Septisemi temperaments: Difference between revisions
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m Text replacement - "Category:Temperament collections" to "Category:Temperament collections Category:Pages with mostly numerical content" |
m Units & misc. cleanup |
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* ''[[Pelogic]]'' (+135/128) → [[Mavila family #Pelogic|Mavila family]] | * ''[[Pelogic]]'' (+135/128) → [[Mavila family #Pelogic|Mavila family]] | ||
* ''[[Flattie]]'' (+25/24) → [[Dicot family #Flattie|Dicot family]] | * ''[[Flattie]]'' (+25/24) → [[Dicot family #Flattie|Dicot family]] | ||
* | * [[Beep]] (+27/25) → [[Bug family #Beep|Bug family]] | ||
* ''[[Deflated]]'' (+128/125) → [[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]] | ||
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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 | |||
: | |||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 666.499 | * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 666.499{{c}} | ||
: [[ | : [[error map]]: {{val| 0.000 -35.456 +12.682 }} | ||
* [[POTE]]: ~2 = 1200.000, ~3/2 = 661.593 | * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 661.593{{c}} | ||
: | : 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 42: | Line 41: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 668.748 | * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 668.748{{c}} | ||
: [[ | : [[error map]]: {{val| 0.000 -33.207 +26.177 -25.084 }} | ||
* [[POTE]]: ~2 = 1200.000, ~3/2 = 663.059 | * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 663.059{{c}} | ||
: | : 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 }} | ||
| Line 57: | Line 56: | ||
{{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 | |||
: | |||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~7/6 = 325.425 | * [[CTE]]: ~2 = 1200.000{{c}}, ~7/6 = 325.425{{c}} | ||
: [[ | : [[error map]]: {{val| 0.000 -51.104 +40.813 +7.450 }} | ||
* [[POTE]]: ~2 = 1200.000, ~7/6 = 320.182 | * [[POTE]]: ~2 = 1200.000{{c}}, ~7/6 = 320.182{{c}} | ||
: | : 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 14:39, 19 November 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:
- Mother (+16/15) → Father family
- Sharptone (+28/27) → Meantone family
- Pelogic (+135/128) → Mavila family
- Flattie (+25/24) → Dicot family
- Beep (+27/25) → Bug family
- Deflated (+128/125) → Augmented family
- Gidorah (+144/125) → Gamelismic clan
- Oxygen (+175/162) → Very low accuracy temperaments
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
- 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]]
- 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
- 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