TempoSection::tempo_at methods return a Tempo, document the opposite direction.

3 files changed, 122 insertions, 113 deletions

diff --git a/libs/ardour/ardour/tempo.h b/libs/ardour/ardour/tempo.h
index 16cca3b7b4..e820a1cbdc 100644
--- a/libs/ardour/ardour/tempo.h
+++ b/libs/ardour/ardour/tempo.h
@@ -207,17 +207,20 @@ class LIBARDOUR_API TempoSection : public MetricSection, public Tempo {
 	bool locked_to_meter ()  const { return _locked_to_meter; }
 	void set_locked_to_meter (bool yn) { _locked_to_meter = yn; }
 
-	double tempo_at_minute (const double& minute) const;
-	double minute_at_tempo (const double& bpm, const double& pulse) 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& bpm, const double& minute) const;
+	Tempo tempo_at_pulse (const double& pulse) const;
+	double pulse_at_ntpm (const double& ntpm, const double& minute) 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;
-	double compute_c_func_minute (const double& end_bpm, const double& end_minute) 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; }
 
@@ -450,11 +453,11 @@ class LIBARDOUR_API TempoMap : public PBD::StatefulDestructible
 	/* 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);
-	double quarter_note_at_frame_rt (const framepos_t frame);
-	framepos_t frame_at_quarter_note (const double quarter_note);
+	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;
 
-	framecnt_t frames_between_quarter_notes (const double start, const double end);
+	framecnt_t frames_between_quarter_notes (const double start, const double end) const;
 
 	double quarter_note_at_beat (const double beat);
 	double beat_at_quarter_note (const double beat);
@@ -511,7 +514,7 @@ private:
 	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;
 
-	double minutes_between_quarter_notes_locked (const Metrics& metrics, const double start_qn, const double end_qn);
+	double minutes_between_quarter_notes_locked (const Metrics& metrics, const double start_qn, const double end_qn) 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;
diff --git a/libs/ardour/tempo.cc b/libs/ardour/tempo.cc
index 8d9f06db75..0279007a21 100644
--- a/libs/ardour/tempo.cc
+++ b/libs/ardour/tempo.cc
@@ -238,63 +238,79 @@ TempoSection::set_type (Type type)
 	_type = type;
 }
 
-/** returns the tempo on note types per minute at the zero-based (relative to session) minute.
+/** returns the Tempo at the session-relative minute.
 */
-double
+Tempo
 TempoSection::tempo_at_minute (const double& m) const
 {
 
 	if (_type == Constant || _c_func == 0.0) {
-		return note_types_per_minute();
+		return Tempo (note_types_per_minute(), note_type());
 	}
 
-	return _tempo_at_time (m - minute());
+	return Tempo (_tempo_at_time (m - minute()), _note_type);
 }
 
-/** returns the zero-based minute (relative to session)
-   where the tempo in note types per minute occurs in this section.
-   pulse p is only used for constant tempi.
-   note that the tempo map may have multiple such values.
+/** returns the session relative minute where the supplied tempo in note types per minute occurs.
+ *  @param ntpm the tempo in mote types per minute used to calculate the returned minute
+ *  @param p the pulse used to calculate the returned minute for constant tempi
+ *  @return the minute at the supplied tempo
+ *
+ *  note that the note_type is currently ignored in this function. see below.
+ *
+*/
+
+/** 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.
+ *  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_tempo (const double& npm, const double& p) const
+TempoSection::minute_at_ntpm (const double& ntpm, const double& p) const
 {
 	if (_type == Constant || _c_func == 0.0) {
 		return ((p - pulse()) / pulses_per_minute()) + minute();
 	}
 
-	return _time_at_tempo (npm) + minute();
+	return _time_at_tempo (ntpm) + minute();
 }
 
-/** returns the tempo in note types per minute at the supplied pulse.
-*/
-double
+/** returns the Tempo at the supplied whole-note pulse.
+ */
+Tempo
 TempoSection::tempo_at_pulse (const double& p) const
 {
 
 	if (_type == Constant || _c_func == 0.0) {
-		return note_types_per_minute();
+		return Tempo (note_types_per_minute(), note_type());
 	}
 
