diff --git a/libs/ardour/session_time.cc b/libs/ardour/session_time.cc
index a84d5802b7..b98d1d9d08 100644
--- a/libs/ardour/session_time.cc
+++ b/libs/ardour/session_time.cc
@@ -236,7 +236,7 @@ Session::convert_to_samples (AnyTime const & position)
 
 	switch (position.type) {
 	case AnyTime::BBT:
-		return Temporal::superclock_to_samples (TempoMap::use()->superclock_at (BBT_Argument (timepos_t::zero (Temporal::BeatTime), position.bbt)), _current_sample_rate);
+		return Temporal::superclock_to_samples (TempoMap::use()->superclock_at (BBT_Argument (superclock_t (0), position.bbt)), _current_sample_rate);
 		break;
 
 	case AnyTime::Timecode:
diff --git a/libs/ardour/triggerbox.cc b/libs/ardour/triggerbox.cc
index c161c59ff4..26c70bb900 100644
--- a/libs/ardour/triggerbox.cc
+++ b/libs/ardour/triggerbox.cc
@@ -1447,7 +1447,7 @@ AudioTrigger::compute_end (Temporal::TempoMap::SharedPtr const & tmap, Temporal:
            _beatcnt : the expected duration of the trigger, based on analysis of its tempo .. can be overridden by the user later
 	*/
 
-	const Temporal::BBT_Argument transition_bba (timepos_t::zero (Temporal::BeatTime), transition_bbt);
+	const Temporal::BBT_Argument transition_bba (superclock_t (0), transition_bbt);
 
 	samplepos_t end_by_follow_length = tmap->sample_at (tmap->bbt_walk (transition_bba, _follow_length));
 	samplepos_t end_by_data_length = transition_sample + (data.length - _start_offset);
@@ -2315,7 +2315,7 @@ MIDITrigger::start_and_roll_to (samplepos_t start_pos, samplepos_t end_position,
 timepos_t
 MIDITrigger::compute_end (Temporal::TempoMap::SharedPtr const & tmap, Temporal::BBT_Time const & transition_bbt, samplepos_t, Temporal::Beats & effective_length)
 {
-	const Temporal::BBT_Argument transition_bba (timepos_t::zero(Temporal::BeatTime), transition_bbt);
+	const Temporal::BBT_Argument transition_bba (superclock_t (0), transition_bbt);
 
 	Temporal::Beats end_by_follow_length = tmap->quarters_at (tmap->bbt_walk (transition_bba, _follow_length));
 	Temporal::Beats end_by_data_length = tmap->quarters_at (tmap->bbt_walk (transition_bba, Temporal::BBT_Offset (0, data_length.get_beats(), data_length.get_ticks())));
diff --git a/libs/temporal/tempo.cc b/libs/temporal/tempo.cc
index e0c3295dfc..ae0279e904 100644
--- a/libs/temporal/tempo.cc
+++ b/libs/temporal/tempo.cc
@@ -663,13 +663,13 @@ MeterPoint::get_state () const
 	return base;
 }
 
-timepos_t
+superclock_t
 TempoMetric::reftime() const
 {
 	return _tempo->map().reftime (*this);
 }
 
-timepos_t
+superclock_t
 TempoMap::reftime (TempoMetric const &tm) const
 {
 	Points::const_iterator pi;
@@ -689,7 +689,7 @@ TempoMap::reftime (TempoMetric const &tm) const
 		--pi;
 	}
 
-	return timepos_t (pi->sclock());
+	return pi->sclock();
 }
 
 Temporal::BBT_Argument
@@ -731,7 +731,7 @@ TempoMetric::bbt_at (timepos_t const & pos) const
 
 	DEBUG_TRACE (DEBUG::TemporalMap, string_compose ("BBT offset from %3 @ %1: %2\n", (_tempo->beats() < _meter->beats() ?  _meter->bbt() : _tempo->bbt()), bbt_offset,
 	                                                 (_tempo->beats() < _meter->beats() ? "meter" : "tempo")));
-	timepos_t ref (std::min (_meter->sclock(), _tempo->sclock()));
+	superclock_t ref (std::min (_meter->sclock(), _tempo->sclock()));
 
 	return BBT_Argument (ref, _meter->bbt_add (reference_point->bbt(), bbt_offset));
 }
@@ -2079,7 +2079,7 @@ TempoMap::bbt_at (superclock_t s) const
 {
 	TempoMetric metric (metric_at (s));
 
-	timepos_t ref (std::min (metric.tempo().sclock(), metric.meter().sclock()));
+	superclock_t ref (std::min (metric.tempo().sclock(), metric.meter().sclock()));
 	return BBT_Argument (ref, metric.bbt_at (timepos_t::from_superclock (s)));
 }
 
