Wrap MusicalTime in a class.

This lets us get a more explicit handle on time conversions, and is the main
step towards using actual beat:tick time and getting away from floating point
precision problems.

20 files changed, 173 insertions, 128 deletions

diff --git a/libs/ardour/ardour/automation_control.h b/libs/ardour/ardour/automation_control.h
index 639c5b5287..d73b2fc822 100644
--- a/libs/ardour/ardour/automation_control.h
+++ b/libs/ardour/ardour/automation_control.h
@@ -24,6 +24,7 @@
 #include <boost/shared_ptr.hpp>
 #include <boost/enable_shared_from_this.hpp>
 
+#include "evoral/types.hpp"
 #include "pbd/controllable.h"
 #include "evoral/Control.hpp"
 
diff --git a/libs/ardour/ardour/automation_list.h b/libs/ardour/ardour/automation_list.h
index 72c26420c0..28f9be3fd4 100644
--- a/libs/ardour/ardour/automation_list.h
+++ b/libs/ardour/ardour/automation_list.h
@@ -27,6 +27,9 @@
 
 #include <glibmm/threads.h>
 
+#include "evoral/ControlList.hpp"
+#include "evoral/Parameter.hpp"
+
 #include "pbd/undo.h"
 #include "pbd/xml++.h"
 #include "pbd/statefuldestructible.h"
@@ -34,8 +37,6 @@
 
 #include "ardour/ardour.h"
 
-#include "evoral/ControlList.hpp"
-
 namespace ARDOUR {
 
 class AutomationList;
diff --git a/libs/ardour/ardour/beats_frames_converter.h b/libs/ardour/ardour/beats_frames_converter.h
index 2e170d278a..ada09b1179 100644
--- a/libs/ardour/ardour/beats_frames_converter.h
+++ b/libs/ardour/ardour/beats_frames_converter.h
@@ -20,6 +20,8 @@
 */
 
 #include "evoral/TimeConverter.hpp"
+#include "evoral/types.hpp"
+
 #include "ardour/libardour_visibility.h"
 #include "ardour/types.h"
 
@@ -34,15 +36,35 @@ class TempoMap;
  *  from some origin (supplied to the constructor in frames), and converts
  *  them to the opposite unit, taking tempo changes into account.
  */
-class LIBARDOUR_API BeatsFramesConverter : public Evoral::TimeConverter<double,framepos_t> {
+class LIBARDOUR_API BeatsFramesConverter
+	: public Evoral::TimeConverter<Evoral::MusicalTime,framepos_t> {
 public:
 	BeatsFramesConverter (TempoMap& tempo_map, framepos_t origin)
+		: Evoral::TimeConverter<Evoral::MusicalTime, framepos_t> (origin)
+		, _tempo_map(tempo_map)
+	{}
+
+	framepos_t          to (Evoral::MusicalTime beats) const;
+	Evoral::MusicalTime from (framepos_t frames) const;
+
+private:
+	TempoMap& _tempo_map;
+};
+
+/** Converter between beats and frames.  Takes distances in beats or frames
+ *  from some origin (supplied to the constructor in frames), and converts
+ *  them to the opposite unit, taking tempo changes into account.
+ */
+class LIBARDOUR_API DoubleBeatsFramesConverter
+	: public Evoral::TimeConverter<double,framepos_t> {
+public:
+	DoubleBeatsFramesConverter (TempoMap& tempo_map, framepos_t origin)
 		: Evoral::TimeConverter<double, framepos_t> (origin)
 		, _tempo_map(tempo_map)
 	{}
 
-	framepos_t to (double beats)        const;
-	double     from (framepos_t frames) const;
+	framepos_t          to (double beats) const;
+	double from (framepos_t frames) const;
 
 private:
 	TempoMap& _tempo_map;
diff --git a/libs/ardour/ardour/midi_model.h b/libs/ardour/ardour/midi_model.h
index dc1c7af0e9..31df5ef040 100644
--- a/libs/ardour/ardour/midi_model.h
+++ b/libs/ardour/ardour/midi_model.h
@@ -116,16 +116,11 @@ public:
 		struct NoteChange {
 			NoteDiffCommand::Property property;
 			NotePtr note;
-		        uint32_t note_id; 
-		    
-			union {
-				uint8_t  old_value;
-				TimeType old_time;
-			};
-			union {
-				uint8_t  new_value;
-				TimeType new_time;
-			};
+			uint32_t note_id;
+			uint8_t  old_value;  // or...
+			TimeType old_time;   // this
+			uint8_t  new_value;  // or...
+			TimeType new_time;   // this
 		};
 
 		typedef std::list<NoteChange> ChangeList;
@@ -209,16 +204,16 @@ public:
 		struct Change {
 			PatchChangePtr patch;
 			Property       property;
-		        gint           patch_id;
+			gint           patch_id;
+			TimeType       old_time;
 			union {
-				TimeType   old_time;
 				uint8_t    old_channel;
 				int        old_bank;
 				uint8_t    old_program;
 			};
+			TimeType       new_time;
 			union {
 				uint8_t    new_channel;
-				TimeType   new_time;
 				uint8_t    new_program;
 				int        new_bank;
 			};
@@ -311,7 +306,5 @@ private:
 
 } /* namespace ARDOUR */
 
-/* This is a very long comment and stuff oh my god it's so long what are we going to do oh no oh no*/
-
 #endif /* __ardour_midi_model_h__ */
 
diff --git a/libs/ardour/ardour/midi_region.h b/libs/ardour/ardour/midi_region.h
index 38229b998b..2a4e3a6190 100644
--- a/libs/ardour/ardour/midi_region.h
+++ b/libs/ardour/ardour/midi_region.h
@@ -23,6 +23,8 @@
 
 #include <vector>
 
+#include "evoral/types.hpp"
+
 #include "ardour/ardour.h"
 #include "ardour/region.h"
 
diff --git a/libs/ardour/ardour/midi_source.h b/libs/ardour/ardour/midi_source.h
index 65e382c4b7..2ce92ba3cf 100644
--- a/libs/ardour/ardour/midi_source.h
+++ b/libs/ardour/ardour/midi_source.h
@@ -43,7 +43,7 @@ template<typename T> class MidiRingBuffer;
 class LIBARDOUR_API MidiSource : virtual public Source, public boost::enable_shared_from_this<MidiSource>
 {
   public:
-	typedef double TimeType;
+	typedef Evoral::MusicalTime TimeType;
 
