49/48: Difference between revisions

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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]]. It 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-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.

{{Infobox Interval

| Icon =

| Ratio = 49/48

| Monzo = -4 -1 0 2

| Cents = 35.69681

| Name = large septimal diesis <br> slendro diesis

| Color name = zz2, zozo comma

| Sound = Ji-{{#regex:{{PAGENAME}}|/(\S+)\/(\S+)/|\1-\2}}-csound-foscil-220hz.mp3

}}

The '''large septimal diesis''' (or '''slendro diesis'''), '''49/48''' (35.6968 [[cent]]s), 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]]). It 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-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.

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

In classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo]].

[[Category:~~interval~~]]

== See also ==

[[Category:~~septimal~~]]

* [[Medium comma]]

* [[Gallery of just intervals]]

* [https://en.wikipedia.org/wiki/Septimal_diesis Septimal diesis - Wikipedia]

[[Category:7-limit]]

[[Category:Septimal]]

[[Category:Interval ratio]]

[[Category:Medium comma]]

[[Category:Superparticular]]

[[Category:Listen]]

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-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]]. It 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-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.
+{{Infobox Interval
+| Icon =
+| Ratio = 49/48
+| Monzo = -4 -1 0 2
+| Cents = 35.69681
+| Name = large septimal diesis <br> slendro diesis
+| Color name = zz2, zozo comma
+| Sound = Ji-{{#regex:{{PAGENAME}}|/(\S+)\/(\S+)/|\1-\2}}-csound-foscil-220hz.mp3
+}}
+The '''large septimal diesis''' (or '''slendro diesis'''), '''49/48''' (35.6968 [[cent]]s), 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]]). It 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-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.
-[http://en.wikipedia.org/wiki/Septimal_diesis http://en.wikipedia.org/wiki/Septimal_diesis]
+In classical Western music, this interval is not known as a [[comma]] as it is not tempered out in [[12edo]].
-[[Category:interval]]
+== See also ==
-[[Category:septimal]]
+* [[Medium comma]]
+* [[Gallery of just intervals]]
+* [https://en.wikipedia.org/wiki/Septimal_diesis Septimal diesis &#45; Wikipedia]
+[[Category:7-limit]]
+[[Category:Septimal]]
+[[Category:Interval ratio]]
+[[Category:Medium comma]]
+[[Category:Superparticular]]
+[[Category:Listen]]