Note Frequency Reference (A4 Tuning Offset) mechanism

Model scope

The frequency formula passes under the stated equal-temperament assumptions, but the instrument cannot be fully verified until the cents-deviation formula and baseline, note-name parsing rules, and supported MIDI range are specified.

• The frequency formula is correct for 12-tone equal temperament when n is the MIDI note number, A4 is MIDI note 69, and A4 is expressed in Hz.
• No formula is supplied for the declared output 'cents deviation from 12-TET'. The baseline is ambiguous: it could mean deviation from 440 Hz tuning, deviation from the selected A4 reference, or deviation from another standard.
• The note-name-to-MIDI-number conversion is unspecified, including accidental spelling, octave numbering, and valid MIDI range.

Units and conventions

• A4 is a positive frequency in Hz, such as 440 Hz, 432 Hz, or 442 Hz.
• n is a dimensionless integer MIDI note number; standard MIDI range is 0 through 127 unless a wider range is explicitly supported.
• The formula assumes 12-tone equal temperament with A4 assigned to MIDI note 69.
• For these test vectors, cents deviation is interpreted relative to 440-Hz 12-TET for the same MIDI note: 1200*log2(actual_frequency/reference_440_TET_frequency).

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "note_name": "A4",
    "octave": 4,
    "midi_note": 69,
    "A4_reference_Hz": 440
  },
  "expected_outputs": {
    "frequency_Hz": 440,
    "cents_deviation_from_440_TET": 0
  },
  "working": "n=69, so (n-69)/12=(69-69)/12=0. 2^0=1.  frequency=440*1=440 Hz.  The 440-Hz reference is exactly the 440-Hz 12-TET A4, so cents deviation=1200*log2(440/440)=1200*log2(1)=0 cents."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification does not state rejection behavior for zero or negative A4 references, producing zero or negative frequencies and undefined cents results. It also leaves the cents comparison reference and sign convention ambiguous; the same 432-Hz tuning can reasonably be reported as either -31.766653633 cents relative to 440-Hz TET or 0 cents relative to its own supplied tuning.

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-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json