2 Copyright (C) 2000 Paul Davis
4 This program is free software; you can redistribute it and/or modify
5 it under the terms of the GNU General Public License as published by
6 the Free Software Foundation; either version 2 of the License, or
7 (at your option) any later version.
9 This program is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12 GNU General Public License for more details.
14 You should have received a copy of the GNU General Public License
15 along with this program; if not, write to the Free Software
16 Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
20 #ifndef __ardour_tempo_h__
21 #define __ardour_tempo_h__
27 #include <glibmm/threads.h>
30 #include "pbd/enum_convert.h"
32 #include "pbd/stateful.h"
33 #include "pbd/statefuldestructible.h"
35 #include "temporal/beats.h"
37 #include "ardour/ardour.h"
40 class FrameposPlusBeatsTest;
41 class FrameposMinusBeatsTest;
50 // Find a better place for these
51 LIBARDOUR_API bool bbt_time_to_string (const Timecode::BBT_Time& bbt, std::string& str);
52 LIBARDOUR_API bool string_to_bbt_time (const std::string& str, Timecode::BBT_Time& bbt);
54 /** Tempo, the speed at which musical time progresses (BPM). */
55 class LIBARDOUR_API Tempo {
58 * @param npm Note Types per minute
59 * @param type Note Type (default `4': quarter note)
61 Tempo (double npm, double type=4.0) // defaulting to quarter note
62 : _note_types_per_minute (npm), _note_type (type), _end_note_types_per_minute (npm) {}
63 Tempo (double start_npm, double type, double end_npm)
64 : _note_types_per_minute (start_npm), _note_type (type), _end_note_types_per_minute (end_npm) {}
66 double note_types_per_minute () const { return _note_types_per_minute; }
67 double note_types_per_minute (double note_type) const { return (_note_types_per_minute / _note_type) * note_type; }
68 void set_note_types_per_minute (double npm) { _note_types_per_minute = npm; }
69 double note_type () const { return _note_type; }
71 double quarter_notes_per_minute () const { return note_types_per_minute (4.0); }
72 double pulses_per_minute () const { return note_types_per_minute (1.0); }
74 double end_note_types_per_minute () const { return _end_note_types_per_minute; }
75 double end_note_types_per_minute (double note_type) const { return (_end_note_types_per_minute / _note_type) * note_type; }
76 void set_end_note_types_per_minute (double npm) { _end_note_types_per_minute = npm; }
78 double end_quarter_notes_per_minute () const { return end_note_types_per_minute (4.0); }
79 double end_pulses_per_minute () const { return end_note_types_per_minute (1.0); }
81 /** audio samples per note type.
82 * if you want an instantaneous value for this, use TempoMap::samples_per_quarter_note_at() instead.
83 * @param sr samplerate
85 double samples_per_note_type (samplecnt_t sr) const {
86 return (60.0 * sr) / _note_types_per_minute;
88 /** audio samples per quarter note.
89 * if you want an instantaneous value for this, use TempoMap::samples_per_quarter_note_at() instead.
90 * @param sr samplerate
92 double samples_per_quarter_note (samplecnt_t sr) const {
93 return (60.0 * sr) / quarter_notes_per_minute ();
97 double _note_types_per_minute;
99 double _end_note_types_per_minute;
102 /** Meter, or time signature (beats per bar, and which note type is a beat). */
103 class LIBARDOUR_API Meter {
105 Meter (double dpb, double bt)
106 : _divisions_per_bar (dpb), _note_type (bt) {}
108 double divisions_per_bar () const { return _divisions_per_bar; }
109 double note_divisor() const { return _note_type; }
111 double samples_per_bar (const Tempo&, samplecnt_t sr) const;
112 double samples_per_grid (const Tempo&, samplecnt_t sr) const;
114 inline bool operator==(const Meter& other)
115 { return _divisions_per_bar == other.divisions_per_bar() && _note_type == other.note_divisor(); }
118 /** The number of divisions in a bar. This is a floating point value because
119 there are musical traditions on our planet that do not limit
120 themselves to integral numbers of beats per bar.
122 double _divisions_per_bar;
124 /** The type of "note" that a division represents. For example, 4.0 is
125 a quarter (crotchet) note, 8.0 is an eighth (quaver) note, etc.
