the syntonic comma pump. four familiar chords (C, A minor, D minor, G), each tuned purely from a note the previous chord leaves behind. no voice ever moves by anything but a pure interval, yet every time the progression comes home, home has sunk by 81/80, a syntonic comma, 21.5 cents. escher's staircase is an illusion; this one really descends. about 56 cycles to fall a full octave. reverse to climb, temper to stand still. the G chord's root is 40/27, one comma under the 3/2 you started from.
click the canvas to start · esc stops and frees the voices · gold bars are notes held over from the previous chord · the pure links the comma sneaks through · − marks a note one syntonic comma (81/80) under its just C-major self