position of the supplied sample. Ignores meter.
  *
 */
 double
-TempoMap::quarter_note_at_frame (const framepos_t frame) const
+TempoMap::quarter_note_at_sample (const samplepos_t sample) const
 {
-       Glib::Threads::RWLock::ReaderLock lm (lock);
+       const double minute =  minute_at_sample (sample);
 
-       const double ret = quarter_note_at_minute_locked (_metrics, minute_at_frame (frame));
+       Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return ret;
+       return pulse_at_minute_locked (_metrics, minute) * 4.0;
 }
 
 double
-TempoMap::quarter_note_at_minute_locked (const Metrics& metrics, const double minute) const
+TempoMap::quarter_note_at_sample_rt (const samplepos_t sample) const
 {
-       const double ret = pulse_at_minute_locked (metrics, minute) * 4.0;
-
-       return ret;
-}
+       const double minute =  minute_at_sample (sample);
 
-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");
+               throw std::logic_error ("TempoMap::quarter_note_at_sample_rt() could not lock tempo map");
        }
 
-       const double ret = pulse_at_minute_locked (_metrics, minute_at_frame (frame)) * 4.0;
-
-       return ret;
+       return pulse_at_minute_locked (_metrics, minute) * 4.0;
 }
 
 /**
- * Returns the frame position corresponding to the supplied quarter-note beat.
+ * Returns the sample 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.
+ * @return the sample position of the supplied quarter-note. Ignores meter.
  *
  *
 */
-framepos_t
-TempoMap::frame_at_quarter_note (const double quarter_note) const
+samplepos_t
+TempoMap::sample_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 minute;
+       {
+               Glib::Threads::RWLock::ReaderLock lm (lock);
 
-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);
+               minute = minute_at_pulse_locked (_metrics, quarter_note / 4.0);
+       }
 
-       return ret;
+       return sample_at_minute (minute);
 }
 
 /** 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.
+ * a quarter-note may be compared with and assigned to Temporal::Beats.
  *
  */
 double
-TempoMap::quarter_note_at_beat (const double beat)
+TempoMap::quarter_note_at_beat (const double beat) const
 {
        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;
+       return pulse_at_beat_locked (_metrics, beat) * 4.0;
 }
 
 /** Returns the BBT (meter-based) beat position corresponding to the supplied quarter-note beats.
  * @param quarter_note The position in quarter-note beats.
  * @return the BBT (meter-based) beat position of the supplied quarter-note beats.
  *
- * a quarter-note is the musical unit of Evoral::Beats.
+ * a quarter-note is the musical unit of Temporal::Beats.
  *
  */
 double
-TempoMap::beat_at_quarter_note (const double quarter_note)
+TempoMap::beat_at_quarter_note (const double quarter_note) const
 {
        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);
+       return beat_at_pulse_locked (_metrics, quarter_note / 4.0);
 }
 
-/** Returns the duration in frames between two supplied quarter-note beat positions.
+/** Returns the duration in samples 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.
+ * @return the sample 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,
+ * sample_at-quarter_note (end_beats) - sample_at_quarter_note (start_beats).
+ * samples_between_quarter_notes() doesn't round to audio samples as an intermediate step,
  *
  */
-framecnt_t
-TempoMap::frames_between_quarter_notes (const double start, const double end) const
+samplecnt_t
+TempoMap::samples_between_quarter_notes (const double start, const double end) const
 {
-       Glib::Threads::RWLock::ReaderLock lm (lock);
+       double minutes;
 
-       return frame_at_minute (minutes_between_quarter_notes_locked (_metrics, start, end));
+       {
+               Glib::Threads::RWLock::ReaderLock lm (lock);
+               minutes = minutes_between_quarter_notes_locked (_metrics, start, end);
+       }
+
+       return sample_at_minute (minutes);
 }
 
 double
@@ -2392,15 +2482,15 @@ TempoMap::minutes_between_quarter_notes_locked (const Metrics& metrics, const do
 }
 
 double
-TempoMap::quarter_notes_between_frames (const framecnt_t start, const framecnt_t end) const
+TempoMap::quarter_notes_between_samples (const samplecnt_t start, const samplecnt_t end) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return quarter_notes_between_frames_locked (_metrics, start, end);
+       return quarter_notes_between_samples_locked (_metrics, start, end);
 }
 
 double
-TempoMap::quarter_notes_between_frames_locked (const Metrics& metrics, const framecnt_t start, const framecnt_t end) const
+TempoMap::quarter_notes_between_samples_locked (const Metrics& metrics, const samplecnt_t start, const samplecnt_t end) const
 {
        const TempoSection* prev_t = 0;
 
@@ -2412,13 +2502,14 @@ TempoMap::quarter_notes_between_frames_locked (const Metrics& metrics, const fra
                        if (!t->active()) {
                                continue;
                        }
-                       if (prev_t && t->frame() > start) {
+                       if (prev_t && t->sample() > start) {
                                break;
                        }
                        prev_t = t;
                }
        }
-       const double start_qn = prev_t->pulse_at_frame (start);
+       assert (prev_t);
+       const double start_qn = prev_t->pulse_at_sample (start);
 
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                TempoSection* t;
@@ -2428,13 +2519,13 @@ TempoMap::quarter_notes_between_frames_locked (const Metrics& metrics, const fra
                        if (!t->active()) {
                                continue;
                        }
-                       if (prev_t && t->frame() > end) {
+                       if (prev_t && t->sample() > end) {
                                break;
                        }
                        prev_t = t;
                }
        }
-       const double end_qn = prev_t->pulse_at_frame (end);
+       const double end_qn = prev_t->pulse_at_sample (end);
 
        return (end_qn - start_qn) * 4.0;
 }
@@ -2459,8 +2550,8 @@ TempoMap::check_solved (const Metrics& metrics) const
                                        return false;
                                }
 
-                               /* precision check ensures tempo and frames align.*/
-                               if (t->frame() != frame_at_minute (prev_t->minute_at_ntpm (t->note_types_per_minute(), t->pulse()))) {
+                               /* precision check ensures tempo and samples align.*/
+                               if (t->sample() != sample_at_minute (prev_t->minute_at_ntpm (prev_t->end_note_types_per_minute(), t->pulse()))) {
                                        if (!t->locked_to_meter()) {
                                                return false;
                                        }
@@ -2469,8 +2560,8 @@ TempoMap::check_solved (const Metrics& metrics) const
                                /* gradient limit - who knows what it should be?
                                   things are also ok (if a little chaotic) without this
                                */
-                               if (fabs (prev_t->c_func()) > 1000.0) {
-                                       //std::cout << "c : " << prev_t->c_func() << std::endl;
+                               if (fabs (prev_t->c()) > 1000.0) {
+                                       //std::cout << "c : " << prev_t->c() << std::endl;
                                        return false;
                                }
                        }
@@ -2480,11 +2571,11 @@ TempoMap::check_solved (const Metrics& metrics) const
                if (!(*i)->is_tempo()) {
                        m = static_cast<MeterSection*> (*i);
                        if (prev_m && m->position_lock_style() == AudioTime) {
-                               const TempoSection* t = &tempo_section_at_minute_locked (metrics, minute_at_frame (m->frame() - 1));
-                               const double nascent_m_minute = t->minute_at_pulse (m->pulse());
+                               const TempoSection* t = &tempo_section_at_minute_locked (metrics, minute_at_sample (m->sample() - 1));
+                               const samplepos_t nascent_m_sample = sample_at_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)) {
+                               if (t && (nascent_m_sample > m->sample() || nascent_m_sample < 0)) {
                                        return false;
                                }
                        }
@@ -2498,23 +2589,23 @@ TempoMap::check_solved (const Metrics& metrics) const
 }
 
 bool
-TempoMap::set_active_tempos (const Metrics& metrics, const framepos_t& frame)
+TempoMap::set_active_tempi (const Metrics& metrics, const samplepos_t sample)
 {
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                TempoSection* t;
                if ((*i)->is_tempo()) {
                        t = static_cast<TempoSection*> (*i);
-                       if (!t->movable()) {
-                               t->set_active (true);
-                               continue;
-                       }
-                       if (t->movable() && t->active () && t->position_lock_style() == AudioTime && t->frame() < frame) {
-                               t->set_active (false);
-                               t->set_pulse (0.0);
-                       } else if (t->movable() && t->position_lock_style() == AudioTime && t->frame() > frame) {
+                       if (t->locked_to_meter()) {
                                t->set_active (true);
-                       } else if (t->movable() && t->position_lock_style() == AudioTime && t->frame() == frame) {
-                               return false;
+                       } else if (t->position_lock_style() == AudioTime) {
+                               if (t->sample() < sample) {
+                                       t->set_active (false);
+                                       t->set_pulse (-1.0);
+                               } else if (t->sample() > sample) {
+                                       t->set_active (true);
+                               } else if (t->sample() == sample) {
+                                       return false;
+                               }
                        }
                }
        }
@@ -2527,19 +2618,20 @@ TempoMap::solve_map_minute (Metrics& imaginary, TempoSection* section, const dou
        TempoSection* prev_t = 0;
        TempoSection* section_prev = 0;
        double first_m_minute = 0.0;
+       const bool sml = section->locked_to_meter();
 
        /* can't move a tempo before the first meter */
        for (Metrics::iterator i = imaginary.begin(); i != imaginary.end(); ++i) {
                MeterSection* m;
                if (!(*i)->is_tempo()) {
                        m = static_cast<MeterSection*> (*i);
-                       if (!m->movable()) {
+                       if (m->initial()) {
                                first_m_minute = m->minute();
                                break;
                        }
                }
        }
-       if (section->movable() && minute <= first_m_minute) {
+       if (!section->initial() && minute <= first_m_minute) {
                return false;
        }
 
