Septiennealimmal clan: Difference between revisions

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== Ennealimmal ==

: ''For the 5-limit version, see [[~~Ennealimma~~ #Ennealimmal]].''

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Ennealimmal]].''

Ennealimmal tempers out the two smallest 7-limit [[superparticular]] commas, [[2401/2400]] and [[4375/4374]], leading to a temperament of unusual [[efficiency]]. It also tempers out the [[landscape comma]], which is (2401/2400)/(4375/4374), and the [[wizma]], which is (2401/2400)⋅(4375/4374). 7-limit ennealimmal's [[S-expression]]-based comma list is {[[4375/4374|S25/S27]], [[2401/2400|S49]]}.

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Badness (Sintel): 0.912

===== 2.3.5.7.11.13.19 subgroup =====

Subgroup: 2.3.5.7.11.13.19

Comma list: 1216/1215, 1540/1539, 2080/2079, 2376/2375, 2401/2400

Subgroup-val mapping: {{mapping| 9 1 1 12 -75 -106 -48 | 0 2 3 2 16 21 13 }}

Optimal tunings:

* WE: ~27/25 = 133.3209{{c}}, ~5/3 = 884.3968{{c}} (~36/35 = 48.8494{{c}})

* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.4722{{c}} (~36/35 = 48.8612{{c}})

{{Optimal ET sequence|legend=0| 99ef, 171ef, 270, 639h, 909h, 1179h }}

Badness (Sintel): 0.684

==== Enneabio ====

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[[Category:Septiennealimmal clan| ]]

[[Category:Temperament clans]]

[[Category:Catalogs of rank-2 temperaments]]

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 == Ennealimmal ==
 {{Main| Ennealimmal }}
-: ''For the 5-limit version, see [[Ennealimma #Ennealimmal]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Ennealimmal]].''
 Ennealimmal tempers out the two smallest 7-limit [[superparticular]] commas, [[2401/2400]] and [[4375/4374]], leading to a temperament of unusual [[efficiency]]. It also tempers out the [[landscape comma]], which is (2401/2400)/(4375/4374), and the [[wizma]], which is (2401/2400)⋅(4375/4374). 7-limit ennealimmal's [[S-expression]]-based comma list is {[[4375/4374|S25/S27]], [[2401/2400|S49]]}.
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 Badness (Sintel): 0.912
+===== 2.3.5.7.11.13.19 subgroup =====
+Subgroup: 2.3.5.7.11.13.19
+Comma list: 1216/1215, 1540/1539, 2080/2079, 2376/2375, 2401/2400
+Subgroup-val mapping: {{mapping| 9 1 1 12 -75 -106 -48 | 0 2 3 2 16 21 13 }}
+Optimal tunings:
+* WE: ~27/25 = 133.3209{{c}}, ~5/3 = 884.3968{{c}} (~36/35 = 48.8494{{c}})
+* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.4722{{c}} (~36/35 = 48.8612{{c}})
+{{Optimal ET sequence|legend=0| 99ef, 171ef, 270, 639h, 909h, 1179h }}
+Badness (Sintel): 0.684
 ==== Enneabio ====
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 [[Category:Septiennealimmal clan| ]] <!-- main article -->
 [[Category:Temperament clans]]
+[[Category:Catalogs of rank-2 temperaments]]