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The '''7-limit''' or "7 prime-limit" refers to a constraint on rational intervals such that 7 is the highest allowable [[prime_number|prime number]], so that every such interval may be written as a ratio of integers which are products of 2, 3, 5 and 7. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the octave include [[9/7]], [[14/9]], [[15/14]], [[28/15]], [[21/16]], [[32/21]], [[25/14]], [[28/25]], [[25/21]], [[42/25]], [[28/27]], [[27/14]], [[35/27]], 54/35, 45/28, 56/45, 49/32, 64/49, 49/36, 72/49, 49/30, 60/49, 49/25, 50/49, 49/27, 54/49, 49/35, 70/49, 49/45, 90/49.
{{Prime limit navigation|7}}
{{Wikipedia|7-limit tuning}}
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.  


"7 odd-limit" refers to a constraint on the selection of [[JustIntonation|just]] [[Interval class|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|1/1]], [[8/7|8/7]], [[7/6|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-limit [http://en.wikipedia.org/wiki/Tonality_diamond tonality diamond].
These things are contained by the 7-limit, but not the 5-limit:
* The [[7-odd-limit|7-]] and [[9-odd-limit]];
* Mode 4 and 5 of the harmonic or subharmonic series.  


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 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]].


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-limit|11-]] or [[13-limit]], which usually sound much more exotic.
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.


Relative to their size, the equal divisions [[1edo]], [[2edo]], [[3edo]], [[4edo]], [[5edo]], [[7edo]], [[9edo]], [[10edo]], [[12edo]], [[15edo|15edo]], [[19edo]], [[21edo]], [[22edo]], [[31edo]], [[53edo]], [[84edo]], [[87edo]], [[94edo]], [[99edo]], [[118edo]], [[130edo]], [[140edo]], [[171edo]], [[270edo]], [[410edo]], [[441edo]] and [[612edo]] provide good approximations to the 7-limit.
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.


== List of Intervals in the 7-Prime Limit and 81-Odd Limit ==
== Edo approximation ==
Here is a list of [[edo]]s which tunes the 7-limit with more accuracy ([[monotonicity limit]] ≥ 7 and decreasing [[TE error]]): {{EDOs| 5, 8d, 9, 10, 12, 19, 27, 31, 41, 53, 72, 99, 171, 441, 612, … }}. For a more comprehensive list, see [[Sequence of equal temperaments by error]].


{| class="wikitable"
Here is a list of edos which tunes the 7-limit well relative to their size ([[TE relative error]] < 5%): {{EDOs| 12, 19, 31, 41, 53, 72, 99, 118, 130, 140, 152, 171, 183, 202, 212, 217, 224, 229, 239, 243, 251, 270, 282, 289, 301, 311, 323, 354, 369, 373, 383, 388, 395, 400, 410, 414, 422, 441, 453, 460, 472, 482, 494, 525, 544, 566, 571, 581, 593, 612, … }}.
 
{{Note| [[Wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "8d" means taking the second closest approximation of harmonic 7. }}
 
== Intervals ==
{{See also| User:Lériendil/Table of 21-odd-limit 7-limit intervals }}
 
Here is a table of intervals in the 7-prime-limit and 81-odd-limit.