@@ -2554,21 +2646,36 @@ TempoMap::solve_map_minute (Metrics& imaginary, TempoSection* section, const dou
                        if (!t->active()) {
                                continue;
                        }
+
                        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->note_types_per_minute(), t->pulse()));
-                                       t->set_minute (prev_t->minute_at_ntpm (t->note_types_per_minute(), t->pulse()));
+
+                               if (t->sample() == sample_at_minute (minute)) {
+                                       return false;
+                               }
+
+                               const bool tlm = t->position_lock_style() == MusicTime;
+
+                               if (prev_t && !section_prev && ((sml && tlm && t->pulse() > section->pulse()) || (!tlm && t->minute() > minute))) {
+                                       section_prev = prev_t;
+
+                                       section_prev->set_c (section_prev->compute_c_minute (section_prev->end_note_types_per_minute(), minute));
+                                       if (!section->locked_to_meter()) {
+                                               section->set_pulse (section_prev->pulse_at_ntpm (section_prev->end_note_types_per_minute(), minute));
+                                       }
+                                       prev_t = section;
+                               }
+
+                               if (t->position_lock_style() == MusicTime) {
+                                       prev_t->set_c (prev_t->compute_c_pulse (prev_t->end_note_types_per_minute(), t->pulse()));
+                                       t->set_minute (prev_t->minute_at_ntpm (prev_t->end_note_types_per_minute(), t->pulse()));
                                } else {
-                                       prev_t->set_c_func (prev_t->compute_c_func_minute (t->note_types_per_minute(), t->minute()));
+                                       prev_t->set_c (prev_t->compute_c_minute (prev_t->end_note_types_per_minute(), t->minute()));
                                        if (!t->locked_to_meter()) {
-                                               t->set_pulse (prev_t->pulse_at_ntpm (t->note_types_per_minute(), t->minute()));
+                                               t->set_pulse (prev_t->pulse_at_ntpm (prev_t->end_note_types_per_minute(), t->minute()));
                                        }
                                }
                        }
@@ -2576,23 +2683,6 @@ TempoMap::solve_map_minute (Metrics& imaginary, TempoSection* section, const dou
                }
        }
 
-       if (section_prev) {
-               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_ntpm (section->note_types_per_minute(), minute));
-               }
-       }
-
-#if (0)
-       recompute_tempi (imaginary);
-
-       if (check_solved (imaginary)) {
-               return true;
-       } else {
-               dunp (imaginary, std::cout);
-       }
-#endif
-
        MetricSectionFrameSorter fcmp;
        imaginary.sort (fcmp);
 
@@ -2620,7 +2710,7 @@ TempoMap::solve_map_pulse (Metrics& imaginary, TempoSection* section, const doub
                        if (!t->active()) {
                                continue;
                        }
-                       if (!t->movable()) {
+                       if (t->initial()) {
                                t->set_pulse (0.0);
                                prev_t = t;
                                continue;
@@ -2630,13 +2720,14 @@ TempoMap::solve_map_pulse (Metrics& imaginary, TempoSection* section, const doub
                                        section_prev = prev_t;
                                        continue;
                                }
+
                                if (t->position_lock_style() == MusicTime) {
-                                       prev_t->set_c_func (prev_t->compute_c_func_pulse (t->note_types_per_minute(), t->pulse()));
-                                       t->set_minute (prev_t->minute_at_ntpm (t->note_types_per_minute(), t->pulse()));
+                                       prev_t->set_c (prev_t->compute_c_pulse (prev_t->end_note_types_per_minute(), t->pulse()));
+                                       t->set_minute (prev_t->minute_at_ntpm (prev_t->end_note_types_per_minute(), t->pulse()));
                                } else {
-                                       prev_t->set_c_func (prev_t->compute_c_func_minute (t->note_types_per_minute(), t->minute()));
+                                       prev_t->set_c (prev_t->compute_c_minute (prev_t->end_note_types_per_minute(), t->minute()));
                                        if (!t->locked_to_meter()) {
-                                               t->set_pulse (prev_t->pulse_at_ntpm (t->note_types_per_minute(), t->minute()));
+                                               t->set_pulse (prev_t->pulse_at_ntpm (prev_t->end_note_types_per_minute(), t->minute()));
                                        }
                                }
                        }
@@ -2645,20 +2736,10 @@ 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->note_types_per_minute(), pulse));
-               section->set_minute (section_prev->minute_at_ntpm (section->note_types_per_minute(), pulse));
+               section_prev->set_c (section_prev->compute_c_pulse (section_prev->end_note_types_per_minute(), pulse));
+               section->set_minute (section_prev->minute_at_ntpm (section_prev->end_note_types_per_minute(), pulse));
        }
 
-#if (0)
-       recompute_tempi (imaginary);
-
-       if (check_solved (imaginary)) {
-               return true;
-       } else {
-               dunp (imaginary, std::cout);
-       }
-#endif
-
        MetricSectionSorter cmp;
        imaginary.sort (cmp);
 
@@ -2683,15 +2764,15 @@ TempoMap::solve_map_pulse (Metrics& imaginary, TempoSection* section, const doub
 bool
 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 */
+       /* disallow moving first meter past any subsequent one, and any initial meter before the first one */
        const MeterSection* other =  &meter_section_at_minute_locked (imaginary, minute);
-       if ((!section->movable() && other->movable()) || (!other->movable() && section->movable() && other->minute() >= minute)) {
+       if ((section->initial() && !other->initial()) || (other->initial() && !section->initial() && other->minute() >= minute)) {
                return false;
        }
 
-       if (!section->movable()) {
+       if (section->initial()) {
                /* lock the first tempo to our first meter */
-               if (!set_active_tempos (imaginary, section->frame_at_minute (minute))) {
+               if (!set_active_tempi (imaginary, sample_at_minute (minute))) {
                        return false;
                }
        }
@@ -2702,7 +2783,7 @@ TempoMap::solve_map_minute (Metrics& imaginary, MeterSection* section, const dou
                TempoSection* t;
                if ((*ii)->is_tempo()) {
                        t = static_cast<TempoSection*> (*ii);
-                       if ((t->locked_to_meter() || !t->movable()) && t->minute() == section->minute()) {
+                       if (t->locked_to_meter() && t->sample() == section->sample()) {
                                meter_locked_tempo = t;
                                break;
                        }
@@ -2723,7 +2804,7 @@ TempoMap::solve_map_minute (Metrics& imaginary, MeterSection* section, const dou
                if (!(*i)->is_tempo()) {
                        m = static_cast<MeterSection*> (*i);
                        if (m == section){
-                               if (prev_m && section->movable()) {
+                               if (prev_m && !section->initial()) {
                                        const double beats = (pulse_at_minute_locked (imaginary, minute) - prev_m->pulse()) * prev_m->note_divisor();
                                        if (beats + prev_m->beat() < section->beat()) {
                                                /* set the section pulse according to its musical position,
@@ -2757,7 +2838,7 @@ TempoMap::solve_map_minute (Metrics& imaginary, MeterSection* section, const dou
                                                }
                                        } else {
                                                /* all is ok. set section's locked tempo if allowed.
-                                                  possibly disallowed if there is an adjacent audio-locked tempo.
+                                                  possibly disallow if there is an adjacent audio-locked tempo.
                                                   XX this check could possibly go. its never actually happened here.
                                                */
                                                MeterSection* meter_copy = const_cast<MeterSection*>
@@ -2785,7 +2866,7 @@ TempoMap::solve_map_minute (Metrics& imaginary, MeterSection* section, const dou
                                                }
                                        }
                                } else {
-                                       /* not movable (first meter atm) */
+                                       /* initial (first meter atm) */
 
                                        tempo_copy->set_minute (minute);
                                        tempo_copy->set_pulse (0.0);
@@ -2850,11 +2931,17 @@ TempoMap::solve_map_bbt (Metrics& imaginary, MeterSection* section, const BBT_Ti
                MeterSection* m;
                if (!(*i)->is_tempo()) {
                        m = static_cast<MeterSection*> (*i);
+
+                       if (m == section) {
+                               continue;
+                       }
+
                        pair<double, BBT_Time> b_bbt;
                        double new_pulse = 0.0;
 
                        if (prev_m && m->bbt().bars > when.bars && !section_prev){
                                section_prev = prev_m;
+
                                const double beats = (when.bars - section_prev->bbt().bars) * section_prev->divisions_per_bar();
                                const double pulse = (beats / section_prev->note_divisor()) + section_prev->pulse();
                                pair<double, BBT_Time> b_bbt = make_pair (beats + section_prev->beat(), when);
@@ -2863,7 +2950,6 @@ TempoMap::solve_map_bbt (Metrics& imaginary, MeterSection* section, const BBT_Ti
                                section->set_pulse (pulse);
                                section->set_minute (minute_at_pulse_locked (imaginary, pulse));
                                prev_m = section;
-                               continue;
                        }
 
                        if (m->position_lock_style() == AudioTime) {
@@ -2873,7 +2959,7 @@ TempoMap::solve_map_bbt (Metrics& imaginary, MeterSection* section, const BBT_Ti
                                        TempoSection* t;
                                        if ((*ii)->is_tempo()) {
                                                t = static_cast<TempoSection*> (*ii);
-                                               if ((t->locked_to_meter() || !t->movable()) && t->frame() == m->frame()) {
+                                               if (t->locked_to_meter() && t->sample() == m->sample()) {
                                                        meter_locked_tempo = t;
                                                        break;
                                                }
@@ -2885,14 +2971,21 @@ TempoMap::solve_map_bbt (Metrics& imaginary, MeterSection* section, const BBT_Ti
                                }
 
                                if (prev_m) {
-                                       const double beats = ((m->bbt().bars - prev_m->bbt().bars) * prev_m->divisions_per_bar());
+                                       double beats = ((m->bbt().bars - prev_m->bbt().bars) * prev_m->divisions_per_bar());
 
                                        if (beats + prev_m->beat() != m->beat()) {
                                                /* tempo/ meter change caused a change in beat (bar). */
+
+                                               /* the user has requested that the previous section of music overlaps this one.
+                                                  we have no choice but to change the bar number here, as being locked to audio means
+                                                  we must stay where we are on the timeline.
+                                               */
+                                               beats = m->beat() - prev_m->beat();
                                                b_bbt = make_pair (beats + prev_m->beat()
                                                                   , BBT_Time ((beats / prev_m->divisions_per_bar()) + prev_m->bbt().bars, 1, 0));
                                                new_pulse = prev_m->pulse() + (beats / prev_m->note_divisor());
-                                       } else if (m->movable()) {
+
+                                       } else if (!m->initial()) {
                                                b_bbt = make_pair (m->beat(), m->bbt());
                                                new_pulse = prev_m->pulse() + (beats / prev_m->note_divisor());
                                        }
@@ -2948,15 +3041,13 @@ TempoMap::solve_map_bbt (Metrics& imaginary, MeterSection* section, const BBT_Ti
  *  to section's equivalent in copy.
  */
 TempoSection*
-TempoMap::copy_metrics_and_point (const Metrics& metrics, Metrics& copy, TempoSection* section)
+TempoMap::copy_metrics_and_point (const Metrics& metrics, Metrics& copy, TempoSection* section) const
 {
        TempoSection* ret = 0;
 
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
-               TempoSection* t;
-               MeterSection* m;
                if ((*i)->is_tempo()) {
-                       t = static_cast<TempoSection*> (*i);
+                       TempoSection const * const t = dynamic_cast<TempoSection const * const> (*i);
                        if (t == section) {
                                ret = new TempoSection (*t);
                                copy.push_back (ret);
@@ -2965,9 +3056,8 @@ TempoMap::copy_metrics_and_point (const Metrics& metrics, Metrics& copy, TempoSe
 