 	MidiSource (Session& session, std::string name, Source::Flag flags = Source::Flag(0));
 	MidiSource (Session& session, const XMLNode&);
@@ -120,7 +120,7 @@ class LIBARDOUR_API MidiSource : virtual public Source, public boost::enable_sha
 	 */
 	virtual void mark_midi_streaming_write_completed (
 		Evoral::Sequence<Evoral::MusicalTime>::StuckNoteOption stuck_option,
-		Evoral::MusicalTime                                    when = 0);
+		Evoral::MusicalTime                                    when = Evoral::MusicalTime());
 
 	virtual void session_saved();
 
@@ -134,8 +134,8 @@ class LIBARDOUR_API MidiSource : virtual public Source, public boost::enable_sha
 
 	bool length_mutable() const { return true; }
 
-	void set_length_beats(double l) { _length_beats = l; }
-	double length_beats() const { return _length_beats; }
+	void     set_length_beats(TimeType l) { _length_beats = l; }
+	TimeType length_beats() const         { return _length_beats; }
 
 	virtual void load_model(bool lock=true, bool force_reload=false) = 0;
 	virtual void destroy_model() = 0;
@@ -194,8 +194,8 @@ class LIBARDOUR_API MidiSource : virtual public Source, public boost::enable_sha
 	mutable Evoral::Sequence<Evoral::MusicalTime>::const_iterator _model_iter;
 	mutable bool                                                  _model_iter_valid;
 
-	mutable double     _length_beats;
-	mutable framepos_t _last_read_end;
+	mutable Evoral::MusicalTime _length_beats;
+	mutable framepos_t          _last_read_end;
 
 	/** The total duration of the current capture. */
 	framepos_t _capture_length;
diff --git a/libs/ardour/ardour/smf_source.h b/libs/ardour/ardour/smf_source.h
index 84c45f9b3c..1c1f2bbcba 100644
--- a/libs/ardour/ardour/smf_source.h
+++ b/libs/ardour/ardour/smf_source.h
@@ -56,7 +56,8 @@ public:
 
 	void mark_streaming_midi_write_started (NoteMode mode);
 	void mark_streaming_write_completed ();
-	void mark_midi_streaming_write_completed (Evoral::Sequence<Evoral::MusicalTime>::StuckNoteOption, Evoral::MusicalTime when = 0);
+	void mark_midi_streaming_write_completed (Evoral::Sequence<Evoral::MusicalTime>::StuckNoteOption,
+	                                          Evoral::MusicalTime when = Evoral::MusicalTime());
 
 	XMLNode& get_state ();
 	int set_state (const XMLNode&, int version);
@@ -88,8 +89,8 @@ public:
 	                           framepos_t                  position,
 	                           framecnt_t                  cnt);
 
-	double    _last_ev_time_beats;
-	framepos_t _last_ev_time_frames;
+	Evoral::MusicalTime _last_ev_time_beats;
+	framepos_t          _last_ev_time_frames;
 	/** end time (start + duration) of last call to read_unlocked */
 	mutable framepos_t _smf_last_read_end;
 	/** time (in SMF ticks, 1 tick per _ppqn) of the last event read by read_unlocked */
diff --git a/libs/ardour/beats_frames_converter.cc b/libs/ardour/beats_frames_converter.cc
index 94042b1b03..b99edbf51e 100644
--- a/libs/ardour/beats_frames_converter.cc
+++ b/libs/ardour/beats_frames_converter.cc
@@ -31,26 +31,43 @@ namespace ARDOUR {
  *  taking tempo changes into account.
  */
 framepos_t
-BeatsFramesConverter::to (double beats) const
+BeatsFramesConverter::to (Evoral::MusicalTime beats) const
 {
-	if (beats < 0) {
+	if (beats < Evoral::MusicalTime()) {
 		std::cerr << "negative beats passed to BFC: " << beats << std::endl;
 		PBD::stacktrace (std::cerr, 30);
+		return 0;
 	}
-	assert (beats >= 0);
-	framecnt_t r = _tempo_map.framepos_plus_beats (_origin_b, beats) - _origin_b;
-	return r;
+	return _tempo_map.framepos_plus_beats (_origin_b, beats) - _origin_b;
 }
 
 /** Takes a duration in frames and considers it as a distance from the origin
  *  supplied to the constructor.  Returns the equivalent number of beats,
  *  taking tempo changes into account.
  */
-double
+Evoral::MusicalTime
 BeatsFramesConverter::from (framepos_t frames) const
 {
-	double b = _tempo_map.framewalk_to_beats (_origin_b, frames);
-	return b;
+	return _tempo_map.framewalk_to_beats (_origin_b, frames);
+}
+
+/** As above, but with beats in double instead (for GUI). */
+framepos_t
+DoubleBeatsFramesConverter::to (double beats) const
+{
+	if (beats < 0.0) {
+		std::cerr << "negative beats passed to BFC: " << beats << std::endl;
+		PBD::stacktrace (std::cerr, 30);
+		return 0;
+	}
+	return _tempo_map.framepos_plus_beats (_origin_b, Evoral::MusicalTime(beats)) - _origin_b;
+}
+
+/** As above, but with beats in double instead (for GUI). */
+double
+DoubleBeatsFramesConverter::from (framepos_t frames) const
+{
+	return _tempo_map.framewalk_to_beats (_origin_b, frames).to_double();
 }
 