-	return _tempo_at_pulse (p - pulse());
+	return Tempo (_tempo_at_pulse (p - pulse()), _note_type);
 }
 
-/** returns the pulse where the tempo in note types per minute occurs given minute m.
-    minute m is only used for constant tempi.
-    note that the session tempo map may have multiple locations where a given tempo occurs.
+/** returns the whole-note pulse where a tempo in note types per minute occurs.
+ *  constant tempi require minute m.
+ *  @param ntpm the note types per minute value used to calculate the returned pulse
+ *  @param m the minute used to calculate the returned pulse if the tempo is constant
+ *  @return the whole-note pulse at the supplied tempo
+ *
+ *  note that note_type is currently ignored in this function. see minute_at_tempo().
+ *
+ *  for constant tempi, this is anaologous to pulse_at_minute().
 */
 double
-TempoSection::pulse_at_tempo (const double& npm, const double& m) const
+TempoSection::pulse_at_ntpm (const double& ntpm, const double& m) const
 {
 	if (_type == Constant || _c_func == 0.0) {
-		const double pulses = ((m - minute()) * pulses_per_minute()) + pulse();
-		return pulses;
+		return ((m - minute()) * pulses_per_minute()) + pulse();
 	}
 
-	return _pulse_at_tempo (npm) + pulse();
+	return _pulse_at_tempo (ntpm) + pulse();
 }
 
-/** returns the pulse at the supplied session-relative minute.
+/** returns the whole-note pulse at the supplied session-relative minute.
 */
 double
 TempoSection::pulse_at_minute (const double& m) const
@@ -306,7 +322,7 @@ TempoSection::pulse_at_minute (const double& m) const
 	return _pulse_at_time (m - minute()) + pulse();
 }
 
-/** returns the minute (relative to session start) at the supplied pulse.
+/** returns the session-relative minute at the supplied whole-note pulse.
 */
 double
 TempoSection::minute_at_pulse (const double& p) const
@@ -439,16 +455,16 @@ TempoSection::_tempo_at_time (const double& time) const
 
 /* time in minutes at tempo in note types per minute */
 double
-TempoSection::_time_at_tempo (const double& tempo) const
+TempoSection::_time_at_tempo (const double& npm) const
 {
-	return log (tempo / note_types_per_minute()) / _c_func;
+	return log (npm / note_types_per_minute()) / _c_func;
 }
 
 /* pulse at tempo in note types per minute */
 double
-TempoSection::_pulse_at_tempo (const double& tempo) const
+TempoSection::_pulse_at_tempo (const double& npm) const
 {
-	return ((tempo - note_types_per_minute()) / _c_func) / _note_type;
+	return ((npm - note_types_per_minute()) / _c_func) / _note_type;
 }
 
 /* tempo in note types per minute at pulse */
@@ -1312,12 +1328,12 @@ TempoMap::recompute_tempi (Metrics& metrics)
 				if (t->position_lock_style() == AudioTime) {
 					prev_t->set_c_func (prev_t->compute_c_func_minute (t->note_types_per_minute(), t->minute()));
 					if (!t->locked_to_meter()) {
-						t->set_pulse (prev_t->pulse_at_tempo (t->note_types_per_minute(), t->minute()));
+						t->set_pulse (prev_t->pulse_at_ntpm (t->note_types_per_minute(), t->minute()));
 					}
 
 				} else {
 					prev_t->set_c_func (prev_t->compute_c_func_pulse (t->note_types_per_minute(), t->pulse()));
-					t->set_minute (prev_t->minute_at_tempo (t->note_types_per_minute(), t->pulse()));
+					t->set_minute (prev_t->minute_at_ntpm (t->note_types_per_minute(), t->pulse()));
 
 				}
 			}
@@ -1606,18 +1622,13 @@ TempoMap::tempo_at_minute_locked (const Metrics& metrics, const double& minute)
 			}
 			if ((prev_t) && t->minute() > minute) {
 				/* t is the section past frame */
-				const double ret_bpm = prev_t->tempo_at_minute (minute);
-				const Tempo ret_tempo (ret_bpm, prev_t->note_type());
-				return ret_tempo;
+				return prev_t->tempo_at_minute (minute);
 			}
 			prev_t = t;
 		}
 	}
 
