Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited


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


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