Septiennealimmal clan: Difference between revisions
m Units & misc. cleanup. + category |
Switch to Sintel's badness, WE & CWE tunings (1/) |
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== No-five septiennealimmal == | == No-five septiennealimmal == | ||
This rank-2 temperament is of interest to anyone who wants a different generator for the ennealimmal-like structure because it represents the part of ennealimmal supported by non-ennealimmal equal temperaments of interest that do well in the 2.3.7 subgroup, such as [[36edo]], which adds the [[1029/1024|gamelisma]], or [[63edo]], which in the 7-limit can be used for [[magic]] and in higher limits for [[parapyth]] among other things. | This rank-2 temperament simply equates a stack of nine [[7/6]] subminor thirds with two octaves. It is of interest to anyone who wants a different generator for the ennealimmal-like structure because it represents the part of ennealimmal supported by non-ennealimmal equal temperaments of interest that do well in the [[2.3.7 subgroup]], such as [[36edo]], which adds the [[1029/1024|gamelisma]], or [[63edo]], which in the 7-limit can be used for [[magic]] and in higher limits for [[parapyth]] among other things. | ||
[[Subgroup]]: 2.3.7 | [[Subgroup]]: 2.3.7 | ||
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[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[ | * [[WE]]: ~2592/2401 = 133.3357{{c}}, ~3/2 = 701.9772{{c}} | ||
: [[error map]]: {{val| 0. | : [[error map]]: {{val| +0.021 +0.043 -0.135 }} | ||
* [[ | * [[CWE]]: ~2592/2401 = 133.3333{{c}}, ~3/2 = 701.9833{{c}} | ||
: error map: {{val| 0.0000 +0. | : error map: {{val| 0.0000 +0.028 -0.176 }} | ||
{{Optimal ET sequence|legend=1| 27, 36, 99, 135, 171, 306, 4419d, 4725d, …, 8397dd, 8703dd }} | {{Optimal ET sequence|legend=1| 27, 36, 99, 135, 171, 306, 4419d, 4725d, …, 8397dd, 8703dd }} | ||
[[Badness]] (Sintel): 0.191 | |||
=== Septiennealic === | === Septiennealic === | ||
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A notable tuning of septiennealic not appearing in the optimal ET sequence is [[63edo]]. If we include a somewhat more complex mapping for 11 via {{nowrap| 36e & 63 }}, it will become the optimal patent val and largest in the sequence. | A notable tuning of septiennealic not appearing in the optimal ET sequence is [[63edo]]. If we include a somewhat more complex mapping for 11 via {{nowrap| 36e & 63 }}, it will become the optimal patent val and largest in the sequence. | ||
Subgroup: 2.3.7.13 | |||
Comma list: 169/168, 31213/31104 | |||
{{ | Subgroup-val mapping: {{mapping| 9 0 11 19 | 0 1 1 1 }} | ||
Optimal tunings: | |||
* WE: ~13/12 = 133.3847{{c}}, ~3/2 = 701.9342{{c}} | |||
* CWE: ~13/12 = 133.3333{{c}}, ~3/2 = 702.0763{{c}} | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 27, 36, 99, 135f, 171f }} | ||
Badness (Sintel): 0.540 | |||
=== Ennea === | === Ennea === | ||
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Comma list: 41503/41472, 43923/43904 | Comma list: 41503/41472, 43923/43904 | ||
Subgroup-val mapping: {{mapping| 9 0 11 24 | 0 2 2 1 }} | |||
: mapping generators: ~121/112, ~343/198 | |||
Optimal tunings: | Optimal tunings: | ||
* | * WE: ~121/112 = 133.3392{{c}}, 343/198 = 951.0013{{c}} (~99/98 = 17.6266{{c}}) | ||
* | * CWE: ~121/112 = 133.3333{{c}}, 343/198 = 950.9799{{c}} (~99/98 = 17.6466{{c}}) | ||
{{Optimal ET sequence|legend=0| 63, 72, 135, 342, 477, 1089, 1566 }} | |||
Badness (Sintel): 0.161 | |||
== Ennealimmal == | == Ennealimmal == | ||