-	const double ret = prev_t->note_types_per_minute();
-	const Tempo ret_tempo (ret, prev_t->note_type ());
-
-	return ret_tempo;
+	return Tempo (prev_t->note_types_per_minute(), prev_t->note_type());
 }
 
 /** returns the frame at which the supplied tempo occurs, or
@@ -1660,7 +1671,7 @@ TempoMap::minute_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) co
 				const double prev_t_bpm = prev_t->note_types_per_minute();
 
 				if ((t_bpm > tempo_bpm && prev_t_bpm < tempo_bpm) || (t_bpm < tempo_bpm && prev_t_bpm > tempo_bpm)) {
-					return prev_t->minute_at_tempo (tempo_bpm, prev_t->pulse());
+					return prev_t->minute_at_ntpm (prev_t->note_types_per_minute(), prev_t->pulse());
 				}
 			}
 			prev_t = t;
@@ -1685,18 +1696,13 @@ TempoMap::tempo_at_pulse_locked (const Metrics& metrics, const double& pulse) co
 			}
 			if ((prev_t) && t->pulse() > pulse) {
 				/* t is the section past frame */
-				const double ret_bpm = prev_t->tempo_at_pulse (pulse);
-				const Tempo ret_tempo (ret_bpm, prev_t->note_type());
-				return ret_tempo;
+				return prev_t->tempo_at_pulse (pulse);
 			}
 			prev_t = t;
 		}
 	}
 
-	const double ret = prev_t->note_types_per_minute();
-	const Tempo ret_tempo (ret, prev_t->note_type ());
-
-	return ret_tempo;
+	return Tempo (prev_t->note_types_per_minute(), prev_t->note_type());
 }
 
 double
@@ -1726,7 +1732,7 @@ TempoMap::pulse_at_tempo_locked (const Metrics& metrics, const Tempo& tempo) con
 				const double prev_t_bpm = prev_t->note_types_per_minute();
 
 				if ((t_bpm > tempo_bpm && prev_t_bpm < tempo_bpm) || (t_bpm < tempo_bpm && prev_t_bpm > tempo_bpm)) {
-					return prev_t->pulse_at_tempo (tempo_bpm, prev_t->minute());
+					return prev_t->pulse_at_ntpm (prev_t->note_types_per_minute(), prev_t->minute());
 				}
 			}
 			prev_t = t;
@@ -2255,7 +2261,7 @@ TempoMap::minute_at_bbt_locked (const Metrics& metrics, const BBT_Time& bbt) con
  *
 */
 double
-TempoMap::quarter_note_at_frame (const framepos_t frame)
+TempoMap::quarter_note_at_frame (const framepos_t frame) const
 {
 	Glib::Threads::RWLock::ReaderLock lm (lock);
 
@@ -2273,7 +2279,7 @@ TempoMap::quarter_note_at_minute_locked (const Metrics& metrics, const double mi
 }
 
 double
-TempoMap::quarter_note_at_frame_rt (const framepos_t frame)
+TempoMap::quarter_note_at_frame_rt (const framepos_t frame) const
 {
 	Glib::Threads::RWLock::ReaderLock lm (lock, Glib::Threads::TRY_LOCK);
 
@@ -2295,7 +2301,7 @@ TempoMap::quarter_note_at_frame_rt (const framepos_t frame)
  *
 */
 framepos_t
-TempoMap::frame_at_quarter_note (const double quarter_note)
+TempoMap::frame_at_quarter_note (const double quarter_note) const
 {
 	Glib::Threads::RWLock::ReaderLock lm (lock);
 
@@ -2372,7 +2378,7 @@ TempoMap::beat_at_quarter_note_locked (const Metrics& metrics, const double quar
  *
  */
 framecnt_t
-TempoMap::frames_between_quarter_notes (const double start, const double end)
+TempoMap::frames_between_quarter_notes (const double start, const double end) const
 {
 	Glib::Threads::RWLock::ReaderLock lm (lock);
 
