Septisemi temperaments: Difference between revisions
-oxygen (addressed in porcupine family) |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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[[POTE generator]]: ~3/2 = 661.593 | [[POTE generator]]: ~3/2 = 661.593 | ||
{{ | {{Optimal ET sequence|legend=1| 2c, 7c, 9, 20b, 29b }} | ||
[[Badness]]: 0.181941 | [[Badness]]: 0.181941 | ||
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[[POTE generator]]: ~3/2 = 663.059 | [[POTE generator]]: ~3/2 = 663.059 | ||
{{ | {{Optimal ET sequence|legend=1| 9, 20bdd, 29bdd }} | ||
[[Badness]]: 0.055623 | [[Badness]]: 0.055623 | ||
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[[POTE generator]]: ~7/6 = 320.182 | [[POTE generator]]: ~7/6 = 320.182 | ||
{{ | {{Optimal ET sequence|legend=1| 4, 11, 15b }} | ||
[[Badness]]: 0.055814 | [[Badness]]: 0.055814 | ||
Revision as of 18:19, 7 May 2023
These are very low complexity temperaments tempering out the septimal minor semitone, 21/20, and hence equating 5/3 with 7/4, and 10/7 with 3/2.
Temperaments discussed elsewhere are:
- Mother, {16/15, 21/20} → Father family
- Flat, {21/20, 25/24} → Dicot family
- Beep, {21/20, 27/25} → Bug family
- Sharptone, {21/20, 28/27} → Meantone family
- Pelogic, {21/20, 135/128} → Pelogic family
- Gidorah, {21/20, 144/125} → Gamelismic clan
- Oxygen, {21/20, 175/162} → Porcupine family
Considered below are fluorine and sodium.
Fluorine
5-limit (avila)
Subgroup: 2.3.5
Comma list: 729/640
Mapping: [⟨1 0 -7], ⟨0 1 6]]
POTE generator: ~3/2 = 661.593
Optimal ET sequence: 2c, 7c, 9, 20b, 29b
Badness: 0.181941
7-limit
Subgroup: 2.3.5.7
Comma list: 21/20, 243/224
Mapping: [⟨1 0 -7 -5], ⟨0 1 6 5]]
Wedgie: ⟨⟨ 1 6 5 7 5 -5 ]]
POTE generator: ~3/2 = 663.059
Optimal ET sequence: 9, 20bdd, 29bdd
Badness: 0.055623
Sodium
Subgroup: 2.3.5.7
Comma list: 21/20, 54/49
Mapping: [⟨1 1 1 2], ⟨0 2 5 3]]
Wedgie: ⟨⟨ 2 5 3 3 -1 -7 ]]
POTE generator: ~7/6 = 320.182
Optimal ET sequence: 4, 11, 15b
Badness: 0.055814