130 /** A section of timeline with a certain Tempo or Meter. */
131 class LIBARDOUR_API MetricSection {
133 MetricSection (double pulse, double minute, PositionLockStyle pls, bool is_tempo, samplecnt_t sample_rate)
134 : _pulse (pulse), _minute (minute), _initial (false), _position_lock_style (pls), _is_tempo (is_tempo), _sample_rate (sample_rate) {}
136 virtual ~MetricSection() {}
138 const double& pulse () const { return _pulse; }
139 void set_pulse (double pulse) { _pulse = pulse; }
141 double minute() const { return _minute; }
142 virtual void set_minute (double m) {
146 samplepos_t sample () const { return sample_at_minute (_minute); }
148 void set_initial (bool yn) { _initial = yn; }
149 bool initial() const { return _initial; }
151 /* MeterSections are not stateful in the full sense,
152 but we do want them to control their own
153 XML state information.
155 virtual XMLNode& get_state() const = 0;
157 virtual int set_state (const XMLNode&, int version);
159 PositionLockStyle position_lock_style () const { return _position_lock_style; }
160 void set_position_lock_style (PositionLockStyle ps) { _position_lock_style = ps; }
161 bool is_tempo () const { return _is_tempo; }
163 samplepos_t sample_at_minute (const double& time) const;
164 double minute_at_sample (const samplepos_t sample) const;
167 void add_state_to_node (XMLNode& node) const;
174 PositionLockStyle _position_lock_style;
175 const bool _is_tempo;
176 samplecnt_t _sample_rate;
179 /** A section of timeline with a certain Meter. */
180 class LIBARDOUR_API MeterSection : public MetricSection, public Meter {
182 MeterSection (double pulse, double minute, double beat, const Timecode::BBT_Time& bbt, double bpb, double note_type, PositionLockStyle pls, samplecnt_t sr)
183 : MetricSection (pulse, minute, pls, false, sr), Meter (bpb, note_type), _bbt (bbt), _beat (beat) {}
185 MeterSection (const XMLNode&, const samplecnt_t sample_rate);
187 static const std::string xml_state_node_name;
189 XMLNode& get_state() const;
191 void set_beat (std::pair<double, Timecode::BBT_Time>& w) {
196 const Timecode::BBT_Time& bbt() const { return _bbt; }
197 const double& beat () const { return _beat; }
198 void set_beat (double beat) { _beat = beat; }
201 Timecode::BBT_Time _bbt;
205 /** A section of timeline with a certain Tempo. */
206 class LIBARDOUR_API TempoSection : public MetricSection, public Tempo {
213 TempoSection (const double& pulse, const double& minute, Tempo tempo, PositionLockStyle pls, samplecnt_t sr)
214 : MetricSection (pulse, minute, pls, true, sr), Tempo (tempo), _c (0.0), _active (true), _locked_to_meter (false), _clamped (false) {}
216 TempoSection (const XMLNode&, const samplecnt_t sample_rate);
218 static const std::string xml_state_node_name;
220 XMLNode& get_state() const;
222 double c () const { return _c; }
223 void set_c (double c) { _c = c; }
225 Type type () const { if (note_types_per_minute() == end_note_types_per_minute()) { return Constant; } else { return Ramp; } }
227 bool active () const { return _active; }
228 void set_active (bool yn) { _active = yn; }
230 bool locked_to_meter () const { return _locked_to_meter; }
231 void set_locked_to_meter (bool yn) { _locked_to_meter = yn; }
233 bool clamped () const { return _clamped; }
234 void set_clamped (bool yn) { _clamped = yn; }
236 Tempo tempo_at_minute (const double& minute) const;
237 double minute_at_ntpm (const double& ntpm, const double& pulse) const;
239 Tempo tempo_at_pulse (const double& pulse) const;
240 double pulse_at_ntpm (const double& ntpm, const double& minute) const;
242 double pulse_at_minute (const double& minute) const;
243 double minute_at_pulse (const double& pulse) const;
245 double compute_c_pulse (const double& end_ntpm, const double& end_pulse) const;
246 double compute_c_minute (const double& end_ntpm, const double& end_minute) const;
248 double pulse_at_sample (const samplepos_t sample) const;
249 samplepos_t sample_at_pulse (const double& pulse) const;
251 Timecode::BBT_Time legacy_bbt () { return _legacy_bbt; }
255 /* tempo ramp functions. zero-based with time in minutes,
256 * 'tick tempo' in ticks per minute and tempo in bpm.
