Septimal ennealimma: Difference between revisions

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== Temperaments ==

In the 2.3.7 subgroup, tempering it out leads to the 2.3.7-subgroup [[restriction]] of the [[ennealimmal ~~temperament~~]], which is the head of the [[septiennealimmal clan]]. It can only possibly be tempered out in an edo if that edo is a multiple of 9.

In the 2.3.7 subgroup, tempering it out leads to the 2.3.7-subgroup [[restriction]] of the [[ennealimmal]] temperament, which is the head of the [[septiennealimmal clan]]. It can only possibly be tempered out in an edo if that edo is a multiple of 9.

In the full 7-limit, tempering it out leads to the '''septiennealimmal temperament''' (''cf''. septimal ennealimmal temperament). You may find a list of good equal temperaments that support this temperament below.

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: mapping generators: ~2592/2401, ~3, ~5

[[Optimal tuning]]s:

* [[CTE]]: ~2592/2401 = 133.3333, ~3/2 = 702.0044, ~5/4 = 386.3137

: [[error map]]: {{val| 0.0000 +0.0494 0.0000 -0.1549 }}

* [[CWE]]: ~2592/2401 = 133.3333, ~3/2 = 701.9833, ~5/4 = 386.2877

: error map: {{val| 0.0000 +0.0283 -0.0260 -0.1759 }}

{{Optimal ET sequence|legend=1| 27, 45, 63, 72, 99, 171, 441, 612 }}

Badness (Smith): 0.502 × 10<sup>-3</sup>

[[Badness]] (Smith): 0.502 × 10<sup>-3</sup>

== See also ==

* [[Unnoticeable comma]]

* [[Ennealimma]]

[[Category:Septiennealimmal]]

[[Category:Commas named for their periods per equave]]

@@ Line 8: / Line 8: @@
 == Temperaments ==
-In the 2.3.7 subgroup, tempering it out leads to the 2.3.7-subgroup [[restriction]] of the [[ennealimmal temperament]], which is the head of the [[septiennealimmal clan]]. It can only possibly be tempered out in an edo if that edo is a multiple of 9.
+In the 2.3.7 subgroup, tempering it out leads to the 2.3.7-subgroup [[restriction]] of the [[ennealimmal]] temperament, which is the head of the [[septiennealimmal clan]]. It can only possibly be tempered out in an edo if that edo is a multiple of 9.
 In the full 7-limit, tempering it out leads to the '''septiennealimmal temperament''' (''cf''. septimal ennealimmal temperament). You may find a list of good equal temperaments that support this temperament below.
@@ Line 17: / Line 17: @@
 {{Mapping|legend=1| 9 0 0 11 | 0 1 0 1 | 0 0 1 0 }}
 : mapping generators: ~2592/2401, ~3, ~5
+[[Optimal tuning]]s:
+* [[CTE]]: ~2592/2401 = 133.3333, ~3/2 = 702.0044, ~5/4 = 386.3137
+: [[error map]]: {{val| 0.0000 +0.0494 0.0000 -0.1549 }}
+* [[CWE]]: ~2592/2401 = 133.3333, ~3/2 = 701.9833, ~5/4 = 386.2877
+: error map: {{val| 0.0000 +0.0283 -0.0260 -0.1759 }}
 {{Optimal ET sequence|legend=1| 27, 45, 63, 72, 99, 171, 441, 612 }}
-Badness (Smith): 0.502 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.502 × 10<sup>-3</sup>
 == See also ==
-* [[Unnoticeable comma]]
 * [[Ennealimma]]
 [[Category:Septiennealimmal]]
 [[Category:Commas named for their periods per equave]]