49/48: Difference between revisions
m septimal is synonymous to 7-limit |
Undo revision 230355 by VectorGraphics (talk) Tag: Undo |
||
| (32 intermediate revisions by 13 users not shown) | |||
| Line 6: | Line 6: | ||
}} | }} | ||
{{Infobox Interval | {{Infobox Interval | ||
| Name = large septimal diesis, large septimal sixth-tone, slendro diesis, semaphore comma, semaphoresma | |||
| Color name = zz2, zozo 2nd,<br>zzM, zozoma | |||
| Name = large septimal diesis, | |||
| Color name = zz2, zozo | |||
| Sound = Ji-49-48-csound-foscil-220hz.mp3 | | Sound = Ji-49-48-csound-foscil-220hz.mp3 | ||
| Comma = yes | |||
}} | }} | ||
{{Wikipedia|Septimal diesis}} | |||
'''49/48''', the '''large septimal diesis''' (a.k.a. '''large septimal sixth-tone''' or '''slendro diesis'''), is a [[7-limit]] [[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|12tet]]. | |||
This interval has a function similar to [[25/24]] in that it separates the [[7/6]] and [[8/7]] intervals in a [[6:7:8]] triad, similarly to how [[25/24]] separates [[5/4]] and [[6/5]] in a [[4:5:6]] triad. The 6:7:8 triad consists of odd [[harmonic]]s [[1/1|1]], [[3/1|3]], and [[7/1|7]] [[octave reduced]] to span the [[4/3|perfect fourth]], while the 4:5:6 triad consists of odd harmonics 1, 3, and 5 octave reduced to span the [[3/2|perfect fifth]]. In that regard, tempering out 49/48 can be considered a form of [[exotemperament|exotempering]] that neutralizes the 6:7:8 chord and equates it with its inverse [[21:24:28|1/(8:7:6)]], just like how [[dicot]], which tempers out 25/24, neutralizes the 4:5:6 chord and equates it with its inverse [[10:12:15|1/(6:5:4)]]. | |||
In | == Temperaments == | ||
49/48 is [[tempered out]] in [[15edo]] and [[19edo]], where 7/6 and 8/7 are equated, and the fourth is split in a perfect half. 3/1 is also split into two [[7/4]]~[[12/7]]'s. 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. | |||
== Approximations == | |||
{{interval edo approximation|min_edo=5}} | |||
== 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]] | ||
[[Category: | [[Category:Commas named for how they divide the fourth]] | ||
[[Category: | [[Category:Commas named after musical traditions]] | ||