Lesson 05 · The division field - Build a MIDI Parser

The division field

The division field has two meanings hiding in one 16-bit number, chosen by its top bit - ticks per quarter note, or an SMPTE frame rate. Today you tell them apart so later lessons can turn ticks into time.

The goal

Interpret a division value as either ticks-per-quarter or an SMPTE rate.

Start here - the target

TO DO

Scenario: The top bit selects ticks-per-quarter or SMPTE timing

Givena division value of 0x0060 (top bit clear)

Whenit is interpreted

Thenit is metrical timing with 96 ticks per quarter note

Anda division of 0xE250 (top bit set) is SMPTE timing at 30 frames per second with 80 ticks per frame

Background

The division is the file’s clock. When its top bit (bit 15) is clear, the whole 16-bit value is ticks per quarter note - the metrical mode almost every file uses. 0x0060 is 96, so 96 delta-ticks make one quarter note, and once you know the tempo you can turn ticks into seconds.

When the top bit is set, the field is SMPTE timing instead. The high byte is a negative frame rate stored as a signed 8-bit value - 0xE2 is -30, so 30 frames per second - and the low byte is ticks per frame, 0x50 is 80. That gives absolute frame-based timing independent of tempo. This project does its time math in the metrical mode; recognising SMPTE now means later code can flag it rather than compute a wrong number.

Make it work

// bit 15 set means SMPTE; the high byte is a signed negative frame rate
func divisionKind(d uint16) (smpte bool, a int, b int) {
  if d&0x8000 == 0 {
    return false, int(d), 0 // ticks per quarter note
  }
  fps := -int(int8(d >> 8)) // high byte is a signed 8-bit value
  return true, fps, int(d & 0xFF)
}

CheckpointDONE

You can classify a division as metrical or SMPTE timing. Commit and stop here.