@@ -2380,7 +2386,7 @@ TempoMap::frames_between_quarter_notes (const double start, const double end)
 }
 
 double
-TempoMap::minutes_between_quarter_notes_locked (const Metrics& metrics, const double start, const double end)
+TempoMap::minutes_between_quarter_notes_locked (const Metrics& metrics, const double start, const double end) const
 {
 
 	return minute_at_pulse_locked (metrics, end / 4.0) - minute_at_pulse_locked (metrics, start / 4.0);
@@ -2407,7 +2413,7 @@ TempoMap::check_solved (const Metrics& metrics) const
 				}
 
 				/* precision check ensures tempo and frames align.*/
-				if (t->frame() != frame_at_minute (prev_t->minute_at_tempo (t->note_types_per_minute(), t->pulse()))) {
+				if (t->frame() != frame_at_minute (prev_t->minute_at_ntpm (t->note_types_per_minute(), t->pulse()))) {
 					if (!t->locked_to_meter()) {
 						return false;
 					}
@@ -2511,11 +2517,11 @@ TempoMap::solve_map_minute (Metrics& imaginary, TempoSection* section, const dou
 				}
 				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_tempo (t->note_types_per_minute(), t->pulse()));
+					t->set_minute (prev_t->minute_at_ntpm (t->note_types_per_minute(), t->pulse()));
 				} else {
 					prev_t->set_c_func (prev_t->compute_c_func_minute (t->note_types_per_minute(), t->minute()));
 					if (!t->locked_to_meter()) {
-						t->set_pulse (prev_t->pulse_at_tempo (t->note_types_per_minute(), t->minute()));
+						t->set_pulse (prev_t->pulse_at_ntpm (t->note_types_per_minute(), t->minute()));
 					}
 				}
 			}
@@ -2526,7 +2532,7 @@ 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_tempo (section->note_types_per_minute(), minute));
+			section->set_pulse (section_prev->pulse_at_ntpm (section->note_types_per_minute(), minute));
 		}
 	}
 
@@ -2579,11 +2585,11 @@ TempoMap::solve_map_pulse (Metrics& imaginary, TempoSection* section, const doub
 				}
 				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_tempo (t->note_types_per_minute(), t->pulse()));
+					t->set_minute (prev_t->minute_at_ntpm (t->note_types_per_minute(), t->pulse()));
 				} else {
 					prev_t->set_c_func (prev_t->compute_c_func_minute (t->note_types_per_minute(), t->minute()));
 					if (!t->locked_to_meter()) {
-						t->set_pulse (prev_t->pulse_at_tempo (t->note_types_per_minute(), t->minute()));
+						t->set_pulse (prev_t->pulse_at_ntpm (t->note_types_per_minute(), t->minute()));
 					}
 				}
 			}
@@ -2593,7 +2599,7 @@ 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_tempo (section->note_types_per_minute(), pulse));
+		section->set_minute (section_prev->minute_at_ntpm (section->note_types_per_minute(), pulse));
 	}
 
 #if (0)
@@ -3874,7 +3880,7 @@ TempoMap::frames_per_quarter_note_at (const framepos_t& frame, const framecnt_t&
 	}
 
 	if (ts_after) {
-		return  (60.0 * _frame_rate) / ((ts_at->tempo_at_minute (minute_at_frame (frame)) / ts_at->note_type()) * 4.0);
+		return  (60.0 * _frame_rate) / ts_at->tempo_at_minute (minute_at_frame (frame)).quarter_notes_per_minute();
 	}
 	/* must be treated as constant tempo */
 	return ts_at->frames_per_quarter_note (_frame_rate);
@@ -4154,9 +4160,9 @@ TempoMap::dump (const Metrics& metrics, std::ostream& o) const
 				o << "  previous     : " << prev_t->note_types_per_minute()
 				  << " | " << prev_t->pulse() << " | " << prev_t->frame() << " | " << prev_t->minute() << std::endl;
 				o << "  calculated   : " << prev_t->tempo_at_pulse (t->pulse())
-				  << " | " << prev_t->pulse_at_tempo (t->note_types_per_minute(), t->minute())
-				  << " | " << frame_at_minute (prev_t->minute_at_tempo (t->note_types_per_minute(), t->pulse()))
-				  << " | " << prev_t->minute_at_tempo (t->note_types_per_minute(), t->pulse()) << std::endl;
+				  << " | " << prev_t->pulse_at_ntpm (t->note_types_per_minute(), t->minute())
+				  << " | " << frame_at_minute (prev_t->minute_at_ntpm (t->note_types_per_minute(), t->pulse()))
+				  << " | " << prev_t->minute_at_ntpm (t->note_types_per_minute(), t->pulse()) << std::endl;
 			}
 			prev_t = t;
 		} else if ((m = dynamic_cast<const MeterSection*>(*i)) != 0) {
diff --git a/libs/ardour/test/tempo_test.cc b/libs/ardour/test/tempo_test.cc
index 02c1e3ccab..6d84e67db1 100644
--- a/libs/ardour/test/tempo_test.cc
+++ b/libs/ardour/test/tempo_test.cc
@@ -60,8 +60,8 @@ TempoTest::recomputeMapTest48 ()
 
