Harmonisma: Difference between revisions
Rewrite opening paragraph to make it coherent |
Added alfheim |
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Here, for example 33/32 is 4/3 vs. 11/8; 91/88 is 22/13 vs. 7/4; 121/117 is 13/11 vs. 11/9; and 28/27 is 9/8 vs. 7/6. | Here, for example 33/32 is 4/3 vs. 11/8; 91/88 is 22/13 vs. 7/4; 121/117 is 13/11 vs. 11/9; and 28/27 is 9/8 vs. 7/6. | ||
=== Harmonismatic === | === Harmonismatic === | ||
Harmonismatic is a natural detemperament of parapyth where the last generator can be taken to be 352/351~364/363. [[Kalimera]] | Harmonismatic is a natural detemperament of [[parapyth]] where the last generator can be taken to be 352/351~364/363. [[Kalimera]] and [[Catalog of rank-4 temperaments#Alfheim (10648/10647, 1664000/1663893)|alfheim]] are [[weak extension]]<nowiki/>s to the whole 13-limit. | ||
[[Subgroup]]: 2.3.7.11.13 | [[Subgroup]]: 2.3.7.11.13 | ||
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[[Comma list]]: 10648/10647 | [[Comma list]]: 10648/10647 | ||
{ | [[Mapping]]: | ||
{| class="right-all" | |||
|[⟨ | |||
|1 | |||
|0 | |||
|0 | |||
|1 | |||
|3 | |||
|], | |||
|- | |||
|⟨ | |||
|0 | |||
|1 | |||
|0 | |||
|0 | |||
| -1 | |||
|], | |||
|- | |||
|⟨ | |||
|0 | |||
|0 | |||
|1 | |||
|1 | |||
|1 | |||
|], | |||
|- | |||
|⟨ | |||
|0 | |||
|0 | |||
|0 | |||
| -2 | |||
| -3 | |||
|]] | |||
|} | |||
: mapping generators: ~2, ~3, ~7, ~44/39 | : mapping generators: ~2, ~3, ~7, ~44/39 | ||
[[Optimal tuning]]: | [[Optimal tuning]]: | ||
* [[WE]]: ~2 = 1199.9974{{c}}, ~3/2 = 701.9619{{c}}, ~7/4 = 968.8378{{c}}, ~44/39 = 208.7715{{c}} | * [[WE]]: ~2 = 1199.9974{{c}}, ~3/2 = 701.9619{{c}}, ~7/4 = 968.8378{{c}}, ~44/39 = 208.7715{{c}} | ||
: [[error map]]: {{val| -0.003 +0.004 +0.007 -0.031 +0.024 }} | |||
: [[error map]]: {{val|-0.003 +0.004 +0.007 -0.031 +0.024}} | |||
* [[CWE]]: ~99/70 = 1200.0000{{c}}, ~3/2 = 701.9615{{c}}, ~7/4 = 968.8365{{c}}, ~44/39 = 208.7728{{c}} | * [[CWE]]: ~99/70 = 1200.0000{{c}}, ~3/2 = 701.9615{{c}}, ~7/4 = 968.8365{{c}}, ~44/39 = 208.7728{{c}} | ||
{{Optimal ET sequence | : error map: {{val|0.000 +0.007 +0.011 -0.027 +0.029}} | ||
{{Optimal ET sequence|12f, 16, 17, 41, 46, 58, 87, 103, 104, 149, 166, 207, 270, 431, 477, 701, 971, 1012, 1178, 1282, 1489, 1506, 1983, 7455, 7662, 9645, 11628, 13134, 15117|legend=1}} | |||
[[Badness]] (Sintel): 0.0382 | [[Badness]] (Sintel): 0.0382 | ||