class LIBARDOUR_API Tempo {
public:
/**
- * @param bpm Beats Per Minute
+ * @param npm Note Types per minute
* @param type Note Type (default `4': quarter note)
*/
- Tempo (double bpm, double type=4.0) // defaulting to quarter note
- : _beats_per_minute (bpm), _note_type(type) {}
+ Tempo (double npm, double type=4.0) // defaulting to quarter note
+ : _note_types_per_minute (npm), _note_type(type) {}
- /*
- quarter note beats as distinct from a beat derived from meter and pulse.
- */
- double beats_per_minute () const { return _beats_per_minute; }
- void set_beats_per_minute (double bpm) { _beats_per_minute = bpm; }
+ double note_types_per_minute () const { return _note_types_per_minute; }
+ double note_types_per_minute (double note_type) const { return (_note_types_per_minute / _note_type) * note_type; }
+ void set_note_types_per_minute (double npm) { _note_types_per_minute = npm; }
double note_type () const { return _note_type; }
- double pulses_per_minute () const { return _beats_per_minute / _note_type; }
- /** audio samples per beat
+
+ double quarter_notes_per_minute () const { return note_types_per_minute (4.0); }
+ double pulses_per_minute () const { return note_types_per_minute (1.0); }
+ /** audio samples per note type.
+ * if you want an instantaneous value for this, use TempoMap::frames_per_quarter_note_at() instead.
* @param sr samplerate
*/
- double frames_per_beat (framecnt_t sr) const {
- return (60.0 * sr) / _beats_per_minute;
+ double frames_per_note_type (framecnt_t sr) const {
+ return (60.0 * sr) / _note_types_per_minute;
}
- double frames_per_pulse (framecnt_t sr) const {
- return (_note_type * 60.0 * sr) / _beats_per_minute;
+ /** audio samples per quarter note.
+ * if you want an instantaneous value for this, use TempoMap::frames_per_quarter_note_at() instead.
+ * @param sr samplerate
+ */
+ double frames_per_quarter_note (framecnt_t sr) const {
+ return (60.0 * sr) / quarter_notes_per_minute ();
}
protected:
- double _beats_per_minute;
+ double _note_types_per_minute;
double _note_type;
};
double frames_per_bar (const Tempo&, framecnt_t sr) const;
double frames_per_grid (const Tempo&, framecnt_t sr) const;
+ inline bool operator==(const Meter& other)
+ { return _divisions_per_bar == other.divisions_per_bar() && _note_type == other.note_divisor(); }
+
protected:
/** The number of divisions in a bar. This is a floating point value because
there are musical traditions on our planet that do not limit
/** A section of timeline with a certain Tempo or Meter. */
class LIBARDOUR_API MetricSection {
public:
- MetricSection (double pulse, framepos_t frame, PositionLockStyle pls, bool is_tempo)
- : _pulse (pulse), _frame (frame), _movable (true), _position_lock_style (pls), _is_tempo (is_tempo) {}
+ MetricSection (double pulse, double minute, PositionLockStyle pls, bool is_tempo, framecnt_t sample_rate)
+ : _pulse (pulse), _minute (minute), _initial (false), _position_lock_style (pls), _is_tempo (is_tempo), _sample_rate (sample_rate) {}
virtual ~MetricSection() {}
const double& pulse () const { return _pulse; }
void set_pulse (double pulse) { _pulse = pulse; }
- framepos_t frame() const { return _frame; }
- virtual void set_frame (framepos_t f) {
- _frame = f;
+ double minute() const { return _minute; }
+ virtual void set_minute (double m) {
+ _minute = m;
}
- void set_movable (bool yn) { _movable = yn; }
- bool movable() const { return _movable; }
+ framepos_t frame () const { return frame_at_minute (_minute); }
+
+ void set_initial (bool yn) { _initial = yn; }
+ bool initial() const { return _initial; }
/* MeterSections are not stateful in the full sense,
but we do want them to control their own
void set_position_lock_style (PositionLockStyle ps) { _position_lock_style = ps; }
