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 "evoral/Beats.hpp"
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::frames_per_quarter_note_at() instead.
83 * @param sr samplerate
85 double frames_per_note_type (framecnt_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::frames_per_quarter_note_at() instead.
90 * @param sr samplerate
92 double frames_per_quarter_note (framecnt_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 frames_per_bar (const Tempo&, framecnt_t sr) const;
112 double frames_per_grid (const Tempo&, framecnt_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, framecnt_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 framepos_t frame () const { return frame_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 framepos_t frame_at_minute (const double& time) const;
164 double minute_at_frame (const framepos_t& frame) const;
167 void add_state_to_node (XMLNode& node) const;
174 PositionLockStyle _position_lock_style;
175 const bool _is_tempo;
176 framecnt_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, framecnt_t sr)
183 : MetricSection (pulse, minute, pls, false, sr), Meter (bpb, note_type), _bbt (bbt), _beat (beat) {}
185 MeterSection (const XMLNode&, const framecnt_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, framecnt_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 framecnt_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_frame (const framepos_t& frame) const;
249 framepos_t frame_at_pulse (const double& pulse) const;
251 Timecode::BBT_Time legacy_bbt () { return _legacy_bbt; }
252 bool legacy_end () { return _legacy_end; }
256 /* tempo ramp functions. zero-based with time in minutes,
257 * 'tick tempo' in ticks per minute and tempo in bpm.
258 * time relative to section start.
260 double a_func (double end_tpm, double c_func) const;
261 double c_func (double end_tpm, double end_time) const;
263 double _tempo_at_time (const double& time) const;
264 double _time_at_tempo (const double& tempo) const;
266 double _tempo_at_pulse (const double& pulse) const;
267 double _pulse_at_tempo (const double& tempo) const;
269 double _pulse_at_time (const double& time) const;
270 double _time_at_pulse (const double& pulse) const;
272 /* this value provides a fractional offset into the bar in which
273 the tempo section is located in. A value of 0.0 indicates that
274 it occurs on the first beat of the bar, a value of 0.5 indicates
275 that it occurs halfway through the bar and so on.
277 this enables us to keep the tempo change at the same relative
278 position within the bar if/when the meter changes.
283 bool _locked_to_meter;
285 Timecode::BBT_Time _legacy_bbt;
289 typedef std::list<MetricSection*> Metrics;
291 /** Helper class to keep track of the Meter *AND* Tempo in effect
292 at a given point in time.
294 class LIBARDOUR_API TempoMetric {
296 TempoMetric (const Meter& m, const Tempo& t)
297 : _meter (&m), _tempo (&t), _minute (0.0), _pulse (0.0) {}
299 void set_tempo (const Tempo& t) { _tempo = &t; }
300 void set_meter (const Meter& m) { _meter = &m; }
301 void set_minute (double m) { _minute = m; }
302 void set_pulse (const double& p) { _pulse = p; }
304 void set_metric (const MetricSection* section) {
305 const MeterSection* meter;
306 const TempoSection* tempo;
307 if ((meter = dynamic_cast<const MeterSection*>(section))) {
309 } else if ((tempo = dynamic_cast<const TempoSection*>(section))) {
313 set_minute (section->minute());
314 set_pulse (section->pulse());
317 const Meter& meter() const { return *_meter; }
318 const Tempo& tempo() const { return *_tempo; }
319 double minute() const { return _minute; }
320 const double& pulse() const { return _pulse; }
329 /** Tempo Map - mapping of timecode to musical time.
