Catalog of rank-4 temperaments: Difference between revisions
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A '''rank-4 temperament''' has a [[period]] and three additional independent [[generator]]s, for a total of four [[rank and codimension|dimensions]]. Typical examples include [[7-limit]] [[JI]], full 11-limit temperament with a one-dimensional [[comma basis]], and full 13-limit temperament with a two-dimensional comma basis. | A '''rank-4 temperament''' has a [[period]] and three additional independent [[generator]]s, for a total of four [[rank and codimension|dimensions]]. Typical examples include [[7-limit]] [[JI]], full 11-limit temperament with a one-dimensional [[comma basis]], and full 13-limit temperament with a two-dimensional comma basis. | ||
Temperaments in this catalog are ordered by [[Tenney height]]; temperaments whose commas have bigger denominators are listed first. | |||
== Cake (45/44) == | == Cake (45/44) == | ||
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[[Badness]] (Sintel): 0.164 | [[Badness]] (Sintel): 0.164 | ||
== Alfheim (10648/10647, 1664000/1663893) == | |||
A weak extension of [[Harmonisma#Harmonismatic|harmonismatic]] to add prime 5, which instead tempers out the [[Yggdrasil comma]], equating 2080/2079 with 2401/2400. It is a detemperament of [[freyr]]. | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Comma list]]: 10648/10647, 1664000/1663893 | |||
{{Mapping|1 0 0 0 −23 −33|0 1 0 0 6 8|0 0 1 0 −6 −9|0 0 0 1 11 16|legend=1}} | |||
: mapping generators: ~2, ~3, ~5, ~7 | |||
[[Optimal tuning]]: | |||
* [[WE]]: ~2 = 1199.9949{{c}}, ~3/2 = 701.9656{{c}}, ~5/4 = 386.3197{{c}}, ~7/4 = 968.8528{{c}} | |||
: [[error map]]: {{val|−0.0051 +0.0055 −0.0041 +0.0167 −0.0270 +0.0194}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9658{{c}}, ~5/4 = 386.3152{{c}}, ~7/4 = 968.8543{{c}} | |||
: error map: {{val|0.0000 +0.0108 +0.0015 +0.0284 −0.0172 +0.0305}} | |||
{{Optimal ET sequence|16, 17c, 25e, 33, 41, 58, 99ef, 154cef, 171ef, 212, 270, 581, 851, 867, 966, 1137, 1178, 1236, 1448, 1506, 2684, 4190, 4771, 7185, 7455, 17594…|legend=1}} | |||
[[Badness]] (Sintel): 0.637 | |||
== Unisquary (12005/11979) == | == Unisquary (12005/11979) == | ||