49/48: Difference between revisions
Good opportunity to set this straight now |
→Temperaments: Improve readability |
||
| Line 15: | Line 15: | ||
== 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''' or '''semaphoresma''' | 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'''. | ||
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. | 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 == | ||
Revision as of 02:13, 14 October 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.