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Encyclopedia of Microtonal Music Theory

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Fokker periodicity-block

[Joe Monzo]

A term used by Paul Erlich to specify a periodicity-block whose boundaries define a parallelepiped (or N-dimensional equivalent) shape. (See Erlich, A Gentle Introduction to Fokker Periodicity Blocks: part 1 and continue to follow the links to part 2, an excursion, and part3.)

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[Gene Ward Smith]

Yahoo tuning group, Message 55480
From: "Gene Ward Smith"
Date: Fri Aug 13, 2004 11:11 pm
Subject: Re: JI 12-tone 7-limit epimorphic scales?

--- In tuning@yahoogroups.com, Kurt Bigler wrote:

> So does the Fokker block approach generate epimorphic scales of the
> non-monotonic variety? Or is it monotonic only (I hope)?

It can easily enough be non-monotonic; in fact the Dona Nobis Pacem scale I used recently here is exactly that. Not only that, it's a good example of where some 5-limit chords will mostly likely be assimilated to a 7-limit interpretation, the sort of thing Carl [Lumma] was talking about.

> I looked up Fokker block and saw that it is a parallelepiped structure,
> which then somehow reinforced my original (incorrect) intuition. Hmm.

Of course, paralleopideds are not the only thing which works; various other sorts of convex bodies will also [see Erlich, A Gentle Introduction to Fokker Periodicity Blocks: An Excursion]. Simply detempering a MOS with respect to a distance measure such as the Hahn norm works also as a means of concocting epimorphic scales.

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See also:

Erlich, Paul and Monzo, Joe. 1999. The Indian Sruti System as a Periodicity-Block

Erlich, Paul. 1999. Partch's 43-tone Scale as a Periodicity-Block

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