                        TempoSection* cp = new TempoSection (*t);
                        copy.push_back (cp);
-               }
-               if (!(*i)->is_tempo()) {
-                       m = static_cast<MeterSection *> (*i);
+               } else {
+                       MeterSection const * const m = dynamic_cast<MeterSection const * const> (*i);
                        MeterSection* cp = new MeterSection (*m);
                        copy.push_back (cp);
                }
@@ -2977,21 +3067,17 @@ TempoMap::copy_metrics_and_point (const Metrics& metrics, Metrics& copy, TempoSe
 }
 
 MeterSection*
-TempoMap::copy_metrics_and_point (const Metrics& metrics, Metrics& copy, MeterSection* section)
+TempoMap::copy_metrics_and_point (const Metrics& metrics, Metrics& copy, MeterSection* section) const
 {
        MeterSection* ret = 0;
 
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
-               TempoSection* t;
-               MeterSection* m;
                if ((*i)->is_tempo()) {
-                       t = static_cast<TempoSection*> (*i);
+                       TempoSection const * const t = dynamic_cast<TempoSection const * const> (*i);
                        TempoSection* cp = new TempoSection (*t);
                        copy.push_back (cp);
-               }
-
-               if (!(*i)->is_tempo()) {
-                       m = static_cast<MeterSection *> (*i);
+               } else {
+                       MeterSection const * const m = dynamic_cast<MeterSection const * const> (*i);
                        if (m == section) {
                                ret = new MeterSection (*m);
                                copy.push_back (ret);
@@ -3038,17 +3124,17 @@ 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,
+* This is for a gui that needs to know the pulse or sample 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 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.
+* @return returns - the position in pulses and samples (as a pair) where the new tempo section will lie.
 */
-pair<double, framepos_t>
+pair<double, samplepos_t>
 TempoMap::predict_tempo_position (TempoSection* section, const BBT_Time& bbt)
 {
        Metrics future_map;
-       pair<double, framepos_t> ret = make_pair (0.0, 0);
+       pair<double, samplepos_t> ret = make_pair (0.0, 0);
 
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
@@ -3056,12 +3142,16 @@ TempoMap::predict_tempo_position (TempoSection* section, const BBT_Time& bbt)
 
        const double beat = beat_at_bbt_locked (future_map, bbt);
 
+       if (section->position_lock_style() == AudioTime) {
+               tempo_copy->set_position_lock_style (MusicTime);
+       }
+
        if (solve_map_pulse (future_map, tempo_copy, pulse_at_beat_locked (future_map, beat))) {
                ret.first = tempo_copy->pulse();
-               ret.second = tempo_copy->frame();
+               ret.second = tempo_copy->sample();
        } else {
                ret.first = section->pulse();
-               ret.second = section->frame();
+               ret.second = section->sample();
        }
 
        Metrics::const_iterator d = future_map.begin();
@@ -3074,35 +3164,35 @@ TempoMap::predict_tempo_position (TempoSection* section, const BBT_Time& bbt)
 
 /** 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 sample - the new position in samples 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
+ * if sub_num is non-zero, the sample 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
+ *  0        | no snap - use audio sample 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.
+ * if sub_num is zero, the musical position will be taken from the supplied sample.
  */
 void
-TempoMap::gui_move_tempo (TempoSection* ts, const framepos_t& frame, const int& sub_num)
+TempoMap::gui_set_tempo_position (TempoSection* ts, const samplepos_t sample, 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. */
+                       /* if we're snapping to a musical grid, set the pulse exactly instead of via the supplied sample. */
                        Glib::Threads::RWLock::WriterLock lm (lock);
                        TempoSection* tempo_copy = copy_metrics_and_point (_metrics, future_map, ts);
 
                        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);
+                       if (solve_map_minute (future_map, tempo_copy, minute_at_sample (sample))) {
+                               const double beat = exact_beat_at_sample_locked (future_map, sample, sub_num);
                                const double pulse = pulse_at_beat_locked (future_map, beat);
 
                                if (solve_map_pulse (future_map, tempo_copy, pulse)) {
@@ -3118,30 +3208,25 @@ TempoMap::gui_move_tempo (TempoSection* ts, const framepos_t& frame, const int&
                        Glib::Threads::RWLock::WriterLock lm (lock);
                        TempoSection* tempo_copy = copy_metrics_and_point (_metrics, future_map, ts);
 
-                       if (solve_map_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));
+                       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 sample 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).
+                                * We fudge around this by doing this in the musical domain and then swapping back for the recompute.
+                                */
+                               const double qn = exact_qn_at_sample_locked (_metrics, sample, sub_num);
+                               tempo_copy->set_position_lock_style (MusicTime);
+                               if (solve_map_pulse (future_map, tempo_copy, qn / 4.0)) {
+                                       ts->set_position_lock_style (MusicTime);
+                                       solve_map_pulse (_metrics, ts, qn / 4.0);
+                                       ts->set_position_lock_style (AudioTime);
+                                       recompute_meters (_metrics);
+                               }
+                       } else {
+                               if (solve_map_minute (future_map, tempo_copy, minute_at_sample (sample))) {
+                                       solve_map_minute (_metrics, ts, minute_at_sample (sample));
                                        recompute_meters (_metrics);
                                }
                        }
@@ -3154,19 +3239,19 @@ TempoMap::gui_move_tempo (TempoSection* ts, const framepos_t& frame, const int&
                ++d;
        }
 
-       MetricPositionChanged (); // Emit Signal
+       MetricPositionChanged (PropertyChange ()); // Emit Signal
 }
 
 /** moves a MeterSection to a specified position.
  * @param ms - the section to be moved
- * @param frame - the new position in frames for the meter
+ * @param sample - the new position in samples for the meter
  *
  * as a meter cannot snap to anything but bars,
- * the supplied frame is rounded to the nearest bar, possibly
+ * the supplied sample is rounded to the nearest bar, possibly
  * leaving the meter position unchanged.
  */
 void
-TempoMap::gui_move_meter (MeterSection* ms, const framepos_t& frame)
+TempoMap::gui_set_meter_position (MeterSection* ms, const samplepos_t sample)
 {
        Metrics future_map;
 
@@ -3176,8 +3261,8 @@ TempoMap::gui_move_meter (MeterSection* ms, const framepos_t& frame)
                        Glib::Threads::RWLock::WriterLock lm (lock);
                        MeterSection* copy = copy_metrics_and_point (_metrics, future_map, ms);
 
-                       if (solve_map_minute (future_map, copy, minute_at_frame (frame))) {
-                               solve_map_minute (_metrics, ms, minute_at_frame (frame));
+                       if (solve_map_minute (future_map, copy, minute_at_sample (sample))) {
+                               solve_map_minute (_metrics, ms, minute_at_sample (sample));
                                recompute_tempi (_metrics);
                        }
                }
@@ -3186,7 +3271,7 @@ TempoMap::gui_move_meter (MeterSection* ms, const framepos_t& frame)
                        Glib::Threads::RWLock::WriterLock lm (lock);
                        MeterSection* copy = copy_metrics_and_point (_metrics, future_map, ms);
 
-                       const double beat = beat_at_minute_locked (_metrics, minute_at_frame (frame));
+                       const double beat = beat_at_minute_locked (_metrics, minute_at_sample (sample));
                        const Timecode::BBT_Time bbt = bbt_at_beat_locked (_metrics, beat);
 
                        if (solve_map_bbt (future_map, copy, bbt)) {
@@ -3202,7 +3287,7 @@ TempoMap::gui_move_meter (MeterSection* ms, const framepos_t& frame)
                ++d;
        }
 
-       MetricPositionChanged (); // Emit Signal
+       MetricPositionChanged (PropertyChange ()); // Emit Signal
 }
 
 bool
@@ -3213,11 +3298,40 @@ 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_note_types_per_minute (bpm.note_types_per_minute());
+
+               if (tempo_copy->type() == TempoSection::Constant) {
+                       tempo_copy->set_end_note_types_per_minute (bpm.note_types_per_minute());
+                       tempo_copy->set_note_types_per_minute (bpm.note_types_per_minute());
+               } else {
+                       tempo_copy->set_note_types_per_minute (bpm.note_types_per_minute());
+                       tempo_copy->set_end_note_types_per_minute (bpm.end_note_types_per_minute());
+               }
+
+               if (ts->clamped()) {
+                       TempoSection* prev = 0;
+                       if ((prev = previous_tempo_section_locked (future_map, tempo_copy)) != 0) {
+                               prev->set_end_note_types_per_minute (tempo_copy->note_types_per_minute());
+                       }
+               }
+
                recompute_tempi (future_map);
 
                if (check_solved (future_map)) {
-                       ts->set_note_types_per_minute (bpm.note_types_per_minute());
+                       if (ts->type() == TempoSection::Constant) {
+                               ts->set_end_note_types_per_minute (bpm.note_types_per_minute());
+                               ts->set_note_types_per_minute (bpm.note_types_per_minute());
+                       } else {
+                               ts->set_end_note_types_per_minute (bpm.end_note_types_per_minute());
+                               ts->set_note_types_per_minute (bpm.note_types_per_minute());
+                       }
+
+                       if (ts->clamped()) {
+                               TempoSection* prev = 0;
+                               if ((prev = previous_tempo_section_locked (_metrics, ts)) != 0) {
+                                       prev->set_end_note_types_per_minute (ts->note_types_per_minute());
+                               }
+                       }
+
                        recompute_map (_metrics);
                        can_solve = true;
                }
@@ -3229,20 +3343,21 @@ TempoMap::gui_change_tempo (TempoSection* ts, const Tempo& bpm)
                ++d;
        }
        if (can_solve) {
-               MetricPositionChanged (); // Emit Signal
+               MetricPositionChanged (PropertyChange ()); // Emit Signal
        }
+
        return can_solve;
 }
 
 void
-TempoMap::gui_dilate_tempo (TempoSection* ts, const framepos_t& frame, const framepos_t& end_frame)
+TempoMap::gui_stretch_tempo (TempoSection* ts, const samplepos_t sample, const samplepos_t end_sample, const double start_qnote, const double end_qnote)
 {
        /*
          Ts (future prev_t)   Tnext
          |                    |
          |     [drag^]        |
          |----------|----------
-               e_f  qn_beats(frame)
+               e_f  qn_beats(sample)
        */
 
