7-limit: Difference between revisions

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The '''7-limit''' ~~or 7-prime-limit~~ consists of [[just intonation|rational intervals]] where 7 is the highest allowable [[prime]] factor, so that every such interval may be written as a [[ratio]] of integers which are products of 2, 3, 5 and 7. The 7-limit is the fourth prime limit and is a superset of the [[5-limit]] and a subset of the [[11-limit]]. Some examples of 7-limit intervals include [[7/4]], [[7/5]], [[7/6]], [[9/7]], [[15/14]], [[21/16]], [[21/20]], [[35/27]], [[49/36]], and so on.

The '''7-limit''' (a.k.a. ''yaza'' in [[color notation]]) consists of [[just intonation|rational intervals]] where 7 is the highest allowable [[prime]] factor, so that every such interval may be written as a [[ratio]] of integers which are products of 2, 3, 5 and 7. The 7-limit is the fourth prime limit and is a superset of the [[5-limit]] and a subset of the [[11-limit]]. Some examples of 7-limit intervals include [[7/4]], [[7/5]], [[7/6]], [[9/7]], [[15/14]], [[21/16]], [[21/20]], [[35/27]], [[49/36]], and so on.

These things are contained by the 7-limit, but not the 5-limit:

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The 7-odd-limit is a constraint on the selection of just intervals for a scale or composition such that 7 is the highest allowable odd number, either for the intervals of the scale, or the ratios between successive or simultaneously sounding notes of the composition. The complete list of 7 odd-limit intervals within the octave is [[1/1]], [[8/7]], [[7/6]], [[6/5]], [[5/4]], [[4/3]], [[7/5]], [[10/7]], [[3/2]], [[8/5]], [[5/3]], [[12/7]], [[7/4]], [[2/1]], which is known as the 7-odd-limit [[tonality diamond]].

The phrase "7-limit just intonation" usually refers to the 7-prime-limit and includes primes 2, 3, 5, and 7. When octave equivalence is assumed, an interval can be taken as representing that interval in every possible voicing. This leaves primes 3, 5, and 7, which can be represented in [[~~The Seven Limit Symmetrical Lattices~~|3-dimensional lattice diagrams]], each prime represented by a different dimension. Lattices describing scales beyond the 7-limit require more than three dimensions, and in the 7-limit, such lattices have unique features which simplify the relations between 7-limit chords.

The phrase "7-limit just intonation" usually refers to the 7-prime-limit and includes primes 2, 3, 5, and 7. When octave equivalence is assumed, an interval can be taken as representing that interval in every possible voicing. This leaves primes 3, 5, and 7, which can be represented in [[7-limit symmetrical lattices|3-dimensional lattice diagrams]], each prime represented by a different dimension. Lattices describing scales beyond the 7-limit require more than three dimensions, and in the 7-limit, such lattices have unique features which simplify the relations between 7-limit chords.

For a variety of reasons, common-practice music has been somewhat stuck at the 5-limit for centuries, though 7-limit intervals have a characteristic jazzy sound which is at least partially familiar. Music in the 7-limit thus represents a large step forward, although not as much as 11- or [[13-limit]], which usually sound much more exotic.

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; {{W|Johann Pachelbel}}

* ''{{w|Pachelbel's Canon|Canon in D}}'' (''c''. 1680–1706) – [https://web.archive.org/web/20201127013008/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Pachelbel_s%20Canon%20in%20D%20-%20Relaxing%20music,%20with%20mountain%20views.mp3 play] | [https://www.youtube.com/watch?v=HzQmaxDIxnc YouTube] – arranged by [[Claudi Meneghin]] (2011)

; Traditional (unknown composer)

* [https://www.youtube.com/shorts/uXxfy6r39hI ''Scarborough Fair''] – arranged by [[Claudi Meneghin]] (2026)

=== 20th century ===

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; [[Jacob Adler]]

* [https://m.youtube.com/watch?v=IUePyH2C9Y0 ''7-Limit Harmony''] (2024)

; [[Amanda Cole]]

