Septiennealimmal clan: Difference between revisions

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@@ Line 82: / Line 82: @@
 [[Badness]] (Sintel): 0.0914
-=== 11-limit ===
+=== Enneabiotic ===
-The undecimal ennealimmal temperament can be described as {{nowrap| 99e & 171e }}, which tempers out [[5632/5625]] (vishdel comma) and [[19712/19683]] (symbiotic comma).
+Enneabiotic ({{nowrap| 99e & 171e }}) tempers out [[5632/5625]] (vishdel comma) and [[19712/19683]] (symbiotic comma). It is catalogued as ''undecimal ennealimmal'' in [[Graham Breed]]'s [https://x31eq.com/temper/ Temperament Finder].
 Subgroup: 2.3.5.7.11
@@ Line 100: / Line 100: @@
 ==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 2080/2079, 2401/2400, 4375/4374, 5632/5625
+Mapping: {{mapping| 9 1 1 12 -75 -106 | 0 2 3 2 16 21 }}
+Optimal tunings:
+* WE: ~27/25 = 133.3215{{c}}, ~5/3 = 884.4027{{c}} (~36/35 = 48.8479{{c}})
+* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.4745{{c}} (~36/35 = 48.8589{{c}})
+{{Optimal ET sequence|legend=0| 99ef, 171ef, 270, 639, 909, 1179, 2088bce }}
+Badness (Sintel): 0.912
+==== Enneabio ====
 Subgroup: 2.3.5.7.11.13
@@ Line 144: / Line 159: @@
 Badness (Sintel): 1.25
-==== Ennealimmalis ====
+=== Ennealympic ===
-Subgroup: 2.3.5.7.11.13
+Ennealympic ({{nowrap| 99 & 171 }}, formerly ''ennealimmia'') is an alternative extension which tempers out [[131072/130977]] (olympia).
-Comma list: 2080/2079, 2401/2400, 4375/4374, 5632/5625
-Mapping: {{mapping| 9 1 1 12 -75 -106 | 0 2 3 2 16 21 }}
-Optimal tunings:
-* WE: ~27/25 = 133.3215{{c}}, ~5/3 = 884.4027{{c}} (~36/35 = 48.8479{{c}})
-* CWE: ~27/25 = 133.3333{{c}}, ~5/3 = 884.4745{{c}} (~36/35 = 48.8589{{c}})
-{{Optimal ET sequence|legend=0| 99ef, 171ef, 270, 639, 909, 1179, 2088bce }}
-Badness (Sintel): 0.912
-=== Ennealimmia ===
-The ennealimmia temperament is an alternative extension and can be described as {{nowrap| 99 & 171 }}, which tempers out [[131072/130977]] (olympia).
 Subgroup: 2.3.5.7.11
@@ Line 223: / Line 223: @@
 === Ennealimnic ===
 {{Distinguish| Ennealimmic }}
+{{See also| Chords of ennealimnic }}
 Ennealimnic ({{nowrap| 72 & 171 }}) equates 11/9 with 27/22, 49/40, and 60/49 as a neutral third interval.
@@ Line 243: / Line 244: @@
 Badness (Sintel): 0.673
-See also: [[Chords of ennealimnic]]
 ==== 13-limit ====
@@ Line 473: / Line 472: @@
 * CWE: ~27/26 = 66.6667{{c}}, ~26/15 = 951.0386{{c}}
-{{Optimal ET sequence|legend=1| 72, 198g, 270 }}
+{{Optimal ET sequence|legend=0| 72, 198g, 270 }}
 Badness (Sintel): 0.812
@@ Line 523: / Line 522: @@
 Badness (Sintel): 0.927
-=== Semiennealimmal ===
+=== Ennealimmapine ===
-Semiennealimmal tempers out [[4000/3993]], and uses a ~140/121 semifourth generator. Notably, however, two generator steps do not reach ~4/3, despite that the name may suggest so. In fact, it splits the generator of ennealimmal into three.
+Ennealimmapine (formerly ''semiennealimmal'') tempers out [[4000/3993]], and uses a ~140/121 semifourth generator, six of which and 1/3 octave give the 3rd harmonic. Perhaps a better generator is the [[secor]], ~77/72, six of which give the perfect fifth, or the [[ptolemisma]], six of which and 1/3 octave give the perfect fourth.
 Subgroup: 2.3.5.7.11