525/512: Difference between revisions

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.

Temperaments

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

Subgroup: 2.3.5.7

Mapping: [⟨1 0 0 9], ⟨0 1 0 -1], ⟨0 0 1 -2]]

POTE generators: ~3/2 = 695.5265, ~5/4 = 374.1745

Badness: 0.4765 × 10^-3

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| JI glyph =
+| Name = Avicenna's enharmonic diesis, avicennma
-| Ratio = 525/512
+| Color name = Lzyy1, lazoyoyo unison
-| Monzo = -9 1 2 1
+| Comma = yes
-| Cents = 43.40834
-| Name = Avicenna's enharmonic diesis, <br>avicennma
-| Color name =
-| FJS name = A1<sup>25, 7</sup>
-| Sound =
 }}
-'''525/512''', known as '''Avicenna's enharmonic diesis''' or '''avicennma''', is the interval between [[64/63]] and [[25/24]]. Tempering it out equates the two and leads to [[avicennmic temperaments]].
+'''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]].
+== Temperaments ==
+Tempering it out equates 64/63 with 25/24 and leads to the avicennmic temperament.
+=== Avicennmic temperament ===
+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]]
+* [[Avicennmic temperaments]], a collection of rank-2 temperaments where it is tempered out
-[[Category:7-limit]]
-[[Category:Medium comma]]
-[[Category:Interval]]
 [[Category:Avicennmic]]
+[[Category:Commas named after polymaths]]