257 * time relative to section start.
259 double a_func (double end_tpm, double c_func) const;
260 double c_func (double end_tpm, double end_time) const;
262 double _tempo_at_time (const double& time) const;
263 double _time_at_tempo (const double& tempo) const;
265 double _tempo_at_pulse (const double& pulse) const;
266 double _pulse_at_tempo (const double& tempo) const;
268 double _pulse_at_time (const double& time) const;
269 double _time_at_pulse (const double& pulse) const;
271 /* this value provides a fractional offset into the bar in which
272 the tempo section is located in. A value of 0.0 indicates that
273 it occurs on the first beat of the bar, a value of 0.5 indicates
274 that it occurs halfway through the bar and so on.
276 this enables us to keep the tempo change at the same relative
277 position within the bar if/when the meter changes.
282 bool _locked_to_meter;
284 Timecode::BBT_Time _legacy_bbt;
287 typedef std::list<MetricSection*> Metrics;
289 /** Helper class to keep track of the Meter *AND* Tempo in effect
290 at a given point in time.
292 class LIBARDOUR_API TempoMetric {
294 TempoMetric (const Meter& m, const Tempo& t)
295 : _meter (&m), _tempo (&t), _minute (0.0), _pulse (0.0) {}
297 void set_tempo (const Tempo& t) { _tempo = &t; }
298 void set_meter (const Meter& m) { _meter = &m; }
299 void set_minute (double m) { _minute = m; }
300 void set_pulse (const double& p) { _pulse = p; }
302 void set_metric (const MetricSection* section) {
303 const MeterSection* meter;
304 const TempoSection* tempo;
305 if ((meter = dynamic_cast<const MeterSection*>(section))) {
307 } else if ((tempo = dynamic_cast<const TempoSection*>(section))) {
311 set_minute (section->minute());
312 set_pulse (section->pulse());
315 const Meter& meter() const { return *_meter; }
316 const Tempo& tempo() const { return *_tempo; }
317 double minute() const { return _minute; }
318 const double& pulse() const { return _pulse; }
327 /** Tempo Map - mapping of timecode to musical time.
328 * convert audio-samples, sample-rate to Bar/Beat/Tick, Meter/Tempo
330 class LIBARDOUR_API TempoMap : public PBD::StatefulDestructible
333 TempoMap (samplecnt_t sample_rate);
336 TempoMap& operator= (TempoMap const &);
338 /* measure-based stuff */
353 BBTPoint (const MeterSection& m, const Tempo& t, samplepos_t f,
354 uint32_t b, uint32_t e, double qnote)
355 : meter (m), tempo (t), sample (f), bar (b), beat (e), qn (qnote) {}
357 Timecode::BBT_Time bbt() const { return Timecode::BBT_Time (bar, beat, 0); }
358 operator Timecode::BBT_Time() const { return bbt(); }
359 operator samplepos_t() const { return sample; }
360 bool is_bar() const { return beat == 1; }
363 template<class T> void apply_with_metrics (T& obj, void (T::*method)(const Metrics&)) {
364 Glib::Threads::RWLock::ReaderLock lm (lock);
365 (obj.*method)(_metrics);
368 void get_grid (std::vector<BBTPoint>&,
369 samplepos_t start, samplepos_t end, uint32_t bar_mod = 0);
371 static const Tempo& default_tempo() { return _default_tempo; }
372 static const Meter& default_meter() { return _default_meter; }
374 /* because tempi may be ramped, this is only valid for the instant requested.*/
375 double samples_per_quarter_note_at (const samplepos_t, const samplecnt_t sr) const;
377 const TempoSection& tempo_section_at_sample (samplepos_t sample) const;
378 TempoSection& tempo_section_at_sample (samplepos_t sample);
379 const MeterSection& meter_section_at_sample (samplepos_t sample) const;
380 const MeterSection& meter_section_at_beat (double beat) const;
382 TempoSection* previous_tempo_section (TempoSection*) const;
383 TempoSection* next_tempo_section (TempoSection*) const;
385 /** add a tempo section locked to pls. ignored values will be set in recompute_tempi()
386 * @param pulse pulse position of new section. ignored if pls == AudioTime
387 * @param sample frame position of new section. ignored if pls == MusicTime
388 * @param type type of new tempo section (Ramp, Constant)
390 TempoSection* add_tempo (const Tempo&, const double& pulse, const samplepos_t sample, PositionLockStyle pls);
392 /** add a meter section locked to pls.. ignored values will be set in recompute_meters()
393 * @param meter the Meter to be added
394 * @param where bbt position of new section
395 * @param sample frame position of new section. ignored if pls == MusicTime
396 * note that @sample may also be ignored if it would create an un-solvable map
397 * (previous audio-locked tempi may place the requested beat at an earlier time than sample)
398 * in which case the new meter will be placed at the specified BBT.