        Metrics future_map;
@@ -3254,402 +3369,565 @@ TempoMap::gui_dilate_tempo (TempoSection* ts, const framepos_t& frame, const fra
                        return;
                }
 
-               TempoSection* prev_t = copy_metrics_and_point (_metrics, future_map, ts);
-               TempoSection* prev_to_prev_t = 0;
-               const frameoffset_t fr_off = end_frame - frame;
-
-               if (prev_t && prev_t->pulse() > 0.0) {
-                       prev_to_prev_t = const_cast<TempoSection*>(&tempo_section_at_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 ((*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;
+               TempoSection* ts_copy = copy_metrics_and_point (_metrics, future_map, ts);
 
-               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());
+               if (!ts_copy) {
+                       return;
                }
 
-               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));
+               /* minimum allowed measurement distance in samples */
+               samplepos_t const min_dframe = 2;
 
                double new_bpm;
+               if (ts_copy->clamped()) {
+                       TempoSection* next_t = next_tempo_section_locked (future_map, ts_copy);
+                       TempoSection* prev_to_ts_copy = previous_tempo_section_locked (future_map, ts_copy);
+                        /* the change in samples is the result of changing the slope of at most 2 previous tempo sections.
+                          constant to constant is straightforward, as the tempo prev to ts_copy has constant slope.
+                        */                     double contribution = 0.0;
+                       if (next_t && prev_to_ts_copy && prev_to_ts_copy->type() == TempoSection::Ramp) {
+                               contribution = (ts_copy->pulse() - prev_to_ts_copy->pulse()) / (double) (next_t->pulse() - prev_to_ts_copy->pulse());
+                       }
+                       samplepos_t const fr_off = end_sample - sample;
+                       sampleoffset_t const ts_copy_sample_contribution = fr_off - (contribution * (double) fr_off);
 
-               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->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() && 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->note_types_per_minute();
-                                       }
-                               }
+                       if (sample > prev_to_ts_copy->sample() + min_dframe && (sample + ts_copy_sample_contribution) > prev_to_ts_copy->sample() + min_dframe) {
+                               new_bpm = ts_copy->note_types_per_minute() * ((start_qnote - (prev_to_ts_copy->pulse() * 4.0))
+                                                                            / (end_qnote - (prev_to_ts_copy->pulse() * 4.0)));
                        } else {
-                               /* AudioTime */
-                               if (prev_to_prev_t && prev_to_prev_t->type() == TempoSection::Ramp) {
-                                       if (frame > prev_to_prev_t->frame() + min_dframe && end_frame > prev_to_prev_t->frame() + min_dframe) {
-
-                                               new_bpm = prev_t->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 (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->note_types_per_minute();
-                                       }
-                               }
+                               new_bpm = ts_copy->note_types_per_minute();
                        }
                } else {
+                       if (sample > ts_copy->sample() + min_dframe && end_sample > ts_copy->sample() + min_dframe) {
 
-                       double frame_ratio = 1.0;
-                       double pulse_ratio = 1.0;
-                       const double pulse_pos = frame;
-
-                       if (prev_to_prev_t) {
-                               if (pulse_pos > prev_to_prev_t->frame() + min_dframe && (pulse_pos - fr_off) > prev_to_prev_t->frame() + min_dframe) {
-                                       frame_ratio = (((pulse_pos - fr_off) - prev_to_prev_t->frame()) / (double) ((pulse_pos) - prev_to_prev_t->frame()));
-                               }
-                               if (end_pulse > prev_to_prev_t->pulse() && start_pulse > prev_to_prev_t->pulse()) {
-                                       pulse_ratio = ((start_pulse - prev_to_prev_t->pulse()) / (end_pulse - prev_to_prev_t->pulse()));
-                               }
+                               new_bpm = ts_copy->note_types_per_minute() * ((sample - ts_copy->sample())
+                                                                            / (double) (end_sample - ts_copy->sample()));
                        } else {
-                               if (pulse_pos > prev_t->frame() + min_dframe && (pulse_pos - fr_off) > prev_t->frame() + min_dframe) {
-                                       frame_ratio = (((pulse_pos - fr_off) - prev_t->frame()) / (double) ((pulse_pos) - prev_t->frame()));
-                               }
-                               pulse_ratio = (start_pulse / end_pulse);
+                               new_bpm = ts_copy->note_types_per_minute();
                        }
-                       new_bpm = prev_t->note_types_per_minute() * (pulse_ratio * frame_ratio);
-               }
 
+                       new_bpm = min (new_bpm, (double) 1000.0);
+               }
                /* don't clamp and proceed here.
                   testing has revealed that this can go negative,
                   which is an entirely different thing to just being too low.
                */
+
                if (new_bpm < 0.5) {
-                       return;
+                       goto out;
                }
-               new_bpm = min (new_bpm, (double) 1000.0);
-               prev_t->set_note_types_per_minute (new_bpm);
+
+               ts_copy->set_note_types_per_minute (new_bpm);
+
+               if (ts_copy->clamped()) {
+                       TempoSection* prev = 0;
+                       if ((prev = previous_tempo_section_locked (future_map, ts_copy)) != 0) {
+                               prev->set_end_note_types_per_minute (ts_copy->note_types_per_minute());
+                       }
+               }
+
                recompute_tempi (future_map);
                recompute_meters (future_map);
 
                if (check_solved (future_map)) {
                        ts->set_note_types_per_minute (new_bpm);
+
+                       if (ts->clamped()) {
+                               TempoSection* prev = 0;
+                               if ((prev = previous_tempo_section_locked (_metrics, ts)) != 0) {
+                                       prev->set_end_note_types_per_minute (ts->note_types_per_minute());
+                               }
+                       }
+
                        recompute_tempi (_metrics);
                        recompute_meters (_metrics);
                }
        }
 
+
+out:
        Metrics::const_iterator d = future_map.begin();
        while (d != future_map.end()) {
                delete (*d);
                ++d;
        }
+       MetricPositionChanged (PropertyChange ()); // Emit Signal
 
-       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)
+void
+TempoMap::gui_stretch_tempo_end (TempoSection* ts, const samplepos_t sample, const samplepos_t end_sample)
 {
-       return beat_at_pulse_locked (_metrics, exact_qn_at_frame_locked (metrics, frame, divisions) / 4.0);
-}
+       /*
+         Ts (future prev_t)   Tnext
+         |                    |
+         |     [drag^]        |
+         |----------|----------
+               e_f  qn_beats(sample)
+       */
 
-/** 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);
+       Metrics future_map;
 
-       return exact_qn_at_frame_locked (_metrics, frame, sub_num);
-}
+       {
+               Glib::Threads::RWLock::WriterLock lm (lock);
 
-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 (!ts) {
+                       return;
+               }
 
-       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;
+               TempoSection* prev_t = copy_metrics_and_point (_metrics, future_map, ts);
 
-               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 (!prev_t) {
+                       return;
+               }
 
-               if ((qn - prev_b) > (next_b - prev_b) / 2.0) {
-                       qn = next_b;
+               /* minimum allowed measurement distance in samples */
+               samplepos_t const min_dframe = 2;
+               double new_bpm;
+
+               if (sample > prev_t->sample() + min_dframe && end_sample > prev_t->sample() + min_dframe) {
+                       new_bpm = prev_t->end_note_types_per_minute() * ((prev_t->sample() - sample)
+                                                                                / (double) (prev_t->sample() - end_sample));
                } else {
-                       qn = prev_b;
+                       new_bpm = prev_t->end_note_types_per_minute();
                }
-       }
-
-       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);
+               new_bpm = min (new_bpm, (double) 1000.0);
 
-       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 (new_bpm < 0.5) {
+                       goto out;
+               }
 
-       if (dir > 0) {
-               pos_bbt.bars += bbt.bars;
+               prev_t->set_end_note_types_per_minute (new_bpm);
 
-               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;
+               TempoSection* next = 0;
+               if ((next = next_tempo_section_locked (future_map, prev_t)) != 0) {
+                       if (next->clamped()) {
+                               next->set_note_types_per_minute (prev_t->end_note_types_per_minute());
+                       }
                }
 
-               pos_bbt.beats += bbt.beats;
-               if ((double) pos_bbt.beats > divisions) {
-                       pos_bbt.bars += 1;
-                       pos_bbt.beats -= divisions;
-               }
+               recompute_tempi (future_map);
+               recompute_meters (future_map);
 
-               return frame_at_minute (minute_at_bbt_locked (_metrics, pos_bbt)) - offset;
-       } else {
-               pos_bbt.bars -= bbt.bars;
+               if (check_solved (future_map)) {
+                       ts->set_end_note_types_per_minute (new_bpm);
 
-               if (pos_bbt.ticks < bbt.ticks) {
-                       if (pos_bbt.beats == 1) {
-                               pos_bbt.bars--;
-                               pos_bbt.beats = divisions;
-                       } else {
-                               pos_bbt.beats--;
+                       TempoSection* true_next = 0;
+                       if ((true_next = next_tempo_section_locked (_metrics, ts)) != 0) {
+                               if (true_next->clamped()) {
+                                       true_next->set_note_types_per_minute (ts->end_note_types_per_minute());
+                               }
                        }
-                       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;
+                       recompute_tempi (_metrics);
+                       recompute_meters (_metrics);
                }
-
-               return offset - frame_at_minute (minute_at_bbt_locked (_metrics, pos_bbt));
        }
 
-       return 0;
-}
 
-framepos_t
-TempoMap::round_to_bar (framepos_t fr, RoundMode dir)
-{
-       return round_to_type (fr, dir, Bar);
-}
+out:
+       Metrics::const_iterator d = future_map.begin();
+       while (d != future_map.end()) {
+               delete (*d);
+               ++d;
+       }
 
-framepos_t
-TempoMap::round_to_beat (framepos_t fr, RoundMode dir)
-{
-       return round_to_type (fr, dir, Beat);
+       MetricPositionChanged (PropertyChange ()); // Emit Signal
 }
 
-framepos_t
-TempoMap::round_to_beat_subdivision (framepos_t fr, int sub_num, RoundMode dir)
+bool
+TempoMap::gui_twist_tempi (TempoSection* ts, const Tempo& bpm, const samplepos_t sample, const samplepos_t end_sample)
 {
-       Glib::Threads::RWLock::ReaderLock lm (lock);
-       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;
+       TempoSection* next_t = 0;
+       TempoSection* next_to_next_t = 0;
+       Metrics future_map;
+       bool can_solve = false;
 
-       ticks -= beats * BBT_Time::ticks_per_beat;
+       /* minimum allowed measurement distance in samples */
+       samplepos_t const min_dframe = 2;
 
