MIDI Note Number ↔ Note Name Converter mechanism

Model scope

The arithmetic is correct under the standard MIDI convention, but the specification needs an explicit note-name mapping, reverse-conversion rule, valid input ranges, and enharmonic spelling policy. Because these behaviors are ambiguous, the instrument requires review before being considered fully specified.

• The forward formula is standard for integer MIDI note numbers: note_index = MIDI % 12 and octave = floor(MIDI / 12) - 1, with MIDI 60 = C4.
• The note-index-to-name mapping is not specified. A canonical spelling convention is required; the vectors below assume sharp spellings: C, C#, D, D#, E, F, F#, G, G#, A, A#, B.
• The reverse conversion algorithm is not stated. It should be MIDI = 12 × (octave + 1) + note_index.
• The supported MIDI-number domain is not stated. Standard MIDI note numbers are integers from 0 through 127; values outside that range should be rejected unless an extended domain is intentionally supported.
• The accepted note-name syntax and enharmonic aliases are not specified. For example, C#4 and Db4 represent the same pitch but require an explicit policy.

Units and conventions

• MIDI note numbers are dimensionless integer values in the standard range 0–127.
• Note names use scientific pitch notation with an integer octave, such as C4 or G#5.
• The octave convention is MIDI/scientific pitch notation: MIDI 60 = C4 and MIDI 69 = A4.
• The canonical output uses sharps rather than flats: C#, D#, F#, G#, and A#.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "midi_number": 0
  },
  "expected_outputs": {
    "note_name": "C-1",
    "note_index": 0,
    "octave": -1
  },
  "working": "note_index = 0 % 12 = 0. octave = floor(0 / 12) - 1 = 0 - 1 = -1. Index 0 maps to C, so the result is C-1."
}

Failure boundary

• Reject non-integer MIDI inputs, MIDI values below 0, and MIDI values above 127 unless the product explicitly supports a nonstandard range.
• Avoid language-specific remainder behavior for negative values; validate the MIDI range before applying modulo.
• Define whether note names are case-sensitive and whether formats such as Bb4, DB4, C♭4, or B#3 are accepted.
• Define behavior for enharmonic spellings and normalize aliases to one canonical output spelling.
• Ensure octave -1 is formatted unambiguously as C-1 rather than being confused with a negative note number.
• Do not silently clamp invalid inputs or return a plausible-looking result for malformed note names.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json