 } /* namespace ARDOUR */
diff --git a/libs/ardour/import.cc b/libs/ardour/import.cc
index ae5f751767..38a3da2fdc 100644
--- a/libs/ardour/import.cc
+++ b/libs/ardour/import.cc
@@ -389,10 +389,11 @@ write_midi_data_to_new_files (Evoral::SMF* source, ImportStatus& status,
 				}
 
 				smfs->append_event_unlocked_beats(
-					Evoral::Event<double>(0,
-					                      (double)t / (double)source->ppqn(),
-					                      size,
-					                      buf));
+					Evoral::Event<Evoral::MusicalTime>(
+						0,
+						Evoral::MusicalTime::ticks_at_rate(t, source->ppqn()),
+						size,
+						buf));
 
 				if (status.progress < 0.99) {
 					status.progress += 0.01;
@@ -403,10 +404,10 @@ write_midi_data_to_new_files (Evoral::SMF* source, ImportStatus& status,
 
 				/* we wrote something */
 
-				const framepos_t pos = 0;
-				const double length_beats = ceil(t / (double)source->ppqn());
-				BeatsFramesConverter converter(smfs->session().tempo_map(), pos);
-				smfs->update_length(pos + converter.to(length_beats));
+				const framepos_t          pos = 0;
+				const Evoral::MusicalTime length_beats = Evoral::MusicalTime::ticks_at_rate(t, source->ppqn());
+				BeatsFramesConverter      converter(smfs->session().tempo_map(), pos);
+				smfs->update_length(pos + converter.to(length_beats.round_up_to_beat()));
 				smfs->mark_streaming_write_completed ();
 
 				if (status.cancel) {
diff --git a/libs/ardour/midi_diskstream.cc b/libs/ardour/midi_diskstream.cc
index 69eca996aa..40d333d584 100644
--- a/libs/ardour/midi_diskstream.cc
+++ b/libs/ardour/midi_diskstream.cc
@@ -927,7 +927,7 @@ MidiDiskstream::transport_stopped_wallclock (struct tm& /*when*/, time_t /*twhen
 			/* set length in beats to entire capture length */
 
 			BeatsFramesConverter converter (_session.tempo_map(), capture_info.front()->start);
-			const double total_capture_beats = converter.from (total_capture);
+			const Evoral::MusicalTime total_capture_beats = converter.from (total_capture);
 			_write_source->set_length_beats (total_capture_beats);
 
 			/* flush to disk: this step differs from the audio path,
diff --git a/libs/ardour/midi_model.cc b/libs/ardour/midi_model.cc
index 259a04bc0f..6c2132562a 100644
--- a/libs/ardour/midi_model.cc
+++ b/libs/ardour/midi_model.cc
@@ -226,13 +226,13 @@ MidiModel::NoteDiffCommand::change (const NotePtr note, Property prop,
 		break;
 
 	case StartTime:
-		if (Evoral::musical_time_equal (note->time(), new_time)) {
+		if (note->time() == new_time) {
 			return;
 		}
 		change.old_time = note->time();
 		break;
 	case Length:
-		if (Evoral::musical_time_equal (note->length(), new_time)) {
+		if (note->length() == new_time) {
 			return;
 		}
 		change.old_time = note->length();
@@ -556,7 +556,7 @@ MidiModel::NoteDiffCommand::unmarshal_note (XMLNode *xml_note)
 		time_str >> time;
 	} else {
 		warning << "note information missing time" << endmsg;
-		time = 0;
+		time = MidiModel::TimeType();
 	}
 
 	if ((prop = xml_note->property("length")) != 0) {
@@ -564,7 +564,7 @@ MidiModel::NoteDiffCommand::unmarshal_note (XMLNode *xml_note)
 		length_str >> length;
 	} else {
 		warning << "note information missing length" << endmsg;
-		length = 1;
+		length = MidiModel::TimeType(1);
 	}
 
 	if ((prop = xml_note->property("velocity")) != 0) {
@@ -1253,7 +1253,7 @@ MidiModel::PatchChangeDiffCommand::unmarshal_patch_change (XMLNode* n)
 {
 	XMLProperty* prop;
 	Evoral::event_id_t id = 0;
-	Evoral::MusicalTime time = 0;
+	Evoral::MusicalTime time = Evoral::MusicalTime();
 	int channel = 0;
 	int program = 0;
 	int bank = 0;
@@ -1439,7 +1439,7 @@ MidiModel::write_to (boost::shared_ptr<MidiSource> source)
 	source->drop_model();
 	source->mark_streaming_midi_write_started (note_mode());
 
-	for (Evoral::Sequence<TimeType>::const_iterator i = begin(0, true); i != end(); ++i) {
+	for (Evoral::Sequence<TimeType>::const_iterator i = begin(TimeType(), true); i != end(); ++i) {
 		source->append_event_unlocked_beats(*i);
 	}
 
@@ -1469,7 +1469,7 @@ MidiModel::sync_to_source ()
 
 	ms->mark_streaming_midi_write_started (note_mode());
 
-	for (Evoral::Sequence<TimeType>::const_iterator i = begin(0, true); i != end(); ++i) {
+	for (Evoral::Sequence<TimeType>::const_iterator i = begin(TimeType(), true); i != end(); ++i) {
 		ms->append_event_unlocked_beats(*i);
 	}
 
@@ -1503,7 +1503,7 @@ MidiModel::write_section_to (boost::shared_ptr<MidiSource> source, Evoral::Music
 	source->drop_model();
 	source->mark_streaming_midi_write_started (note_mode());
 
-	for (Evoral::Sequence<TimeType>::const_iterator i = begin(0, true); i != end(); ++i) {
+	for (Evoral::Sequence<TimeType>::const_iterator i = begin(TimeType(), true); i != end(); ++i) {
 		const Evoral::Event<Evoral::MusicalTime>& ev (*i);
 
 		if (ev.time() >= begin_time && ev.time() < end_time) {
@@ -1662,7 +1662,7 @@ MidiModel::resolve_overlaps_unlocked (const NotePtr note, void* arg)
 	TimeType ea  = note->end_time();
 