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (1.0, tsa.minute_at_frame (60.0 * sampling_rate), 1e-17);
 
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (0.1, tsa.minute_at_tempo (240.0, 3.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (0.1, tsa.minute_at_tempo (240.0, 3.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (0.1, tsa.minute_at_ntpm (240.0, 3.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (0.1, tsa.minute_at_ntpm (240.0, 3.0), 1e-17);
 
 	/* do the same via the map */
 
@@ -84,7 +84,7 @@ TempoTest::recomputeMapTest48 ()
 	/* tempo */
 
 	/* tempo - frame */
-	CPPUNIT_ASSERT_EQUAL (framepos_t (288e3), map.frame_at_tempo (240.0));
+	CPPUNIT_ASSERT_EQUAL (framepos_t (288e3), map.frame_at_tempo (tempoB));
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (240.0, map.tempo_at_frame (288e3).note_types_per_minute(), 1e-17);
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (120.0, map.tempo_at_frame (288e3 - 1).note_types_per_minute(), 1e-17);
 
@@ -94,8 +94,8 @@ TempoTest::recomputeMapTest48 ()
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (120.0, map.tempo_at_quarter_note (6.0).note_types_per_minute(), 1e-17);
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (120.0, map.tempo_at_quarter_note (0.0).note_types_per_minute(), 1e-17);
 
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (12.0, map.quarter_note_at_tempo (240.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (0.0, map.quarter_note_at_tempo (120.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (12.0, map.quarter_note_at_tempo (tempoB), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (0.0, map.quarter_note_at_tempo (tempoA), 1e-17);
 
 	/* tempo - internal minute interface  */
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (240.0, map.tempo_at_minute_locked (map._metrics, 0.1).note_types_per_minute(), 1e-17);
@@ -158,7 +158,7 @@ TempoTest::recomputeMapTest44 ()
 
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (1.0, tsa.minute_at_frame (60.0 * sampling_rate), 1e-17);
 
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (0.1, tsa.minute_at_tempo (240.0, 3.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (0.1, tsa.minute_at_ntpm (240.0, 3.0), 1e-17);
 
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (0.1, tsa.minute_at_pulse (3.0), 1e-17);
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (3.0, tsa.pulse_at_minute (0.1), 1e-17);
@@ -194,8 +194,8 @@ TempoTest::recomputeMapTest44 ()
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (120.0, map.tempo_at_quarter_note (6.0).note_types_per_minute(), 1e-17);
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (120.0, map.tempo_at_quarter_note (0.0).note_types_per_minute(), 1e-17);
 
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (12.0, map.quarter_note_at_tempo (240.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (0.0, map.quarter_note_at_tempo (120.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (12.0, map.quarter_note_at_tempo (tempoB), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (0.0, map.quarter_note_at_tempo (tempoA), 1e-17);
 
 	/* tempo - internal minute interface  */
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (240.0, map.tempo_at_minute_locked (map._metrics, 0.1).note_types_per_minute(), 1e-17);
@@ -395,26 +395,26 @@ TempoTest::rampTest48 ()
 	TempoSection& tA = map.first_tempo();
 	const TempoSection& tB = map.tempo_section_at_frame ((framepos_t) 60 * sampling_rate);
 
