Mystery comma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 70368744177664/68630377364883 | |||
| Ratio = 70368744177664 / 68630377364883 | | Name = mystery comma, 29-comma, Pythagorean quadruple-diminished fourth, Pythagorean tridietic semilimma | ||
| Color name = Wa-29, s<sup>4</sup>w4 | |||
| Comma = yes | |||
| Name = 29-comma, | |||
| Color name = s<sup>4</sup>w4 | |||
| | |||
}} | }} | ||
{{monzo|46 -29}}, the '''29-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 '''mystery comma''' or '''29-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>. When treated as an interval in its own right, there are actually two very good descriptive names for this interval. Firstly, and most obviously, it can be called the '''Pythagorean quadruple-diminished fourth''', however, because it is also almost exactly half of the traditional [[Pythagorean limma]] (a stack of two mystery commas differing from the limma by [[Mercator's comma]]) 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 == | ||
Tempering out | 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|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]]. | ||
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== See also == | == See also == | ||
* [[ | * [[Medium comma]] | ||
* [[ | * [[29th-octave temperaments]] | ||
[[Category:29edo]] | [[Category:29edo]] | ||
[[Category: | [[Category:Mystery]] | ||
[[Category:Commas with unknown etymology]] | |||
Latest revision as of 01:26, 29 January 2025
| Interval information |
29-comma,
Pythagorean quadruple-diminished fourth,
Pythagorean tridietic semilimma
reduced subharmonic
[46 -29⟩, the mystery comma or 29-comma of 43.305 cents, is the difference between 46 octaves and 29 fifths, in other words 246/329. When treated as an interval in its own right, there are actually two very good descriptive names for this interval. Firstly, and most obviously, it can be called the Pythagorean quadruple-diminished fourth, however, because it is also almost exactly half of the traditional Pythagorean limma (a stack of two mystery commas differing from the limma by Mercator's comma) 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.