 	const Pitches& p (pitches (note->channel()));
-	NotePtr search_note(new Note<TimeType>(0, 0, 0, note->note()));
+	NotePtr search_note(new Note<TimeType>(0, TimeType(), TimeType(), note->note()));
 	set<NotePtr> to_be_deleted;
 	bool set_note_length = false;
 	bool set_note_time = false;
@@ -1979,7 +1979,7 @@ MidiModel::insert_silence_at_start (TimeType t)
 	for (Controls::iterator i = controls().begin(); i != controls().end(); ++i) {
 		boost::shared_ptr<AutomationControl> ac = boost::dynamic_pointer_cast<AutomationControl> (i->second);
 		XMLNode& before = ac->alist()->get_state ();
-		i->second->list()->shift (0, t);
+		i->second->list()->shift (0, t.to_double());
 		XMLNode& after = ac->alist()->get_state ();
 		s->session().add_command (new MementoCommand<AutomationList> (new MidiAutomationListBinder (s, i->first), &before, &after));
 	}
diff --git a/libs/ardour/midi_region.cc b/libs/ardour/midi_region.cc
index 71fd796b81..f6631b9de5 100644
--- a/libs/ardour/midi_region.cc
+++ b/libs/ardour/midi_region.cc
@@ -28,6 +28,8 @@
 #include <glibmm/fileutils.h>
 #include <glibmm/miscutils.h>
 
+#include "evoral/types.hpp"
+
 #include "pbd/xml++.h"
 #include "pbd/basename.h"
 
@@ -78,7 +80,7 @@ MidiRegion::register_properties ()
 /* Basic MidiRegion constructor (many channels) */
 MidiRegion::MidiRegion (const SourceList& srcs)
 	: Region (srcs)
-	, _start_beats (Properties::start_beats, 0)
+	, _start_beats (Properties::start_beats, Evoral::MusicalTime())
 	, _length_beats (Properties::length_beats, midi_source(0)->length_beats())
 {
 	register_properties ();
@@ -92,7 +94,7 @@ MidiRegion::MidiRegion (const SourceList& srcs)
 MidiRegion::MidiRegion (boost::shared_ptr<const MidiRegion> other)
 	: Region (other)
 	, _start_beats (Properties::start_beats, other->_start_beats)
-	, _length_beats (Properties::length_beats, (Evoral::MusicalTime) 0)
+	, _length_beats (Properties::length_beats, Evoral::MusicalTime())
 {
 	update_length_beats ();
 	register_properties ();
@@ -105,14 +107,14 @@ MidiRegion::MidiRegion (boost::shared_ptr<const MidiRegion> other)
 /** Create a new MidiRegion that is part of an existing one */
 MidiRegion::MidiRegion (boost::shared_ptr<const MidiRegion> other, frameoffset_t offset)
 	: Region (other, offset)
-	, _start_beats (Properties::start_beats, (Evoral::MusicalTime) 0)
-	, _length_beats (Properties::length_beats, (Evoral::MusicalTime) 0)
+	, _start_beats (Properties::start_beats, Evoral::MusicalTime())
+	, _length_beats (Properties::length_beats, Evoral::MusicalTime())
 {
 	BeatsFramesConverter bfc (_session.tempo_map(), _position);
 	Evoral::MusicalTime const offset_beats = bfc.from (offset);
 
-	_start_beats = other->_start_beats + offset_beats;
-	_length_beats = other->_length_beats - offset_beats;
+	_start_beats  = other->_start_beats.val() + offset_beats;
+	_length_beats = other->_length_beats.val() - offset_beats;
 
 	register_properties ();
 
@@ -216,7 +218,7 @@ MidiRegion::set_position_internal (framepos_t pos, bool allow_bbt_recompute)
 	/* zero length regions don't exist - so if _length_beats is zero, this object
 	   is under construction.
 	*/
-	if (_length_beats) {
+	if (_length_beats.val() == Evoral::MusicalTime()) {
 		/* leave _length_beats alone, and change _length to reflect the state of things
 		   at the new position (tempo map may dictate a different number of frames
 		*/
@@ -440,7 +442,7 @@ MidiRegion::fix_negative_start ()
 
 	model()->insert_silence_at_start (c.from (-_start));
 	_start = 0;
-	_start_beats = 0;
+	_start_beats = Evoral::MusicalTime();
 }
 
 /** Transpose the notes in this region by a given number of semitones */
diff --git a/libs/ardour/midi_source.cc b/libs/ardour/midi_source.cc
index 823ca9dc5c..1c050733c2 100644
--- a/libs/ardour/midi_source.cc
+++ b/libs/ardour/midi_source.cc
@@ -153,13 +153,13 @@ MidiSource::set_state (const XMLNode& node, int /*version*/)
 bool
 MidiSource::empty () const
 {
-	return _length_beats == 0;
+	return !_length_beats;
 }
 
 framecnt_t
 MidiSource::length (framepos_t pos) const
 {
-	if (_length_beats == 0) {
+	if (!_length_beats) {
 		return 0;
 	}
 
@@ -198,7 +198,7 @@ MidiSource::midi_read (Evoral::EventSink<framepos_t>&     dst,
 
 	if (_model) {
 		// Find appropriate model iterator
-		Evoral::Sequence<double>::const_iterator& i = _model_iter;
+		Evoral::Sequence<Evoral::MusicalTime>::const_iterator& i = _model_iter;
 		if (_last_read_end == 0 || start != _last_read_end || !_model_iter_valid) {
 			// Cached iterator is invalid, search for the first event past start
 			i                 = _model->begin(converter.from(start), false, filtered);
diff --git a/libs/ardour/midi_state_tracker.cc b/libs/ardour/midi_state_tracker.cc
index f006004621..0eac3819f2 100644
--- a/libs/ardour/midi_state_tracker.cc
+++ b/libs/ardour/midi_state_tracker.cc
@@ -173,7 +173,7 @@ MidiStateTracker::resolve_notes (MidiSource& src, Evoral::MusicalTime time)
 										       this, (int) note, (int) channel, time));
 				_active_notes[note + 128 * channel]--;
 				/* don't stack events up at the same time */
-				time += 1.0/128.0;
+				time += Evoral::MusicalTime::tick();
 			}
 		}
 	}
diff --git a/libs/ardour/midi_stretch.cc b/libs/ardour/midi_stretch.cc
index 38cab08ace..f5b3a47b41 100644
--- a/libs/ardour/midi_stretch.cc
+++ b/libs/ardour/midi_stretch.cc
@@ -95,9 +95,9 @@ MidiStretch::run (boost::shared_ptr<Region> r, Progress*)
 	/* Note: pass true into force_discrete for the begin() iterator so that the model doesn't
 	 * do interpolation of controller data when we stretch.
 	 */
-	for (Evoral::Sequence<MidiModel::TimeType>::const_iterator i = old_model->begin (0, true);
+	for (Evoral::Sequence<MidiModel::TimeType>::const_iterator i = old_model->begin (MidiModel::TimeType(), true);
 			i != old_model->end(); ++i) {
-		const double new_time = i->time() * _request.time_fraction;
+		const MidiModel::TimeType new_time = i->time() * (double)_request.time_fraction;
 