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (1.0, tA.minute_at_tempo (tB.note_types_per_minute(), 300.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (217.0, tA.tempo_at_minute (1.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (1.0, tA.minute_at_ntpm (217.0, 300.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (217.0, tA.tempo_at_minute (1.0).note_types_per_minute(), 1e-17);
 
 	/* note 1e-14 here. pulse is two derivatives away from time */
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB.pulse(), tA.pulse_at_minute (1.0), 1e-14);
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (1.0, tA.minute_at_pulse (tB.pulse()), 1e-15);
 
 	/* note 1e-17 here. tempo is one derivative away from pulse, so we can get the same stuff with more precision */
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB.pulse(), tA.pulse_at_tempo (217.0, 1.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (1.0, tA.minute_at_tempo (217.0, tB.pulse()), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB.pulse(), tA.pulse_at_ntpm (217.0, 1.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (1.0, tA.minute_at_ntpm (217.0, tB.pulse()), 1e-17);
 
 	/* self-check tempo at pulse @ 125 bpm. */
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (125.0, tA.tempo_at_pulse (tA.pulse_at_tempo (125.0, 0)), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (125.0, tA.tempo_at_pulse (tA.pulse_at_ntpm (125.0, 0)).note_types_per_minute(), 1e-17);
 
 	/* check that tB's pulse is what tA thinks it should be */
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB.pulse(), tA.pulse_at_tempo (217.0, 0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB.pulse(), tA.pulse_at_ntpm (217.0, 0), 1e-17);
 
 	/* check that the tempo at the halfway mark (in pulses) is half the tempo delta.*/
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (147.0, tA.tempo_at_pulse (tB.pulse() / 2.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL ((tB.pulse() - tA.pulse()) / 2.0, tA.pulse_at_tempo (147.0, 0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (147.0, tA.tempo_at_pulse (tB.pulse() / 2.0).note_types_per_minute(), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL ((tB.pulse() - tA.pulse()) / 2.0, tA.pulse_at_ntpm (147.0, 0), 1e-17);
 
 	/* self-check frame at pulse 20 seconds in. */
 	const double target = 20.0 / 60.0;
@@ -457,26 +457,26 @@ TempoTest::rampTest44 ()
 	TempoSection& tA = map.first_tempo();
 	const TempoSection& tB = map.tempo_section_at_frame ((framepos_t) 60 * sampling_rate);
 
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (1.0, tA.minute_at_tempo (tB.note_types_per_minute(), 300.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (217.0, tA.tempo_at_minute (1.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (1.0, tA.minute_at_ntpm (217.0, 300.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (217.0, tA.tempo_at_minute (1.0).note_types_per_minute(), 1e-17);
 
 	/* note 1e-14 here. pulse is two derivatives away from time */
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB.pulse(), tA.pulse_at_minute (1.0), 1e-14);
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (1.0, tA.minute_at_pulse (tB.pulse()), 1e-15);
 
 	/* note 1e-17 here. tempo is one derivative away from pulse, so we can get the same stuff with more precision */
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB.pulse(), tA.pulse_at_tempo (217.0, 1.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (1.0, tA.minute_at_tempo (217.0, tB.pulse()), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB.pulse(), tA.pulse_at_ntpm (217.0, 1.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (1.0, tA.minute_at_ntpm (217.0, tB.pulse()), 1e-17);
 
 	/* self-check tempo at pulse @ 125 bpm. */
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (125.0, tA.tempo_at_pulse (tA.pulse_at_tempo (125.0, 0)), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (125.0, tA.tempo_at_pulse (tA.pulse_at_ntpm (125.0, 0)).note_types_per_minute(), 1e-17);
 
 	/* check that tB's pulse is what tA thinks it should be */
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB.pulse(), tA.pulse_at_tempo (217.0, 0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB.pulse(), tA.pulse_at_ntpm (217.0, 0), 1e-17);
 
 	/* check that the tempo at the halfway mark (in pulses) is half the tempo delta.*/
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (147.0, tA.tempo_at_pulse (tB.pulse() / 2.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL ((tB.pulse() - tA.pulse()) / 2.0, tA.pulse_at_tempo (147.0, 0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (147.0, tA.tempo_at_pulse (tB.pulse() / 2.0).note_types_per_minute(), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL ((tB.pulse() - tA.pulse()) / 2.0, tA.pulse_at_ntpm (147.0, 0), 1e-17);
 
