525/512: Difference between revisions

(3 intermediate revisions by 2 users not shown)

Line 1:

{{Infobox Interval

| Name = Avicenna's enharmonic diesis~~, avicennma~~

| Name = avicennma, Avicenna's enharmonic diesis

| Color name = Lzyy1, lazoyoyo unison

| Comma = yes

}}

'''525/512''', the '''avicennma''', also known as ''Avicenna's enharmonic diesis'', is a [[medium comma|medium]] [[7-limit]] [[comma]] measuring about 43.4 [[cent]]s. It is the difference between [[64/63]] and [[25/24]], or between [[32/25]] and [[21/16]].

~~'''525/512''', known as '''Avicenna's enharmonic diesis''' or '''avicennma''', is~~ the ~~[[7~~-limit]] [[~~medium comma~~]] ~~between~~ [[64/63]] and [[~~25/24~~]], ~~or between~~ [[32/25]] ~~and~~ [[21/16]].

In the 11-limit, it factors into ([[45/44]])⋅([[385/384]]), and in the [[2.3.5.7.13 subgroup]], ([[65/64]])⋅([[105/104]]).

== Temperaments ==

Tempering it out equates 64/63 with 25/24 and leads to the avicennmic temperament.

[[Tempering out]] this comma equates 64/63 with 25/24 and leads to the [[avicennmic]] temperament. Because it flattens [[3/2]] and [[5/4]], it is a natural choice to further temper out [[81/80]], resulting in [[flattone]] temperament.

~~=== Avicennmic temperament ===~~

See [[Avicennmic temperaments]] for a collection of rank-2 temperaments where it is tempered out.

~~Subgroup: 2.3.5.7~~

~~[[Comma list]]: 525/512~~

~~[[Mapping]]: [{{val| 1 0 0 9 }}, {{val| 0 1 0 -1 }}, {{val| 0 0 1 -2 }}]~~

~~[[POTE generator]]s: ~3/2 = 695.5265, ~5/4 = 374.1745~~

~~{{Optimal ET sequence|legend=1| 7, 9, 10, 16, 19, 45, 64cd, 93cdd, 119bccdd, 138bccdd }}~~

~~[[Badness]]: 0.4765 × 10<sup>-3</sup>~~

== See ~~also ==~~

* [[Medium comma]]

* [[Avicennmic temperaments]], a collection of rank-2 temperaments where it is tempered out

[[Category:Avicennmic]]

[[Category:Commas named after polymaths]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = Avicenna's enharmonic diesis, avicennma
+| Name = avicennma, Avicenna's enharmonic diesis
 | Color name = Lzyy1, lazoyoyo unison
 | Comma = yes
 }}
+'''525/512''', the '''avicennma''', also known as ''Avicenna's enharmonic diesis'', is a [[medium comma|medium]] [[7-limit]] [[comma]] measuring about 43.4 [[cent]]s. It is the difference between [[64/63]] and [[25/24]], or between [[32/25]] and [[21/16]].
-'''525/512''', known as '''Avicenna's enharmonic diesis''' or '''avicennma''', is the [[7-limit]] [[medium comma]] between [[64/63]] and [[25/24]], or between [[32/25]] and [[21/16]].
+In the 11-limit, it factors into ([[45/44]])⋅([[385/384]]), and in the [[2.3.5.7.13 subgroup]], ([[65/64]])⋅([[105/104]]).
 == Temperaments ==
-Tempering it out equates 64/63 with 25/24 and leads to the avicennmic temperament.
+[[Tempering out]] this comma equates 64/63 with 25/24 and leads to the [[avicennmic]] temperament. Because it flattens [[3/2]] and [[5/4]], it is a natural choice to further temper out [[81/80]], resulting in [[flattone]] temperament.
-=== Avicennmic temperament ===
+See [[Avicennmic temperaments]] for a collection of rank-2 temperaments where it is tempered out.
-Subgroup: 2.3.5.7
-[[Comma list]]: 525/512
-[[Mapping]]: [{{val| 1 0 0 9 }}, {{val| 0 1 0 -1 }}, {{val| 0 0 1 -2 }}]
-[[POTE generator]]s: ~3/2 = 695.5265, ~5/4 = 374.1745
-{{Optimal ET sequence|legend=1| 7, 9, 10, 16, 19, 45, 64cd, 93cdd, 119bccdd, 138bccdd }}
-[[Badness]]: 0.4765 × 10<sup>-3</sup>
-== See also ==
-* [[Medium comma]]
-* [[Avicennmic temperaments]], a collection of rank-2 temperaments where it is tempered out
 [[Category:Avicennmic]]
 [[Category:Commas named after polymaths]]