5th-octave temperaments: Difference between revisions
m →Thunderclysmic: clarify |
→Quint: explain how it's unexplained |
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== Quint == | == Quint == | ||
Quint preserves the 5-limit mapping of 5edo, and harmonic 7 is mapped to an independent generator. As harmonic 7 is way more accurately approximated than 5 by 5edo, this temperament provides little improvement to 5edo'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 2.3.7-subgroup structure of 5edo and give prime 5 an indepedent generator instead, which is exactly what [[blacksmith]] does. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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{{Multival|legend=1| 0 0 5 0 8 12 }} | {{Multival|legend=1| 0 0 5 0 8 12 }} | ||
[[Optimal tuning]] ([[POTE]]): ~9/8 = | [[Optimal tuning]] ([[POTE]]): ~9/8 = 1\5, ~7/4 = 1017.903 | ||
{{Optimal ET sequence|legend=1| 5, 15ccd }} | {{Optimal ET sequence|legend=1| 5, 15ccd }} | ||
[[Badness]]: 0.048312 | [[Badness]]: 0.048312 | ||