Very low accuracy temperaments: Difference between revisions
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== Sept == | == Sept == | ||
{{See also| Apotome 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. | ||
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Badness (Sintel): 0.681 | Badness (Sintel): 0.681 | ||
== Sixseven == | |||
{{Main| 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. | |||
[[Subgroup]]: 2.3.7 | |||
[[Comma list]]: 7/6 | |||
{{Mapping|legend=1| 1 0 1 | 0 1 1 }} | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1218.135{{c}}, ~3/2 = 734.187{{c}} | |||
: [[error map]]: {{val| +18.135 +50.367 -198.368 }} | |||
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 738.927{{c}} | |||
: error map: {{val| 0.000 +36.972 -229.899 }} | |||
{{Optimal ET sequence|legend=1| 1, 2d, 3, 5dd }} | |||
[[Badness]] (Sintel): 0.329 | |||
=== 2.3.7.13 subgroup === | |||
This temperament is extended to the 2.3.7.13 subgroup naturally, tempering out both [[13/12]] and [[14/13]], tridecimal neutral seconds. | |||
Subgroup: 2.3.7.13 | |||
Comma list: 7/6, 13/12 | |||
Mapping: {{mapping| 1 0 1 2 | 0 1 1 1 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1220.937{{c}}, ~3/2 = 734.003{{c}} | |||
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 739.780{{c}} | |||
{{Optimal ET sequence|legend=0| 1, 2d, 3, 5ddf }} | |||
Badness (Sintel): 0.422 | |||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||