 		// FIXME: double copy
 		Evoral::Event<MidiModel::TimeType> ev(*i, true);
diff --git a/libs/ardour/quantize.cc b/libs/ardour/quantize.cc
index 7da1edaaa1..13b1cf3b36 100644
--- a/libs/ardour/quantize.cc
+++ b/libs/ardour/quantize.cc
@@ -58,6 +58,8 @@ Quantize::operator () (boost::shared_ptr<MidiModel> model,
                        double position,
                        std::vector<Evoral::Sequence<Evoral::MusicalTime>::Notes>& seqs)
 {
+	/* TODO: Rewrite this to be precise with fixed point? */
+
 	/* Calculate offset from start of model to next closest quantize step,
 	   to quantize relative to actual session beats (etc.) rather than from the
 	   start of the model.
@@ -77,8 +79,8 @@ Quantize::operator () (boost::shared_ptr<MidiModel> model,
 		 */
 		for (Evoral::Sequence<MidiModel::TimeType>::Notes::iterator i = (*s).begin(); i != (*s).end(); ++i) {
 
-			double new_start = round (((*i)->time() - offset) / _start_grid) * _start_grid + offset;
-			double new_end = round (((*i)->end_time() - offset) / _end_grid) * _end_grid + offset;
+			double new_start = round (((*i)->time().to_double() - offset) / _start_grid) * _start_grid + offset;
+			double new_end = round (((*i)->end_time().to_double() - offset) / _end_grid) * _end_grid + offset;
 
 			if (_swing > 0.0 && !even) {
 
@@ -104,18 +106,18 @@ Quantize::operator () (boost::shared_ptr<MidiModel> model,
 
 			}
 
-			double delta = new_start - (*i)->time();
+			double delta = new_start - (*i)->time().to_double();
 
 			if (fabs (delta) >= _threshold) {
 				if (_snap_start) {
 					delta *= _strength;
 					cmd->change ((*i), MidiModel::NoteDiffCommand::StartTime,
-						     (*i)->time() + delta);
+					             (*i)->time().to_double() + delta);
 				}
 			}
 
 			if (_snap_end) {
-				delta = new_end - (*i)->end_time();
+				delta = new_end - (*i)->end_time().to_double();
 
 				if (fabs (delta) >= _threshold) {
 					double new_dur = new_end - new_start;
diff --git a/libs/ardour/smf_source.cc b/libs/ardour/smf_source.cc
index 8a956495a5..1ffcdac1b2 100644
--- a/libs/ardour/smf_source.cc
+++ b/libs/ardour/smf_source.cc
@@ -225,7 +225,7 @@ SMFSource::read_unlocked (Evoral::EventSink<framepos_t>& destination,
 
 	BeatsFramesConverter converter(_session.tempo_map(), source_start);
 
-	const uint64_t start_ticks = (uint64_t)(converter.from(start) * ppqn());
+	const uint64_t start_ticks = converter.from(start).to_ticks();
 	DEBUG_TRACE (DEBUG::MidiSourceIO, string_compose ("SMF read_unlocked: start in ticks %1\n", start_ticks));
 
 	if (_smf_last_read_end == 0 || start != _smf_last_read_end) {
@@ -273,7 +273,7 @@ SMFSource::read_unlocked (Evoral::EventSink<framepos_t>& destination,
 		/* Note that we add on the source start time (in session frames) here so that ev_frame_time
 		   is in session frames.
 		*/
-		const framepos_t ev_frame_time = converter.to(time / (double)ppqn()) + source_start;
+		const framepos_t ev_frame_time = converter.to(Evoral::MusicalTime::ticks_at_rate(time, ppqn())) + source_start;
 
 		if (ev_frame_time < start + duration) {
 			destination.write (ev_frame_time, ev_type, ev_size, ev_buffer);
@@ -377,9 +377,9 @@ SMFSource::write_unlocked (MidiRingBuffer<framepos_t>& source,
 	return cnt;
 }
 
-/** Append an event with a timestamp in beats (double) */
+/** Append an event with a timestamp in beats */
 void
-SMFSource::append_event_unlocked_beats (const Evoral::Event<double>& ev)
+SMFSource::append_event_unlocked_beats (const Evoral::Event<Evoral::MusicalTime>& ev)
 {
 	if (!_writing || ev.size() == 0)  {
 		return;
@@ -389,10 +389,10 @@ SMFSource::append_event_unlocked_beats (const Evoral::Event<double>& ev)
                name().c_str(), ev.id(), ev.time(), ev.size());
 	       for (size_t i = 0; i < ev.size(); ++i) printf("%X ", ev.buffer()[i]); printf("\n");*/
 
-	double time = ev.time();
+	Evoral::MusicalTime time = ev.time();
 	if (time < _last_ev_time_beats) {
-		const double difference = _last_ev_time_beats - time;
-		if (difference / (double)ppqn() < 1.0) {
+		const Evoral::MusicalTime difference = _last_ev_time_beats - time;
+		if (difference.to_double() / (double)ppqn() < 1.0) {
 			/* Close enough.  This problem occurs because Sequence is not
 			   actually ordered due to fuzzy time comparison.  I'm pretty sure
 			   this is inherently a bad idea which causes problems all over the
@@ -401,7 +401,7 @@ SMFSource::append_event_unlocked_beats (const Evoral::Event<double>& ev)
 		} else {
 			/* Out of order by more than a tick. */
 			warning << string_compose(_("Skipping event with unordered beat time %1 < %2 (off by %3 beats, %4 ticks)"),
-			                          ev.time(), _last_ev_time_beats, difference, difference / (double)ppqn())
+			                          ev.time(), _last_ev_time_beats, difference, difference.to_double() / (double)ppqn())
 			        << endmsg;
 			return;
 		}
@@ -421,8 +421,8 @@ SMFSource::append_event_unlocked_beats (const Evoral::Event<double>& ev)
 