-       if (dir > 0) {
-               /* round to next (or same iff dir == RoundUpMaybe) */
+       {
+               Glib::Threads::RWLock::WriterLock lm (lock);
+               if (!ts) {
+                       return false;
+               }
 
-               uint32_t mod = ticks % ticks_one_subdivisions_worth;
+               TempoSection* tempo_copy = copy_metrics_and_point (_metrics, future_map, ts);
+               TempoSection* prev_to_prev_t = 0;
+               const sampleoffset_t fr_off = end_sample - sample;
 
-               if (mod == 0 && dir == RoundUpMaybe) {
-                       /* right on the subdivision, which is fine, so do nothing */
+               if (!tempo_copy) {
+                       return false;
+               }
 
-               } else if (mod == 0) {
-                       /* right on the subdivision, so the difference is just the subdivision ticks */
-                       ticks += ticks_one_subdivisions_worth;
+               if (tempo_copy->pulse() > 0.0) {
+                       prev_to_prev_t = const_cast<TempoSection*>(&tempo_section_at_minute_locked (future_map, minute_at_sample (tempo_copy->sample() - 1)));
+               }
 
-               } else {
-                       /* not on subdivision, compute distance to next subdivision */
+               for (Metrics::const_iterator i = future_map.begin(); i != future_map.end(); ++i) {
+                       if ((*i)->is_tempo() && (*i)->minute() >  tempo_copy->minute()) {
+                               next_t = static_cast<TempoSection*> (*i);
+                               break;
+                       }
+               }
 
-                       ticks += ticks_one_subdivisions_worth - mod;
+               if (!next_t) {
+                       return false;
                }
 
-               if (ticks >= BBT_Time::ticks_per_beat) {
-                       ticks -= BBT_Time::ticks_per_beat;
+               for (Metrics::const_iterator i = future_map.begin(); i != future_map.end(); ++i) {
+                       if ((*i)->is_tempo() && (*i)->minute() >  next_t->minute()) {
+                               next_to_next_t = static_cast<TempoSection*> (*i);
+                               break;
+                       }
                }
-       } else if (dir < 0) {
 
-               /* round to previous (or same iff dir == RoundDownMaybe) */
+               if (!next_to_next_t) {
+                       return false;
+               }
 
-               uint32_t difference = ticks % ticks_one_subdivisions_worth;
+               double prev_contribution = 0.0;
 
-               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 (next_t && prev_to_prev_t && prev_to_prev_t->type() == TempoSection::Ramp) {
+                       prev_contribution = (tempo_copy->sample() - prev_to_prev_t->sample()) / (double) (next_t->sample() - prev_to_prev_t->sample());
                }
 
-               if (ticks < difference) {
-                       ticks = BBT_Time::ticks_per_beat - ticks;
+               const sampleoffset_t tempo_copy_sample_contribution = fr_off - (prev_contribution * (double) fr_off);
+
+
+               samplepos_t old_tc_minute = tempo_copy->minute();
+               double old_next_minute = next_t->minute();
+               double old_next_to_next_minute = next_to_next_t->minute();
+
+               double new_bpm;
+               double new_next_bpm;
+               double new_copy_end_bpm;
+
+               if (sample > tempo_copy->sample() + min_dframe && (sample + tempo_copy_sample_contribution) > tempo_copy->sample() + min_dframe) {
+                       new_bpm = tempo_copy->note_types_per_minute() * ((sample - tempo_copy->sample())
+                                                                                      / (double) (end_sample - tempo_copy->sample()));
                } else {
-                       ticks -= difference;
+                       new_bpm = tempo_copy->note_types_per_minute();
                }
 
-       } else {
-               /* round to nearest */
-               double rem;
+               /* don't clamp and proceed here.
+                  testing has revealed that this can go negative,
+                  which is an entirely different thing to just being too low.
+               */
+               if (new_bpm < 0.5) {
+                       return false;
+               }
 
-               /* compute the distance to the previous and next subdivision */
+               new_bpm = min (new_bpm, (double) 1000.0);
 
-               if ((rem = fmod ((double) ticks, (double) ticks_one_subdivisions_worth)) > ticks_one_subdivisions_worth/2.0) {
+               tempo_copy->set_note_types_per_minute (new_bpm);
+               if (tempo_copy->type() == TempoSection::Constant) {
+                       tempo_copy->set_end_note_types_per_minute (new_bpm);
+               }
 
-                       /* closer to the next subdivision, so shift forward */
+               recompute_tempi (future_map);
 
-                       ticks = lrint (ticks + (ticks_one_subdivisions_worth - rem));
+               if (check_solved (future_map)) {
 
-                       DEBUG_TRACE (DEBUG::SnapBBT, string_compose ("moved forward to %1\n", ticks));
+                       if (!next_t) {
+                               return false;
+                       }
 
-                       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));
+                       ts->set_note_types_per_minute (new_bpm);
+                       if (ts->type() == TempoSection::Constant) {
+                               ts->set_end_note_types_per_minute (new_bpm);
                        }
 
-               } else if (rem > 0) {
+                       recompute_map (_metrics);
 
-                       /* closer to previous subdivision, so shift backward */
+                       can_solve = true;
+               }
 
-                       if (rem > ticks) {
-                               if (beats == 0) {
-                                       /* can't go backwards past zero, so ... */
-                                       return 0;
+               if (next_t->type() == TempoSection::Constant || next_t->c() == 0.0) {
+                       if (sample > tempo_copy->sample() + min_dframe && end_sample > tempo_copy->sample() + min_dframe) {
+
+                               new_next_bpm = next_t->note_types_per_minute() * ((next_to_next_t->minute() - old_next_minute)
+                                                                                 / (double) ((old_next_to_next_minute) - old_next_minute));
+
+                       } else {
+                               new_next_bpm = next_t->note_types_per_minute();
+                       }
+
+                       next_t->set_note_types_per_minute (new_next_bpm);
+                       recompute_tempi (future_map);
+
+                       if (check_solved (future_map)) {
+                               for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
+                                       if ((*i)->is_tempo() && (*i)->minute() >  ts->minute()) {
+                                               next_t = static_cast<TempoSection*> (*i);
+                                               break;
+                                       }
                                }
-                               /* step back to previous beat */
-                               --beats;
-                               ticks = lrint (BBT_Time::ticks_per_beat - rem);
-                               DEBUG_TRACE (DEBUG::SnapBBT, string_compose ("step back beat to %1\n", beats));
+
+                               if (!next_t) {
+                                       return false;
+                               }
+                               next_t->set_note_types_per_minute (new_next_bpm);
+                               recompute_map (_metrics);
+                               can_solve = true;
+                       }
+               } else {
+                       double next_sample_ratio = 1.0;
+                       double copy_sample_ratio = 1.0;
+
+                       if (next_to_next_t) {
+                               next_sample_ratio = (next_to_next_t->minute() - old_next_minute) / (old_next_to_next_minute -  old_next_minute);
+
+                               copy_sample_ratio = ((old_tc_minute - next_t->minute()) / (double) (old_tc_minute - old_next_minute));
+                       }
+
+                       new_next_bpm = next_t->note_types_per_minute() * next_sample_ratio;
+                       new_copy_end_bpm = tempo_copy->end_note_types_per_minute() * copy_sample_ratio;
+
+                       tempo_copy->set_end_note_types_per_minute (new_copy_end_bpm);
+
+                       if (next_t->clamped()) {
+                               next_t->set_note_types_per_minute (new_copy_end_bpm);
                        } else {
-                               ticks = lrint (ticks - rem);
-                               DEBUG_TRACE (DEBUG::SnapBBT, string_compose ("moved backward to %1\n", ticks));
+                               next_t->set_note_types_per_minute (new_next_bpm);
                        }
+
+                       recompute_tempi (future_map);
+
+                       if (check_solved (future_map)) {
+                               for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
+                                       if ((*i)->is_tempo() && (*i)->minute() >  ts->minute()) {
+                                               next_t = static_cast<TempoSection*> (*i);
+                                               break;
+                                       }
+                               }
+
+                               if (!next_t) {
+                                       return false;
+                               }
+
+                               if (next_t->clamped()) {
+                                       next_t->set_note_types_per_minute (new_copy_end_bpm);
+                               } else {
+                                       next_t->set_note_types_per_minute (new_next_bpm);
+                               }
+
+                               ts->set_end_note_types_per_minute (new_copy_end_bpm);
+                               recompute_map (_metrics);
+                               can_solve = true;
+                       }
+               }
+       }
+
+       Metrics::const_iterator d = future_map.begin();
+       while (d != future_map.end()) {
+               delete (*d);
+               ++d;
+       }
+
+       MetricPositionChanged (PropertyChange ()); // Emit Signal
+
+       return can_solve;
+}
+
+/** Returns the sample position of the musical position zero */
+samplepos_t
+TempoMap::music_origin ()
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       return first_tempo().sample();
+}
+
+/** Returns the exact bbt-based beat corresponding to the bar, beat or quarter note subdivision nearest to
+ * the supplied sample, possibly returning a negative value.
+ *
+ * @param sample  The session sample 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_sample()).
+ * @return The beat position of the supplied sample.
+ *
+ * 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 sample 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_sample (const samplepos_t sample, const int32_t sub_num) const
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       return exact_beat_at_sample_locked (_metrics, sample, sub_num);
+}
+
+double
+TempoMap::exact_beat_at_sample_locked (const Metrics& metrics, const samplepos_t sample, const int32_t divisions) const
+{
+       return beat_at_pulse_locked (_metrics, exact_qn_at_sample_locked (metrics, sample, divisions) / 4.0);
+}
+
+/** Returns the exact quarter note corresponding to the bar, beat or quarter note subdivision nearest to
+ * the supplied sample, possibly returning a negative value.
+ *
+ * @param sample  The session sample 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_sample()).
+ * @return The quarter note position of the supplied sample.
+ *
+ * When working to a musical grid, the use of sub_nom indicates that
+ * the sample 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 sample 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_sample (const samplepos_t sample, const int32_t sub_num) const
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       return exact_qn_at_sample_locked (_metrics, sample, sub_num);
+}
+
+double
+TempoMap::exact_qn_at_sample_locked (const Metrics& metrics, const samplepos_t sample, const int32_t sub_num) const
+{
+       double qn = pulse_at_minute_locked (metrics, minute_at_sample (sample)) * 4.0;
+
+       if (sub_num > 1) {
+               qn = floor (qn) + (floor (((qn - floor (qn)) * (double) sub_num) + 0.5) / sub_num);
+       } else if (sub_num == 1) {
+               /* the gui requested exact musical (BBT) beat */
+               qn = pulse_at_beat_locked (metrics, (floor (beat_at_minute_locked (metrics, minute_at_sample (sample)) + 0.5))) * 4.0;
+       } else if (sub_num == -1) {
+               /* snap to  bar */
+               Timecode::BBT_Time bbt = bbt_at_pulse_locked (metrics, qn / 4.0);
+               bbt.beats = 1;
+               bbt.ticks = 0;
+
+               const double prev_b = pulse_at_bbt_locked (metrics, bbt) * 4.0;
+               ++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 {
-                       /* on the subdivision, do nothing */
+                       qn = prev_b;
+               }
+       }
+
+       return qn;
+}
+
+/** returns the sample duration of the supplied BBT time at a specified sample position in the tempo map.
+ * @param pos the sample 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 samples between pos and bbt
+*/
+samplecnt_t
+TempoMap::bbt_duration_at (samplepos_t pos, const BBT_Time& bbt, int dir)
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       BBT_Time pos_bbt = bbt_at_minute_locked (_metrics, minute_at_sample (pos));
+
+       const double divisions = meter_section_at_minute_locked (_metrics, minute_at_sample (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;
+               }
+               const samplecnt_t pos_bbt_sample = sample_at_minute (minute_at_bbt_locked (_metrics, pos_bbt));
+
+               return pos_bbt_sample - pos;
+
+       } else {
+
+               if (pos_bbt.bars <= bbt.bars) {
+                       pos_bbt.bars = 1;
+               } else {
+                       pos_bbt.bars -= bbt.bars;
                }
+
+               if (pos_bbt.ticks < bbt.ticks) {
+                       if (pos_bbt.bars > 1) {
+                               if (pos_bbt.beats == 1) {
+                                       pos_bbt.bars--;
+                                       pos_bbt.beats = divisions;
+                               } else {
+                                       pos_bbt.beats--;
+                               }
+                               pos_bbt.ticks = BBT_Time::ticks_per_beat - (bbt.ticks - pos_bbt.ticks);
+                       } else {
+                               pos_bbt.beats = 1;
+                               pos_bbt.ticks = 0;
+                       }
+               } else {
+                       pos_bbt.ticks -= bbt.ticks;
+               }
+
+               if (pos_bbt.beats <= bbt.beats) {
+                       if (pos_bbt.bars > 1) {
+                               pos_bbt.bars--;
+                               pos_bbt.beats = divisions - (bbt.beats - pos_bbt.beats);
+                       } else {
+                               pos_bbt.beats = 1;
+                       }
+               } else {
+                       pos_bbt.beats -= bbt.beats;
+               }
+
+               return pos - sample_at_minute (minute_at_bbt_locked (_metrics, pos_bbt));
        }
 
