unison vector

A term used by Fokker to describe what I call a xenharmonic bridge: an interval which is small enough that it can be disregarded, thereby enabling a ratio with one set of prime-factors to substitute for a ratio with a different set of factors.

The most frequently-used one by Fokker was the 225/224 variety of the septimal schisma, allowing 7/4 and 225/128 to be perceived as being interchangeable with each other.

In Fokker's lattice theory, the spanning of lattice regions by these unison vectors would demarcate a boundary of a periodicity block.

[Paul Erlich comments:

That language is a little strange -- I'd simply say, the unison vectors divide the lattice into regions called periodicity blocks.]

[from Joe Monzo, JustMusic: A New Harmony]

See also: periodicity block, xenharmonic bridge

REFERENCE: The earliest reference I've found to this concept is: Tanaka, Shohé. "Studien im Gebiete der reinen Stimmung", Vierteljahrsschrift für Musikwissenschaft vol. 6 no. 1, Friedrich Chrysander, Philipp Spitta, Guido Adler (eds.), Breitkopf und Härtel, Leipzig, 1890, pp. 1-90. English translation of pages 8 to 18 by Daniel J. Wolf, "Studies in the Realm of Just Intonation", Xenharmonikôn vol. 16, autumn 1995, pp. 118-125; reproduced on the web at The Wilson Archives

---

(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

I welcome feedback about this webpage: corrections, improvements, good links. Let me know if you don't understand something. return to the Microtonal Dictionary index return to my home page return to the Sonic Arts home page