Quadratic Prime Just Intonation

Paul and others have asked me what I mean by "quadratic prime just
intonation" and this is now the time. I used this tuning exclusively in
a solo trombone work called _Rama_ based on the Arthur C. Clarke & Gentry
Lee series of books. I later used it for a section of my string quartet
_Cosmic Rays_.

Firstly, I'd like to quote a passage of _Rama_ which lead me to the tuning:

"What comes first? Do we use models to help us find the truth? Or do we
know the truth first, and then develop the mathematics to explain it?"
- a lead character Nicole les Jardins

Quadratic Primes 41, 43, 47, 53, 61, 71, 83, 97
Each successive number is computed by increasing the difference from the
previous number by two, resulting in exactly forty consecutive prome
dollars. The sequence of primes ends only when the 41st number in the
string turns out to be a non-prime, namely 41 X 41 = 1681.

The ratios are:
43/41 = 82 cents
47/43 = 179 cents
53/47 = 193 cents
61/53 = 244 cents
71/61 = 263 cents
83/71 = 271 cents
97/83 = 270 cents
and continues to diminish down to 1681/1601 = 84 cents

In the _Rama_ books, the alien sentients that rule their lives use
quadratic primes as the basis for their computer software. I found in
using what at first seem like arcane relationships actually make
consonance of all possible combinations. Thats why its just intonation.

Johnny Reinhard
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@ios.com


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