399 * @param pls the position lock style
401 * adding an audio-locked meter will add a meter-locked tempo section at the meter position.
402 * the meter-locked tempo tempo will be the Tempo at @beat
404 MeterSection* add_meter (const Meter& meter, const Timecode::BBT_Time& where, samplepos_t sample, PositionLockStyle pls);
406 void remove_tempo (const TempoSection&, bool send_signal);
407 void remove_meter (const MeterSection&, bool send_signal);
409 void replace_tempo (TempoSection&, const Tempo&, const double& pulse, const samplepos_t sample, PositionLockStyle pls);
411 void replace_meter (const MeterSection&, const Meter&, const Timecode::BBT_Time& where, samplepos_t sample, PositionLockStyle pls);
413 MusicSample round_to_bar (samplepos_t sample, RoundMode dir);
414 MusicSample round_to_beat (samplepos_t sample, RoundMode dir);
415 MusicSample round_to_quarter_note_subdivision (samplepos_t fr, int sub_num, RoundMode dir);
417 void set_length (samplepos_t samples);
419 XMLNode& get_state (void);
420 int set_state (const XMLNode&, int version);
422 void dump (std::ostream&) const;
425 TempoMetric metric_at (Timecode::BBT_Time bbt) const;
427 /** Return the TempoMetric at sample @p t, and point @p last to the latest
428 * metric change <= t, if it is non-NULL.
430 TempoMetric metric_at (samplepos_t, Metrics::const_iterator* last=NULL) const;
432 Metrics::const_iterator metrics_end() { return _metrics.end(); }
434 void change_existing_tempo_at (samplepos_t, double bpm, double note_type, double end_ntpm);
435 void change_initial_tempo (double ntpm, double note_type, double end_ntpm);
437 void insert_time (samplepos_t, samplecnt_t);
438 bool remove_time (samplepos_t where, samplecnt_t amount); //returns true if anything was moved
440 int n_tempos () const;
441 int n_meters () const;
443 samplecnt_t sample_rate () const { return _sample_rate; }
445 /* TEMPO- AND METER-SENSITIVE FUNCTIONS
447 bbt_at_sample(), sample_at_bbt(), beat_at_sample(), sample_at_beat()
448 and bbt_duration_at()
449 are all sensitive to tempo and meter, and will give answers
450 that align with the grid formed by tempo and meter sections.
452 They SHOULD NOT be used to determine the position of events
453 whose location is canonically defined in Temporal::Beats.
456 double beat_at_sample (const samplecnt_t sample) const;
457 samplepos_t sample_at_beat (const double& beat) const;
459 const Meter& meter_at_sample (samplepos_t) const;
461 /* bbt - it's nearly always better to use meter-based beat (above)
462 unless tick resolution is desirable.
