Definitions of tuning terms
© 1998 by Joseph L. Monzo
All definitions by Joe Monzo unless otherwise cited
Pythagorean Comma
Commas are small musical intervals between a note formed by one cycle of just intervals and the same note formed by another cycle of different just intervals. These commas prove important in constructing musical scales, and in notating musical chords and musical pitches.
The Pythagorean comma is the difference between 12 just perfect fifths up and 7 octaves up:
[from Brian McLaren]
The ratio 531441/ 524288, in
JustMusic prime-factor notation
designated as 312, with an
interval size of approximately 0.23 Semitones
[= 23.460+ cents].
It is the difference between the
Pythagorean or 3-Limit "tritone"
or "augmented 4th" of approximately 6.12 Semitones
[= 729/512 = 36 = 611.730+ cents] and the
Pythagorean or 3-Limit "diminished 5th"
of approximately 5.88 Semitones [= 1024/729 = 3-6 = 588.269+ cents].
It was first described c. 300 BC by pseudo-Euclid in Divisions of
the Canon.
[from Joe Monzo, JustMusic: A New Harmony]
(to download a zip file of the entire Dictionary, click here) |
|
I welcome
feedback about this webpage:
![]() ![]() ![]() |