330 * convert audio-samples, sample-rate to Bar/Beat/Tick, Meter/Tempo
332 class LIBARDOUR_API TempoMap : public PBD::StatefulDestructible
335 TempoMap (framecnt_t frame_rate);
338 TempoMap& operator= (TempoMap const &);
340 /* measure-based stuff */
355 BBTPoint (const MeterSection& m, const Tempo& t, framepos_t f,
356 uint32_t b, uint32_t e, double func_c)
357 : frame (f), meter (m.divisions_per_bar(), m.note_divisor()), tempo (t.note_types_per_minute(), t.note_type(), t.end_note_types_per_minute()), c (func_c), bar (b), beat (e) {}
359 Timecode::BBT_Time bbt() const { return Timecode::BBT_Time (bar, beat, 0); }
360 operator Timecode::BBT_Time() const { return bbt(); }
361 operator framepos_t() const { return frame; }
362 bool is_bar() const { return beat == 1; }
365 template<class T> void apply_with_metrics (T& obj, void (T::*method)(const Metrics&)) {
366 Glib::Threads::RWLock::ReaderLock lm (lock);
367 (obj.*method)(_metrics);
370 void get_grid (std::vector<BBTPoint>&,
371 framepos_t start, framepos_t end, uint32_t bar_mod = 0);
373 static const Tempo& default_tempo() { return _default_tempo; }
374 static const Meter& default_meter() { return _default_meter; }
376 /* because tempi may be ramped, this is only valid for the instant requested.*/
377 double frames_per_quarter_note_at (const framepos_t&, const framecnt_t& sr) const;
379 const TempoSection& tempo_section_at_frame (framepos_t frame) const;
380 TempoSection& tempo_section_at_frame (framepos_t frame);
381 const MeterSection& meter_section_at_frame (framepos_t frame) const;
382 const MeterSection& meter_section_at_beat (double beat) const;
384 TempoSection* previous_tempo_section (TempoSection*) const;
385 TempoSection* next_tempo_section (TempoSection*) const;
387 /** add a tempo section locked to pls. ignored values will be set in recompute_tempi()
388 * @param pulse pulse position of new section. ignored if pls == AudioTime
389 * @param frame frame position of new section. ignored if pls == MusicTime
390 * @param type type of new tempo section (Ramp, Constant)
392 TempoSection* add_tempo (const Tempo&, const double& pulse, const framepos_t& frame, PositionLockStyle pls);
394 /** add a meter section locked to pls.. ignored values will be set in recompute_meters()
395 * @param meter the Meter to be added
396 * @param beat beat position of new section
397 * @param where bbt position of new section
398 * @param frame frame position of new section. ignored if pls == MusicTime
399 * note that @frame may also be ignored if it would create an un-solvable map
400 * (previous audio-locked tempi may place the requested beat at an earlier time than frame)
401 * in which case the new meter will be placed at the specified BBT.
402 * @param pls the position lock style
404 * adding an audio-locked meter will add a meter-locked tempo section at the meter position.
405 * the meter-locked tempo tempo will be the Tempo at @beat
407 MeterSection* add_meter (const Meter& meter, const double& beat, const Timecode::BBT_Time& where, framepos_t frame, PositionLockStyle pls);
409 void remove_tempo (const TempoSection&, bool send_signal);
410 void remove_meter (const MeterSection&, bool send_signal);
412 void replace_tempo (TempoSection&, const Tempo&, const double& pulse, const framepos_t& frame, PositionLockStyle pls);
414 void replace_meter (const MeterSection&, const Meter&, const Timecode::BBT_Time& where, framepos_t frame, PositionLockStyle pls);
416 MusicFrame round_to_bar (framepos_t frame, RoundMode dir);
417 MusicFrame round_to_beat (framepos_t frame, RoundMode dir);
418 MusicFrame round_to_quarter_note_subdivision (framepos_t fr, int sub_num, RoundMode dir);
420 void set_length (framepos_t frames);
422 XMLNode& get_state (void);
423 int set_state (const XMLNode&, int version);
425 void dump (std::ostream&) const;
428 TempoMetric metric_at (Timecode::BBT_Time bbt) const;
430 /** Return the TempoMetric at frame @p t, and point @p last to the latest
431 * metric change <= t, if it is non-NULL.
433 TempoMetric metric_at (framepos_t, Metrics::const_iterator* last=NULL) const;
435 Metrics::const_iterator metrics_end() { return _metrics.end(); }
437 void change_existing_tempo_at (framepos_t, double bpm, double note_type, double end_ntpm);
438 void change_initial_tempo (double ntpm, double note_type, double end_ntpm);
440 void insert_time (framepos_t, framecnt_t);
441 bool remove_time (framepos_t where, framecnt_t amount); //returns true if anything was moved
443 int n_tempos () const;
444 int n_meters () const;
446 framecnt_t frame_rate () const { return _frame_rate; }
448 /* TEMPO- AND METER-SENSITIVE FUNCTIONS
450 bbt_at_frame(), frame_at_bbt(), beat_at_frame(), frame_at_beat()
451 and bbt_duration_at()
452 are all sensitive to tempo and meter, and will give answers
453 that align with the grid formed by tempo and meter sections.
455 They SHOULD NOT be used to determine the position of events
456 whose location is canonically defined in Evoral::Beats.