bool is_tempo () const { return _is_tempo; }
+ framepos_t frame_at_minute (const double& time) const;
+ double minute_at_frame (const framepos_t& frame) const;
+
private:
+
double _pulse;
- framepos_t _frame;
- bool _movable;
+ double _minute;
+ bool _initial;
PositionLockStyle _position_lock_style;
const bool _is_tempo;
+ framecnt_t _sample_rate;
};
/** A section of timeline with a certain Meter. */
class LIBARDOUR_API MeterSection : public MetricSection, public Meter {
public:
- MeterSection (double pulse, framepos_t frame, double beat, const Timecode::BBT_Time& bbt, double bpb, double note_type, PositionLockStyle pls)
- : MetricSection (pulse, frame, pls, false), Meter (bpb, note_type), _bbt (bbt), _beat (beat) {}
+ MeterSection (double pulse, double minute, double beat, const Timecode::BBT_Time& bbt, double bpb, double note_type, PositionLockStyle pls, framecnt_t sr)
+ : MetricSection (pulse, minute, pls, false, sr), Meter (bpb, note_type), _bbt (bbt), _beat (beat) {}
- MeterSection (const XMLNode&);
+ MeterSection (const XMLNode&, const framecnt_t sample_rate);
static const std::string xml_state_node_name;
Constant,
};
- TempoSection (const double& pulse, const framepos_t& frame, double qpm, double note_type, Type tempo_type, PositionLockStyle pls)
- : MetricSection (pulse, frame, pls, true), Tempo (qpm, note_type), _type (tempo_type), _c_func (0.0), _active (true), _locked_to_meter (false) {}
+ TempoSection (const double& pulse, const double& minute, double qpm, double note_type, Type tempo_type, PositionLockStyle pls, framecnt_t sr)
+ : MetricSection (pulse, minute, pls, true, sr), Tempo (qpm, note_type), _type (tempo_type), _c_func (0.0), _active (true), _locked_to_meter (false) {}
- TempoSection (const XMLNode&);
+ TempoSection (const XMLNode&, const framecnt_t sample_rate);
static const std::string xml_state_node_name;
bool locked_to_meter () const { return _locked_to_meter; }
void set_locked_to_meter (bool yn) { _locked_to_meter = yn; }
- double tempo_at_frame (const framepos_t& frame, const framecnt_t& frame_rate) const;
- framepos_t frame_at_tempo (const double& ppm, const double& beat, const framecnt_t& frame_rate) const;
+ Tempo tempo_at_minute (const double& minute) const;
+ double minute_at_ntpm (const double& ntpm, const double& pulse) const;
- double tempo_at_pulse (const double& pulse) const;
- double pulse_at_tempo (const double& ppm, const framepos_t& frame, const framecnt_t& frame_rate) const;
+ Tempo tempo_at_pulse (const double& pulse) const;
+ double pulse_at_ntpm (const double& ntpm, const double& minute) const;
- double pulse_at_frame (const framepos_t& frame, const framepos_t& frame_rate) const;
- framepos_t frame_at_pulse (const double& pulse, const framecnt_t& frame_rate) const;
+ double pulse_at_minute (const double& minute) const;
+ double minute_at_pulse (const double& pulse) const;
- double compute_c_func_pulse (const double& end_bpm, const double& end_pulse, const framecnt_t& frame_rate);
- double compute_c_func_frame (const double& end_bpm, const framepos_t& end_frame, const framecnt_t& frame_rate) const;
+ double compute_c_func_pulse (const double& end_ntpm, const double& end_pulse) const;
+ double compute_c_func_minute (const double& end_ntpm, const double& end_minute) const;
+
+ double pulse_at_frame (const framepos_t& frame) const;
+ framepos_t frame_at_pulse (const double& pulse) const;
Timecode::BBT_Time legacy_bbt () { return _legacy_bbt; }
private:
- framepos_t minute_to_frame (const double& time, const framecnt_t& frame_rate) const;
- double frame_to_minute (const framepos_t& frame, const framecnt_t& frame_rate) const;
-
/* tempo ramp functions. zero-based with time in minutes,
* 'tick tempo' in ticks per minute and tempo in bpm.
