Prismatic Harmony · Vladan's Matrix
One diminished chord sits at the center of all harmony. Everything else is a step outward.
Barry Harris' family · Tymoczko's Möbius geometry · one method
↓ scroll — then tap a chord to hear it
The wheel
A four-note diminished chord splits the octave into equal parts — the gold diamond at the center. Nudge any note a half-step and you land on a relative: down → a dominant, up → a minor-6, a pair → a major-6. Choose a seed, then tap.
The idea, in three beats
A diminished 7th is four notes a minor-third apart — perfectly symmetric. It divides the octave evenly, so it has no root to pull toward. In Tymoczko's geometry of chords, that puts it at the exact center of the space.
Shift a single note a half-step and the center resolves into a real chord: down gives a dominant 7, up gives a minor-6; move a pair and you get a major-6. One seed, sixteen relatives — Barry Harris called it the family.
The four dominants pair off a tritone apart, sharing the very same guide tones. Travel that tritone once and you're on the mirror side; twice and you're home. A tritone substitution is the family's Möbius half-twist.
In a real tune
The engine keeps a chord's function and swaps it for a family relative — a resolved, singable recolor, not a random substitution. Tap to compare.
The Möbius twist
“The tritone substitution isn't a trick you memorize. It's the half-twist of the diminished family — the same guide tones, seen from the other side of the strip.”
B7 and F7 hold the identical tritone, A and E♭. Rotate the seed a tritone and every dominant swaps with its partner while the guide tones stay fixed — go around once, you're flipped; twice, you're back. That return-flipped-then-restored is the mathematical signature of a Möbius strip.