No-fives subgroup temperaments: Difference between revisions
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[[Tp tuning #T2 tuning|RMS error]]: 0.2054 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.2054 cents | ||
=== Shoal === | |||
The 2.3.13.23 subgroup is remarkable for containing not one but two [[superparticular]] intervals as small as these. Tempering out both of them gives us a rank-2 temperament where a sharp whole tone of [[26/23]] is the generator, two of which stack to a [[23/18]] supermajor third, and eight of which stack to a [[8/3]] perfect eleventh. [[17edo]] is a trivial tuning where 26/23 is equated to [[9/8]], tempering out the comma [[208/207]]. More accurate tunings of shoal create a 17-note [[MOS]] scale, serving as a [[circulating temperament]] of 17edo, where 208/207 is the [[chroma]] between large and small steps. | |||
[[Subgroup]]: 2.3.13.23 | |||
[[Comma list]]: [[3888/3887]], [[12168/12167]] | |||
{{Mapping|legend=2|1 3 6 7|0 -8 -13 -14}} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1/1, ~26/23 = 212.261 | |||
{{Optimal ET sequence|legend=1|11fi, 17, 79, 96, 113, 130, 147, 424, 571, 1289, 1860, 3149 }} | |||
Badness (Dirichlet): 0.021 | |||
== Temperaments with a higher-limit gene == | == Temperaments with a higher-limit gene == | ||