 	_length_beats = max(_length_beats, time);
 
-	const double delta_time_beats   = time - _last_ev_time_beats;
-	const uint32_t delta_time_ticks = (uint32_t)lrint(delta_time_beats * (double)ppqn());
+	const Evoral::MusicalTime delta_time_beats = time - _last_ev_time_beats;
+	const uint32_t            delta_time_ticks = delta_time_beats.to_ticks(ppqn());
 
 	Evoral::SMF::append_event_delta(delta_time_ticks, ev.size(), ev.buffer(), event_id);
 	_last_ev_time_beats = time;
@@ -448,9 +448,9 @@ SMFSource::append_event_unlocked_frames (const Evoral::Event<framepos_t>& ev, fr
 		return;
 	}
 
-	BeatsFramesConverter converter(_session.tempo_map(), position);
-	const double ev_time_beats = converter.from(ev.time());
-	Evoral::event_id_t event_id;
+	BeatsFramesConverter      converter(_session.tempo_map(), position);
+	const Evoral::MusicalTime ev_time_beats = converter.from(ev.time());
+	Evoral::event_id_t        event_id;
 
 	if (ev.id() < 0) {
 		event_id  = Evoral::next_event_id();
@@ -459,10 +459,10 @@ SMFSource::append_event_unlocked_frames (const Evoral::Event<framepos_t>& ev, fr
 	}
 
 	if (_model) {
-		const Evoral::Event<double> beat_ev (ev.event_type(),
-		                                     ev_time_beats,
-		                                     ev.size(),
-		                                     const_cast<uint8_t*>(ev.buffer()));
+		const Evoral::Event<Evoral::MusicalTime> beat_ev (ev.event_type(),
+		                                                  ev_time_beats,
+		                                                  ev.size(),
+		                                                  const_cast<uint8_t*>(ev.buffer()));
 		_model->append (beat_ev, event_id);
 	}
 
@@ -470,7 +470,7 @@ SMFSource::append_event_unlocked_frames (const Evoral::Event<framepos_t>& ev, fr
 
 	const Evoral::MusicalTime last_time_beats  = converter.from (_last_ev_time_frames);
 	const Evoral::MusicalTime delta_time_beats = ev_time_beats - last_time_beats;
-	const uint32_t            delta_time_ticks = (uint32_t)(lrint(delta_time_beats * (double)ppqn()));
+	const uint32_t            delta_time_ticks = delta_time_beats.to_ticks(ppqn());
 
 	Evoral::SMF::append_event_delta(delta_time_ticks, ev.size(), ev.buffer(), event_id);
 	_last_ev_time_frames = ev.time();
@@ -516,7 +516,7 @@ SMFSource::mark_streaming_midi_write_started (NoteMode mode)
 
 	MidiSource::mark_streaming_midi_write_started (mode);
 	Evoral::SMF::begin_write ();
-	_last_ev_time_beats = 0.0;
+	_last_ev_time_beats  = Evoral::MusicalTime();
 	_last_ev_time_frames = 0;
 }
 
@@ -586,8 +586,8 @@ SMFSource::safe_midi_file_extension (const string& file)
 }
 
 static bool compare_eventlist (
-		const std::pair< Evoral::Event<double>*, gint >& a,
-		const std::pair< Evoral::Event<double>*, gint >& b) {
+	const std::pair< Evoral::Event<Evoral::MusicalTime>*, gint >& a,
+	const std::pair< Evoral::Event<Evoral::MusicalTime>*, gint >& b) {
 	return ( a.first->time() < b.first->time() );
 }
 
@@ -620,7 +620,7 @@ SMFSource::load_model (bool lock, bool force_reload)
 	Evoral::SMF::seek_to_start();
 
 	uint64_t time = 0; /* in SMF ticks */
-	Evoral::Event<double> ev;
+	Evoral::Event<Evoral::MusicalTime> ev;
 
 	uint32_t scratch_size = 0; // keep track of scratch and minimize reallocs
 
@@ -632,7 +632,7 @@ SMFSource::load_model (bool lock, bool force_reload)
 	bool have_event_id;
 
 	// TODO simplify event allocation
-	std::list< std::pair< Evoral::Event<double>*, gint > > eventlist;
+	std::list< std::pair< Evoral::Event<Evoral::MusicalTime>*, gint > > eventlist;
 
 	for (unsigned i = 1; i <= num_tracks(); ++i) {
 		if (seek_to_track(i)) continue;
@@ -658,8 +658,8 @@ SMFSource::load_model (bool lock, bool force_reload)
 				if (!have_event_id) {
 					event_id = Evoral::next_event_id();
 				}
-				uint32_t event_type = midi_parameter_type(buf[0]);
-				double   event_time = time / (double) ppqn();
+				const uint32_t            event_type = midi_parameter_type(buf[0]);
+				const Evoral::MusicalTime event_time = Evoral::MusicalTime::ticks_at_rate(time, ppqn());
 #ifndef NDEBUG
 				std::string ss;
 
@@ -674,7 +674,7 @@ SMFSource::load_model (bool lock, bool force_reload)
 #endif
 
 				eventlist.push_back(make_pair (
-							new Evoral::Event<double> (
+							new Evoral::Event<Evoral::MusicalTime> (
 								event_type, event_time,
 								size, buf, true)
 							, event_id));
@@ -693,7 +693,7 @@ SMFSource::load_model (bool lock, bool force_reload)
 
 	eventlist.sort(compare_eventlist);
 