-       const framepos_t ret_frame = frame_at_minute (minute_at_beat_locked (_metrics, beats + (ticks / BBT_Time::ticks_per_beat)));
+       return 0;
+}
+
+MusicSample
+TempoMap::round_to_bar (samplepos_t fr, RoundMode dir)
+{
+       return round_to_type (fr, dir, Bar);
+}
 
-       return ret_frame;
+MusicSample
+TempoMap::round_to_beat (samplepos_t fr, RoundMode dir)
+{
+       return round_to_type (fr, dir, Beat);
 }
 
-framepos_t
-TempoMap::round_to_quarter_note_subdivision (framepos_t fr, int sub_num, RoundMode dir)
+MusicSample
+TempoMap::round_to_quarter_note_subdivision (samplepos_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 ticks = (uint32_t) floor (max (0.0, pulse_at_minute_locked (_metrics, minute_at_sample (fr))) * BBT_Time::ticks_per_beat * 4.0);
        uint32_t beats = (uint32_t) floor (ticks / BBT_Time::ticks_per_beat);
        uint32_t ticks_one_subdivisions_worth = (uint32_t) BBT_Time::ticks_per_beat / sub_num;
 
@@ -3673,9 +3951,14 @@ TempoMap::round_to_quarter_note_subdivision (framepos_t fr, int sub_num, RoundMo
                        ticks += ticks_one_subdivisions_worth - mod;
                }
 
-               if (ticks >= BBT_Time::ticks_per_beat) {
-                       ticks -= BBT_Time::ticks_per_beat;
-               }
+//NOTE:  this code intentionally limits the rounding so we don't advance to the next beat.
+//  For the purposes of "jump-to-next-subdivision", we DO want to advance to the next beat.
+//     And since the "prev" direction DOES move beats, I assume this code is unintended.
+//  But I'm keeping it around, until we determine there are no terrible consequences.
+//             if (ticks >= BBT_Time::ticks_per_beat) {
+//                     ticks -= BBT_Time::ticks_per_beat;
+//             }
+
        } else if (dir < 0) {
 
                /* round to previous (or same iff dir == RoundDownMaybe) */
@@ -3721,7 +4004,7 @@ TempoMap::round_to_quarter_note_subdivision (framepos_t fr, int sub_num, RoundMo
                        if (rem > ticks) {
                                if (beats == 0) {
                                        /* can't go backwards past zero, so ... */
-                                       return 0;
+                                       return MusicSample (0, 0);
                                }
                                /* step back to previous beat */
                                --beats;
@@ -3736,91 +4019,118 @@ TempoMap::round_to_quarter_note_subdivision (framepos_t fr, int sub_num, RoundMo
                }
        }
 
-       const framepos_t ret_frame = frame_at_minute (minute_at_quarter_note_locked (_metrics, beats + (ticks / BBT_Time::ticks_per_beat)));
+       MusicSample ret (0, 0);
+       ret.sample = sample_at_minute (minute_at_pulse_locked (_metrics, (beats + (ticks / BBT_Time::ticks_per_beat)) / 4.0));
+       ret.division = sub_num;
 
-       return ret_frame;
+       return ret;
 }
 
-framepos_t
-TempoMap::round_to_type (framepos_t frame, RoundMode dir, BBTPointType type)
+MusicSample
+TempoMap::round_to_type (samplepos_t sample, RoundMode dir, BBTPointType type)
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-
-       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));
+       const double minute = minute_at_sample (sample);
+       const double beat_at_samplepos = max (0.0, beat_at_minute_locked (_metrics, minute));
+       BBT_Time bbt (bbt_at_beat_locked (_metrics, beat_at_samplepos));
+       MusicSample ret (0, 0);
 
        switch (type) {
        case Bar:
+               ret.division = -1;
+
                if (dir < 0) {
-                       /* find bar previous to 'frame' */
+                       /* find bar previous to 'sample' */
+                       if (bbt.bars > 0)
+                               --bbt.bars;
                        bbt.beats = 1;
                        bbt.ticks = 0;
-                       return frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
+
+                       ret.sample = sample_at_minute (minute_at_bbt_locked (_metrics, bbt));
+
+                       return ret;
 
                } else if (dir > 0) {
-                       /* find bar following 'frame' */
+                       /* find bar following 'sample' */
                        ++bbt.bars;
                        bbt.beats = 1;
                        bbt.ticks = 0;
-                       return frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
+
+                       ret.sample = sample_at_minute (minute_at_bbt_locked (_metrics, bbt));
+
+                       return ret;
                } else {
                        /* true rounding: find nearest bar */
-                       framepos_t raw_ft = frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
+                       samplepos_t raw_ft = sample_at_minute (minute_at_bbt_locked (_metrics, bbt));
                        bbt.beats = 1;
                        bbt.ticks = 0;
-                       framepos_t prev_ft = frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
+                       samplepos_t prev_ft = sample_at_minute (minute_at_bbt_locked (_metrics, bbt));
                        ++bbt.bars;
-                       framepos_t next_ft = frame_at_minute (minute_at_bbt_locked (_metrics, bbt));
+                       samplepos_t next_ft = sample_at_minute (minute_at_bbt_locked (_metrics, bbt));
 
-                       if ((raw_ft - prev_ft) > (next_ft - prev_ft) / 2) { 
-                               return next_ft;
+                       if ((raw_ft - prev_ft) > (next_ft - prev_ft) / 2) {
+                               ret.sample = next_ft;
+
+                               return ret;
                        } else {
-                               return prev_ft;
+                               --bbt.bars;
+                               ret.sample = prev_ft;
+
+                               return ret;
                        }
                }
 
                break;
 
        case Beat:
+               ret.division = 1;
+
                if (dir < 0) {
-                       return frame_at_minute (minute_at_beat_locked (_metrics, floor (beat_at_framepos)));
+                       ret.sample = sample_at_minute (minute_at_beat_locked (_metrics, floor (beat_at_samplepos)));
+
+                       return ret;
                } else if (dir > 0) {
-                       return frame_at_minute (minute_at_beat_locked (_metrics, ceil (beat_at_framepos)));
+                       ret.sample = sample_at_minute (minute_at_beat_locked (_metrics, ceil (beat_at_samplepos)));
+
+                       return ret;
                } else {
-                       return frame_at_minute (minute_at_beat_locked (_metrics, floor (beat_at_framepos + 0.5)));
+                       ret.sample = sample_at_minute (minute_at_beat_locked (_metrics, floor (beat_at_samplepos + 0.5)));
+
+                       return ret;
                }
                break;
        }
 
-       return 0;
+       return MusicSample (0, 0);
 }
 
 void
 TempoMap::get_grid (vector<TempoMap::BBTPoint>& points,
-                   framepos_t lower, framepos_t upper, uint32_t bar_mod)
+                   samplepos_t lower, samplepos_t upper, uint32_t bar_mod)
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       int32_t cnt = ceil (beat_at_minute_locked (_metrics, minute_at_frame (lower)));
-       framecnt_t pos = 0;
+       int32_t cnt = ceil (beat_at_minute_locked (_metrics, minute_at_sample (lower)));
+       samplecnt_t pos = 0;
        /* although the map handles negative beats, bbt doesn't. */
        if (cnt < 0.0) {
                cnt = 0.0;
        }
 
-       if (minute_at_beat_locked (_metrics, cnt) >= minute_at_frame (upper)) {
+       if (minute_at_beat_locked (_metrics, cnt) >= minute_at_sample (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));
+                       pos = sample_at_minute (minute_at_beat_locked (_metrics, cnt));
+                       const MeterSection meter = meter_section_at_minute_locked (_metrics, minute_at_sample (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()));
+                       const double qn = pulse_at_beat_locked (_metrics, cnt) * 4.0;
+
+                       points.push_back (BBTPoint (meter, tempo_at_minute_locked (_metrics, minute_at_sample (pos)), pos, bbt.bars, bbt.beats, qn));
                        ++cnt;
                }
        } else {
-               BBT_Time bbt = bbt_at_minute_locked (_metrics, minute_at_frame (lower));
+               BBT_Time bbt = bbt_at_minute_locked (_metrics, minute_at_sample (lower));
                bbt.beats = 1;
                bbt.ticks = 0;
 
