11-limit: Difference between revisions

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The '''11-limit''' consists of all [[Just intonation|justly tuned]] intervals whose numerators and denominators are both products of the primes 2, 3, 5, 7 and 11. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]]. 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 consonances.

The '''11-limit''' consists of all [[Just intonation|justly tuned]] intervals whose numerators and denominators are both products of the primes 2, 3, 5, 7 and 11. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]]. 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 consonances.

~~== Intervals 1 ==~~

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.

Examples of [[EDO]]s which represent 11-limit intervals well include: {{EDOs|22, 26, 31, 41, 46, 63, 72, 87, 109, 118, 152, and 161edo }}.

== Intervals ==

=== 11-odd-limit intervals ===

{| class="wikitable center-all"

! Ratio

Line 153:

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| do-do

|}

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.

~~Examples of [[EDO]]s which represent 11-limit intervals well include: {{EDOs|22, 26, 31, 41, 46, 63, 72, 87, 109, 118, 152, and 161edo }}.~~

[[File:11-limit_compare.png|alt=11-limit_compare.png|11-limit_compare.png]]

==~~Intervals 2~~==

=== Selected 15-odd-limit intervals ===

Here are all the 15-odd-limit intervals of 11:

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|}

==Music==

== Music ==

* [http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Study #3] [http://sonic-arts.org/hill/10-passages-ji/04_hill_study-3.mp3 play] by [[Dave Hill]]

* [http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Brief 11-ratio composition] [http://sonic-arts.org/hill/10-passages-ji/09_hill_brief-11-ratio-composition.mp3 play] by Dave Hill

* [http://micro.soonlabel.com/just/11-limit/20120210-piano-11-limit.mp3 11 Limit Piano] by [[Chris Vaisvil]]

* [https://soundcloud.com/andrew_heathwaite/11-limit-singtervals 11-limit singtervals] by [[Andrew Heathwaite]]

*[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Study #3] [http://sonic-arts.org/hill/10-passages-ji/04_hill_study-3.mp3 play] by [[Dave Hill]]

== See also ==

*[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Brief 11-ratio composition] [http://sonic-arts.org/hill/10-passages-ji/09_hill_brief-11-ratio-composition.mp3 play] by Dave Hill

* [[Gallery of just intervals]]

*[http://micro.soonlabel.com/just/11-limit/20120210-piano-11-limit.mp3 11 Limit Piano] by [[Chris Vaisvil]]

* [[Harmonic limit]]

*[https://soundcloud.com/andrew_heathwaite/11-limit-singtervals 11-limit singtervals] by [[Andrew Heathwaite]]

* [[11-odd-limit]]

==See also==

*[[Gallery of just intervals]]

*[[Harmonic limit]]

*[[11-odd-limit]]

[[Category:Just intonation]]

[[Category:11-limit]]

[[Category:~~example~~]]

[[Category:Interval]]

[[Category:~~interval~~]]

[[Category:Limit]]

[[Category:~~limit~~]]

[[Category:Listen]]

[[Category:~~listen]]~~

[[Category:Prime limit]]

~~[[Category:prime_limit]]~~

~~[[Category:Todo~~]]

@@ Line 1: / Line 1: @@
-The '''11-limit''' consists of all [[Just intonation|justly tuned]] intervals whose numerators and denominators are both products of the primes 2, 3, 5, 7 and 11. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]]. 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 consonances.
+The '''11-limit''' consists of all [[Just intonation|justly tuned]] intervals whose numerators and denominators are both products of the primes 2, 3, 5, 7 and 11. Some examples of 11-limit intervals are [[14/11]], [[11/8]], [[27/22]] and [[99/98]]. 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 consonances.
-== Intervals 1 ==
+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.
+Examples of [[EDO]]s which represent 11-limit intervals well include: {{EDOs|22, 26, 31, 41, 46, 63, 72, 87, 109, 118, 152, and 161edo }}.
+== Intervals ==
+=== 11-odd-limit intervals ===
 {| class="wikitable center-all"
 ! Ratio
@@ Line 153: / Line 157: @@
 | do-do
 |}
-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.
-Examples of [[EDO]]s which represent 11-limit intervals well include: {{EDOs|22, 26, 31, 41, 46, 63, 72, 87, 109, 118, 152, and 161edo }}.
 [[File:11-limit_compare.png|alt=11-limit_compare.png|11-limit_compare.png]]
-==Intervals 2==
+=== Selected 15-odd-limit intervals ===
 Here are all the 15-odd-limit intervals of 11:
@@ Line 230: / Line 229: @@
 |}
-==Music==
+== Music ==
+* [http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Study #3] [http://sonic-arts.org/hill/10-passages-ji/04_hill_study-3.mp3 play] by [[Dave Hill]]
+* [http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Brief 11-ratio composition] [http://sonic-arts.org/hill/10-passages-ji/09_hill_brief-11-ratio-composition.mp3 play] by Dave Hill
+* [http://micro.soonlabel.com/just/11-limit/20120210-piano-11-limit.mp3 11 Limit Piano] by [[Chris Vaisvil]]
+* [https://soundcloud.com/andrew_heathwaite/11-limit-singtervals 11-limit singtervals] by [[Andrew Heathwaite]]
-*[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Study #3] [http://sonic-arts.org/hill/10-passages-ji/04_hill_study-3.mp3 play] by [[Dave Hill]]
+== See also ==
-*[http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm Brief 11-ratio composition] [http://sonic-arts.org/hill/10-passages-ji/09_hill_brief-11-ratio-composition.mp3 play] by Dave Hill
+* [[Gallery of just intervals]]
-*[http://micro.soonlabel.com/just/11-limit/20120210-piano-11-limit.mp3 11 Limit Piano] by [[Chris Vaisvil]]
+* [[Harmonic limit]]
-*[https://soundcloud.com/andrew_heathwaite/11-limit-singtervals 11-limit singtervals] by [[Andrew Heathwaite]]
+* [[11-odd-limit]]
-==See also==
-*[[Gallery of just intervals]]
-*[[Harmonic limit]]
-*[[11-odd-limit]]
+[[Category:Just intonation]]
 [[Category:11-limit]]
-[[Category:example]]
+[[Category:Interval]]
-[[Category:interval]]
+[[Category:Limit]]
-[[Category:limit]]
+[[Category:Listen]]
-[[Category:listen]]
+[[Category:Prime limit]]
-[[Category:prime_limit]]
-[[Category:Todo]]