11-limit: Difference between revisions

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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-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 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.

These things are contained by the 11-limit, but not the 7-limit:

* The [[11-odd-limit]];

* Mode 6 of the harmonic or subharmonic series.

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.

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== See also ==

* [[11-odd-limit]]

* [[Gallery of just intervals]]

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 {{Prime limit navigation|11}}
-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-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 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.
+These things are contained by the 11-limit, but not the 7-limit:
+* The [[11-odd-limit]];
+* Mode 6 of the harmonic or subharmonic series.
+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.
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 == See also ==
-* [[11-odd-limit]]
 * [[Gallery of just intervals]]