459 double beat_at_frame (const framecnt_t& frame) const;
460 framepos_t frame_at_beat (const double& beat) const;
462 const Meter& meter_at_frame (framepos_t) const;
464 /* bbt - it's nearly always better to use meter-based beat (above)
465 unless tick resolution is desirable.
467 Timecode::BBT_Time bbt_at_frame (framepos_t when);
468 Timecode::BBT_Time bbt_at_frame_rt (framepos_t when);
469 framepos_t frame_at_bbt (const Timecode::BBT_Time&);
471 double beat_at_bbt (const Timecode::BBT_Time& bbt);
472 Timecode::BBT_Time bbt_at_beat (const double& beats);
474 double quarter_note_at_bbt (const Timecode::BBT_Time& bbt);
475 double quarter_note_at_bbt_rt (const Timecode::BBT_Time& bbt);
476 Timecode::BBT_Time bbt_at_quarter_note (const double& quarter_note);
478 framecnt_t bbt_duration_at (framepos_t, const Timecode::BBT_Time&, int dir);
479 framepos_t framepos_plus_bbt (framepos_t pos, Timecode::BBT_Time b) const;
481 /* TEMPO-SENSITIVE FUNCTIONS
483 These next 2 functions will all take tempo in account and should be
484 used to determine position (and in the last case, distance in beats)
485 when tempo matters but meter does not.
487 They SHOULD be used to determine the position of events
488 whose location is canonically defined in Evoral::Beats.
491 framepos_t framepos_plus_qn (framepos_t, Evoral::Beats) const;
492 Evoral::Beats framewalk_to_qn (framepos_t pos, framecnt_t distance) const;
494 /* quarter note related functions are also tempo-sensitive and ignore meter.
495 quarter notes may be compared with and assigned to Evoral::Beats.
497 double quarter_note_at_frame (const framepos_t frame) const;
498 double quarter_note_at_frame_rt (const framepos_t frame) const;
499 framepos_t frame_at_quarter_note (const double quarter_note) const;
501 framecnt_t frames_between_quarter_notes (const double start, const double end) const;
502 double quarter_notes_between_frames (const framecnt_t start, const framecnt_t end) const;
504 double quarter_note_at_beat (const double beat) const;
505 double beat_at_quarter_note (const double beat) const;
507 /* obtain a musical subdivision via a frame position and magic note divisor.*/
508 double exact_qn_at_frame (const framepos_t& frame, const int32_t sub_num) const;
509 double exact_beat_at_frame (const framepos_t& frame, const int32_t sub_num) const;
511 Tempo tempo_at_frame (const framepos_t& frame) const;
512 framepos_t frame_at_tempo (const Tempo& tempo) const;
513 Tempo tempo_at_quarter_note (const double& beat) const;
514 double quarter_note_at_tempo (const Tempo& tempo) const;
516 void gui_set_tempo_position (TempoSection*, const framepos_t& frame, const int& sub_num);
517 void gui_set_meter_position (MeterSection*, const framepos_t& frame);
518 bool gui_change_tempo (TempoSection*, const Tempo& bpm);
519 void gui_stretch_tempo (TempoSection* tempo, const framepos_t frame, const framepos_t end_frame);
520 void gui_stretch_tempo_end (TempoSection* tempo, const framepos_t frame, const framepos_t end_frame);
521 bool gui_twist_tempi (TempoSection* first, const Tempo& bpm, const framepos_t frame, const framepos_t end_frame);
523 std::pair<double, framepos_t> predict_tempo_position (TempoSection* section, const Timecode::BBT_Time& bbt);
524 bool can_solve_bbt (TempoSection* section, const Timecode::BBT_Time& bbt);
526 PBD::Signal1<void,const PBD::PropertyChange&> MetricPositionChanged;
527 void fix_legacy_session();
528 void fix_legacy_end_session();
531 /* prevent copy construction */
532 TempoMap (TempoMap const&);
534 TempoSection* previous_tempo_section_locked (const Metrics& metrics, TempoSection*) const;
535 TempoSection* next_tempo_section_locked (const Metrics& metrics, TempoSection*) const;
537 double beat_at_minute_locked (const Metrics& metrics, const double& minute) const;
538 double minute_at_beat_locked (const Metrics& metrics, const double& beat) const;
540 double pulse_at_beat_locked (const Metrics& metrics, const double& beat) const;
541 double beat_at_pulse_locked (const Metrics& metrics, const double& pulse) const;
543 double pulse_at_minute_locked (const Metrics& metrics, const double& minute) const;
544 double minute_at_pulse_locked (const Metrics& metrics, const double& pulse) const;
