Pleased to present a new matrix "The Pythagorean Harmonic Hybrid"

a better app, cross my heart! Improvisation, demonstration, genuflection using the Pythagorean-Harmonic Hybrid Matrix. You've read about it, but have you ever actually heard the Pythagorean comma? Well, now you have. Please kindly remember you saw and heard this app here first.

Application of Harmonic Matrix Theory by D Bond. [iPad bridge by Fantastick using MMF]

n=16; 1/1=515

Fairly new, this matrix was the basis of my composition "Standard Machine" Feb-Mar 2012 - this is the first time it has been depicted and published online.

It represents the cycles of Pythagorean 5ths ((3/2)^(|y|/y))^|y|) multiplied by the Harmonic Series [S=|x|^|x|/x]. Need I mention that the base term is arbitrary?

The name is provisional. The usefulness of this matrix should be obvious. For example, here are address pairs = I Maj9.

0,4 0,5 0,6

1,4 1,5 1,6

is equivalent to

0,8 0,10 0,12 0,15 0,18

etc...

Other harmonies not available to standard practice can be constructed and readily used. Notice the cycle of colors does indeed loop [y axis] after 12 iterations, but the color is noticeably different, just as the pitch is.

For your edification, here presented are 2 large order versions of the matrix: