Duodene

A tonal lattice with 12 nodes invented by A. J. Ellis as a model for the 12-tone chromatic scale in Just Intonation.

It consists of a chain of four Perfect fifths (F to D) and a three Major Thirds above and below each of these pitch tones.

Analogs may be constructed by replacing the 3/2 and 5/4's with other intervals.

[from John Chalmers, Divisions of the Tetrachord]

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Ellis's Duodene was the original inspiration for my own independent invention of what I used to call "matrices", as published in my initial paper, and which I now refer to, in keeping with the work done by others before me, as lattices.

The Duodene is a periodicity-block whose unison-vectors are the syntonic comma and the diesis. Here is a Monzo lattice of Ellis's Duodene:

Unison-vectors:

     81:80   =  [4 -1]  syntonic comma
    128:125  =  [0 -3]  Ellis's "great diesis", Rameau's "minor diesis"



[from Joe Monzo, JustMusic: A New Harmony]

See also:

Ellis's Duodene as a Periodicity-Block;

Paul Erlich's derivation of the duodene in Gentle Introduction to Fokker Periodicity Blocks, part 2.

My webpage, Ellis's Duodene and a "best-fit" meantone.

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Updated: 2002.1.22, 2002.1.26

(to download a zip file of the entire Dictionary, click here)

For many more diagrams and explanations of historical tunings, see my book. If you don't understand my theory or the terms I've used, start here

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