 
{| class="wikitable center-1 right-3"
|-
|-
! [[Ratio|Ratio]]
! [[Ratio]]
! [[monzo|Monzo]]
! [[Monzo]]
! [[cents|Cents]] Value
! Size in [[cent|¢]]s
! colspan="2" |[[Kite's color notation|Color name]]
! colspan="2" |[[Color name]]
|-
|-
| 1/1
| 1/1
| {{Monzo| 0 }}
| {{Monzo| 0 }}
| 0.000
| 0.000
|w1
| w1
|wa unison
| wa unison
|-
|-
| 81/80
| 81/80
| {{Monzo| -4 4 -1 }}
| {{Monzo| -4 4 -1 }}
| 21.506
| 21.506
|g1
| g1
|gu comma
| gu comma
|-
|-
| 64/63
| 64/63
| {{Monzo| 6 -2 0 -1 }}
| {{Monzo| 6 -2 0 -1 }}
| 27.264
| 27.264
|r1
| r1
|ru comma
| ru comma
|-
|-
| 50/49
| 50/49
| {{Monzo| 1 0 2 -2 }}
| {{Monzo| 1 0 2 -2 }}
| 34.976
| 34.976
|rryy-2
| rryy-2
|biruyo comma
| biruyo comma
|-
|-
|49/48
| 49/48
|{{Monzo| 1 0 2 -2 }}
| {{Monzo| -4 -1 0 2 }}
|35.697
| 35.697
|zz2
| zz2
|zozo comma
| zozo comma
|-
|-
| 36/35
| 36/35
| {{Monzo| 2 2 -1 -1 }}
| {{Monzo| 2 2 -1 -1 }}
| 48.770
| 48.770
|rg1
| rg1
|rugu comma
| rugu comma
|-
|-
| 28/27
| 28/27
| {{Monzo| 2 -3 0 1 }}
| {{Monzo| 2 -3 0 1 }}
| 62.961
| 62.961
|z2
| z2
|zo 2nd
| zo 2nd
|-
|-
| 25/24
| 25/24
| {{Monzo| -3 -1 2 }}
| {{Monzo| -3 -1 2 }}
| 70.672
| 70.672
|yy1
| yy1
|yoyo unison
| yoyo unison
|-
|-
| 21/20
| 21/20
| {{Monzo| -2 1 -1 1 }}
| {{Monzo| -2 1 -1 1 }}
| 84.467
| 84.467
|zg2
| zg2
|zogu 2nd
| zogu 2nd
|-
|-
| 16/15
| 16/15
| {{Monzo| 4 -1 -1 }}
| {{Monzo| 4 -1 -1 }}
| 111.731
| 111.731
|g2
| g2
|gu 2nd
| gu 2nd
|-
|-
| 15/14
| 15/14
| {{Monzo| -1 1 1 -1 }}
| {{Monzo| -1 1 1 -1 }}
| 119.443
| 119.443
|ry1
| ry1
|ruyo unison
| ruyo unison
|-
|-
| 27/25
| 27/25
| |<nowiki> |0 3 -2</nowiki>&gt;
| {{Monzo| 0 3 -2 }}
| 133.238
| 133.238
|gg2
| gg2
|gugu 2nd
| gugu 2nd
|-
|-
| 49/45
| 49/45
| |<nowiki> |0 -2 -1 2</nowiki>&gt;
| {{Monzo| 0 -2 -1 2 }}
| 147.428
| 147.428
|zzg3
| zzg3
|zozogu 3rd
| zozogu 3rd
|-
|-
| 35/32
| 35/32
| |<nowiki> |-5 0 1 1</nowiki>&gt;
| {{Monzo| -5 0 1 1 }}
| 155.140
| 155.140
|zy2
| zy2
|zoyo 2nd
| zoyo 2nd
|-
|-
| 54/49
| 54/49
| |<nowiki> |1 3 0 -2</nowiki>&gt;
| {{Monzo| 1 3 0 -2 }}
| 168.213
| 168.213
|rr1
| rr1
|ruru unison
| ruru unison
|-
|-
|10/9
| 10/9
|{{Monzo| 1 0 2 -2 }}
| {{Monzo| 1 0 2 -2 }}
|182.404
| 182.404
|y2
| y2
|yo 2nd
| yo 2nd
|-
|-
| 28/25
| 28/25
