Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited


diesis


    1. A variety of small intervals were called diesis in ancient Greek theory, including the so-called 'quarter-tones' of Aristoxenus. The term was revived in medieval Europe when the ancient Greek treatises became known and were translated into Latin. There was no one specific measurement.

    2. The infamous "fifth-tones" of Marchetto of Padua were named by him "dieses". According to my analysis, Marchetto's dieses were of five different sizes: approximately 22, 44, 45, 46, and 47 cents.

    This usage has a modern counterpart in the 31-eq [or 31-ET] system, in which the (slightly-smaller-than-)"fifth-tone" was named diesis by Fokker. This interval is 2(1/31) [= 0.39 Semitone = ~38.710 cents].

    3. This term is also used with a qualifying adjective to designate several specific 5-limit intervals. The two named in Ellis's chart [see p 453 of his translation of Helmholtz, On the Sensations of Tone] are the Small Diesis with a ratio of 3072:3125 [= 2-103-155 = 0.29 Semitone = ~29.614 cents], and the Great Diesis with a ratio of 125:128 [= 275-3 = 0.41 Semitone = ~41.059 cents].

    see also anomaly

    [from Joe Monzo, JustMusic: A New Harmony]


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