* [https://www.youtube.com/watch?v=3-3aXAtE574 ''Lumatone Improvisation in 7-limit just intonation tuning with sine tone drone''] (2024)

; [[Ivor Darreg]]

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; [[E8 Heterotic]]

* [https://~~youtu~~.be/~~mecOmJbqbxU~~?si=~~ILByj2hvPIMKRjJT~~ ''Justicar''] (2020)

* [https://www.youtube.com/watch?v=mecOmJbqbxU ''Justicar''] (2020)

; [[Eufalesio]]

* [https://soundcloud.com/eufalesio/mind-ye-a-worse-comelore?in=eufalesio/sets/microtonal-stuff ''Mind Ye A Worse Comelore''] from [https://soundcloud.com/eufalesio/sets/microtonal-stuff ''Microtonal stuff''] (2022)

; [[Francium]]

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; [[Kaiveran Lugheidh]]

* [https://soundcloud.com/vale-10/nostalgic-blue Nostalgic Blue] (2017) – in 2.3.7 subgroup

* [https://soundcloud.com/vale-10/nostalgic-blue ''Nostalgic Blue''] (2017) – in 2.3.7 subgroup

; [[Melanie Martinez]]

* [https://m.youtube.com/watch?v=OKBB1VufWCg ''Training Wheels''] (2015)

; [[Nick, The NRG]]

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; [[Randy Wells]]

* [https://www.youtube.com/watch?v=rTvMMwkH2Z8 ''The Antidote for Entropy''] (2022)

~~== See also ==~~

* [[Wikipedia: Highly composite number]]

[[Category:7-limit| ]]

[[Category:Rank-4 temperaments]]

[[Category:Lists of intervals]]

[[Category:Lattice]]

[[Category:Listen]]

