Subgroup temperaments: Difference between revisions
→Fractional subgroup temperaments: +poggers |
+spog (2.15.55) |
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{{Optimal ET sequence|legend=1| 5, 13, 31 }} | {{Optimal ET sequence|legend=1| 5, 13, 31 }} | ||
== 2.15.55 subgroup == | |||
=== Spog === | |||
This temperament produces [[Slendro_clan#Superpelog|superpelog]]-like [[5L 4s|semiquartal]] scales while being more accurate ([[Subgroup temperaments#2.15.189.55.325.279|see]] rational approximations to their intervals). | |||
[[Subgroup]]: 2.15.55 | |||
[[Comma list]]: [[100663296/100656875]] | |||
{{Mapping|legend=2| 1 0 5 | 0 5 1 }} | |||
[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.655 | |||
[[Support]]ing [[ET]]s: 5, 9, 13[-15], 14, 19[+15], 23, 32, 37, 41, 50, 55, 64, 73, 78, 87, 96, 101, 105, 119, 128, 151, 183, 206, 311 | |||
==== 2.15.55.325 ==== | |||
[[Subgroup]]: 2.15.55.325 | |||
[[Comma list]]: [[4225/4224]], [[6656/6655]] | |||
{{Mapping|legend=2| 1 0 5 6 | 0 5 1 3 }} | |||
[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.647 | |||
[[Support]]ing [[ET]]s: 5, 9, 13[-15], 14, 23, 32, 37, 41, 50, 55, 64, 73, 78, 87, 96, 101, 105, 119, 128, 151, 183, 206, 311 | |||
==== 2.15.189.55.325 ==== | |||
Related temperament: [[Lehmerismic_temperaments#Lux|lux]] | |||
[[Subgroup]]: 2.15.189.55.325 | |||
[[Comma list]]: [[2080/2079]], [[3025/3024]], [[4096/4095]] | |||
{{Mapping|legend=2| 1 0 6 5 6 | 0 5 2 1 3 }} | |||
[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.677 | |||
[[Support]]ing [[ET]]s: 5, 9, 14, 23, 32, 37, 41, 50, 55, 64, 73, 78, 87, 96, 101, 105, 119, 128, 151, 183, 206, 311 | |||
==== 2.15.189.55.325.279 ==== | |||
Here are rational approximations to the intervals of the semiquartal scale. | |||
[[Modal_UDP_notation#Generalizing_to_arbitrary_MOS_scales:_bright_and_dark_generators_.28chroma-positive_and_chroma-negative.29|Chroma-positive]]: 12/11, 25/21, 33/26, 18/13, 65/44 ~ 96/65, 50/31, 55/32, 15/8. | |||
Chroma-negative: 16/15, 64/55, 31/25, 65/48 ~ 88/65, 13/9, 52/33, 42/25, 11/6. | |||
[[Subgroup]]: 2.15.189.55.325.279 | |||
[[Comma list]]: [[2016/2015]], [[2080/2079]], [[3025/3024]], [[4096/4095]] | |||
{{Mapping|legend=2| 1 0 6 5 6 5 | 0 5 2 1 3 4 }} | |||
[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.666 | |||
[[Support]]ing [[ET]]s: 5, 9, 14, 23, 32, 37, 41, 50, 55, 64, 73, 78, 87, 96, 101, 105, 119, 128, 151, 183, 206, 311 | |||
== 4.3.5 subgroup == | == 4.3.5 subgroup == | ||