* time relative to section start.
double a_func (double end_tpm, double c_func) const;
double c_func (double end_tpm, double end_time) const;
- double pulse_tempo_at_time (const double& time) const;
- double time_at_pulse_tempo (const double& pulse_tempo) const;
+ double _tempo_at_time (const double& time) const;
+ double _time_at_tempo (const double& tempo) const;
- double pulse_tempo_at_pulse (const double& pulse) const;
- double pulse_at_pulse_tempo (const double& pulse_tempo) const;
+ double _tempo_at_pulse (const double& pulse) const;
+ double _pulse_at_tempo (const double& tempo) const;
- double pulse_at_time (const double& time) const;
- double time_at_pulse (const double& pulse) const;
+ double _pulse_at_time (const double& time) const;
+ double _time_at_pulse (const double& pulse) const;
/* this value provides a fractional offset into the bar in which
the tempo section is located in. A value of 0.0 indicates that
class LIBARDOUR_API TempoMetric {
public:
TempoMetric (const Meter& m, const Tempo& t)
- : _meter (&m), _tempo (&t), _frame (0) {}
+ : _meter (&m), _tempo (&t), _minute (0.0), _pulse (0.0) {}
void set_tempo (const Tempo& t) { _tempo = &t; }
void set_meter (const Meter& m) { _meter = &m; }
- void set_frame (framepos_t f) { _frame = f; }
+ void set_minute (double m) { _minute = m; }
void set_pulse (const double& p) { _pulse = p; }
void set_metric (const MetricSection* section) {
set_tempo(*tempo);
}
- set_frame (section->frame());
+ set_minute (section->minute());
set_pulse (section->pulse());
}
const Meter& meter() const { return *_meter; }
const Tempo& tempo() const { return *_tempo; }
- framepos_t frame() const { return _frame; }
+ double minute() const { return _minute; }
const double& pulse() const { return _pulse; }
private:
const Meter* _meter;
const Tempo* _tempo;
- framepos_t _frame;
+ double _minute;
double _pulse;
};
{
public:
TempoMap (framecnt_t frame_rate);
+ TempoMap (TempoMap const &);
~TempoMap();
+ TempoMap& operator= (TempoMap const &);
+
/* measure-based stuff */
enum BBTPointType {
BBTPoint (const MeterSection& m, const Tempo& t, framepos_t f,
uint32_t b, uint32_t e, double func_c)
- : frame (f), meter (m.divisions_per_bar(), m.note_divisor()), tempo (t.beats_per_minute(), t.note_type()), c (func_c), bar (b), beat (e) {}
+ : frame (f), meter (m.divisions_per_bar(), m.note_divisor()), tempo (t.note_types_per_minute(), t.note_type()), c (func_c), bar (b), beat (e) {}
Timecode::BBT_Time bbt() const { return Timecode::BBT_Time (bar, beat, 0); }
operator Timecode::BBT_Time() const { return bbt(); }
}
void get_grid (std::vector<BBTPoint>&,
- framepos_t start, framepos_t end);
+ framepos_t start, framepos_t end, uint32_t bar_mod = 0);
static const Tempo& default_tempo() { return _default_tempo; }
static const Meter& default_meter() { return _default_meter; }
- /* because tempos may be ramped, this is only valid for the instant requested.*/
- double frames_per_beat_at (const framepos_t&, const framecnt_t& sr) const;
+ /* because tempi may be ramped, this is only valid for the instant requested.*/
+ double frames_per_quarter_note_at (const framepos_t&, const framecnt_t& sr) const;
const TempoSection& tempo_section_at_frame (framepos_t frame) const;
const MeterSection& meter_section_at_frame (framepos_t frame) const;
*/
TempoSection* add_tempo (const Tempo&, const double& pulse, const framepos_t& frame, TempoSection::Type type, PositionLockStyle pls);
- /** add an meter section locked to pls.. ignored values will be set in recompute_meters()
+ /** add a meter section locked to pls.. ignored values will be set in recompute_meters()
+ * @param meter the Meter to be added
* @param beat beat position of new section
* @param where bbt position of new section
* @param frame frame position of new section. ignored if pls == MusicTime
+ * note that @frame may also be ignored if it would create an un-solvable map
+ * (previous audio-locked tempi may place the requested beat at an earlier time than frame)
+ * in which case the new meter will be placed at the specified BBT.
+ * @param pls the position lock style
+ *
+ * adding an audio-locked meter will add a meter-locked tempo section at the meter position.
