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~~

* [[WE]]: ~2592/2401 = 133.3357{{c}}, ~3/2 = 701.9772{{c}}, ~5/4 = 386.2717{{c}}

: [[error map]]: {{val| 0.~~0000~~ +0.~~0494~~ 0.~~0000~~ -0.~~1549~~ }}

: [[error map]]: {{val| +0.021 +0.043 -0.000 -0.135 }}

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

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

: error map: {{val| 0.~~0000~~ +0.~~0283~~ -0.~~0260~~ -0.~~1759~~ }}

: error map: {{val| 0.000 +0.028 -0.026 -0.176 }}

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

[[Badness]] (~~Smith~~): 0.~~502 × 10<sup>-3</sup>~~

[[Badness]] (Sintel): 2.21

== See also ==

@@ 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 16: / Line 16: @@
 {{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
+* [[WE]]: ~2592/2401 = 133.3357{{c}}, ~3/2 = 701.9772{{c}}, ~5/4 = 386.2717{{c}}
-: [[error map]]: {{val| 0.0000 +0.0494 0.0000 -0.1549 }}
+: [[error map]]: {{val| +0.021 +0.043 -0.000 -0.135 }}
-* [[CWE]]: ~2592/2401 = 133.3333, ~3/2 = 701.9833, ~5/4 = 386.2877
+* [[CWE]]: ~2592/2401 = 133.3333{{c}}, ~3/2 = 701.9833{{c}}, ~5/4 = 386.2877{{c}}
-: error map: {{val| 0.0000 +0.0283 -0.0260 -0.1759 }}
+: error map: {{val| 0.000 +0.028 -0.026 -0.176 }}
 {{Optimal ET sequence|legend=1| 27, 45, 63, 72, 99, 171, 441, 612 }}
-[[Badness]] (Smith): 0.502 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 2.21
 == See also ==