Mystery comma: Difference between revisions
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{{monzo|46 -29}}, the '''29-comma''' or '''mystery comma''' of 43.305 cents, is the difference between 46 octaves and 29 fifths, in other words 2<sup>46</sup>/3<sup>29</sup>. Because this comma is a Pythagorean interval and is almost exactly half of the traditional [[Pythagorean limma]] in addition to being | {{monzo|46 -29}}, the '''29-comma''' or '''mystery comma''' of 43.305 cents, is the difference between 46 octaves and 29 fifths, in other words 2<sup>46</sup>/3<sup>29</sup>. Because this comma is a Pythagorean interval and is almost exactly half of the traditional [[Pythagorean limma]] in addition to being displaced from the unison's scale degree by three, one can also call this interval the '''Pythagorean tridietic semilimma'''. | ||
== Temperaments == | == Temperaments == | ||
Revision as of 01:32, 15 October 2024
| Interval information |
mystery comma,
Pythagorean quadruple-diminished fourth,
Pythagorean tridietic semilimma
reduced subharmonic
[46 -29⟩, the 29-comma or mystery comma of 43.305 cents, is the difference between 46 octaves and 29 fifths, in other words 246/329. Because this comma is a Pythagorean interval and is almost exactly half of the traditional Pythagorean limma in addition to being displaced from the unison's scale degree by three, one can also call this interval the Pythagorean tridietic semilimma.
Temperaments
Tempering out this comma splits the octave into 29 equal parts and maps the harmonic 3 to 17\29, leading to the 5-limit version of mystery temperament. For EDOs up to 400, the 29-comma is tempered out if and only if 29 divides it, for example 29edo, 58edo or 87edo.