49/48: Difference between revisions

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<~~span style~~=~~"display: block; text~~-~~align: right~~;">[[~~:de:49/48~~|~~Deutsch~~]]~~</span>~~

{{interwiki

| de = 49/48

| en = 49/48

| es =

| ja =

}}

{{Infobox Interval

| Name = large septimal diesis, large septimal sixth-tone, slendro diesis, semaphore comma, semaphoresma

| Color name = zz2, zozo 2nd,<br>zzM, zozoma

| Sound = Ji-49-48-csound-foscil-220hz.mp3

| Comma = yes

}}

'''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]].

~~The large septimal or slendro diesis, 49~~/~~48 (35.6968~~ [[~~cent|cents~~]]~~), is a~~ [[~~superparticular|superparticular~~]] ~~ratio spanning the small distance between~~ a ~~subminor third of~~ [[7/6|7/6]] ~~and a supermajor second~~ of [[8/7|8/7]]~~. It is tempered out in~~ [[~~15edo|15edo~~]] ~~and~~ [[~~19edo~~|~~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~~-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~~.

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)]].

[~~http:~~//en.~~wikipedia~~.~~org~~/~~wiki~~/~~Septimal_diesis http:~~//en.~~wikipedia~~.~~org/wiki/Septimal_diesis~~] [[Category:~~interval~~]]

== Temperaments ==

[[Category:~~septimal~~]]

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 ==

== See also ==

* [[Medium comma]]

* [[List of superparticular intervals]]

* [[Gallery of just intervals]]

[[Category:Semaphore]]

[[Category:Semaphoresmic]]

[[Category:Commas named for how they divide the fourth]]

[[Category:Commas named after musical traditions]]

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-<span style="display: block; text-align: right;">[[:de:49/48|Deutsch]]</span>
+{{interwiki
+| de = 49/48
+| en = 49/48
+| es =
+| ja =
+}}
+{{Infobox Interval
+| Name = large septimal diesis, large septimal sixth-tone, slendro diesis, semaphore comma, semaphoresma
+| Color name = zz2, zozo 2nd,<br>zzM, zozoma
+| 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]].
-The large septimal or slendro diesis, 49/48 (35.6968 [[cent|cents]]), is a [[superparticular|superparticular]] ratio spanning the small distance between a subminor third of [[7/6|7/6]] and a supermajor second of [[8/7|8/7]]. It is tempered out in [[15edo|15edo]] and [[19edo|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-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.
+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)]].
-[http://en.wikipedia.org/wiki/Septimal_diesis http://en.wikipedia.org/wiki/Septimal_diesis]      [[Category:interval]]
+== Temperaments ==
-[[Category:septimal]]
+/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 ==
+* [[Medium comma]]
+* [[List of superparticular intervals]]
+* [[Gallery of just intervals]]
+[[Category:Semaphore]]
+[[Category:Semaphoresmic]]
+[[Category:Commas named for how they divide the fourth]]
+[[Category:Commas named after musical traditions]]