49/48: Difference between revisions

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{{Infobox Interval

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

| Color name = zz2, zozo 2nd,<br>~~Zozo comma~~

| 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]].

'''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)]].

== 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 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:

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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 ==

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 {{Infobox Interval
 | Name = large septimal diesis, large septimal sixth-tone, slendro diesis, semaphore comma, semaphoresma
-| Color name = zz2, zozo 2nd,<br>Zozo comma
+| 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]].
+'''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)]].
 == Temperaments ==
-/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'''.
+/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:
@@ Line 26: / Line 28: @@
 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 ==