Symbiotic comma: Difference between revisions
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== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma in the 11-limit results in the rank-4 '''symbiotic''' temperament (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]), or in the 2.3.7.11 subgroup, the '''symbiotian''' temperament. In either case, it identifies [[11/8]] by an apotome over [[9/7]], [[11/6]] by an apotome over [[12/7]], and [[11/9]] by an apotome over [[8/7]]. Finally, it identifies 11/9 by a [[256/243|limma]] below 9/7. | [[Tempering out]] this comma in the 11-limit results in the rank-4 '''symbiotic''' temperament (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]), or in the 2.3.7.11 subgroup, the '''symbiotian''' temperament. In either case, it identifies [[11/8]] by an apotome over [[9/7]], [[11/6]] by an apotome over [[12/7]], and [[11/9]] by an apotome over [[8/7]]. Finally, it identifies 11/9 by a [[256/243|limma]] below 9/7. | ||
=== Symbiotian === | |||
[[Subgroup]]: 2.3.7.11 | |||
[[Comma list]]: 19712/19683 | |||
{{Mapping|legend=2| 1 0 0 -8 | 0 1 0 9 | 0 0 1 -1 }} | |||
: mapping generators: ~2, ~3, ~7 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.9290{{c}}, ~3/2 = 702.2265{{c}}, ~7/4 = 968.8979{{c}} | |||
: [[error map]]: {{val| -0.071 +0.201 -0.070 -0.106 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2440{{c}}, ~7/4 = 968.8593{{c}} | |||
: error map: {{val| 0.000 +0.289 +0.033 +0.019 }} | |||
{{Optimal ET sequence|legend=1| 41, 58, 77, 94, 118, 135, 716, 733, 851, 868, 1003, 1138, 1273, 1449, 1584, 1719, 1854 }} | |||
[[Badness]] (Sintel): 0.336 | |||
== Etymology == | == Etymology == | ||