| |<nowiki> |2 0 -2 1</nowiki>&gt;
| {{Monzo| 2 0 -2 1 }}
| 196.198
| 196.198
|zgg3
| zgg3
|zogugu 3rd
| zogugu 3rd
|-
|-
| 9/8
| 9/8
| |<nowiki> |-3 2</nowiki>&gt;
| {{Monzo| -3 2 }}
| 203.910
| 203.910
|w2
| w2
|wa 2nd
| wa 2nd
|-
|-
| 8/7
| 8/7
| |<nowiki> |3 0 0 -1</nowiki>&gt;
| {{Monzo| 3 0 0 -1 }}
| 231.174
| 231.174
|r2
| r2
|ru 2nd
| ru 2nd
|-
|-
| 81/70
| 81/70
| |<nowiki> |-1 4 -1 -1</nowiki>&gt;
| {{Monzo| -1 4 -1 -1 }}
| 252.68
| 252.680
|rg2
| rg2
|rugu 2nd
| rugu 2nd
|-
|-
| 7/6
| 7/6
| |<nowiki> |-1 -1 0 1</nowiki>&gt;
| {{Monzo| -1 -1 0 1 }}
| 266.871
| 266.871
|z3
| z3
|zo 3rd
| zo 3rd
|-
|-
| 75/64
| 75/64
| |<nowiki> |-6 1 2</nowiki>&gt;
| {{Monzo| -6 1 2 }}
| 274.582
| 274.582
|yy2
| yy2
|yoyo 2nd
| yoyo 2nd
|-
|-
| 32/27
| 32/27
| |<nowiki> |5 -3</nowiki>&gt;
| {{Monzo| 5 -3 }}
| 294.135
| 294.135
|w3
| w3
|wa 3rd
| wa 3rd
|-
|-
| 25/21
| 25/21
| |<nowiki> |0 -1 2 -1</nowiki>&gt;
| {{Monzo| 0 -1 2 -1 }}
| 301.847
| 301.847
|ryy2
| ryy2
|ruyoyo 2nd
| ruyoyo 2nd
|-
|-
| 6/5
| 6/5
| |<nowiki> |1 1 -1</nowiki>&gt;
| {{Monzo| 1 1 -1 }}
| 315.641
| 315.641
|g3
| g3
|gu 3rd
| gu 3rd
|-
|-
| 98/81
| 98/81
| |<nowiki> |1 -4 0 2</nowiki>&gt;
| {{Monzo| 1 -4 0 2 }}
| 329.832
| 329.832
|zz4
| zz4
|zozo 4th
| zozo 4th
|-
|-
| 60/49
| 60/49
| |<nowiki> |2 1 1 -2</nowiki>&gt;
| {{Monzo| 2 1 1 -2 }}
| 350.617
| 350.617
|rry2
| rry2
|ruruyo 2nd
| ruruyo 2nd
|-
|-
| | 49/40
| 49/40
| |<nowiki> |-3 0 -1 2</nowiki>&gt;
| {{Monzo| -3 0 -1 2 }}
| | 351.338
| 351.338
|zzg4
| zzg4
|zozogu 4th
| zozogu 4th
|-
|-
| | 100/81
| 100/81
| |<nowiki> |2 -4 2</nowiki>&gt;
| {{Monzo| 2 -4 2 }}
| | 364.807
| 364.807
|yy3
| yy3
|yoyo 3rd
| yoyo 3rd
|-
|-
| | 56/45
| 56/45
| |<nowiki> |3 -2 -1 1</nowiki>&gt;
| {{Monzo| 3 -2 -1 1 }}
| | 378.602
| 378.602
|zg4
| zg4
|zogu 4th
| zogu 4th
|-
|-
|5/4
| 5/4
|{{Monzo| 0 }}
| {{Monzo| -2 0 1 }}
|386.314
| 386.314
|y3
| y3
|yo 3rd
| yo 3rd
|-
|-
| | 63/50
| 63/50
| |<nowiki> |-1 2 -2 1</nowiki>&gt;
| {{Monzo| -1 2 -2 1 }}
| | 400.108
| 400.108
|zgg4
| zgg4
|zogugu 4th
| zogugu 4th
|-
|-
| | 81/64
| 81/64
| |<nowiki> |-6 4</nowiki>&gt;
| {{Monzo| -6 4 }}
| | 407.820
| 407.820
|Lw3
| Lw3
|large wa 3rd
| lawa 3rd
|-
|-
| | 80/63
| 80/63