+ * the meter-locked tempo tempo will be the Tempo at @beat
*/
- MeterSection* add_meter (const Meter&, const double& beat, const Timecode::BBT_Time& where, const framepos_t& frame, PositionLockStyle pls);
+ MeterSection* add_meter (const Meter& meter, const double& beat, const Timecode::BBT_Time& where, framepos_t frame, PositionLockStyle pls);
void remove_tempo (const TempoSection&, bool send_signal);
void remove_meter (const MeterSection&, bool send_signal);
void replace_tempo (const TempoSection&, const Tempo&, const double& pulse, const framepos_t& frame
, TempoSection::Type type, PositionLockStyle pls);
- void replace_meter (const MeterSection&, const Meter&, const Timecode::BBT_Time& where, const framepos_t& frame
- , PositionLockStyle pls);
+ void replace_meter (const MeterSection&, const Meter&, const Timecode::BBT_Time& where, framepos_t frame, PositionLockStyle pls);
framepos_t round_to_bar (framepos_t frame, RoundMode dir);
framepos_t round_to_beat (framepos_t frame, RoundMode dir);
XMLNode& get_state (void);
int set_state (const XMLNode&, int version);
- void dump (const Metrics& metrics, std::ostream&) const;
+ void dump (std::ostream&) const;
void clear ();
TempoMetric metric_at (Timecode::BBT_Time bbt) const;
/* TEMPO- AND METER-SENSITIVE FUNCTIONS
- bbt_at_frame(), frame_at_bbt(), beat_at_frame(), frame_at_beat(), tempo_at_beat()
+ bbt_at_frame(), frame_at_bbt(), beat_at_frame(), frame_at_beat()
and bbt_duration_at()
are all sensitive to tempo and meter, and will give answers
that align with the grid formed by tempo and meter sections.
double beat_at_frame (const framecnt_t& frame) const;
framepos_t frame_at_beat (const double& beat) const;
- Tempo tempo_at_frame (const framepos_t& frame) const;
- framepos_t frame_at_tempo (const Tempo& tempo) const;
-
- Tempo tempo_at_beat (const double& beat) const;
-
const Meter& meter_at_frame (framepos_t) const;
- double pulse_at_beat (const double& beat) const;
- double beat_at_pulse (const double& pulse) const;
-
- double pulse_at_frame (const framecnt_t& frame) const;
- framepos_t frame_at_pulse (const double& pulse) const;
-
- /* bbt - it's nearly always better to use beats.*/
+ /* bbt - it's nearly always better to use meter-based beat (above)
+ unless tick resolution is desirable.
+ */
Timecode::BBT_Time bbt_at_frame (framepos_t when);
Timecode::BBT_Time bbt_at_frame_rt (framepos_t when);
framepos_t frame_at_bbt (const Timecode::BBT_Time&);
double beat_at_bbt (const Timecode::BBT_Time& bbt);
Timecode::BBT_Time bbt_at_beat (const double& beats);
- double pulse_at_bbt (const Timecode::BBT_Time& bbt);
- double pulse_at_bbt_rt (const Timecode::BBT_Time& bbt);
- Timecode::BBT_Time bbt_at_pulse (const double& pulse);
+ double quarter_note_at_bbt (const Timecode::BBT_Time& bbt);
+ double quarter_note_at_bbt_rt (const Timecode::BBT_Time& bbt);
+ Timecode::BBT_Time bbt_at_quarter_note (const double& quarter_note);
framecnt_t bbt_duration_at (framepos_t, const Timecode::BBT_Time&, int dir);
+ framepos_t framepos_plus_bbt (framepos_t pos, Timecode::BBT_Time b) const;
/* TEMPO-SENSITIVE FUNCTIONS
framepos_t framepos_plus_qn (framepos_t, Evoral::Beats) const;
Evoral::Beats framewalk_to_qn (framepos_t pos, framecnt_t distance) const;
- framepos_t framepos_plus_bbt (framepos_t pos, Timecode::BBT_Time b) const;
+ /* quarter note related functions are also tempo-sensitive and ignore meter.
+ quarter notes may be compared with and assigned to Evoral::Beats.
