11-limit: Difference between revisions
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{{Prime limit navigation|11}} | {{Prime limit navigation|11}} | ||
The '''11-limit''' consists of all [[Just intonation|justly tuned]] [[interval]]s whose numerators and denominators are both products of the | The '''11-limit''' consists of all [[Just intonation|justly tuned]] [[interval]]s whose [[Ratio|numerators and denominators]] are both products of the [[prime]]s 2, 3, 5, 7 and 11. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]]. The 11-limit is the 5th [[prime limit]] and is thus a superset of the [[7-limit]] and a subset of the [[13-limit]]. | ||
The [[11-odd-limit]] consists of intervals whose numerators and denominators, when all factors of two have been removed, are less than or equal to 11. Reduced to an octave, these are the ratios 1/1, 12/11, 11/10, 10/9, 9/8, 8/7, 7/6, 6/5, 11/9, 5/4, 14/11, 9/7, 4/3, 11/8, 7/5, 10/7, 16/11, 3/2, 14/9, 11/7, 8/5, 18/11, 5/3, 12/7, 7/4, 16/9, 9/5, 20/11, 11/6, 2/1. In an 11-limit system, all the ratios of the 11 odd-limit can be treated as potential [[consonance]]s. | |||
While the [[7-limit]] introduces subminor and supermajor intervals, which can sound like dramatic inflections of the familiar interval categories of [[12edo]], the 11-limit introduces neutral intervals, [[superfourth]]s and [[subfifth]]s, which fall in between major, minor and perfect [[interval category|interval categories]] and thus demand new distinctions. It is thus inescapably xenharmonic. | While the [[7-limit]] introduces subminor and supermajor intervals, which can sound like dramatic inflections of the familiar interval categories of [[12edo]], the 11-limit introduces neutral intervals, [[superfourth]]s and [[subfifth]]s, which fall in between major, minor and perfect [[interval category|interval categories]] and thus demand new distinctions. It is thus inescapably xenharmonic. | ||
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== See also == | == See also == | ||
* [[11-odd-limit]] | |||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:11-limit| ]] <!-- main article --> | [[Category:11-limit| ]] <!-- main article --> | ||