| |<nowiki> |4 -2 1 -1</nowiki>&gt;
| {{Monzo| 4 -2 1 -1 }}
| | 413.578
| 413.578
|ry3
| ry3
|ruyo 3rd
| ruyo 3rd
|-
|-
| | 32/25
| 32/25
| |<nowiki> |5 0 -2</nowiki>&gt;
| {{Monzo| 5 0 -2 }}
| | 427.373
| 427.373
|gg4
| gg4
|gugu 4th
| gugu 4th
|-
|-
| | 9/7
| 9/7
| |<nowiki> |0 2 0 -1</nowiki>&gt;
| {{Monzo| 0 2 0 -1 }}
| | 435.084
| 435.084
|r3
| r3
|ru 3rd
| ru 3rd
|-
|-
| | 35/27
| 35/27
| |<nowiki> |0 -3 1 1</nowiki>&gt;
| {{Monzo| 0 -3 1 1 }}
| | 449.275
| 449.275
|zy4
| zy4
|zoyo 4th
| zoyo 4th
|-
|-
| | 64/49
| 64/49
| |<nowiki> |6 0 0 -2</nowiki>&gt;
| {{Monzo| 6 0 0 -2 }}
| | 462.348
| 462.348
|rr3
| rr3
|ruru 3rd
| ruru 3rd
|-
|-
| | 98/75
| 98/75
| |<nowiki> |1 -1 -2 2</nowiki>&gt;
| {{Monzo| 1 -1 -2 2 }}
| | 463.069
| 463.069
|zzgg5
| zzgg5
|double zogu 5th
| bizogu 5th
|-
|-
| | 21/16
| 21/16
| |<nowiki> |-4 1 0 1</nowiki>&gt;
| {{Monzo| -4 1 0 1 }}
| | 470.781
| 470.781
|z4
| z4
|zo 4th
| zo 4th
|-
|-
| | 4/3
| 4/3
| |<nowiki> |2 -1</nowiki>&gt;
| {{Monzo| 2 -1 }}
| | 498.045
| 498.045
|w4
| w4
|wa 4th
| wa 4th
|-
|-
| | 75/56
| 75/56
| |<nowiki> |-3 1 2 -1</nowiki>&gt;
| {{Monzo| -3 1 2 -1 }}
| | 505.757
| 505.757
|ryy3
| ryy3
|ruyoyo 3rd
| ruyoyo 3rd
|-
|-
| | 27/20
| 27/20
| |<nowiki> |-2 3 -1</nowiki>&gt;
| {{Monzo| -2 3 -1 }}
| | 519.551
| 519.551
|g4
| g4
|gu 4th
| gu 4th
|-
|-
| | 49/36
| 49/36
| |<nowiki> |-2 -2 0 2</nowiki>&gt;
| {{Monzo| -2 -2 0 2 }}
| | 533.742
| 533.742
|zz5
| zz5
|zozo 5th
| zozo 5th
|-
|-
| | 48/35
| 48/35
| |<nowiki> |4 1 -1 -1</nowiki>&gt;
| {{Monzo| 4 1 -1 -1 }}
| | 546.815
| 546.815
|rg4
| rg4
|rugu 4th
| rugu 4th
|-
|-
| | 112/81
| 112/81
| |<nowiki> |4 -4 0 1</nowiki>&gt;
| {{Monzo| 4 -4 0 1 }}
| | 561.006
| 561.006
|z5
| z5
|zo 5th
| zo 5th
|-
|-
|25/18
| 25/18
|<nowiki>|-1 -2 2></nowiki>
| {{Monzo| -1 -2 2 }}
|568.717
| 568.717
|yy4
| yy4
|yoyo 4th
| yoyo 4th
|-
|-
| | 7/5
| 7/5
| |<nowiki> |0 0 -1 1</nowiki>&gt;
| {{Monzo| 0 0 -1 1 }}
| | 582.512
| 582.512
|zg5
| zg5
|zogu 5th
| zogu 5th
|-
|-
| | 45/32
| 45/32
| |<nowiki> |-5 2 1</nowiki>&gt;
| {{Monzo| -5 2 1 }}
| | 590.224
| 590.224
|y4
| y4
|yo 4th
| yo 4th
|-
|-
| | 64/45
| 64/45
| |<nowiki> |6 -2 -1</nowiki>&gt;
| {{Monzo| 6 -2 -1 }}
| | 609.776
| 609.776