464 Timecode::BBT_Time bbt_at_sample (samplepos_t when);
465 Timecode::BBT_Time bbt_at_sample_rt (samplepos_t when);
466 samplepos_t sample_at_bbt (const Timecode::BBT_Time&);
468 double beat_at_bbt (const Timecode::BBT_Time& bbt);
469 Timecode::BBT_Time bbt_at_beat (const double& beats);
471 double quarter_note_at_bbt (const Timecode::BBT_Time& bbt);
472 double quarter_note_at_bbt_rt (const Timecode::BBT_Time& bbt);
473 Timecode::BBT_Time bbt_at_quarter_note (const double& quarter_note);
475 samplecnt_t bbt_duration_at (samplepos_t, const Timecode::BBT_Time&, int dir);
476 samplepos_t samplepos_plus_bbt (samplepos_t pos, Timecode::BBT_Time b) const;
478 /* TEMPO-SENSITIVE FUNCTIONS
480 These next 2 functions will all take tempo in account and should be
481 used to determine position (and in the last case, distance in beats)
482 when tempo matters but meter does not.
484 They SHOULD be used to determine the position of events
485 whose location is canonically defined in Temporal::Beats.
488 samplepos_t samplepos_plus_qn (samplepos_t, Temporal::Beats) const;
489 Temporal::Beats framewalk_to_qn (samplepos_t pos, samplecnt_t distance) const;
491 /* quarter note related functions are also tempo-sensitive and ignore meter.
492 quarter notes may be compared with and assigned to Temporal::Beats.
494 double quarter_note_at_sample (const samplepos_t sample) const;
495 double quarter_note_at_sample_rt (const samplepos_t sample) const;
496 samplepos_t sample_at_quarter_note (const double quarter_note) const;
498 samplecnt_t samples_between_quarter_notes (const double start, const double end) const;
499 double quarter_notes_between_samples (const samplecnt_t start, const samplecnt_t end) const;
501 double quarter_note_at_beat (const double beat) const;
502 double beat_at_quarter_note (const double beat) const;
504 /* obtain a musical subdivision via a sample position and magic note divisor.*/
505 double exact_qn_at_sample (const samplepos_t sample, const int32_t sub_num) const;
506 double exact_beat_at_sample (const samplepos_t sample, const int32_t sub_num) const;
508 Tempo tempo_at_sample (const samplepos_t sample) const;
509 samplepos_t sample_at_tempo (const Tempo& tempo) const;
510 Tempo tempo_at_quarter_note (const double& beat) const;
511 double quarter_note_at_tempo (const Tempo& tempo) const;
513 void gui_set_tempo_position (TempoSection*, const samplepos_t sample, const int& sub_num);
514 void gui_set_meter_position (MeterSection*, const samplepos_t sample);
515 bool gui_change_tempo (TempoSection*, const Tempo& bpm);
516 void gui_stretch_tempo (TempoSection* tempo, const samplepos_t sample, const samplepos_t end_sample, const double start_qnote, const double end_qnote);
517 void gui_stretch_tempo_end (TempoSection* tempo, const samplepos_t sample, const samplepos_t end_sample);
518 bool gui_twist_tempi (TempoSection* first, const Tempo& bpm, const samplepos_t sample, const samplepos_t end_sample);
520 std::pair<double, samplepos_t> predict_tempo_position (TempoSection* section, const Timecode::BBT_Time& bbt);
521 bool can_solve_bbt (TempoSection* section, const Timecode::BBT_Time& bbt);
523 PBD::Signal1<void,const PBD::PropertyChange&> MetricPositionChanged;
524 void fix_legacy_session();
525 void fix_legacy_end_session();
527 samplepos_t music_origin ();
530 /* prevent copy construction */
531 TempoMap (TempoMap const&);
533 TempoSection* previous_tempo_section_locked (const Metrics& metrics, TempoSection*) const;
534 TempoSection* next_tempo_section_locked (const Metrics& metrics, TempoSection*) const;
536 double beat_at_minute_locked (const Metrics& metrics, const double& minute) const;
537 double minute_at_beat_locked (const Metrics& metrics, const double& beat) const;
539 double pulse_at_beat_locked (const Metrics& metrics, const double& beat) const;
540 double beat_at_pulse_locked (const Metrics& metrics, const double& pulse) const;
542 double pulse_at_minute_locked (const Metrics& metrics, const double& minute) const;
543 double minute_at_pulse_locked (const Metrics& metrics, const double& pulse) const;
545 Tempo tempo_at_minute_locked (const Metrics& metrics, const double& minute) const;
