Mystery comma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 70368744177664/68630377364883 | | Ratio = 70368744177664/68630377364883 | ||
| Name = 29-comma, mystery comma, Pythagorean semilimma | | Name = 29-comma, mystery comma, Pythagorean quadridietic semilimma | ||
| Color name = Wa-29, s<sup>4</sup>w4 | | Color name = Wa-29, s<sup>4</sup>w4 | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
{{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]], one can also call this interval the '''Pythagorean semilimma'''. | {{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 a quadruple-diminished fourth, one can also call this interval the '''Pythagorean quadridietic semilimma'''. | ||
== Temperaments == | == Temperaments == | ||
Revision as of 01:27, 15 October 2024
| Interval information |
mystery comma,
Pythagorean quadridietic 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 a quadruple-diminished fourth, one can also call this interval the Pythagorean quadridietic 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.