The claim that MMA is the only 7-note scale where all 12 transpositions function over real chords in a single key center is a mathematical claim. Mathematical claims require proof — not demonstration of a few cases but exhaustive verification of all cases. Intuition can suggest a relationship; computation can prove it. The SuperScales discovery required both: musical intuition to formulate the question, and SuperCollider and Python to answer it rigorously.

This article describes the computational verification process — how the test was formulated, how it was implemented, what the results looked like, and why the computational approach was necessary rather than optional.

Why Computation Was Necessary

The verification required testing 66 heptachords × 12 transpositions × (approximately 20 real chord types per key center) = approximately 15,840 scale-chord pairings. Each pairing required determining which scale tones were chord tones, which were tensions, and which were avoid notes relative to the specific chord type. This is a well-defined algorithmic procedure — but doing it 15,840 times by hand would take weeks and introduce human error into the process.

More fundamentally, the claim is a universal statement: “all 12 transpositions of MMA function over real chords.” Universal statements require testing all cases, not just the suggestive ones. Before computational verification, a musician might suspect that MMA had special properties — but suspicion is not proof. The computation is what converts a hypothesis into a confirmed finding.

The Python Implementation

# All 66 heptachords as pitch class arrays (prime forms)
heptachords = {
    '7-34': [0,1,3,4,5,6,8],  # MMA
    '7-35': [0,1,3,5,6,8,10], # Major scale
    # ... all 66 heptachords
}

def has_avoid_note(scale_pcs, chord_root, chord_quality):
    chord_tones = get_chord_tones(chord_root, chord_quality)
    tensions = get_tensions(chord_root, chord_quality)
    for pc in scale_pcs:
        if pc not in chord_tones and pc not in tensions:
            # Check if pc clashes with a chord tone by semitone
            if any(abs(pc - ct) % 12 == 1 for ct in chord_tones):
                return True
    return False

def test_heptachord(forte_name, prime_form):
    passes = 0
    for transpose in range(12):
        scale = [(pc + transpose) % 12 for pc in prime_form]
        for chord in real_chords_in_C:
            if not has_avoid_note(scale, chord.root, chord.quality):
                passes += 1
                break  # This transposition passes
    return passes == 12  # True only if ALL 12 transpositions pass

The Results

SuperCollider — Audio Confirmation

After the Python script identified MMA as the only passing heptachord, SuperCollider was used to generate audio for each of the 12 MMA transpositions — the scale played against a drone plus the corresponding chord — to confirm aurally that the mathematical result was also a musical one. This is the experimental confirmation step: the mathematical proof says it should work; the audio says it does work.

The audio confirmation step revealed something the mathematical test alone cannot capture: the quality of the pass. Some scale-chord pairings that technically have no avoid notes still sound awkward or strained — they pass the algorithm but not the ear. For MMA, every one of the 12 transpositions passed both tests — mathematically zero avoid notes, and musically coherent against the corresponding chord. The algorithm’s definition of “pass” was a reliable predictor of the musical result.

This alignment between mathematical and musical evaluation is itself meaningful. It confirms that the algorithm’s avoid-note definition captures something real about musical perception — not just an arbitrary rule but a genuine acoustic criterion. The computational proof and the auditory proof point to the same conclusion.