-	std::list< std::pair< Evoral::Event<double>*, gint > >::iterator it;
+	std::list< std::pair< Evoral::Event<Evoral::MusicalTime>*, gint > >::iterator it;
 	for (it=eventlist.begin(); it!=eventlist.end(); ++it) {
 		_model->append (*it->first, it->second);
 		delete it->first;
diff --git a/libs/ardour/tempo.cc b/libs/ardour/tempo.cc
index 57bf9fe674..1767c8100d 100644
--- a/libs/ardour/tempo.cc
+++ b/libs/ardour/tempo.cc
@@ -1891,10 +1891,11 @@ TempoMap::framepos_plus_beats (framepos_t pos, Evoral::MusicalTime beats) const
 		framecnt_t distance_frames = (next_tempo == metrics.end() ? max_framepos : ((*next_tempo)->frame() - pos));
 
 		/* Distance to the end in beats */
-		Evoral::MusicalTime distance_beats = distance_frames / tempo->frames_per_beat (_frame_rate);
+		Evoral::MusicalTime distance_beats = Evoral::MusicalTime::ticks_at_rate(
+			distance_frames, tempo->frames_per_beat (_frame_rate));
 
 		/* Amount to subtract this time */
-		double const delta = min (distance_beats, beats);
+		Evoral::MusicalTime const delta = min (distance_beats, beats);
 
 		DEBUG_TRACE (DEBUG::TempoMath, string_compose ("\tdistance to %1 = %2 (%3 beats)\n",
 							       (next_tempo == metrics.end() ? max_framepos : (*next_tempo)->frame()),
@@ -1902,7 +1903,7 @@ TempoMap::framepos_plus_beats (framepos_t pos, Evoral::MusicalTime beats) const
 
 		/* Update */
 		beats -= delta;
-		pos += delta * tempo->frames_per_beat (_frame_rate);
+		pos += delta.to_ticks(tempo->frames_per_beat (_frame_rate));
 
 		DEBUG_TRACE (DEBUG::TempoMath, string_compose ("\tnow at %1, %2 beats left\n", pos, beats));
 
@@ -1999,10 +2000,11 @@ TempoMap::framepos_minus_beats (framepos_t pos, Evoral::MusicalTime beats) const
 		framecnt_t distance_frames = (pos - tempo->frame());
 
 		/* Distance to the start in beats */
-		Evoral::MusicalTime distance_beats = distance_frames / tempo->frames_per_beat (_frame_rate);
+		Evoral::MusicalTime distance_beats = Evoral::MusicalTime::ticks_at_rate(
+			distance_frames, tempo->frames_per_beat (_frame_rate));
 
 		/* Amount to subtract this time */
-		double const sub = min (distance_beats, beats);
+		Evoral::MusicalTime const sub = min (distance_beats, beats);
 
 		DEBUG_TRACE (DEBUG::TempoMath, string_compose ("\tdistance to %1 = %2 (%3 beats)\n",
 							       tempo->frame(), distance_frames, distance_beats));
@@ -2035,7 +2037,7 @@ TempoMap::framepos_minus_beats (framepos_t pos, Evoral::MusicalTime beats) const
 			}
 		} else {
 			pos -= llrint (beats * tempo->frames_per_beat (_frame_rate));
-			beats = 0;
+			beats = Evoral::MusicalTime();
 		}
 	}
 
@@ -2216,7 +2218,7 @@ TempoMap::framewalk_to_beats (framepos_t pos, framecnt_t distance) const
 	             string_compose ("frame %1 walk by %2 frames, start with tempo = %3 @ %4\n",
 	                             pos, distance, *((const Tempo*)tempo), tempo->frame()));
 	
-	Evoral::MusicalTime beats = 0;
+	Evoral::MusicalTime beats = Evoral::MusicalTime();
 
 	while (distance) {
 
@@ -2234,8 +2236,8 @@ TempoMap::framewalk_to_beats (framepos_t pos, framecnt_t distance) const
 			distance_to_end = end - pos;
 		}
 
-		/* Amount to subtract this time */
-		double const sub = min (distance, distance_to_end);
+		/* Amount to subtract this time in frames */
+		framecnt_t const sub = min (distance, distance_to_end);
 
 		DEBUG_TRACE (DEBUG::TempoMath, string_compose ("to reach end at %1 (end ? %2), distance= %3 sub=%4\n", end, (next_tempo == metrics.end()),
 							       distance_to_end, sub));
@@ -2244,7 +2246,7 @@ TempoMap::framewalk_to_beats (framepos_t pos, framecnt_t distance) const
 		pos += sub;
 		distance -= sub;
 		assert (tempo);
-		beats += sub / tempo->frames_per_beat (_frame_rate);
+		beats += Evoral::MusicalTime::ticks_at_rate(sub, tempo->frames_per_beat (_frame_rate));
 
 		DEBUG_TRACE (DEBUG::TempoMath, string_compose ("now at %1, beats = %2 distance left %3\n",
 							       pos, beats, distance));
diff --git a/libs/ardour/test/framepos_minus_beats_test.cc b/libs/ardour/test/framepos_minus_beats_test.cc
index 01bafc1606..e4c4844146 100644
--- a/libs/ardour/test/framepos_minus_beats_test.cc
+++ b/libs/ardour/test/framepos_minus_beats_test.cc
@@ -7,6 +7,7 @@ CPPUNIT_TEST_SUITE_REGISTRATION (FrameposMinusBeatsTest);
 using namespace std;
 using namespace ARDOUR;
 using namespace Timecode;
+using namespace Evoral;
 
 /* Basic tests with no tempo / meter changes */
 void
@@ -25,11 +26,11 @@ FrameposMinusBeatsTest::singleTempoTest ()
 	map.add_tempo (tempo, BBT_Time (1, 1, 0));
 
 	/* Subtract 1 beat from beat 3 of the first bar */
-	framepos_t r = map.framepos_minus_beats (frames_per_beat * 2, 1);
+	framepos_t r = map.framepos_minus_beats (frames_per_beat * 2, MusicalTime(1));
 	CPPUNIT_ASSERT_EQUAL (r, framepos_t (frames_per_beat * 1));
 
 	/* Subtract 4 beats from 3 beats in, to go beyond zero */
-	r = map.framepos_minus_beats (frames_per_beat * 3, 4);
+	r = map.framepos_minus_beats (frames_per_beat * 3, MusicalTime(4));
 	CPPUNIT_ASSERT_EQUAL (r, framepos_t (- frames_per_beat));
 }
 
