Septisemi temperaments: Difference between revisions
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These are very low complexity temperaments tempering out the minor septimal semitone, [[21/20]], and hence equating 5/3 with 7/4, and 10/7 with 3/2. | These are very low complexity temperaments tempering out the minor septimal semitone, [[21/20]], and hence equating 5/3 with 7/4, and 10/7 with 3/2. | ||
Discussed elsewhere are [[Father family #Mother|mother]], [[Dicot family #Flat|flat]], [[Bug family #Beep|beep]], [[Meantone family #Sharptone|sharptone]] and [[Pelogic family #Pelogic|pelogic]]. | Discussed elsewhere are [[Father family #Mother|mother]], [[Dicot family #Flat|flat]], [[Bug family #Beep|beep]], [[Gamelismic clan #Gidorah|gidorah]], [[Meantone family #Sharptone|sharptone]] and [[Pelogic family #Pelogic|pelogic]]. | ||
= Fluorine = | == Fluorine == | ||
=== 5-limit (Avila) === | |||
Subgroup: 2.3.5 | |||
[[Comma]]: 729/640 | |||
[[Mapping]]: [{{val| 1 0 -7 }}, {{val| 0 1 6 }}] | |||
[[POTE generator]]: ~3/2 = 661.593 | |||
{{Val list|legend=1| 2c, 7c, 9, 20b, 29b }} | |||
[[Badness]]: 0.181941 | |||
=== 7-limit === | |||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[POTE generator]]: ~3/2 = 663.059 | [[POTE generator]]: ~3/2 = 663.059 | ||
{{Val list|legend=1| 9, | {{Val list|legend=1| 9, 20bdd, 29bdd }} | ||
[[Badness]]: 0.055623 | |||
== Sodium == | |||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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{{Val list|legend=1| 4, 11, 15b }} | {{Val list|legend=1| 4, 11, 15b }} | ||
[[Badness]]: 0. | [[Badness]]: 0.055814 | ||
== Oxygen == | |||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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{{Val list|legend=1| 7d, 8 }} | {{Val list|legend=1| 7d, 8 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.059866 | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 13:50, 7 August 2021
These are very low complexity temperaments tempering out the minor septimal semitone, 21/20, and hence equating 5/3 with 7/4, and 10/7 with 3/2.
Discussed elsewhere are mother, flat, beep, gidorah, sharptone and pelogic.
Fluorine
5-limit (Avila)
Subgroup: 2.3.5
Comma: 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