On the Poole Just-Intonation Keyboard

© 1999 by Joe Monzo

In the 1860s Henry Ward Poole1 invented a clever keyboard for just-intonation.²

It looked like this:

(sorry, no picture yet)

This keyboard was an ingenious system of the type Partch would call "Poly-pythagorean". This means that it follows cycles of powers of 3, along five different odd-number axes:

3
5
7
25 [=5²]
35 [=5*7]

Here is a lattice diagram depicting the ratios specified by Poole:

(sorry, no lattice diagram yet)

Altogether, there were 100 different keys (meaning keyboard levers) and pitches per "octave" in sound. If built, it would give perfectly-tuned 4:5:6:7 tetrads on 20 different "roots". The layout on the keyboard was cyclical, so that the patterns of finger movement were completely identical in every key.

Here is a graph of the pitches as they fall within one octave:

Notice that there are many schismatic equivalents. These are notes that are very close together in pitch, which I would call "xenharmonic bridges". Therefore, if Poole was willing to accept the "imperceptibility" of these equivalents, he could have reduced the size of the keyboard a great deal. His retention of these tiny intervallic differences does show it, however, to be a truly perfectly in-tune 7-limit just-intonation keyboard.

NOTES

¹ Poole (1826-1890) was born in Salem, Massachusetts, and lived the later part of his life in Mexico City, where he was Professor of Public Instruction in the Government Institute. (back to text)

² REFERENCES

Silliman's American Journal of Science and Arts, vol 44, July 1867. Poole had published his theories on "perfect musical intonation" in the issues of January and March, 1850.

updated:

1999.03.13