Odd limit: Difference between revisions
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This conjecture has two implications. First, a given JI chord has an ideal voicing. This voicing may be rather far-flung, and a more compact voicing may be almost as consonant. For example, 1:3:5:7 has a large gap between the two lowest voices, and 2:3:5:7 is more practical. Second, a voicing can imply a tuning. For example, if a piece has a minor chord with the 3rd voiced as a 10th, 7/3 may be preferred over 12/5 for the 3rd. If it's voiced as a 10th plus an octave, either 14/3 or 19/4 may be preferred to 24/5. | This conjecture has two implications. First, a given JI chord has an ideal voicing. This voicing may be rather far-flung, and a more compact voicing may be almost as consonant. For example, 1:3:5:7 has a large gap between the two lowest voices, and 2:3:5:7 is more practical. Second, a voicing can imply a tuning. For example, if a piece has a minor chord with the 3rd voiced as a 10th, 7/3 may be preferred over 12/5 for the 3rd. If it's voiced as a 10th plus an octave, either 14/3 or 19/4 may be preferred to 24/5. | ||
== | ==Lists of intervals by odd limit== | ||
* [[1-odd-limit]] | * [[1-odd-limit]] | ||
* [[3-odd-limit]] | * [[3-odd-limit]] | ||
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* [[17-odd-limit]] | * [[17-odd-limit]] | ||
* [[19-odd-limit]] | * [[19-odd-limit]] | ||
* [[21-odd-limit]] | |||
* [[23-odd-limit]] | |||
== See also == | |||
* [[p-limit]] - or prime harmonic limit | |||
* [http://en.wikipedia.org/wiki/Limit_(music) Limit (music) - Wikipedia, the free encyclopedia] (covers also the distinction between odd-limit and prime-limit) | * [http://en.wikipedia.org/wiki/Limit_(music) Limit (music) - Wikipedia, the free encyclopedia] (covers also the distinction between odd-limit and prime-limit) | ||
* [http://tonalsoft.com/enc/l/limit.aspx Limit - Tonalsoft Encyclopedia of Microtonal Music Theory] | * [http://tonalsoft.com/enc/l/limit.aspx Limit - Tonalsoft Encyclopedia of Microtonal Music Theory] | ||
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[[Category:Limit]] | [[Category:Limit]] | ||
[[Category:Term]] | [[Category:Term]] | ||
[[Category:todo:improve synopsis]] | [[Category:todo:improve synopsis]] | ||