Septisemi temperaments: Difference between revisions

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* ''[[Flattie]]'' (+25/24) → [[Dicot family #Flattie|Dicot family]]
* ''[[Flattie]]'' (+25/24) → [[Dicot family #Flattie|Dicot family]]
* ''[[Beep]]'' (+27/25) → [[Bug family #Beep|Bug family]]
* ''[[Beep]]'' (+27/25) → [[Bug family #Beep|Bug family]]
* ''[[Deflated]]'' (+21/20) → [[Augmented family #Deflated|Augmented family]]
* ''[[Deflated]]'' (+128/125) → [[Augmented family #Deflated|Augmented family]]
* ''[[Gidorah]]'' (+144/125) → [[Gamelismic clan #Gidorah|Gamelismic clan]]
* ''[[Gidorah]]'' (+144/125) → [[Gamelismic clan #Gidorah|Gamelismic clan]]
* ''[[Oxygen]]'' (+175/162) → [[Porcupine family #Oxygen|Porcupine family]]
* ''[[Oxygen]]'' (+175/162) → [[Porcupine family #Oxygen|Porcupine family]]
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{{Mapping|legend=1| 1 0 -7 | 0 1 6 }}
{{Mapping|legend=1| 1 0 -7 | 0 1 6 }}


: mapping generators: ~2, ~3
: Mapping generators: ~2, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 666.499
* [[CTE]]: ~2 = 1200.000, ~3/2 = 666.499
: [[error map]]: {{val| 0.000 -35.456 +12.682 }}
: [[Error map]]: {{val| 0.000 -35.456 +12.682 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 661.593
* [[POTE]]: ~2 = 1200.000, ~3/2 = 661.593
: error map: {{val| 0.000 -40.362 -16.754 }}
: Error map: {{val| 0.000 -40.362 -16.754 }}


{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20b, 29b }}
{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20b, 29b }}
Line 45: Line 45:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 668.748
* [[CTE]]: ~2 = 1200.000, ~3/2 = 668.748
: [[error map]]: {{val| 0.000 -33.207 +26.177 -25.084 }}
: [[Error map]]: {{val| 0.000 -33.207 +26.177 -25.084 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 663.059
* [[POTE]]: ~2 = 1200.000, ~3/2 = 663.059
: error map: {{val| 0.000 -38.896 -7.960 -53.531 }}
: Error map: {{val| 0.000 -38.896 -7.960 -53.531 }}


{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20bdd, 29bdd }}
{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20bdd, 29bdd }}
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{{Mapping|legend=1| 1 1 1 2 | 0 2 5 3 }}
{{Mapping|legend=1| 1 1 1 2 | 0 2 5 3 }}


: mapping generators: ~2, ~7/6
: Mapping generators: ~2, ~7/6


{{Multival|legend=1| 2 5 3 3 -1 -7 }}
{{Multival|legend=1| 2 5 3 3 -1 -7 }}
Line 66: Line 66:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/6 = 325.425
* [[CTE]]: ~2 = 1200.000, ~7/6 = 325.425
: [[error map]]: {{val| 0.000 -51.104 +40.813 +7.450 }}
: [[Error map]]: {{val| 0.000 -51.104 +40.813 +7.450 }}
* [[POTE]]: ~2 = 1200.000, ~7/6 = 320.182
* [[POTE]]: ~2 = 1200.000, ~7/6 = 320.182
: error map: {{val| 0.000 -61.591 +14.597 -8.280 }}
: Error map: {{val| 0.000 -61.591 +14.597 -8.280 }}


{{Optimal ET sequence|legend=1| 4, 11, 15b }}
{{Optimal ET sequence|legend=1| 4, 11, 15b }}

Revision as of 12:50, 18 May 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

This is a collection of 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:

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 tunings:

  • CTE: ~2 = 1200.000, ~3/2 = 666.499
Error map: ⟨0.000 -35.456 +12.682]
  • POTE: ~2 = 1200.000, ~3/2 = 661.593
Error map: ⟨0.000 -40.362 -16.754]

Optimal ET sequence: 2c, 7c, 9, 20b, 29b

Badness (Smith): 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 tunings:

  • CTE: ~2 = 1200.000, ~3/2 = 668.748
Error map: ⟨0.000 -33.207 +26.177 -25.084]
  • POTE: ~2 = 1200.000, ~3/2 = 663.059
Error map: ⟨0.000 -38.896 -7.960 -53.531]

Optimal ET sequence: 2c, 7c, 9, 20bdd, 29bdd

Badness (Smith): 0.055623

Sodium

Subgroup: 2.3.5.7

Comma list: 21/20, 54/49

Mapping: [⟨1 1 1 2], ⟨0 2 5 3]]

Mapping generators: ~2, ~7/6

Wedgie: ⟨⟨ 2 5 3 3 -1 -7 ]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~7/6 = 325.425
Error map: ⟨0.000 -51.104 +40.813 +7.450]
  • POTE: ~2 = 1200.000, ~7/6 = 320.182
Error map: ⟨0.000 -61.591 +14.597 -8.280]

Optimal ET sequence: 4, 11, 15b

Badness (Smith): 0.055814

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