|g5
| g5
|gu 5th
| gu 5th
|-
|-
| | 10/7
| 10/7
| |<nowiki> |1 0 1 -1</nowiki>&gt;
| {{Monzo| 1 0 1 -1 }}
| | 617.488
| 617.488
|ry4
| ry4
|ruyo 4th
| ruyo 4th
|-
|-
|36/25
| 36/25
|<nowiki>|2 2 -2></nowiki>
| {{Monzo| 2 2 -2 }}
|631.283
| 631.283
|gg5
| gg5
|gugu 5th
| gugu 5th
|-
|-
| | 81/56
| 81/56
| |<nowiki> |-3 4 0 -1</nowiki>&gt;
| {{Monzo| -3 4 0 -1 }}
| | 638.994
| 638.994
|r4
| r4
|ru 4th
| ru 4th
|-
|-
| | 35/24
| 35/24
| |<nowiki> |-3 -1 1 1</nowiki>&gt;
| {{Monzo| -3 -1 1 1 }}
| | 653.185
| 653.185
|zy5
| zy5
|zoyo 5th
| zoyo 5th
|-
|-
| | 72/49
| 72/49
| |<nowiki> |3 2 0 -2</nowiki>&gt;
| {{Monzo| 3 2 0 -2 }}
| | 666.258
| 666.258
|rr4
| rr4
|ruru 4th
| ruru 4th
|-
|-
| | 40/27
| 40/27
| |<nowiki> |3 -3 1</nowiki>&gt;
| {{Monzo| 3 -3 1 }}
| | 680.449
| 680.449
|y5
| y5
|yo 5th
| yo 5th
|-
|-
| | 112/75
| 112/75
| |<nowiki> |4 -1 -2 1</nowiki>&gt;
| {{Monzo| 4 -1 -2 1 }}
| | 694.243
| 694.243
|zgg6
| zgg6
|zogugu 6th
| zogugu 6th
|-
|-
| | 3/2
| 3/2
| |<nowiki> |-1 1</nowiki>&gt;
| {{Monzo| -1 1 }}
| | 701.955
| 701.955
|w5
| w5
|wa 5th
| wa 5th
|-
|-
| | 32/21
| 32/21
| |<nowiki> |5 -1 0 -1</nowiki>&gt;
| {{Monzo| 5 -1 0 -1 }}
| | 729.219
| 729.219
|r5
| r5
|ru 5th
| ru 5th
|-
|-
| | 75/49
| 75/49
| |<nowiki> |0 1 2 -2</nowiki>&gt;
| {{Monzo| 0 1 2 -2 }}
| | 736.931
| 736.931
|rryy4
| rryy4
|double ruyo 4th
| biruyo 4th
|-
|-
| | 49/32
| 49/32
| |<nowiki> |-5 0 0 2</nowiki>&gt;
| {{Monzo| -5 0 0 2 }}
| | 737.652
| 737.652
|zz6
| zz6
|zozo 6th
| zozo 6th
|-
|-
| | 54/35
| 54/35
| |<nowiki> |1 3 -1 -1</nowiki>&gt;
| {{Monzo| 1 3 -1 -1 }}
| | 750.725
| 750.725
|rg5
| rg5
|rugu 5th
| rugu 5th
|-
|-
| | 14/9
| 14/9
| |<nowiki> |1 -2 0 1</nowiki>&gt;
| {{Monzo| 1 -2 0 1 }}
| | 764.916
| 764.916
|z6
| z6
|zo 6th
| zo 6th
|-
|-
| | 25/16
| 25/16
| |<nowiki> |-4 0 2</nowiki>&gt;
| {{Monzo| -4 0 2 }}
| | 772.627
| 772.627
|yy5
| yy5
|yoyo 5th
| yoyo 5th
|-
|-
| | 63/40
| 63/40
| |<nowiki> |-3 2 -1 1</nowiki>&gt;
| {{Monzo| -3 2 -1 1 }}
| | 786.422
| 786.422
|zg6
| zg6
|zogu 6th
| zogu 6th
|-
|-
| | 128/81
| 128/81
| |<nowiki> |7 -4</nowiki>&gt;
| {{Monzo| 7 -4 }}
| | 792.180
| 792.180
|sw6
| sw6
|small wa 6th
| sawa 6th
|-
|-
| | 100/63
| 100/63
