Septisemi temperaments: Difference between revisions
Jump to navigation
Jump to search
m Update linking |
+CTE tunings; +error maps; spell out 1\1 in decimal; note the badness metric being used |
||
| Line 1: | Line 1: | ||
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: | Temperaments discussed elsewhere are: | ||
| Line 23: | Line 23: | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 666.499 | |||
: [[error map]]: {{val| 0.000 -35.456 +12.682 }} | |||
* [[POTE]]: ~2 = 1200.000, ~3/2 = 661.593 | |||
: 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]]: 0.181941 | [[Badness]] (Smith): 0.181941 | ||
=== 7-limit === | === 7-limit === | ||
| Line 38: | Line 42: | ||
{{Multival|legend=1| 1 6 5 7 5 -5 }} | {{Multival|legend=1| 1 6 5 7 5 -5 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 668.748 | |||
: [[error map]]: {{val| 0.000 -33.207 +26.177 -25.084 }} | |||
* [[POTE]]: ~2 = 1200.000, ~3/2 = 663.059 | |||
: error map: {{val| 0.000 -38.896 -7.960 -53.531 }} | |||
{{Optimal ET sequence|legend=1| 9, 20bdd, 29bdd }} | {{Optimal ET sequence|legend=1| 2c, 7c, 9, 20bdd, 29bdd }} | ||
[[Badness]]: 0.055623 | [[Badness]] (Smith): 0.055623 | ||
== Sodium == | == Sodium == | ||
| Line 53: | Line 61: | ||
{{Multival|legend=1| 2 5 3 3 -1 -7 }} | {{Multival|legend=1| 2 5 3 3 -1 -7 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~2 = 1200.000, ~7/6 = 325.425 | |||
: [[error map]]: {{val| 0.000 -51.104 +40.813 +7.450 }} | |||
* [[POTE]]: ~2 = 1200.000, ~7/6 = 320.182 | |||
: 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 }} | ||
[[Badness]]: 0.055814 | [[Badness]] (Smith): 0.055814 | ||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Septisemi temperaments| ]] <!-- main article --> | [[Category:Septisemi temperaments| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 11:14, 25 December 2024
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 (+21/20) → Augmented family
- Gidorah (+144/125) → Gamelismic clan
- Oxygen (+175/162) → Porcupine family
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]]
Wedgie: ⟨⟨ 1 6 5 7 5 -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]]
Wedgie: ⟨⟨ 2 5 3 3 -1 -7 ]]
- 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