@@ -2087,7 +2087,7 @@ Temporal::BBT_Argument
 TempoMap::bbt_at (Temporal::Beats const & qn) const
 {
 	TempoMetric metric (metric_at (qn));
-	timepos_t ref (std::min (metric.tempo().sclock(), metric.meter().sclock()));
+	superclock_t ref (std::min (metric.tempo().sclock(), metric.meter().sclock()));
 	return BBT_Argument (ref, metric.bbt_at (qn));
 }
 
diff --git a/libs/temporal/temporal/bbt_argument.h b/libs/temporal/temporal/bbt_argument.h
index 76a1a2e65f..04d3da2c9b 100644
--- a/libs/temporal/temporal/bbt_argument.h
+++ b/libs/temporal/temporal/bbt_argument.h
@@ -27,19 +27,19 @@ namespace Temporal {
 struct LIBTEMPORAL_API BBT_Argument : public BBT_Time
 {
   public:
-	BBT_Argument () : BBT_Time (), _reference (Temporal::timepos_t (Temporal::BeatTime)) {}
-	BBT_Argument (int32_t B, int32_t b, int32_t t) : BBT_Time (B, b, t),  _reference (Temporal::timepos_t (Temporal::BeatTime)) {}
+	BBT_Argument () : BBT_Time (), _reference (0) {}
+	BBT_Argument (int32_t B, int32_t b, int32_t t) : BBT_Time (B, b, t),  _reference (0) {}
 
-	BBT_Argument (Temporal::timepos_t const & r) : BBT_Time (), _reference (r) {}
-	BBT_Argument (Temporal::timepos_t const & r, int32_t B, int32_t b, int32_t t) : BBT_Time (B, b, t), _reference (r) {}
+	BBT_Argument (superclock_t r) : BBT_Time (), _reference (r) {}
+	BBT_Argument (superclock_t r, int32_t B, int32_t b, int32_t t) : BBT_Time (B, b, t), _reference (r) {}
 
-	explicit BBT_Argument (BBT_Time const & bbt) : BBT_Time (bbt),  _reference (Temporal::timepos_t (Temporal::BeatTime)) {}
-	BBT_Argument (Temporal::timepos_t const & r, BBT_Time const & bbt) : BBT_Time (bbt),  _reference (r) {}
+	explicit BBT_Argument (BBT_Time const & bbt) : BBT_Time (bbt),  _reference (0) {}
+	BBT_Argument (superclock_t r, BBT_Time const & bbt) : BBT_Time (bbt),  _reference (r) {}
 
-	Temporal::timepos_t reference() const { return _reference; }
+	superclock_t reference() const { return _reference; }
 
   private:
-	Temporal::timepos_t _reference;
+	superclock_t _reference;
 
 };
 
diff --git a/libs/temporal/temporal/tempo.h b/libs/temporal/temporal/tempo.h
index 672fb73046..182e5ec72a 100644
--- a/libs/temporal/temporal/tempo.h
+++ b/libs/temporal/temporal/tempo.h
@@ -481,7 +481,7 @@ class LIBTEMPORAL_API TempoMetric
 	TempoMetric (TempoPoint const & t, MeterPoint const & m) : _tempo (&t), _meter (&m) {}
 	virtual ~TempoMetric () {}
 
-	timepos_t reftime() const;
+	superclock_t reftime() const;
 
 	TempoPoint const & tempo() const { return *_tempo; }
 	MeterPoint const & meter() const { return *_meter; }
@@ -720,7 +720,7 @@ class /*LIBTEMPORAL_API*/ TempoMap : public PBD::StatefulDestructible
 	LIBTEMPORAL_API static void abort_update ();
 
 	/* not part of public API */
-	timepos_t reftime(TempoMetric const &) const;
+	superclock_t reftime(TempoMetric const &) const;
 
 	/* and now on with the rest of the show ... */
 
diff --git a/libs/temporal/timeline.cc b/libs/temporal/timeline.cc
index 07f1c6d462..bfaf83d076 100644
--- a/libs/temporal/timeline.cc
+++ b/libs/temporal/timeline.cc
@@ -664,7 +664,7 @@ timepos_t::earlier (Temporal::BBT_Offset const & offset) const
 	TempoMap::SharedPtr tm (TempoMap::use());
 
 	if (is_superclock()) {
-		return timepos_t (tm->superclock_at (BBT_Argument (*this, tm->bbt_walk (BBT_Argument (*this, tm->bbt_at (*this)), -offset))));
+		return timepos_t (tm->superclock_at (BBT_Argument (this->superclocks(), tm->bbt_walk (BBT_Argument (this->superclocks(), tm->bbt_at (*this)), -offset))));
 	}
 
 	return timepos_t (tm->bbtwalk_to_quarters (beats(), -offset));
@@ -763,7 +763,7 @@ timepos_t::shift_earlier (Temporal::BBT_Offset const & offset)
 	TempoMap::SharedPtr tm (TempoMap::use());
 
 	if (is_superclock()) {
-		v = build (false, (tm->superclock_at (tm->bbt_walk (BBT_Argument (*this, tm->bbt_at (*this)), -offset))));
+		v = build (false, (tm->superclock_at (tm->bbt_walk (BBT_Argument (this->superclocks(), tm->bbt_at (*this)), -offset))));
 	} else {
 		v = build (true, tm->bbtwalk_to_quarters (beats(), -offset).to_ticks());
 	}
@@ -780,7 +780,7 @@ timepos_t::operator+= (Temporal::BBT_Offset const & offset)
 	if (is_beats()) {
 		v = build (true, tm->bbtwalk_to_quarters (beats(), offset).to_ticks());
 	} else {
-		v = build (false, tm->superclock_at (tm->bbt_walk (BBT_Argument (*this, tm->bbt_at (*this)), offset)));
+		v = build (false, tm->superclock_at (tm->bbt_walk (BBT_Argument (this->superclocks(), tm->bbt_at (*this)), offset)));
 	}
 
 	return *this;