@@ -3830,21 +4140,30 @@ TempoMap::get_grid (vector<TempoMap::BBTPoint>& points,
                }
 
                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()));
+                       pos = sample_at_minute (minute_at_bbt_locked (_metrics, bbt));
+                       const MeterSection meter = meter_section_at_minute_locked (_metrics, minute_at_sample (pos));
+                       const double qn = pulse_at_bbt_locked (_metrics, bbt) * 4.0;
+
+                       points.push_back (BBTPoint (meter, tempo_at_minute_locked (_metrics, minute_at_sample (pos)), pos, bbt.bars, bbt.beats, qn));
                        bbt.bars += bar_mod;
                }
        }
 }
 
 const TempoSection&
-TempoMap::tempo_section_at_frame (framepos_t frame) const
+TempoMap::tempo_section_at_sample (samplepos_t sample) const
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       return tempo_section_at_minute_locked (_metrics, minute_at_sample (sample));
+}
+
+TempoSection&
+TempoMap::tempo_section_at_sample (samplepos_t sample)
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return tempo_section_at_minute_locked (_metrics, minute_at_frame (frame));
+       return tempo_section_at_minute_locked (_metrics, minute_at_sample (sample));
 }
 
 const TempoSection&
@@ -3876,7 +4195,35 @@ TempoMap::tempo_section_at_minute_locked (const Metrics& metrics, double minute)
 
        return *prev;
 }
+TempoSection&
+TempoMap::tempo_section_at_minute_locked (const Metrics& metrics, double minute)
+{
+       TempoSection* prev = 0;
+
+       TempoSection* t;
+
+       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
+
+               if ((*i)->is_tempo()) {
+                       t = static_cast<TempoSection*> (*i);
+                       if (!t->active()) {
+                               continue;
+                       }
+                       if (prev && t->minute() > minute) {
+                               break;
+                       }
+
+                       prev = t;
+               }
+       }
+
+       if (prev == 0) {
+               fatal << endmsg;
+               abort(); /*NOTREACHED*/
+       }
 
+       return *prev;
+}
 const TempoSection&
 TempoMap::tempo_section_at_beat_locked (const Metrics& metrics, const double& beat) const
 {
@@ -3888,6 +4235,11 @@ TempoMap::tempo_section_at_beat_locked (const Metrics& metrics, const double& be
        for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
                if ((*i)->is_tempo()) {
                        t = static_cast<TempoSection*> (*i);
+
+                       if (!t->active()) {
+                               continue;
+                       }
+
                        if (prev_t && ((t->pulse() - prev_m->pulse()) * prev_m->note_divisor()) + prev_m->beat() > beat) {
                                break;
                        }
@@ -3898,11 +4250,97 @@ TempoMap::tempo_section_at_beat_locked (const Metrics& metrics, const double& be
        return *prev_t;
 }
 
-/* don't use this to calculate length (the tempo is only correct for this frame).
-   do that stuff based on the beat_at_frame and frame_at_beat api
+TempoSection*
+TempoMap::previous_tempo_section (TempoSection* ts) const
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       return previous_tempo_section_locked (_metrics, ts);
+
+}
+
+TempoSection*
+TempoMap::previous_tempo_section_locked (const Metrics& metrics, TempoSection* ts) const
+{
+       if (!ts) {
+               return 0;
+       }
+
+       TempoSection* prev = 0;
+
+       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
+
+               if ((*i)->is_tempo()) {
+                       TempoSection* t = static_cast<TempoSection*> (*i);
+
+                       if (!t->active()) {
+                               continue;
+                       }
+
+                       if (prev && t == ts) {
+
+                               return prev;
+                       }
+
+                       prev = t;
+               }
+       }
+
+       if (prev == 0) {
+               fatal << endmsg;
+               abort(); /*NOTREACHED*/
+       }
+
+       return 0;
+}
+
+TempoSection*
+TempoMap::next_tempo_section (TempoSection* ts) const
+{
+       Glib::Threads::RWLock::ReaderLock lm (lock);
+
+       return next_tempo_section_locked (_metrics, ts);
+}
+
+TempoSection*
+TempoMap::next_tempo_section_locked (const Metrics& metrics, TempoSection* ts) const
+{
+       if (!ts) {
+               return 0;
+       }
+
+       TempoSection* prev = 0;
+
+       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
+
+               if ((*i)->is_tempo()) {
+                       TempoSection* t = static_cast<TempoSection*> (*i);
+
+                       if (!t->active()) {
+                               continue;
+                       }
+
+                       if (prev && prev == ts) {
+
+                               return t;
+                       }
+
+                       prev = t;
+               }
+       }
+
+       if (prev == 0) {
+               fatal << endmsg;
+               abort(); /*NOTREACHED*/
+       }
+
+       return 0;
+}
+/* don't use this to calculate length (the tempo is only correct for this sample).
+   do that stuff based on the beat_at_sample and sample_at_beat api
 */
 double
-TempoMap::frames_per_quarter_note_at (const framepos_t& frame, const framecnt_t& sr) const
+TempoMap::samples_per_quarter_note_at (const samplepos_t sample, const samplecnt_t sr) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
@@ -3918,26 +4356,27 @@ TempoMap::frames_per_quarter_note_at (const framepos_t& frame, const framecnt_t&
                        if (!t->active()) {
                                continue;
                        }
-                       if (ts_at && (*i)->frame() > frame) {
+                       if (ts_at && (*i)->sample() > sample) {
                                ts_after = t;
                                break;
                        }
                        ts_at = t;
                }
        }
+       assert (ts_at);
 
        if (ts_after) {
-               return  (60.0 * _frame_rate) / ts_at->tempo_at_minute (minute_at_frame (frame)).quarter_notes_per_minute();
+               return  (60.0 * _sample_rate) / ts_at->tempo_at_minute (minute_at_sample (sample)).quarter_notes_per_minute();
        }
        /* must be treated as constant tempo */
-       return ts_at->frames_per_quarter_note (_frame_rate);
+       return ts_at->samples_per_quarter_note (_sample_rate);
 }
 
 const MeterSection&
-TempoMap::meter_section_at_frame (framepos_t frame) const
+TempoMap::meter_section_at_sample (samplepos_t sample) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       return meter_section_at_minute_locked (_metrics, minute_at_frame (frame));
+       return meter_section_at_minute_locked (_metrics, minute_at_sample (sample));
 }
 
 const MeterSection&
@@ -3996,9 +4435,9 @@ TempoMap::meter_section_at_beat (double beat) const
 }
 
 const Meter&
-TempoMap::meter_at_frame (framepos_t frame) const
+TempoMap::meter_at_sample (samplepos_t sample) const
 {
-       TempoMetric m (metric_at (frame));
+       TempoMetric m (metric_at (sample));
        return m.meter();
 }
 
@@ -4007,13 +4446,14 @@ TempoMap::fix_legacy_session ()
 {
        MeterSection* prev_m = 0;
        TempoSection* prev_t = 0;
+       bool have_initial_t = false;
 
        for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
                MeterSection* m;
                TempoSection* t;
 
                if ((m = dynamic_cast<MeterSection*>(*i)) != 0) {
-                       if (!m->movable()) {
+                       if (m->initial()) {
                                pair<double, BBT_Time> bbt = make_pair (0.0, BBT_Time (1, 1, 0));
                                m->set_beat (bbt);
                                m->set_pulse (0.0);
@@ -4039,16 +4479,29 @@ TempoMap::fix_legacy_session ()
                        if (!t->active()) {
                                continue;
                        }
+                       /* Ramp type never existed in the era of this tempo section */
+                       t->set_end_note_types_per_minute (t->note_types_per_minute());
 
-                       if (!t->movable()) {
+                       if (t->initial()) {
                                t->set_pulse (0.0);
                                t->set_minute (0.0);
                                t->set_position_lock_style (AudioTime);
                                prev_t = t;
+                               have_initial_t = true;
                                continue;
                        }
 
                        if (prev_t) {
+                               /* some 4.x sessions have no initial (non-movable) tempo. */
+                               if (!have_initial_t) {
+                                       prev_t->set_pulse (0.0);
+                                       prev_t->set_minute (0.0);
+                                       prev_t->set_position_lock_style (AudioTime);
+                                       prev_t->set_initial (true);
+                                       prev_t->set_locked_to_meter (true);
+                                       have_initial_t = true;
+                               }
+
                                const double beat = ((t->legacy_bbt().bars - 1) * ((prev_m) ? prev_m->note_divisor() : 4.0))
                                        + (t->legacy_bbt().beats - 1)
                                        + (t->legacy_bbt().ticks / BBT_Time::ticks_per_beat);
@@ -4063,6 +4516,34 @@ TempoMap::fix_legacy_session ()
                }
        }
 }
+void
+TempoMap::fix_legacy_end_session ()
+{
+       TempoSection* prev_t = 0;
+
+       for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
+               TempoSection* t;
+
+               if ((t = dynamic_cast<TempoSection*>(*i)) != 0) {
+
+                       if (!t->active()) {
+                               continue;
+                       }
+
+                       if (prev_t) {
+                               if (prev_t->end_note_types_per_minute() < 0.0) {
+                                       prev_t->set_end_note_types_per_minute (t->note_types_per_minute());
+                               }
+                       }
+
+                       prev_t = t;
+               }
+       }
+
+       if (prev_t) {
+               prev_t->set_end_note_types_per_minute (prev_t->note_types_per_minute());
+       }
+}
 
 XMLNode&
 TempoMap::get_state ()
@@ -4099,7 +4580,7 @@ TempoMap::set_state (const XMLNode& node, int /*version*/)
                        if (child->name() == TempoSection::xml_state_node_name) {
 
                                try {
-                                       TempoSection* ts = new TempoSection (*child, _frame_rate);
+                                       TempoSection* ts = new TempoSection (*child, _sample_rate);
                                        _metrics.push_back (ts);
                                }
 
@@ -4113,7 +4594,7 @@ TempoMap::set_state (const XMLNode& node, int /*version*/)
                        } else if (child->name() == MeterSection::xml_state_node_name) {
 
                                try {
-                                       MeterSection* ms = new MeterSection (*child, _frame_rate);
+                                       MeterSection* ms = new MeterSection (*child, _sample_rate);
                                        _metrics.push_back (ms);
                                }
 
@@ -4126,11 +4607,6 @@ TempoMap::set_state (const XMLNode& node, int /*version*/)
                        }
                }
 
