Septisemi temperaments: Difference between revisions
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m Units & misc. cleanup |
Switch to Sintel's badness, WE & CWE tunings, per community consensus |
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| Line 24: | Line 24: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 666.499{{c}} | * [[WE]]: ~2 = 1210.600{{c}}, ~3/2 = 667.437{{c}} | ||
: [[error map]]: {{val| +10.600 -23.917 +7.711 }} | |||
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 663.474{{c}} | |||
: error map: {{val| 0.000 -38.481 -5.472 }} | |||
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 666.499{{c}} | |||
: [[error map]]: {{val| 0.000 -35.456 +12.682 }} | : [[error map]]: {{val| 0.000 -35.456 +12.682 }} | ||
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 661.593{{c}} | * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 661.593{{c}} | ||
: 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 }} | ||
[[Badness]] ( | [[Badness]] (Sintel): 4.27 | ||
=== 7-limit === | === 7-limit === | ||
| Line 41: | Line 45: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 668.748{{c}} | * [[WE]]: ~2 = 1211.420{{c}}, ~3/2 = 669.369{{c}} | ||
: [[error map]]: {{val| +11.420 -21.165 +18.481 -21.980 }} | |||
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 665.210{{c}} | |||
: error map: {{val| 0.000 -36.745 +4.945 -42.777 }} | |||
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 668.748{{c}} | |||
: [[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{{c}}, ~3/2 = 663.059{{c}} | * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 663.059{{c}} | ||
: 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 }} | ||
[[Badness]] ( | [[Badness]] (Sintel): 1.41 | ||
== Sodium == | == Sodium == | ||
| Line 59: | Line 67: | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000{{c}}, ~7/6 = 325.425{{c}} | * [[WE]]: ~2 = 1207.624{{c}}, ~7/6 = 322.216{{c}} | ||
: [[error map]]: {{val| +7.624 -49.898 +32.393 +13.072 }} | |||
* [[CWE]]: ~2 = 1200.000{{c}}, ~7/6 = 322.210{{c}} | |||
: error map: {{val| 0.000 -57.535 +24.737 -2.196 }} | |||
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~7/6 = 325.425{{c}} | |||
: [[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{{c}}, ~7/6 = 320.182{{c}} | * [[POTE]]: ~2 = 1200.000{{c}}, ~7/6 = 320.182{{c}} | ||
: 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 | {{Optimal ET sequence|legend=1| 4, 11 }} | ||
[[Badness]] ( | [[Badness]] (Sintel): 1.41 | ||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
Revision as of 14:45, 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
- WE: ~2 = 1210.600 ¢, ~3/2 = 667.437 ¢
- error map: ⟨+10.600 -23.917 +7.711]
- CWE: ~2 = 1200.000 ¢, ~3/2 = 663.474 ¢
- error map: ⟨0.000 -38.481 -5.472]
Optimal ET sequence: 2c, 7c, 9, 20b, 29b
Badness (Sintel): 4.27
7-limit
Subgroup: 2.3.5.7
Comma list: 21/20, 243/224
Mapping: [⟨1 0 -7 -5], ⟨0 1 6 5]]
- WE: ~2 = 1211.420 ¢, ~3/2 = 669.369 ¢
- error map: ⟨+11.420 -21.165 +18.481 -21.980]
- CWE: ~2 = 1200.000 ¢, ~3/2 = 665.210 ¢
- error map: ⟨0.000 -36.745 +4.945 -42.777]
Optimal ET sequence: 2c, 7c, 9, 20bdd, 29bdd
Badness (Sintel): 1.41
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
- WE: ~2 = 1207.624 ¢, ~7/6 = 322.216 ¢
- error map: ⟨+7.624 -49.898 +32.393 +13.072]
- CWE: ~2 = 1200.000 ¢, ~7/6 = 322.210 ¢
- error map: ⟨0.000 -57.535 +24.737 -2.196]
Badness (Sintel): 1.41