| |<nowiki> |2 -2 2 -1</nowiki>&gt;
| {{Monzo| 2 -2 2 -1 }}
| | 799.892
| 799.892
|ryy5
| ryy5
|ruyoyo 5th
| ruyoyo 5th
|-
|-
|8/5
| 8/5
|{{Monzo| 0 }}
| {{Monzo| 3 0 -1 }}
|813.686
| 813.686
|g6
| g6
|gu 6th
| gu 6th
|-
|-
| | 45/28
| 45/28
| |<nowiki> |-2 2 1 -1</nowiki>&gt;
| {{Monzo| -2 2 1 -1 }}
| | 821.398
| 821.398
|ry5
| ry5
|ruyo 5th
| ruyo 5th
|-
|-
| | 81/50
| 81/50
| |<nowiki> |-1 4 -2</nowiki>&gt;
| {{Monzo| -1 4 -2 }}
| | 835.193
| 835.193
|gg6
| gg6
|gugu 6th
| gugu 6th
|-
|-
| | 80/49
| 80/49
| |<nowiki> |4 0 1 -2</nowiki>&gt;
| {{Monzo| 4 0 1 -2 }}
| | 848.662
| 848.662
|rry5
| rry5
|ruruyo 5th
| ruruyo 5th
|-
|-
| | 49/30
| 49/30
| |<nowiki> |-1 -1 -1 2</nowiki>&gt;
| {{Monzo| -1 -1 -1 2 }}
| | 849.383
| 849.383
|zzg7
| zzg7
|zozogu 7th
| zozogu 7th
|-
|-
| | 81/49
| 81/49
| |<nowiki> |0 4 0 -2</nowiki>&gt;
| {{Monzo| 0 4 0 -2 }}
| | 870.168
| 870.168
|rr5
| rr5
|ruru 5th
| ruru 5th
|-
|-
| | 5/3
| 5/3
| |<nowiki> |0 -1 1</nowiki>&gt;
| {{Monzo| 0 -1 1 }}
| | 884.359
| 884.359
|y6
| y6
|yo 6th
| yo 6th
|-
|-
| | 42/25
| 42/25
| |<nowiki> |1 1 -2 1</nowiki>&gt;
| {{Monzo| 1 1 -2 1 }}
| | 898.153
| 898.153
|zgg7
| zgg7
|zogugu 7th
| zogugu 7th
|-
|-
| | 27/16
| 27/16
| |<nowiki> |-4 3</nowiki>&gt;
| {{Monzo| -4 3 }}
| | 905.865
| 905.865
|w6
| w6
|wa 6th
| wa 6th
|-
|-
| | 128/75
| 128/75
| |<nowiki> |7 -1 -2</nowiki>&gt;
| {{Monzo| 7 -1 -2 }}
| | 925.418
| 925.418
|gg7
| gg7
|gugu 7th
| gugu 7th
|-
|-
| | 12/7
| 12/7
| |<nowiki> |2 1 0 -1</nowiki>&gt;
| {{Monzo| 2 1 0 -1 }}
| | 933.129
| 933.129
|r6
| r6
|ru 6th
| ru 6th
|-
|-
| | 140/81
| 140/81
| |<nowiki> |2 -4 1 1</nowiki>&gt;
| {{Monzo| 2 -4 1 1 }}
| | 947.320
| 947.320
|zy7
| zy7
|zoyo 7th
| zoyo 7th
|-
|-
| | 7/4
| 7/4
| |<nowiki> |-2 0 0 1</nowiki>&gt;
| {{Monzo| -2 0 0 1 }}
| | 968.826
| 968.826
|z7
| z7
|zo 7th
| zo 7th
|-
|-
| | 16/9
| 16/9
| |<nowiki> |4 -2</nowiki>&gt;
| {{Monzo| 4 -2 }}
| | 996.090
| 996.090
|w7
| w7
|wa 7th
| wa 7th
|-
|-
| | 25/14
| 25/14
| |<nowiki> |-1 0 2 -1</nowiki>&gt;
| {{Monzo| -1 0 2 -1 }}
| | 1003.802
| 1003.802
|ryy6
| ryy6
|ruyoyo 6th
| ruyoyo 6th
|-
|-
| [[9/5]]
| [[9/5]]
|{{Monzo|0 2 -1}}
| {{Monzo| 0 2 -1 }}
|1017.596
| 1017.596
|g7
| g7
|gu 7th
| gu 7th
|-
|-
