Drag your cursor across the black unstemmed noteheads.
THE PI TONE is derived from multiplying a tone, any tone, by the transcendental number Pi. In the above example, when the E is multiplied by Pi, you get a tone slightly flatter than a high C. This is the Pi tone. Written out as an equation in Hertz, it looks like this:
E 4 * π = C 6
329.6 Hz * 3.14159 = 1035.5 (10 Hz less than an equal-tempered C)
The Pi Tone covers the interval of a Minor Thirteenth. When transposed down an octave to a C5, it covers the interval of a Minor Sixth: (13 – 7 [8ve] = 6). There are three Minor Sixths’ in every diatonic key. In the key of C Major (C D E F G A B), they are E—C, A—F, and B—G. Play with them.
Tone * Pi. If you repeat this operation twice, and arrange all the tones in the same octave, you get the Pi Chord or augmented chord. The augmented is built up of Major Thirds. E G# C.
“Don’t disturb my circles!” screamed Archimedes as the pike entered his gut.
“Have a bath, Archimedes,” quipped the soldier, “In hell.”