49/48: Difference between revisions
+"semaphore comma" as a name |
Good opportunity to set this straight now |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = large septimal diesis, slendro diesis, semaphore comma | | Name = large septimal diesis, slendro diesis, semaphore comma, semaphoresma | ||
| Color name = zz2, zozo 2nd,<br>Zozo comma | | Color name = zz2, zozo 2nd,<br>Zozo comma | ||
| Sound = Ji-49-48-csound-foscil-220hz.mp3 | | Sound = Ji-49-48-csound-foscil-220hz.mp3 | ||
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== Temperaments == | == Temperaments == | ||
49/48 is [[tempered out]] in [[15edo]] and [[19edo]], where the two intervals are equated, and the fourth is split in a perfect half. In the 2.3.7 [[subgroup]], this is known as the [[semaphore]] temperament, and the comma is thus known as the '''semaphore comma'''. It cannot be tempered out if all of the consonances of the 7-odd-limit are [[distinct]], but it ''can'' be equated with other commas; for example (49/48)/([[81/80]]) = [[245/243]], (49/48)/([[64/63]]) = [[1029/1024]], (49/48)/([[3125/3072]]) = [[3136/3125]], (49/48)/([[50/49]]) = [[2401/2400]], ([[128/125]])/(49/48) = [[6144/6125]], ([[36/35]])/(49/48) = [[1728/1715]]. | 49/48 is [[tempered out]] in [[15edo]] and [[19edo]], where the two intervals are equated, and the fourth is split in a perfect half. In the 2.3.7 [[subgroup]], this is known as the [[semaphore]] temperament, and the comma is thus known as the '''semaphore comma''' or '''semaphoresma'''. It cannot be tempered out if all of the consonances of the 7-odd-limit are [[distinct]], but it ''can'' be equated with other commas; for example (49/48)/([[81/80]]) = [[245/243]], (49/48)/([[64/63]]) = [[1029/1024]], (49/48)/([[3125/3072]]) = [[3136/3125]], (49/48)/([[50/49]]) = [[2401/2400]], ([[128/125]])/(49/48) = [[6144/6125]], ([[36/35]])/(49/48) = [[1728/1715]]. | ||
See [[Semaphoresmic family]] for the rank-3 family where it is tempered out. See [[Semaphoresmic clan]] for the rank-2 clan where it is tempered out. | |||
== See also == | == See also == | ||
* [[Medium comma]] | * [[Medium comma]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category: | [[Category:Semaphore]] | ||
[[Category: | [[Category:Semaphoresmic]] | ||
Revision as of 10:11, 25 August 2024
| Interval information |
slendro diesis,
semaphore comma,
semaphoresma
Zozo comma
reduced
[sound info]
49/48, the large septimal diesis (or slendro diesis), is a superparticular ratio spanning the small distance between a subminor third (7/6) and a supermajor second (8/7) or between the supermajor sixth (12/7) and the harmonic seventh (7/4). Measuring about 35.7 ¢, it is a medium comma; however, in classical Western music, this interval is not known as a comma as it is not tempered out in 12edo.
Temperaments
49/48 is tempered out in 15edo and 19edo, where the two intervals are equated, and the fourth is split in a perfect half. In the 2.3.7 subgroup, this is known as the semaphore temperament, and the comma is thus known as the semaphore comma or semaphoresma. It cannot be tempered out if all of the consonances of the 7-odd-limit are distinct, but it can be equated with other commas; for example (49/48)/(81/80) = 245/243, (49/48)/(64/63) = 1029/1024, (49/48)/(3125/3072) = 3136/3125, (49/48)/(50/49) = 2401/2400, (128/125)/(49/48) = 6144/6125, (36/35)/(49/48) = 1728/1715.
See Semaphoresmic family for the rank-3 family where it is tempered out. See Semaphoresmic clan for the rank-2 clan where it is tempered out.