Lesson 28 · Ticks to seconds and beats

Ticks to seconds and beats

The whole point of the division and the tempo was to turn abstract ticks into real time. Today you convert a tick to seconds and to beats, the calculation the capstone reports.

The goal

Convert an absolute tick to seconds and to beats using the division and tempo.

Start here - the target

TO DO

Scenario: A tick converts to seconds and beats at a known tempo

Givena division of 96 ticks per quarter and a tempo of 500000 microseconds per quarter (120 BPM)

Whentick 96 is converted

Thenit is 0.5 seconds and 1.0 beats

Andtick 48 is 0.25 seconds and 0.5 beats, and tick 0 is 0.0 seconds and 0.0 beats

Background

This is the conversion the whole timing chapter was heading toward. The division (ticks per quarter note) turns ticks into beats: beats = tick / ppqn, so at a division of 96, tick 96 is exactly 1.0 beat. The tempo (microseconds per quarter) turns beats into seconds: each beat lasts usPerQuarter / 1000000 seconds, so at 500000 microseconds a beat is half a second and tick 96 is 0.5 seconds.

Keep it a constant-tempo calculation for now - one division, one tempo - which is exactly right for the many files that never change tempo. When the tempo map has several entries the honest version sums the seconds segment by segment between tempo changes, but the arithmetic per segment is this same formula; converting across a changing tempo is a natural extension noted in the caveats. Today, pin the clean values: 96 ticks is half a second, 48 is a quarter second, 0 is zero.

Make it work

// beats = tick / ppqn ; seconds = beats * usPerQuarter / 1e6
beats := float64(tick) / float64(ppqn)
seconds := beats * float64(usPerQuarter) / 1000000.0

CheckpointDONE

You can convert a tick to seconds and beats. Commit and stop here.