Limmic temperaments: Difference between revisions
Community poll result: 7-limit {28/27, 49/48} is the canonical extension of 5-limit {256/243}, hence *septimal blackwood* and no need of a distinct name. |
→Blackwood: update |
||
| Line 9: | Line 9: | ||
== Blackwood == | == Blackwood == | ||
{{Main| Blackwood }} | |||
Blackwood is the 5edo [[circle of fifths]] with an independent dimension for the harmonic 5. It can be described as the {{nowrap| 5 & 10 }} temperament. [[15edo]] is an obvious tuning. | Blackwood is the 5edo [[circle of fifths]] with an independent dimension for the harmonic 5. It can be described as the {{nowrap| 5 & 10 }} temperament. [[15edo]] is an obvious tuning. | ||
| Line 21: | Line 23: | ||
: mapping generators: ~9/8, ~5 | : mapping generators: ~9/8, ~5 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~9/8 = 240.000, ~5/4 = 386.314 | |||
: [[error map]]: {{val| 0.000 +18.045 0.000 }} | |||
* [[POTE]]: ~9/8 = 240.000, ~5/4 = 399.594 | |||
: error map: {{val| 0.000 +18.045 +13.280 }} | |||
{{Optimal ET sequence|legend=1| 5, 10, 15 }} | {{Optimal ET sequence|legend=1| 5, 10, 15 }} | ||
[[Badness]] (Smith): 0.063760 | [[Badness]] (Smith): 0.063760 | ||
=== 7-limit (blacksmith) === | === 7-limit (blacksmith) === | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 42: | Line 42: | ||
{{Multival|legend=1| 0 5 0 8 0 -14 }} | {{Multival|legend=1| 0 5 0 8 0 -14 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~8/7 = 240.000, ~5/4 = 386.313 | |||
: [[error map]]: {{val| 0.000 +18.045 0.000 -8.826 }} | |||
* [[POTE]]: ~8/7 = 240.000, ~5/4 = 392.767 | |||
: error map: {{val| 0.000 +18.045 +6.454 -8.826 }} | |||
{{Optimal ET sequence|legend=1| 5, 10, 15, 40b | {{Optimal ET sequence|legend=1| 5, 10, 15, 40b }} | ||
[[Badness]] (Smith): 0.025640 | [[Badness]] (Smith): 0.025640 | ||