 	/* self-check frame at pulse 20 seconds in. */
 	const double target = 20.0 / 60.0;
@@ -524,35 +524,35 @@ TempoTest::tempoAtPulseTest ()
 			}
 		}
 	}
-
-	CPPUNIT_ASSERT_EQUAL (160.0, tA->tempo_at_pulse (20.0));
-	CPPUNIT_ASSERT_EQUAL (123.0, tB->tempo_at_pulse (30.0));
+	std::cout << std::setprecision (18) << "  tA->tempo_at_pulse (20.0).note_types_per_minute(): " << tA->tempo_at_pulse (20.0).note_types_per_minute() << std::endl;
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (160.0, tA->tempo_at_pulse (20.0).note_types_per_minute(), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (123.0, tB->tempo_at_pulse (30.0).note_types_per_minute(), 1e-17);
 
 	/* check that the tempo at the halfway mark (in pulses) is half the tempo delta.*/
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (((80.0 - 160.0)  / 2.0) + 160.0, tA->tempo_at_pulse (10.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (20.0 / 2.0, tA->pulse_at_tempo (120, 0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (((160.0 - 123.0)  / 2.0) + 123.0, tB->tempo_at_pulse (25.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (((20.0 - 30.0)  / 2.0) + 30.0, tB->pulse_at_tempo (141.5, 0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (((80.0 - 160.0)  / 2.0) + 160.0, tA->tempo_at_pulse (10.0).note_types_per_minute(), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (20.0 / 2.0, tA->pulse_at_ntpm (120.0, 0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (((160.0 - 123.0)  / 2.0) + 123.0, tB->tempo_at_pulse (25.0).note_types_per_minute(), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (((20.0 - 30.0)  / 2.0) + 30.0, tB->pulse_at_ntpm (141.5, 0), 1e-17);
 
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB->minute(), tA->minute_at_pulse (20.0), 1e-17);
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (tC->minute(), tB->minute_at_pulse (30.0), 1e-17);
 
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB->minute(), tA->minute_at_tempo (160.0, 20.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (tC->minute(), tB->minute_at_tempo (123.0, 30.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB->minute(), tA->minute_at_ntpm (160.0, 20.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (tC->minute(), tB->minute_at_ntpm (123.0, 30.0), 1e-17);
 
 	/* self-check tempo at pulse @ 125 bpm. */
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (125.0, tA->tempo_at_pulse (tA->pulse_at_tempo (125.0, 0)), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (160.0, tA->tempo_at_pulse (20.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (123.0, tB->tempo_at_pulse (30.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (125.0, tA->tempo_at_pulse (tA->pulse_at_ntpm (125.0, 0)).note_types_per_minute(), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (160.0, tA->tempo_at_pulse (20.0).note_types_per_minute(), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (123.0, tB->tempo_at_pulse (30.0).note_types_per_minute(), 1e-17);
 	/* test minute based measurements */
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB->minute(), tA->minute_at_pulse (20.0), 1e-17);
 	CPPUNIT_ASSERT_DOUBLES_EQUAL (tC->minute(), tB->minute_at_pulse (30.0), 1e-17);
 
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB->minute(), tA->minute_at_tempo (160.0, 20.0), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (tC->minute(), tB->minute_at_tempo (123.0, 30.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (tB->minute(), tA->minute_at_ntpm (160.0, 20.0), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (tC->minute(), tB->minute_at_ntpm (123.0, 30.0), 1e-17);
 
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (160.0, tA->tempo_at_minute (tB->minute()), 1e-17);
-	CPPUNIT_ASSERT_DOUBLES_EQUAL (123.0, tB->tempo_at_minute (tC->minute()), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (160.0, tA->tempo_at_minute (tB->minute()).note_types_per_minute(), 1e-17);
+	CPPUNIT_ASSERT_DOUBLES_EQUAL (123.0, tB->tempo_at_minute (tC->minute()).note_types_per_minute(), 1e-17);
 }
 
 void