+ */
+ double quarter_note_at_frame (const framepos_t frame) const;
+ double quarter_note_at_frame_rt (const framepos_t frame) const;
+ framepos_t frame_at_quarter_note (const double quarter_note) const;
- double quarter_note_at_frame (const framepos_t frame);
- double quarter_note_at_frame_rt (const framepos_t frame);
- framepos_t frame_at_quarter_note (const double quarter_note);
- double quarter_note_at_beat (const double beat);
- double beat_at_quarter_note (const double beat);
+ framecnt_t frames_between_quarter_notes (const double start, const double end) const;
+ double quarter_notes_between_frames (const framecnt_t start, const framecnt_t end) const;
- void gui_move_tempo (TempoSection*, const framepos_t& frame, const int& sub_num);
- void gui_move_meter (MeterSection*, const framepos_t& frame);
- bool gui_change_tempo (TempoSection*, const Tempo& bpm);
- void gui_dilate_tempo (TempoSection* tempo, const framepos_t& frame, const framepos_t& end_frame, const double& pulse);
+ double quarter_note_at_beat (const double beat) const;
+ double beat_at_quarter_note (const double beat) const;
+
+ /* obtain a musical subdivision via a frame position and magic note divisor.*/
+ double exact_qn_at_frame (const framepos_t& frame, const int32_t sub_num) const;
+ double exact_beat_at_frame (const framepos_t& frame, const int32_t sub_num) const;
- double exact_beat_at_frame (const framepos_t& frame, const int32_t sub_num);
- double exact_qn_at_frame (const framepos_t& frame, const int32_t sub_num);
+ Tempo tempo_at_frame (const framepos_t& frame) const;
+ framepos_t frame_at_tempo (const Tempo& tempo) const;
+ Tempo tempo_at_quarter_note (const double& beat) const;
+ double quarter_note_at_tempo (const Tempo& tempo) const;
+
+ void gui_set_tempo_position (TempoSection*, const framepos_t& frame, const int& sub_num);
+ void gui_set_meter_position (MeterSection*, const framepos_t& frame);
+ bool gui_change_tempo (TempoSection*, const Tempo& bpm);
+ void gui_stretch_tempo (TempoSection* tempo, const framepos_t& frame, const framepos_t& end_frame);
std::pair<double, framepos_t> predict_tempo_position (TempoSection* section, const Timecode::BBT_Time& bbt);
bool can_solve_bbt (TempoSection* section, const Timecode::BBT_Time& bbt);
private:
- double beat_at_frame_locked (const Metrics& metrics, const framecnt_t& frame) const;
- framepos_t frame_at_beat_locked (const Metrics& metrics, const double& beat) const;
+ double beat_at_minute_locked (const Metrics& metrics, const double& minute) const;
+ double minute_at_beat_locked (const Metrics& metrics, const double& beat) const;
double pulse_at_beat_locked (const Metrics& metrics, const double& beat) const;
double beat_at_pulse_locked (const Metrics& metrics, const double& pulse) const;
- double pulse_at_frame_locked (const Metrics& metrics, const framepos_t& frame) const;
- framepos_t frame_at_pulse_locked (const Metrics& metrics, const double& pulse) const;
+ double pulse_at_minute_locked (const Metrics& metrics, const double& minute) const;
+ double minute_at_pulse_locked (const Metrics& metrics, const double& pulse) const;
- Tempo tempo_at_frame_locked (const Metrics& metrics, const framepos_t& frame) const;
- framepos_t frame_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) const;
+ Tempo tempo_at_minute_locked (const Metrics& metrics, const double& minute) const;
+ double minute_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) const;
- Timecode::BBT_Time bbt_at_frame_locked (const Metrics& metrics, const framepos_t& frame) const;
- framepos_t frame_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time&) const;
+ Tempo tempo_at_pulse_locked (const Metrics& metrics, const double& pulse) const;
+ double pulse_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) const;
+
+ Timecode::BBT_Time bbt_at_minute_locked (const Metrics& metrics, const double& minute) const;
+ double minute_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time&) const;
double beat_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time& bbt) const ;
Timecode::BBT_Time bbt_at_beat_locked (const Metrics& metrics, const double& beats) const;