546 Tempo tempo_at_minute_locked (const Metrics& metrics, const double& minute) const;
547 double minute_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) const;
549 Tempo tempo_at_pulse_locked (const Metrics& metrics, const double& pulse) const;
550 double pulse_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) const;
552 Timecode::BBT_Time bbt_at_minute_locked (const Metrics& metrics, const double& minute) const;
553 double minute_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time&) const;
555 double beat_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time& bbt) const ;
556 Timecode::BBT_Time bbt_at_beat_locked (const Metrics& metrics, const double& beats) const;
558 double pulse_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time& bbt) const;
559 Timecode::BBT_Time bbt_at_pulse_locked (const Metrics& metrics, const double& pulse) const;
561 double minutes_between_quarter_notes_locked (const Metrics& metrics, const double start_qn, const double end_qn) const;
562 double quarter_notes_between_frames_locked (const Metrics& metrics, const framecnt_t start, const framecnt_t end) const;
564 const TempoSection& tempo_section_at_minute_locked (const Metrics& metrics, double minute) const;
565 TempoSection& tempo_section_at_minute_locked (const Metrics& metrics, double minute);
566 const TempoSection& tempo_section_at_beat_locked (const Metrics& metrics, const double& beat) const;
568 const MeterSection& meter_section_at_minute_locked (const Metrics& metrics, double minute) const;
569 const MeterSection& meter_section_at_beat_locked (const Metrics& metrics, const double& beat) const;
571 bool check_solved (const Metrics& metrics) const;
572 bool set_active_tempi (const Metrics& metrics, const framepos_t& frame);
574 bool solve_map_minute (Metrics& metrics, TempoSection* section, const double& minute);
575 bool solve_map_pulse (Metrics& metrics, TempoSection* section, const double& pulse);
576 bool solve_map_minute (Metrics& metrics, MeterSection* section, const double& minute);
577 bool solve_map_bbt (Metrics& metrics, MeterSection* section, const Timecode::BBT_Time& bbt);
579 double exact_beat_at_frame_locked (const Metrics& metrics, const framepos_t& frame, const int32_t sub_num) const;
580 double exact_qn_at_frame_locked (const Metrics& metrics, const framepos_t& frame, const int32_t sub_num) const;
582 double minute_at_frame (const framepos_t frame) const;
583 framepos_t frame_at_minute (const double minute) const;
585 friend class ::BBTTest;
586 friend class ::FrameposPlusBeatsTest;
587 friend class ::FrameposMinusBeatsTest;
588 friend class ::TempoTest;
590 static Tempo _default_tempo;
591 static Meter _default_meter;
594 framecnt_t _frame_rate;
595 mutable Glib::Threads::RWLock lock;
597 void recompute_tempi (Metrics& metrics);
598 void recompute_meters (Metrics& metrics);
599 void recompute_map (Metrics& metrics, framepos_t end = -1);
601 MusicFrame round_to_type (framepos_t fr, RoundMode dir, BBTPointType);
603 const MeterSection& first_meter() const;
604 MeterSection& first_meter();
605 const TempoSection& first_tempo() const;
606 TempoSection& first_tempo();
608 void do_insert (MetricSection* section);
610 TempoSection* add_tempo_locked (const Tempo&, double pulse, double minute
611 , PositionLockStyle pls, bool recompute, bool locked_to_meter = false);
613 MeterSection* add_meter_locked (const Meter&, double beat, const Timecode::BBT_Time& where, framepos_t frame, PositionLockStyle pls, bool recompute);
615 bool remove_tempo_locked (const TempoSection&);
616 bool remove_meter_locked (const MeterSection&);
618 TempoSection* copy_metrics_and_point (const Metrics& metrics, Metrics& copy, TempoSection* section) const;
619 MeterSection* copy_metrics_and_point (const Metrics& metrics, Metrics& copy, MeterSection* section) const;
622 }; /* namespace ARDOUR */
624 LIBARDOUR_API std::ostream& operator<< (std::ostream&, const ARDOUR::Meter&);
625 LIBARDOUR_API std::ostream& operator<< (std::ostream&, const ARDOUR::Tempo&);
626 LIBARDOUR_API std::ostream& operator<< (std::ostream&, const ARDOUR::MetricSection&);
629 DEFINE_ENUM_CONVERT (ARDOUR::TempoSection::Type)
632 #endif /* __ardour_tempo_h__ */