Septisemi temperaments: Difference between revisions
Jump to navigation
Jump to search
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
Update keys |
||
| Line 2: | Line 2: | ||
Temperaments discussed elsewhere are: | Temperaments discussed elsewhere are: | ||
* ''[[Mother]]'' | * ''[[Mother]]'' (+16/15) → [[Father family #Mother|Father family]] | ||
* ''[[Flat (temperament)|Flat]]'' | * ''[[Flat (temperament)|Flat]]'' (+25/24) → [[Dicot family #Flat|Dicot family]] | ||
* ''[[Beep]]'' | * ''[[Beep]]'' (+27/25) → [[Bug family #Beep|Bug family]] | ||
* ''[[Sharptone]]'' | * ''[[Sharptone]]'' (+28/27) → [[Meantone family #Sharptone|Meantone family]] | ||
* ''[[Pelogic]]'' | * ''[[Pelogic]]'' (+135/128) → [[Pelogic family #Pelogic|Pelogic family]] | ||
* ''[[Gidorah]]'' | * ''[[Gidorah]]'' (+144/125) → [[Gamelismic clan #Gidorah|Gamelismic clan]] | ||
* ''[[Oxygen]]'' | * ''[[Oxygen]]'' (+175/162) → [[Porcupine family #Oxygen|Porcupine family]] | ||
Considered below are fluorine and sodium. | Considered below are fluorine and sodium. | ||
| Line 14: | Line 14: | ||
== Fluorine == | == Fluorine == | ||
=== 5-limit (avila) === | === 5-limit (avila) === | ||
Subgroup: 2.3.5 | [[Subgroup]]: 2.3.5 | ||
[[Comma list]]: 729/640 | [[Comma list]]: 729/640 | ||
{{Mapping|legend=1| 1 0 -7 | 0 1 6 }} | |||
[[POTE | : mapping generators: ~2, ~3 | ||
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 661.593 | |||
{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20b, 29b }} | {{Optimal ET sequence|legend=1| 2c, 7c, 9, 20b, 29b }} | ||
| Line 27: | Line 29: | ||
=== 7-limit === | === 7-limit === | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 21/20, 243/224 | [[Comma list]]: 21/20, 243/224 | ||
{{Mapping|legend=1| 1 0 -7 -5 | 0 1 6 5 }} | |||
{{Multival|legend=1| 1 6 5 7 5 -5 }} | {{Multival|legend=1| 1 6 5 7 5 -5 }} | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 663.059 | ||
{{Optimal ET sequence|legend=1| 9, 20bdd, 29bdd }} | {{Optimal ET sequence|legend=1| 9, 20bdd, 29bdd }} | ||
| Line 42: | Line 44: | ||
== Sodium == | == Sodium == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: 21/20, 54/49 | [[Comma list]]: 21/20, 54/49 | ||
{{Mapping|legend=1| 1 1 1 2 | 0 2 5 3 }} | |||
{{Multival|legend=1| 2 5 3 3 -1 -7 }} | {{Multival|legend=1| 2 5 3 3 -1 -7 }} | ||
[[POTE | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 320.182 | ||
{{Optimal ET sequence|legend=1| 4, 11, 15b }} | {{Optimal ET sequence|legend=1| 4, 11, 15b }} | ||
Revision as of 05:38, 5 August 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) → Father family
- Flat (+25/24) → Dicot family
- Beep (+27/25) → Bug family
- Sharptone (+28/27) → Meantone family
- Pelogic (+135/128) → Pelogic family
- Gidorah (+144/125) → Gamelismic clan
- Oxygen (+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]]
- mapping generators: ~2, ~3
Optimal tuning (POTE): ~2 = 1\1, ~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 ]]
Optimal tuning (POTE): ~2 = 1\1, ~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 ]]
Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 320.182
Optimal ET sequence: 4, 11, 15b
Badness: 0.055814