Very low accuracy temperaments: Difference between revisions
No edit summary Tags: Mobile edit Mobile web edit |
No edit summary Tags: Mobile edit Mobile web edit |
||
| Line 334: | Line 334: | ||
== Sept == | == Sept == | ||
{{See also| | {{See also| Whitewood family }} | ||
Sept preserves the 2.3.7-subgroup of mapping of 7edo, and harmonic 5 is mapped to an independent generator. As harmonic 5 is way more accurately approximated than 7 by 7edo, this temperament provides little improvement to 7edo's 7-limit tuning, so in what way this temperament is useful remains unexplained. It would make much more sense to, for example, preserve the 5-limit structure of 7edo and give prime 7 an independent generator instead, which is exactly what [[jamesbond]] does. | Sept preserves the 2.3.7-subgroup of mapping of 7edo, and harmonic 5 is mapped to an independent generator. As harmonic 5 is way more accurately approximated than 7 by 7edo, this temperament provides little improvement to 7edo's 7-limit tuning, so in what way this temperament is useful remains unexplained. It would make much more sense to, for example, preserve the 5-limit structure of 7edo and give prime 7 an independent generator instead, which is exactly what [[jamesbond]] does. | ||
| Line 772: | Line 772: | ||
== Sixseven == | == Sixseven == | ||
Sixseven tempers out the [[7/6|septimal minor third (7/6)]], equating the [[6/1|sixth]] and [[7/1|seventh harmonic]]s. It was named by [[User:Xenllium|Xenllium]] in 2026. | Sixseven tempers out the [[7/6|septimal minor third (7/6)]], equating the [[6/1|sixth]] and [[7/1|seventh harmonic]]s. It was named by [[User:Xenllium|Xenllium]] in 2026. | ||
| Line 807: | Line 806: | ||
Badness (Sintel): 0.422 | Badness (Sintel): 0.422 | ||
=== Heaven === | |||
Heaven tempers out [[11/9]] and [[22/21]] in the 2.3.7.11 subgroup. | |||
Subgroup: 2.3.7.11 | |||
Comma list: 7/6, 11/9 | |||
Mapping: {{mapping| 1 0 1 0 | 0 1 1 2 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1210.810{{c}}, ~3/2 = 783.079{{c}} | |||
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 785.173{{c}} | |||
{{Optimal ET sequence|legend=0| 1e, 2de, 3 }} | |||
Badness (Sintel): 0.577 | |||
==== 2.3.7.11.13 subgroup ==== | |||
Subgroup: 2.3.7.11.13 | |||
Comma list: 7/6, 11/9, 13/12 | |||
Mapping: {{mapping| 1 0 1 0 2 | 0 1 1 2 1 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1210.595{{c}}, ~3/2 = 783.176{{c}} | |||
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 784.989{{c}} | |||
{{Optimal ET sequence|legend=0| 1e, 2de, 3 }} | |||
Badness (Sintel): 0.627 | |||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||