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]
(to download a zip file of the entire Dictionary, click here) |
|
I welcome
feedback about this webpage:
![]() ![]() ![]() |