double pulse_at_bbt_locked (const Metrics& metrics, const Timecode::BBT_Time& bbt) const;
Timecode::BBT_Time bbt_at_pulse_locked (const Metrics& metrics, const double& pulse) const;
- framepos_t frame_at_quarter_note_locked (const Metrics& metrics, const double quarter_note) const;
- double quarter_note_at_frame_locked (const Metrics& metrics, const framepos_t frame) const;
+ double minute_at_quarter_note_locked (const Metrics& metrics, const double quarter_note) const;
+ double quarter_note_at_minute_locked (const Metrics& metrics, const double minute) const;
+
double quarter_note_at_beat_locked (const Metrics& metrics, const double beat) const;
double beat_at_quarter_note_locked (const Metrics& metrics, const double beat) const;
- const TempoSection& tempo_section_at_frame_locked (const Metrics& metrics, framepos_t frame) const;
+ double minutes_between_quarter_notes_locked (const Metrics& metrics, const double start_qn, const double end_qn) const;
+ double quarter_notes_between_frames_locked (const Metrics& metrics, const framecnt_t start, const framecnt_t end) const;
+
+ const TempoSection& tempo_section_at_minute_locked (const Metrics& metrics, double minute) const;
const TempoSection& tempo_section_at_beat_locked (const Metrics& metrics, const double& beat) const;
- const MeterSection& meter_section_at_frame_locked (const Metrics& metrics, framepos_t frame) const;
+ const MeterSection& meter_section_at_minute_locked (const Metrics& metrics, double minute) const;
const MeterSection& meter_section_at_beat_locked (const Metrics& metrics, const double& beat) const;
bool check_solved (const Metrics& metrics) const;
- bool set_active_tempos (const Metrics& metrics, const framepos_t& frame);
+ bool set_active_tempi (const Metrics& metrics, const framepos_t& frame);
- bool solve_map_frame (Metrics& metrics, TempoSection* section, const framepos_t& frame);
+ bool solve_map_minute (Metrics& metrics, TempoSection* section, const double& minute);
bool solve_map_pulse (Metrics& metrics, TempoSection* section, const double& pulse);
- bool solve_map_frame (Metrics& metrics, MeterSection* section, const framepos_t& frame);
+ bool solve_map_minute (Metrics& metrics, MeterSection* section, const double& minute);
bool solve_map_bbt (Metrics& metrics, MeterSection* section, const Timecode::BBT_Time& bbt);
- double exact_beat_at_frame_locked (const Metrics& metrics, const framepos_t& frame, const int32_t sub_num);
- double exact_qn_at_frame_locked (const Metrics& metrics, const framepos_t& frame, const int32_t sub_num);
+ double exact_beat_at_frame_locked (const Metrics& metrics, const framepos_t& frame, const int32_t sub_num) const;
+ double exact_qn_at_frame_locked (const Metrics& metrics, const framepos_t& frame, const int32_t sub_num) const;
+
+ double minute_at_frame (const framepos_t frame) const;
+ framepos_t frame_at_minute (const double minute) const;
friend class ::BBTTest;
friend class ::FrameposPlusBeatsTest;
void do_insert (MetricSection* section);
- TempoSection* add_tempo_locked (const Tempo&, double pulse, framepos_t frame
+ TempoSection* add_tempo_locked (const Tempo&, double pulse, double minute
, TempoSection::Type type, PositionLockStyle pls, bool recompute, bool locked_to_meter = false);
- MeterSection* add_meter_locked (const Meter&, double beat, const Timecode::BBT_Time& where, framepos_t frame
- , PositionLockStyle pls, bool recompute);
+ MeterSection* add_meter_locked (const Meter&, double beat, const Timecode::BBT_Time& where, framepos_t frame, PositionLockStyle pls, bool recompute);
bool remove_tempo_locked (const TempoSection&);
bool remove_meter_locked (const MeterSection&);
}; /* namespace ARDOUR */
-std::ostream& operator<< (std::ostream&, const ARDOUR::Meter&);
-std::ostream& operator<< (std::ostream&, const ARDOUR::Tempo&);
-std::ostream& operator<< (std::ostream&, const ARDOUR::MetricSection&);
+LIBARDOUR_API std::ostream& operator<< (std::ostream&, const ARDOUR::Meter&);
+LIBARDOUR_API std::ostream& operator<< (std::ostream&, const ARDOUR::Tempo&);
+LIBARDOUR_API std::ostream& operator<< (std::ostream&, const ARDOUR::MetricSection&);
#endif /* __ardour_tempo_h__ */