diff --git a/gtk2_ardour/editor_ops.cc b/gtk2_ardour/editor_ops.cc
index e1efaa268b..bccad1d72f 100644
--- a/gtk2_ardour/editor_ops.cc
+++ b/gtk2_ardour/editor_ops.cc
@@ -4331,7 +4331,10 @@ Editor::apply_midi_note_edit_op_to_region (MidiOperator& op, MidiRegionView& mrv
 	vector<Evoral::Sequence<Evoral::MusicalTime>::Notes> v;
 	v.push_back (selected);
 
-	return op (mrv.midi_region()->model(), v);
+	framepos_t pos_frames = mrv.midi_region()->position();
+	double     pos_beats  = _session->tempo_map().framewalk_to_beats(0, pos_frames);
+
+	return op (mrv.midi_region()->model(), pos_beats, v);
 }
 
 void
diff --git a/libs/ardour/ardour/midi_operator.h b/libs/ardour/ardour/midi_operator.h
index 31e412bafe..c5def76384 100644
--- a/libs/ardour/ardour/midi_operator.h
+++ b/libs/ardour/ardour/midi_operator.h
@@ -37,7 +37,9 @@ class MidiOperator {
 	MidiOperator () {}
 	virtual ~MidiOperator() {}
 
-	virtual Command* operator() (boost::shared_ptr<ARDOUR::MidiModel>, std::vector<Evoral::Sequence<Evoral::MusicalTime>::Notes>&) = 0;
+	virtual Command* operator() (boost::shared_ptr<ARDOUR::MidiModel>,
+	                             double,
+	                             std::vector<Evoral::Sequence<Evoral::MusicalTime>::Notes>&) = 0;
 	virtual std::string name() const = 0;
 };
 
diff --git a/libs/ardour/ardour/quantize.h b/libs/ardour/ardour/quantize.h
index bf046e6c50..e1ca2b2395 100644
--- a/libs/ardour/ardour/quantize.h
+++ b/libs/ardour/ardour/quantize.h
@@ -36,7 +36,9 @@ public:
 			float strength, float swing, float threshold);
 	~Quantize ();
 
-	Command* operator() (boost::shared_ptr<ARDOUR::MidiModel>, std::vector<Evoral::Sequence<Evoral::MusicalTime>::Notes>&);
+	Command* operator() (boost::shared_ptr<ARDOUR::MidiModel>,
+	                     double position,
+	                     std::vector<Evoral::Sequence<Evoral::MusicalTime>::Notes>&);
 	std::string name() const { return std::string ("quantize"); }
 
 private:
diff --git a/libs/ardour/quantize.cc b/libs/ardour/quantize.cc
index db2cbb1d21..7ede60b578 100644
--- a/libs/ardour/quantize.cc
+++ b/libs/ardour/quantize.cc
@@ -60,8 +60,17 @@ Quantize::~Quantize ()
 }
 
 Command*
-Quantize::operator () (boost::shared_ptr<MidiModel> model, std::vector<Evoral::Sequence<Evoral::MusicalTime>::Notes>& seqs)
+Quantize::operator () (boost::shared_ptr<MidiModel> model,
+                       double position,
+                       std::vector<Evoral::Sequence<Evoral::MusicalTime>::Notes>& seqs)
 {
+	/* 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.
+	*/
+	const double round_pos = ceil(position / _start_grid) * _start_grid;
+	const double offset    = round_pos - position;
+
 	bool even;
 	MidiModel::NoteDiffCommand* cmd = new MidiModel::NoteDiffCommand (model, "quantize");
 
@@ -71,9 +80,8 @@ Quantize::operator () (boost::shared_ptr<MidiModel> model, std::vector<Evoral::S
 
 		for (Evoral::Sequence<MidiModel::TimeType>::Notes::iterator i = (*s).begin(); i != (*s).end(); ++i) {
 
-			double new_start = round ((*i)->time() / _start_grid) * _start_grid;
-			double new_end = round ((*i)->end_time() / _end_grid) * _end_grid;
-			double delta;
+			double new_start = round ((*i)->time() / _start_grid) * _start_grid + offset;
+			double new_end = round ((*i)->end_time() / _end_grid) * _end_grid + offset;
 
 			if (_swing > 0.0 && !even) {
 
@@ -97,7 +105,7 @@ Quantize::operator () (boost::shared_ptr<MidiModel> model, std::vector<Evoral::S
 
 			}
 
-			delta = new_start - (*i)->time();
+			double delta = new_start - (*i)->time();
 
 			if (fabs (delta) >= _threshold) {
 				if (_snap_start) {