-               if (niter == nlist.end()) {
-                       MetricSectionSorter cmp;
-                       _metrics.sort (cmp);
-               }
-
                /* check for legacy sessions where bbt was the base musical unit for tempo */
                for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
                        TempoSection* t;
@@ -4139,10 +4615,19 @@ TempoMap::set_state (const XMLNode& node, int /*version*/)
                                        fix_legacy_session();
                                        break;
                                }
-                               break;
+
+                               if (t->end_note_types_per_minute() < 0.0) {
+                                       fix_legacy_end_session();
+                                       break;
+                               }
                        }
                }
 
+               if (niter == nlist.end()) {
+                       MetricSectionSorter cmp;
+                       _metrics.sort (cmp);
+               }
+
                /* check for multiple tempo/meters at the same location, which
                   ardour2 somehow allowed.
                */
@@ -4155,9 +4640,9 @@ TempoMap::set_state (const XMLNode& node, int /*version*/)
                                TempoSection* ts;
                                TempoSection* prev_t;
                                if ((prev_m = dynamic_cast<MeterSection*>(*prev)) != 0 && (ms = dynamic_cast<MeterSection*>(*i)) != 0) {
-                                       if (prev_m->pulse() == ms->pulse()) {
-                                               cerr << string_compose (_("Multiple meter definitions found at %1"), prev_m->pulse()) << endmsg;
-                                               error << string_compose (_("Multiple meter definitions found at %1"), prev_m->pulse()) << endmsg;
+                                       if (prev_m->beat() == ms->beat()) {
+                                               cerr << string_compose (_("Multiple meter definitions found at %1"), prev_m->beat()) << endmsg;
+                                               error << string_compose (_("Multiple meter definitions found at %1"), prev_m->beat()) << endmsg;
                                                return -1;
                                        }
                                } else if ((prev_t = dynamic_cast<TempoSection*>(*prev)) != 0 && (ts = dynamic_cast<TempoSection*>(*i)) != 0) {
@@ -4187,35 +4672,36 @@ TempoMap::set_state (const XMLNode& node, int /*version*/)
 }
 
 void
-TempoMap::dump (const Metrics& metrics, std::ostream& o) const
+TempoMap::dump (std::ostream& o) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock, Glib::Threads::TRY_LOCK);
        const MeterSection* m;
        const TempoSection* t;
        const TempoSection* prev_t = 0;
 
-       for (Metrics::const_iterator i = metrics.begin(); i != metrics.end(); ++i) {
+       for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
 
                if ((t = dynamic_cast<const TempoSection*>(*i)) != 0) {
-                       o << "Tempo @ " << *i << t->note_types_per_minute() << " BPM (pulse = 1/" << t->note_type()
+                       o << "Tempo @ " << *i << " start : " << t->note_types_per_minute() << " end : " << t->end_note_types_per_minute() << " BPM (pulse = 1/" << t->note_type()
                          << " type= " << enum_2_string (t->type()) << ") "  << " at pulse= " << t->pulse()
-                         << " minute= " << t->minute() << " frame= " << t->frame() << " (movable? " << t->movable() << ')'
+                         << " minute= " << t->minute() << " sample= " << t->sample() << " (initial? " << t->initial() << ')'
                          << " pos lock: " << enum_2_string (t->position_lock_style()) << std::endl;
                        if (prev_t) {
-                               o << std::setprecision (17) << "  current      : " << t->note_types_per_minute()
-                                 << " | " << t->pulse() << " | " << t->frame() << " | " << t->minute() << std::endl;
+                               o <<  "  current start  : " << t->note_types_per_minute()
+                                 <<  "  current end  : " << t->end_note_types_per_minute()
+                                 << " | " << t->pulse() << " | " << t->sample() << " | " << t->minute() << std::endl;
                                o << "  previous     : " << prev_t->note_types_per_minute()
-                                 << " | " << prev_t->pulse() << " | " << prev_t->frame() << " | " << prev_t->minute() << std::endl;
+                                 << " | " << prev_t->pulse() << " | " << prev_t->sample() << " | " << 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->pulse_at_ntpm (prev_t->end_note_types_per_minute(), t->minute())
+                                 << " | " << sample_at_minute (prev_t->minute_at_ntpm (prev_t->end_note_types_per_minute(), t->pulse()))
+                                 << " | " << prev_t->minute_at_ntpm (prev_t->end_note_types_per_minute(), t->pulse()) << std::endl;
                        }
                        prev_t = t;
                } else if ((m = dynamic_cast<const MeterSection*>(*i)) != 0) {
                        o << "Meter @ " << *i << ' ' << m->divisions_per_bar() << '/' << m->note_divisor() << " at " << m->bbt()
-                         << " frame= " << m->frame() << " pulse: " << m->pulse() <<  " beat : " << m->beat()
-                         << " pos lock: " << enum_2_string (m->position_lock_style()) << " (movable? " << m->movable() << ')' << endl;
+                         << " sample= " << m->sample() << " pulse: " << m->pulse() <<  " beat : " << m->beat()
+                         << " pos lock: " << enum_2_string (m->position_lock_style()) << " (initial? " << m->initial() << ')' << endl;
                }
        }
        o << "------" << std::endl;
@@ -4252,19 +4738,19 @@ TempoMap::n_meters() const
 }
 
 void
-TempoMap::insert_time (framepos_t where, framecnt_t amount)
+TempoMap::insert_time (samplepos_t where, samplecnt_t amount)
 {
        for (Metrics::reverse_iterator i = _metrics.rbegin(); i != _metrics.rend(); ++i) {
-               if ((*i)->frame() >= where && (*i)->movable ()) {
+               if ((*i)->sample() >= where && !(*i)->initial ()) {
                        MeterSection* ms;
                        TempoSection* ts;
 
                        if ((ms = dynamic_cast <MeterSection*>(*i)) != 0) {
-                               gui_move_meter (ms, (*i)->frame() + amount);
+                               gui_set_meter_position (ms, (*i)->sample() + amount);
                        }
 
                        if ((ts = dynamic_cast <TempoSection*>(*i)) != 0) {
-                               gui_move_tempo (ts, (*i)->frame() + amount, 0);
+                               gui_set_tempo_position (ts, (*i)->sample() + amount, 0);
                        }
                }
        }
@@ -4273,7 +4759,7 @@ TempoMap::insert_time (framepos_t where, framecnt_t amount)
 }
 
 bool
-TempoMap::remove_time (framepos_t where, framecnt_t amount)
+TempoMap::remove_time (samplepos_t where, samplecnt_t amount)
 {
        bool moved = false;
 
@@ -4286,7 +4772,7 @@ TempoMap::remove_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)->frame() < where+amount) {
+                       if ((*i)->sample() >= where && (*i)->sample() < where+amount) {
                                metric_kill_list.push_back(*i);
                                TempoSection *lt = dynamic_cast<TempoSection*> (*i);
                                if (lt)
@@ -4295,10 +4781,10 @@ TempoMap::remove_time (framepos_t where, framecnt_t amount)
                                if (lm)
                                        last_meter = lm;
                        }
-                       else if ((*i)->frame() >= where) {
+                       else if ((*i)->sample() >= where) {
                                // TODO: make sure that moved tempo/meter markers are rounded to beat/bar boundaries
-                               (*i)->set_minute ((*i)->minute() - minute_at_frame (amount));
-                               if ((*i)->frame() == where) {
+                               (*i)->set_minute ((*i)->minute() - minute_at_sample (amount));
+                               if ((*i)->sample() == where) {
                                        // marker was immediately after end of range
                                        tempo_after = dynamic_cast<TempoSection*> (*i);
                                        meter_after = dynamic_cast<MeterSection*> (*i);
@@ -4310,12 +4796,12 @@ 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_minute (minute_at_frame (where));
+                       last_tempo->set_minute (minute_at_sample (where));
                        moved = true;
                }
                if (last_meter && !meter_after) {
                        metric_kill_list.remove(last_meter);
-                       last_meter->set_minute (minute_at_frame (where));
+                       last_meter->set_minute (minute_at_sample (where));
                        moved = true;
                }
 
@@ -4333,24 +4819,24 @@ 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 sample position, and return the result in samples.
  *  pos can be -ve, if required.
  */
-framepos_t
-TempoMap::framepos_plus_qn (framepos_t frame, Evoral::Beats beats) const
+samplepos_t
+TempoMap::samplepos_plus_qn (samplepos_t sample, Temporal::Beats beats) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
-       const double frame_qn = quarter_notes_between_frames_locked (_metrics, 0, frame);
+       const double sample_qn = pulse_at_minute_locked (_metrics, minute_at_sample (sample)) * 4.0;
 
-       return frame_at_minute (minute_at_quarter_note_locked (_metrics, frame_qn + beats.to_double()));
+       return sample_at_minute (minute_at_pulse_locked (_metrics, (sample_qn + beats.to_double()) / 4.0));
 }
 
-framepos_t
-TempoMap::framepos_plus_bbt (framepos_t pos, BBT_Time op) const
+samplepos_t
+TempoMap::samplepos_plus_bbt (samplepos_t pos, BBT_Time op) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       BBT_Time pos_bbt = bbt_at_beat_locked (_metrics, beat_at_minute_locked (_metrics, minute_at_frame (pos)));
+       BBT_Time pos_bbt = bbt_at_beat_locked (_metrics, beat_at_minute_locked (_metrics, minute_at_sample (pos)));
        pos_bbt.ticks += op.ticks;
        if (pos_bbt.ticks >= BBT_Time::ticks_per_beat) {
                ++pos_bbt.beats;
@@ -4366,18 +4852,18 @@ TempoMap::framepos_plus_bbt (framepos_t pos, BBT_Time op) const
        }
        pos_bbt.bars += op.bars;
 
-       return frame_at_minute (minute_at_bbt_locked (_metrics, pos_bbt));
+       return sample_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_qn (framepos_t pos, framecnt_t distance) const
+Temporal::Beats
+TempoMap::framewalk_to_qn (samplepos_t pos, samplecnt_t distance) const
 {
        Glib::Threads::RWLock::ReaderLock lm (lock);
 
-       return Evoral::Beats (quarter_notes_between_frames_locked (_metrics, pos, pos + distance));
+       return Temporal::Beats (quarter_notes_between_samples_locked (_metrics, pos, pos + distance));
 }
 
 struct bbtcmp {
@@ -4399,7 +4885,7 @@ operator<< (std::ostream& o, const Tempo& t) {
 std::ostream&
 operator<< (std::ostream& o, const MetricSection& section) {
 
-       o << "MetricSection @ " << section.frame() << ' ';
+       o << "MetricSection @ " << section.sample() << ' ';
 
        const TempoSection* ts;
        const MeterSection* ms;