Interval / Chord / Scale Reference Builder mechanism

Model scope

The listed major and natural-minor scale patterns, dominant-seventh chord pattern, and octave interval are standard for 12-TET. The specification needs an explicit data schema for scale types, chord qualities, interval inputs, octave/register notation, accidentals, enharmonic spelling, and ascending versus descending intervals. The honest label should state the supported theory scope, such as '12-TET Western note, scale, chord, and interval reference; supported types and enharmonic spelling as listed.'

• The major-scale semitone pattern [0,2,4,5,7,9,11] is correct for a major scale in 12-tone equal temperament, but the algorithm does not specify modulo-12 handling, octave handling, or enharmonic note spelling.
• The chord expression root+third+fifth(+seventh) is incomplete: third quality must be defined as major (4 semitones) or minor (3 semitones), and seventh quality must distinguish major (11), minor/dominant (10), and diminished (9).
• The claimed interval-name computation has no stated algorithm or lookup table. It must define semitone distance, direction, octave crossing, and diatonic spelling; pitch-class distance alone cannot distinguish, for example, augmented fourth from diminished fifth.
• The supported scale and chord types are unspecified. Natural minor, harmonic minor, melodic minor, suspended chords, diminished chords, and seventh-chord qualities require explicit table entries.
• Accidental and note-spelling behavior is unspecified. A pitch-class-only implementation cannot correctly render scales such as F-sharp major or C-sharp major with the required letter names.
• The input specification omits the two-note inputs required for interval computation and does not define whether note registers such as C4 are accepted.

Units and conventions

• All semitone offsets assume standard 12-tone equal temperament (12-TET), with one semitone equal to 100 cents.
• Root and note names are assumed to use conventional letter names with optional sharps or flats; octave/register handling is required when intervals cross octaves.
• Pitch classes are numbered C=0, C-sharp/D-flat=1, ..., B=11 for the vectors below.
• No physical unit conversion is involved; the relevant unit is semitones, with interval names interpreted according to standard Western music theory.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "operation": "scale",
    "root": "C",
    "scale_type": "major"
  },
  "expected_outputs": {
    "notes": [
      "C",
      "D",
      "E",
      "F",
      "G",
      "A",
      "B"
    ],
    "scale_degrees": [
      1,
      2,
      3,
      4,
      5,
      6,
      7
    ],
    "pitch_classes": [
      0,
      2,
      4,
      5,
      7,
      9,
      11
    ]
  },
  "reference_data": {
    "root_pitch_class": {
      "C": 0,
      "source_convention": "Widely tabulated standard 12-TET music-theory value"
    },
    "major_scale_offsets_semitones": {
      "values": [
        0,
        2,
        4,
        5,
        7,
        9,
        11
      ],
      "source_convention": "Widely tabulated standard Western major-scale formula"
    },
    "pitch_class_note_names": {
      "values": [
        "C",
        "C-sharp/D-flat",
        "D",
        "D-sharp/E-flat",
        "E",
        "F",
        "F-sharp/G-flat",
        "G",
        "G-sharp/A-flat",
        "A",
        "A-sharp/B-flat",
        "B"
      ],
      "source_convention": "Widely tabulated standard 12-TET chromatic pitch-class convention"
    }
  },
  "working": "Start at C, pitch class 0. Add the major offsets: 0 -> 0 = C; 0+2=2 = D; 0+4=4 = E; 0+5=5 = F; 0+7=7 = G; 0+9=9 = A; 0+11=11 = B. Therefore the scale is C-D-E-F-G-A-B with degrees 1-7 and pitch classes [0,2,4,5,7,9,11]."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The extreme-octave vector exceeds signed 64-bit MIDI range and must be rejected or handled with arbitrary precision; the interval vector also exposes an unspecified signed-versus-modulo direction convention.

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-tranche7/tranche7-results.json
• BOUNDARY_HAZARD_CATALOG.json