@@ -69,15 +70,15 @@ FrameposMinusBeatsTest::doubleTempoTest ()
 	/* Now some tests */
 
 	/* Subtract 1 beat from 1|2 */
-	framepos_t r = map.framepos_minus_beats (24e3, 1);
+	framepos_t r = map.framepos_minus_beats (24e3, MusicalTime(1));
 	CPPUNIT_ASSERT_EQUAL (r, framepos_t (0));
 
 	/* Subtract 2 beats from 4|2 (over the tempo change) */
-	r = map.framepos_minus_beats (288e3 + 12e3, 2);
+	r = map.framepos_minus_beats (288e3 + 12e3, MusicalTime(2));
 	CPPUNIT_ASSERT_EQUAL (r, framepos_t (288e3 - 24e3));
 
 	/* Subtract 2.5 beats from 4|2 (over the tempo change) */
-	r = map.framepos_minus_beats (288e3 + 12e3, 2.5);
+	r = map.framepos_minus_beats (288e3 + 12e3, MusicalTime(2.5));
 	CPPUNIT_ASSERT_EQUAL (r, framepos_t (288e3 - 24e3 - 12e3));
 }
 
@@ -123,15 +124,15 @@ FrameposMinusBeatsTest::doubleTempoWithMeterTest ()
 	/* Now some tests */
 
 	/* Subtract 1 beat from 1|2 */
-	framepos_t r = map.framepos_minus_beats (24e3, 1);
+	framepos_t r = map.framepos_minus_beats (24e3, MusicalTime(1));
 	CPPUNIT_ASSERT_EQUAL (r, framepos_t (0));
 
 	/* Subtract 2 beats from 4|2 (over the tempo change) */
-	r = map.framepos_minus_beats (288e3 + 12e3, 2);
+	r = map.framepos_minus_beats (288e3 + 12e3, MusicalTime(2));
 	CPPUNIT_ASSERT_EQUAL (r, framepos_t (288e3 - 24e3));
 
 	/* Subtract 2.5 beats from 4|2 (over the tempo change) */
-	r = map.framepos_minus_beats (288e3 + 12e3, 2.5);
+	r = map.framepos_minus_beats (288e3 + 12e3, MusicalTime(2.5));
 	CPPUNIT_ASSERT_EQUAL (r, framepos_t (288e3 - 24e3 - 12e3));
 }
 
diff --git a/libs/ardour/test/framepos_plus_beats_test.cc b/libs/ardour/test/framepos_plus_beats_test.cc
index c95c2a7a66..abe1310f62 100644
--- a/libs/ardour/test/framepos_plus_beats_test.cc
+++ b/libs/ardour/test/framepos_plus_beats_test.cc
@@ -25,11 +25,11 @@ FrameposPlusBeatsTest::singleTempoTest ()
 	map.add_tempo (tempo, BBT_Time (1, 1, 0));
 
 	/* Add 1 beat to beat 3 of the first bar */
-	framepos_t r = map.framepos_plus_beats (frames_per_beat * 2, 1);
+	framepos_t r = map.framepos_plus_beats (frames_per_beat * 2, Evoral::MusicalTime(1));
 	CPPUNIT_ASSERT_EQUAL (framepos_t (frames_per_beat * 3), r);
 
 	/* Add 4 beats to a -ve frame of 1 beat before zero */
-	r = map.framepos_plus_beats (-frames_per_beat * 1, 4);
+	r = map.framepos_plus_beats (-frames_per_beat * 1, Evoral::MusicalTime(4));
 	CPPUNIT_ASSERT_EQUAL (framepos_t (frames_per_beat * 3), r);
 }
 
@@ -69,15 +69,15 @@ FrameposPlusBeatsTest::doubleTempoTest ()
 	/* Now some tests */
 
 	/* Add 1 beat to 1|2 */
-	framepos_t r = map.framepos_plus_beats (24e3, 1);
+	framepos_t r = map.framepos_plus_beats (24e3, Evoral::MusicalTime(1));
 	CPPUNIT_ASSERT_EQUAL (framepos_t (48e3), r);
 
 	/* Add 2 beats to 3|4 (over the tempo change) */
-	r = map.framepos_plus_beats (264e3, 2);
+	r = map.framepos_plus_beats (264e3, Evoral::MusicalTime(2));
 	CPPUNIT_ASSERT_EQUAL (framepos_t (264e3 + 24e3 + 12e3), r);
 
 	/* Add 2.5 beats to 3|3|960 (over the tempo change) */
-	r = map.framepos_plus_beats (264e3 - 12e3, 2.5);
+	r = map.framepos_plus_beats (264e3 - 12e3, Evoral::MusicalTime(2.5));
 	CPPUNIT_ASSERT_EQUAL (framepos_t (264e3 + 24e3 + 12e3), r);
 }
 
@@ -123,15 +123,15 @@ FrameposPlusBeatsTest::doubleTempoWithMeterTest ()
 	/* Now some tests */
 
 	/* Add 1 beat to 1|2 */
-	framepos_t r = map.framepos_plus_beats (24e3, 1);
+	framepos_t r = map.framepos_plus_beats (24e3, Evoral::MusicalTime(1));
 	CPPUNIT_ASSERT_EQUAL (framepos_t (48e3), r);
 
 	/* Add 2 beats to 3|4 (over the tempo change) */
-	r = map.framepos_plus_beats (264e3, 2);
+	r = map.framepos_plus_beats (264e3, Evoral::MusicalTime(2));
 	CPPUNIT_ASSERT_EQUAL (framepos_t (264e3 + 24e3 + 12e3), r);
 
 	/* Add 2.5 beats to 3|3|960 (over the tempo change) */
-	r = map.framepos_plus_beats (264e3 - 12e3, 2.5);
+	r = map.framepos_plus_beats (264e3 - 12e3, Evoral::MusicalTime(2.5));
 	CPPUNIT_ASSERT_EQUAL (framepos_t (264e3 + 24e3 + 12e3), r);
 }