Septisemi temperaments: Difference between revisions
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These are very low complexity temperaments tempering out the minor | 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 #Mother]] | |||
* [[Flat]], {21/20, 25/24} → [[Dicot family #Flat]] | |||
* [[Beep]], {21/20, 27/25} → [[Bug family #Beep]] | |||
* [[Sharptone]], {21/20, 28/27} → [[Meantone family #Sharptone]] | |||
* [[Pelogic]], {21/20, 135/128} → [[Pelogic family #Pelogic]] | |||
* [[Gidorah]], {21/20, 144/125} → [[Gamelismic clan #Gidorah]] | |||
Considered below are fluorine, sodium and oxygen. | |||
== Fluorine == | == Fluorine == | ||
=== 5-limit ( | === 5-limit (avila) === | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
[[Comma]]: 729/640 | [[Comma list]]: 729/640 | ||
[[Mapping]]: [{{val| 1 0 -7 }}, {{val| 0 1 6 }}] | [[Mapping]]: [{{val| 1 0 -7 }}, {{val| 0 1 6 }}] | ||
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[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament collection]] | [[Category:Temperament collection]] | ||
[[Category:Septisemi]] | [[Category:Septisemi temperaments| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 09:05, 13 September 2021
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 #Mother
- Flat, {21/20, 25/24} → Dicot family #Flat
- Beep, {21/20, 27/25} → Bug family #Beep
- Sharptone, {21/20, 28/27} → Meantone family #Sharptone
- Pelogic, {21/20, 135/128} → Pelogic family #Pelogic
- Gidorah, {21/20, 144/125} → Gamelismic clan #Gidorah
Considered below are fluorine, sodium and oxygen.
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
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
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
Badness: 0.055814
Oxygen
Subgroup: 2.3.5.7
Comma list: 21/20, 175/162
Mapping: [⟨1 2 3 3], ⟨0 -3 -5 -2]]
Wedgie: ⟨⟨ 3 5 2 1 -5 -9 ]]
POTE generator: ~7/6 = 169.112
Badness: 0.059866