49/48: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = large septimal diesis, slendro diesis | | Name = large septimal diesis, slendro diesis, semaphore comma | ||
| 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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'''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{{cent}}, 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]]. | '''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{{cent}}, 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]]. | ||
49/48 is [[tempered out]] in [[15edo]] and [[19edo]], where the two intervals are equated, and the fourth is split in a perfect half. 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]]. | == 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]]. | |||
== See also == | == See also == | ||
Revision as of 08:49, 7 June 2024
| Interval information |
slendro diesis,
semaphore comma
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. 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 also
- Semiphore family, the rank-3 family where it is tempered out
- Slendro clan, the rank-2 clan where it is tempered out
- Medium comma
- List of superparticular intervals
- Gallery of just intervals