~~[[Category:Rank 4]]~~

@@ Line 1: / Line 1: @@
 {{Prime limit navigation|7}}
 {{Wikipedia|7-limit tuning}}
-The '''7-limit''' or 7-prime-limit consists of [[just intonation|rational intervals]] where 7 is the highest allowable [[prime]] factor, so that every such interval may be written as a [[ratio]] of integers which are products of 2, 3, 5 and 7. The 7-limit is the fourth prime limit and is a superset of the [[5-limit]] and a subset of the [[11-limit]]. Some examples of 7-limit intervals include [[7/4]], [[7/5]], [[7/6]], [[9/7]], [[15/14]], [[21/16]], [[21/20]], [[35/27]], [[49/36]], and so on.
+The '''7-limit''' (a.k.a. ''yaza'' in [[color notation]]) consists of [[just intonation|rational intervals]] where 7 is the highest allowable [[prime]] factor, so that every such interval may be written as a [[ratio]] of integers which are products of 2, 3, 5 and 7. The 7-limit is the fourth prime limit and is a superset of the [[5-limit]] and a subset of the [[11-limit]]. Some examples of 7-limit intervals include [[7/4]], [[7/5]], [[7/6]], [[9/7]], [[15/14]], [[21/16]], [[21/20]], [[35/27]], [[49/36]], and so on.
 These things are contained by the 7-limit, but not the 5-limit:
@@ Line 9: / Line 9: @@
 The 7-odd-limit is a constraint on the selection of just intervals for a scale or composition such that 7 is the highest allowable odd number, either for the intervals of the scale, or the ratios between successive or simultaneously sounding notes of the composition. The complete list of 7 odd-limit intervals within the octave is [[1/1]], [[8/7]], [[7/6]], [[6/5]], [[5/4]], [[4/3]], [[7/5]], [[10/7]], [[3/2]], [[8/5]], [[5/3]], [[12/7]], [[7/4]], [[2/1]], which is known as the 7-odd-limit [[tonality diamond]].
-The phrase "7-limit just intonation" usually refers to the 7-prime-limit and includes primes 2, 3, 5, and 7. When octave equivalence is assumed, an interval can be taken as representing that interval in every possible voicing. This leaves primes 3, 5, and 7, which can be represented in [[The Seven Limit Symmetrical Lattices|3-dimensional lattice diagrams]], each prime represented by a different dimension. Lattices describing scales beyond the 7-limit require more than three dimensions, and in the 7-limit, such lattices have unique features which simplify the relations between 7-limit chords.
+The phrase "7-limit just intonation" usually refers to the 7-prime-limit and includes primes 2, 3, 5, and 7. When octave equivalence is assumed, an interval can be taken as representing that interval in every possible voicing. This leaves primes 3, 5, and 7, which can be represented in [[7-limit symmetrical lattices|3-dimensional lattice diagrams]], each prime represented by a different dimension. Lattices describing scales beyond the 7-limit require more than three dimensions, and in the 7-limit, such lattices have unique features which simplify the relations between 7-limit chords.
 For a variety of reasons, common-practice music has been somewhat stuck at the 5-limit for centuries, though 7-limit intervals have a characteristic jazzy sound which is at least partially familiar. Music in the 7-limit thus represents a large step forward, although not as much as 11- or [[13-limit]], which usually sound much more exotic.
@@ Line 639: / Line 639: @@
 ; {{W|Johann Pachelbel}}
 * ''{{w|Pachelbel's Canon|Canon in D}}'' (''c''. 1680–1706) – [https://web.archive.org/web/20201127013008/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Pachelbel_s%20Canon%20in%20D%20-%20Relaxing%20music,%20with%20mountain%20views.mp3 play] | [https://www.youtube.com/watch?v=HzQmaxDIxnc YouTube] – arranged by [[Claudi Meneghin]] (2011)
+; Traditional (unknown composer)
+* [https://www.youtube.com/shorts/uXxfy6r39hI ''Scarborough Fair''] – arranged by [[Claudi Meneghin]] (2026)
 === 20th century ===
@@ Line 650: / Line 653: @@
 ; [[Jacob Adler]]
 * [https://m.youtube.com/watch?v=IUePyH2C9Y0 ''7-Limit Harmony''] (2024)
+; [[Amanda Cole]]
+* [https://www.youtube.com/watch?v=3-3aXAtE574 ''Lumatone Improvisation in 7-limit just intonation tuning with sine tone drone''] (2024)
 ; [[Ivor Darreg]]
@@ Line 658: / Line 664: @@
 ; [[E8 Heterotic]]
-* [https://youtu.be/mecOmJbqbxU?si=ILByj2hvPIMKRjJT ''Justicar''] (2020)
+* [https://www.youtube.com/watch?v=mecOmJbqbxU ''Justicar''] (2020)
+; [[Eufalesio]]
+* [https://soundcloud.com/eufalesio/mind-ye-a-worse-comelore?in=eufalesio/sets/microtonal-stuff ''Mind Ye A Worse Comelore''] from [https://soundcloud.com/eufalesio/sets/microtonal-stuff ''Microtonal stuff''] (2022)
 ; [[Francium]]
@@ Line 673: / Line 682: @@
 ; [[Kaiveran Lugheidh]]
-* [https://soundcloud.com/vale-10/nostalgic-blue Nostalgic Blue] (2017) – in 2.3.7 subgroup
+* [https://soundcloud.com/vale-10/nostalgic-blue ''Nostalgic Blue''] (2017) – in 2.3.7 subgroup
+; [[Melanie Martinez]]
+* [https://m.youtube.com/watch?v=OKBB1VufWCg ''Training Wheels''] (2015)
 ; [[Nick, The NRG]]
@@ Line 690: / Line 702: @@
 ; [[Randy Wells]]
 * [https://www.youtube.com/watch?v=rTvMMwkH2Z8 ''The Antidote for Entropy''] (2022)
-== See also ==
-* [[Wikipedia: Highly composite number]]
 [[Category:7-limit| ]] <!-- main page -->
+[[Category:Rank-4 temperaments]]
 [[Category:Lists of intervals]]
 [[Category:Lattice]]
 [[Category:Listen]]
-[[Category:Rank 4]]