49/48: Difference between revisions

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{{Infobox Interval

| Name = large septimal diesis, slendro diesis

| 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''' (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''' (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]].

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 ~~[[distinctly consistent|~~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)]].

== 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 ==

== 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]]

[[Category:~~Slendro~~]]

[[Category:Semaphore]]

[[Category:~~Semiphore~~]]

[[Category:Semaphoresmic]]

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

[[Category:Commas named after musical traditions]]

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 }}
 {{Infobox Interval
-| Name = large septimal diesis, slendro diesis
+| 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''' (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''' (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]].
-/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 [[distinctly consistent|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)]].
+== Temperaments ==
+/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 ==
-* [[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]]
-[[Category:Slendro]]
+[[Category:Semaphore]]
-[[Category:Semiphore]]
+[[Category:Semaphoresmic]]
+[[Category:Commas named for how they divide the fourth]]
+[[Category:Commas named after musical traditions]]