546 double minute_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) const;
548 Tempo tempo_at_pulse_locked (const Metrics& metrics, const double& pulse) const;
549 double pulse_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) const;
551 Timecode::BBT_Time bbt_at_minute_locked (const Metrics& metrics, const double& minute) const;
552 double minute_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time&) const;
554 double beat_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time& bbt) const ;
555 Timecode::BBT_Time bbt_at_beat_locked (const Metrics& metrics, const double& beats) const;
557 double pulse_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time& bbt) const;
558 Timecode::BBT_Time bbt_at_pulse_locked (const Metrics& metrics, const double& pulse) const;
560 double minutes_between_quarter_notes_locked (const Metrics& metrics, const double start_qn, const double end_qn) const;
561 double quarter_notes_between_samples_locked (const Metrics& metrics, const samplecnt_t start, const samplecnt_t end) const;
563 const TempoSection& tempo_section_at_minute_locked (const Metrics& metrics, double minute) const;
564 TempoSection& tempo_section_at_minute_locked (const Metrics& metrics, double minute);
565 const TempoSection& tempo_section_at_beat_locked (const Metrics& metrics, const double& beat) const;
567 const MeterSection& meter_section_at_minute_locked (const Metrics& metrics, double minute) const;
568 const MeterSection& meter_section_at_beat_locked (const Metrics& metrics, const double& beat) const;
570 bool check_solved (const Metrics& metrics) const;
571 bool set_active_tempi (const Metrics& metrics, const samplepos_t sample);
573 bool solve_map_minute (Metrics& metrics, TempoSection* section, const double& minute);
574 bool solve_map_pulse (Metrics& metrics, TempoSection* section, const double& pulse);
575 bool solve_map_minute (Metrics& metrics, MeterSection* section, const double& minute);
576 bool solve_map_bbt (Metrics& metrics, MeterSection* section, const Timecode::BBT_Time& bbt);
578 double exact_beat_at_sample_locked (const Metrics& metrics, const samplepos_t sample, const int32_t sub_num) const;
579 double exact_qn_at_sample_locked (const Metrics& metrics, const samplepos_t sample, const int32_t sub_num) const;
581 double minute_at_sample (const samplepos_t sample) const;
582 samplepos_t sample_at_minute (const double minute) const;
584 friend class ::BBTTest;
585 friend class ::FrameposPlusBeatsTest;
586 friend class ::FrameposMinusBeatsTest;
587 friend class ::TempoTest;
589 static Tempo _default_tempo;
590 static Meter _default_meter;
593 samplecnt_t _sample_rate;
594 mutable Glib::Threads::RWLock lock;
596 void recompute_tempi (Metrics& metrics);
597 void recompute_meters (Metrics& metrics);
598 void recompute_map (Metrics& metrics, samplepos_t end = -1);
600 MusicSample round_to_type (samplepos_t fr, RoundMode dir, BBTPointType);
602 const MeterSection& first_meter() const;
603 MeterSection& first_meter();
604 const TempoSection& first_tempo() const;
605 TempoSection& first_tempo();
607 void do_insert (MetricSection* section);
609 TempoSection* add_tempo_locked (const Tempo&, double pulse, double minute
610 , PositionLockStyle pls, bool recompute, bool locked_to_meter = false, bool clamped = false);
612 MeterSection* add_meter_locked (const Meter&, const Timecode::BBT_Time& where, samplepos_t sample, PositionLockStyle pls, bool recompute);
614 bool remove_tempo_locked (const TempoSection&);
615 bool remove_meter_locked (const MeterSection&);
617 TempoSection* copy_metrics_and_point (const Metrics& metrics, Metrics& copy, TempoSection* section) const;
618 MeterSection* copy_metrics_and_point (const Metrics& metrics, Metrics& copy, MeterSection* section) const;
621 }; /* namespace ARDOUR */
623 LIBARDOUR_API std::ostream& operator<< (std::ostream&, const ARDOUR::Meter&);
624 LIBARDOUR_API std::ostream& operator<< (std::ostream&, const ARDOUR::Tempo&);
625 LIBARDOUR_API std::ostream& operator<< (std::ostream&, const ARDOUR::MetricSection&);
628 DEFINE_ENUM_CONVERT (ARDOUR::TempoSection::Type)
631 #endif /* __ardour_tempo_h__ */