Mystery comma: Difference between revisions
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m Normalising usage of Infobox Interval |
Added a name based on its size |
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 70368744177664/68630377364883 | | Ratio = 70368744177664/68630377364883 | ||
| Name = 29-comma, mystery comma | | Name = 29-comma, mystery comma, Pythagorean 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>. | {{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'''. | ||
== Temperaments == | == Temperaments == | ||
Revision as of 01:09, 15 October 2024
| Interval information |
mystery comma,
Pythagorean 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, one can also call this interval the Pythagorean 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.