Syntonic–chromatic equivalence continuum: Difference between revisions
- CTE & POTE tunings |
CompactStar (talk | contribs) |
||
| (5 intermediate revisions by 3 users not shown) | |||
| Line 94: | Line 94: | ||
| {{Monzo| -17 21 -7 }} | | {{Monzo| -17 21 -7 }} | ||
|- | |- | ||
| … | |||
| … | | … | ||
| … | | … | ||
| Line 178: | Line 179: | ||
== Deeptone a.k.a. tragicomical == | == Deeptone a.k.a. tragicomical == | ||
{{Main| Deeptone }} | {{Main| Deeptone }} | ||
: ''For the 2.3.5.13 subgroup extension, see [[No-sevens subgroup temperaments#Deeptone a.k.a. tragicomical]].'' | |||
Deeptone is generated by a fifth, which is typically sharper than in [[7edo]] but flatter than in [[flattone]]. The ~5/4 is reached by eleven fifths octave-reduced, which is an augmented third (C–E♯). | Deeptone is generated by a fifth, which is typically sharper than in [[7edo]] but flatter than in [[flattone]]. The ~5/4 is reached by eleven fifths octave-reduced, which is an augmented third (C–E♯). | ||
| Line 186: | Line 188: | ||
{{Mapping|legend=1| 1 0 -15 | 0 1 11 }} | {{Mapping|legend=1| 1 0 -15 | 0 1 11 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
| Line 209: | Line 210: | ||
{{Mapping|legend=1| 1 0 18 | 0 1 -10 }} | {{Mapping|legend=1| 1 0 18 | 0 1 -10 }} | ||
: mapping generators: ~2, ~3 | : mapping generators: ~2, ~3 | ||
| Line 228: | Line 228: | ||
{{Mapping|legend=1| 1 1 -1 | 0 2 15 }} | {{Mapping|legend=1| 1 1 -1 | 0 2 15 }} | ||
: mapping generators: ~2, ~2560/2187 | : mapping generators: ~2, ~2560/2187 | ||
| Line 249: | Line 248: | ||
{{Mapping|legend=1| 1 2 2 | 0 -3 2 }} | {{Mapping|legend=1| 1 2 2 | 0 -3 2 }} | ||
: mapping generators: ~2, ~16/15 | : mapping generators: ~2, ~16/15 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1210.1294{{c}}, ~16/15 = 174.5613{{c}} | * [[WE]]: ~2 = 1210.1294{{c}}, ~16/15 = 174.5613{{c}} | ||
: [[error map]]: {{val| + | : [[error map]]: {{val| +10.129 -5.380 -16.932 }} | ||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 172.4620{{c}} | * [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 172.4620{{c}} | ||
: error map: {{val| 0.000 - | : error map: {{val| 0.000 -19.341 -41.390 }} | ||
{{Optimal ET sequence|legend=1| 6b, 7 }} | {{Optimal ET sequence|legend=1| 6b, 7 }} | ||
| Line 268: | Line 266: | ||
{{Mapping|legend=1| 1 2 5 | 0 -3 -19 }} | {{Mapping|legend=1| 1 2 5 | 0 -3 -19 }} | ||
: mapping generators: ~2, ~729/640 | : mapping generators: ~2, ~729/640 | ||
| Line 289: | Line 286: | ||
{{Mapping|legend=1| 1 3 4 | 0 -5 -6 }} | {{Mapping|legend=1| 1 3 4 | 0 -5 -6 }} | ||
: mapping generators: ~2, ~6/5 | : mapping generators: ~2, ~6/5 | ||
| Line 312: | Line 308: | ||
{{Mapping|legend=1| 7 0 -17 | 0 1 3 }} | {{Mapping|legend=1| 7 0 -17 | 0 1 3 }} | ||
: mapping generators: ~800/729, ~3 | : mapping generators: ~800/729, ~3 | ||
| Line 335: | Line 330: | ||
{{Mapping|legend=1| 7 0 -6 | 0 1 2 }} | {{Mapping|legend=1| 7 0 -6 | 0 1 2 }} | ||
: mapping generators: ~10/9, ~3 | : mapping generators: ~10/9, ~3 | ||
| Line 356: | Line 350: | ||
{{Mapping|legend=1| 7 0 5 | 0 1 1 }} | {{Mapping|legend=1| 7 0 5 | 0 1 1 }} | ||
: mapping generators: ~125/108, ~3 | : mapping generators: ~125/108, ~3 | ||
| Line 379: | Line 372: | ||
{{Mapping|legend=1| 1 -1 -4 | 0 9 22 }} | {{Mapping|legend=1| 1 -1 -4 | 0 9 22 }} | ||
: mapping generators: ~2, ~243/200 | : mapping generators: ~2, ~243/200 | ||
| Line 400: | Line 392: | ||
{{Mapping|legend=1| 1 -3 -10 | 0 16 43 }} | {{Mapping|legend=1| 1 -3 -10 | 0 16 43 }} | ||
: mapping generators: ~2, ~8000/6561 | : mapping generators: ~2, ~8000/6561 | ||
| Line 412: | Line 403: | ||
[[Badness]] (Sintel): 2.78 | [[Badness]] (Sintel): 2.78 | ||
== Undetrita (5-limit) == | |||
: ''For extensions, see [[Hemimean clan #Undetrita]].'' | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: {{monzo| -22 30 -11 }} | |||
{{Mapping|legend=1| 1 0 -2 | 0 11 30 }} | |||
: mapping generators: ~2, ~177147/160000 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1200.0596{{c}}, ~177147/160000 = 172.8864{{c}} | |||
: [[error map]]: {{val| +0.060 -0.204 +0.161 }} | |||
* [[CWE]]: ~2 = 1200.000{{c}}, ~177147/160000 = 172.8804{{c}} | |||
: error map: {{val| 0.000 -0.271 +0.098 }} | |||
{{Optimal ET sequence|legend=1| 7, …, 111, 118, 1541, 1659, 1777, 1895b, …, 2839b, 2957b }} | |||
[[Badness]] (Sintel): 4.09 | |||
[[Category:7edo]] | [[Category:7edo]] | ||
[[Category:Equivalence continua]] | [[Category:Equivalence continua]] | ||