57/56: Difference between revisions
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57/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup, called [[hendrix]]. You can also temper it out in a rank-2 temperament in 2.3.19/7, called surprise. | 57/56 is a comma of the 2.3.7.19 subgroup, and on that subgroup, patent vals tempering it out include those from 9, 12, 14, 17 and 26. The comma defines a rank three temperament on this subgroup, called [[hendrix]]. You can also temper it out in a rank-2 temperament in 2.3.19/7, called surprise. | ||
== Temperaments == | |||
=== Hendrix === | |||
This is the [[rank-3]] temperament tempering out the hendrix comma, 57/56. This is simply the most sensible name for this temperament. | |||
[[Subgroup]]: 2.3.7.19 | |||
[[Comma list]]: 57/56 | |||
{{Mapping|legend=2| 1 0 0 3 | 0 1 0 -1 | 0 0 1 1 }} | |||
: mapping generators: ~2, ~3, ~7 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1202.4345{{c}}, ~3/2 = 697.4314{{c}}, ~7/4 = 970.3487{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 697.3981{{c}}, ~7/4 = 972.1990{{c}} | |||
{{Optimal ET sequence|legend=1| 5, 9, 12, 14, 17, 26, 31h }} | |||
[[Badness]] (Sintel): 0.155 | |||
== See also == | == See also == | ||