Definitions of tuning terms
© 1998 by Joseph L. Monzo
All definitions by Joe Monzo unless otherwise cited
schisma
A term coined by Alexander Ellis in his translation of Helmhotz's
On the Sensations of Tone, and originally spelled skhisma.
It designates an extremely small
interval, just barely discernible
to human
pitch-detection.
Unqualified, it is the difference between
As no combination of different
prime numbers
will ever produce ratios
which have exactly the same interval size,
if cycles of a particular
ratio are calculated far enough, very small
intervals like this eventually appear
between ratios having different sets of prime
factors. When these are under
consideration, the term schisma is qualified
with a latin word designating
the higher prime, with the assumption that the
other prime being compared is
a more familiar one, almost always 3.
Thus, we get the septimal schisma,
which is the difference between
Likewise, there is the nondecimal schisma, which is the difference between
Schismas are a key element in my concept of bridging.
I refer to the three schismas explained here as the 3==5, 3==7, and 3==19 bridges,
respectively.
see also
anomaly
[from Joe Monzo, JustMusic: A New Harmony]
51[= 5/4 = 3.86 Semitone =
~ 386.313 cents]
and
3-8 [= 8192/6561 = 3.84 Semitone = ~ 384.359 cents]
and has an interval size of approximately
0.02 Semitone
[= 3851 = 32805/32768 = ~ 1.953 cents].
71[= 7/4 = 9.69 Semitone = ~ 968.825 cents]
and
3-14 [= 8388608/4782969 = 9.73 Semitone =
~ 972.629 cents]
and has an interval size of approximately
0.04 Semitones [= 3-147-1
= 33554432/33480783 = ~ 3.804 cents].
191
[= 19/16 = 2.98 Semitone = ~ 297.513 cents]
and the 'standard' Pythagorean "minor 3rd"
3-3 [= 32/27 = 2.94 Semitone = ~ 294.134 cents],
and which also has an interval size of approximately
0.04 Semitones [33191 = 513/512 = ~ 3.378 cents].
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