The Fifths Ring

analytical · neon · twelve laws · under keeper eris

neon

{{ act || react || change }} · the sculpture

analytical

Twelve pitches sit on a ring, and a step of seven semitones visits every pitch once before it returns.

LIT Starting at pitch 0, add 7 modulo 12, twelve times. The walk hits every residue exactly once and the thirteenth step is 0 again. That happens because 7 and 12 are coprime.

AMBER Musicians call this the circle of fifths. A fifth is seven semitones in twelve-tone equal temperament. The diagram is old teaching equipment; the modular walk above is the check.

MODEL The token hops one fifth at a time around a horizontal ring. The chords drawn across the ring are the same +7 steps.

Sources AMBER

  1. Circle of fifths (reference)

LIT on load: the identity is recomputed (it throws on mismatch), the training target scores 1, 200 rounds improve the shared sketch, the workspace loop logs 5 entries, and the OBJ and SVG exports match the sketch.

Gallery of kept sketches:

Workspace improvement loop MODEL

  1. Measure: every 40 rounds, record the acceptance rate, the current score and how many rounds since the last improvement.
  2. Try next: if the score has been flat for 40 rounds, widen the mutation step. If acceptance is under 15%, shrink it; over 45%, widen it. Otherwise keep it.
  3. Log back: append {entry, round, measured, tried, step} to the workspace log (it is in the export JSON and the list below).
  4. Repeat: re-check the identity before claiming it. The seal stays write-if-missing.

Live workspace log:

    Shared board MODEL

    localStorage key mayhem-twelve-laws-board. Each page writes its best shared reward.

      Attempt board MODEL

        ← Twelve Laws · Twelve Laws · The Twelfth Root → · ERIS

        Background wash: AMBER MODEL a field seeded from this page's seal. The viewport is a deep colour, not black, over a vivid page.

        proving…

        Seal sha256(name|slug|blurb): 3f0eb65eae44ebf340c058cf82adc4764ddb2207077d3d7cfa58241acffc4ba0