| | 49/27
| 49/27
| |<nowiki> |0 -3 0 2</nowiki>&gt;
| {{Monzo| 0 -3 0 2 }}
| | 1031.787
| 1031.787
|zz8
| zz8
|zozo 8ve
| zozo 8ve
|-
|-
| | 64/35
| 64/35
| |<nowiki> |6 0 -1 -1</nowiki>&gt;
| {{Monzo| 6 0 -1 -1 }}
| | 1044.860
| 1044.860
|rg7
| rg7
|rugu 7th
| rugu 7th
|-
|-
| | 90/49
| 90/49
| |<nowiki> |1 2 1 -2</nowiki>&gt;
| {{Monzo| 1 2 1 -2 }}
| | 1052.572
| 1052.572
|rry6
| rry6
|ruruyo 6th
| ruruyo 6th
|-
|-
| | 50/27
| 50/27
| |<nowiki> |1 -3 2</nowiki>&gt;
| {{Monzo| 1 -3 2 }}
| | 1066.762
| 1066.762
|yy7
| yy7
|yoyo 7th
| yoyo 7th
|-
|-
| | 28/15
| 28/15
| |<nowiki> |2 -1 -1 1</nowiki>&gt;
| {{Monzo| 2 -1 -1 1 }}
| | 1080.557
| 1080.557
|zg8
| zg8
|zogu 8ve
| zogu 8ve
|-
|-
| | 15/8
| 15/8
| |<nowiki> |-3 1 1</nowiki>&gt;
| {{Monzo| -3 1 1 }}
| | 1088.269
| 1088.269
|y7
| y7
|yo 7th
| yo 7th
|-
|-
| | 40/21
| 40/21
| |<nowiki> |3 -1 1 -1</nowiki>&gt;
| {{Monzo| 3 -1 1 -1 }}
| | 1115.533
| 1115.533
|ry7
| ry7
|ruyo 7th
| ruyo 7th
|-
|-
| | 48/25
| 48/25
| |<nowiki> |4 1 -2</nowiki>&gt;
| {{Monzo| 4 1 -2 }}
| | 1129.328
| 1129.328
|gg8
| gg8
|gugu 8ve
| gugu 8ve
|-
|-
| | 27/14
| 27/14
| |<nowiki> |-1 3 0 -1</nowiki>&gt;
| {{Monzo| -1 3 0 -1 }}
| | 1137.039
| 1137.039
|r7
| r7
|ru 7th
| ru 7th
|-
|-
| | 35/18
| 35/18
| |<nowiki> |-1 -2 1 1</nowiki>&gt;
| {{Monzo| -1 -2 1 1 }}
| | 1151.230
| 1151.230
|zy8
| zy8
|zoyo 8ve
| zoyo 8ve
|-
|-
|96/49
| 96/49
|<nowiki>|5 1 0 -2></nowiki>
| {{Monzo| 5 1 0 -2 }}
|1164.303
| 1164.303
|rr7
| rr7
|ruru 7th
| ruru 7th
|-
|-
| | 49/25
| 49/25
| |<nowiki> |0 0 -2 2</nowiki>&gt;
| {{Monzo| 0 0 -2 2 }}
| | 1165.024
| 1165.024
|zzgg9
| zzgg9
|double zogu 9th
| bizogu 9th
|-
|-
| | 63/32
| 63/32
| |<nowiki> |-5 2 0 1</nowiki>&gt;
| {{Monzo| -5 2 0 1 }}
| | 1172.736
| 1172.736
|z8
| z8
|zo 8ve
| zo 8ve
|-
|-
| | 160/81
| 160/81
| |<nowiki> |5 -4 1</nowiki>&gt;
| {{Monzo| 5 -4 1 }}
| | 1178.494
| 1178.494
|y8
| y8
|yo 8ve
| yo 8ve
|-
|-
| | 2/1
| 2/1
| |<nowiki> |1</nowiki>&gt;
| {{Monzo| 1 }}
| | 1200.000
| 1200.000
|w8
| w8
|wa 8ve
| wa 8ve
|}
|}
== Subgroups of the 7-limit ==
* [[2.3.7 subgroup]]
* [[2.5.7 subgroup]]
* [[3.5.7 subgroup]]


== Music ==
== Music ==
* [http://micro.soonlabel.com/0-praxis/audio/August/august_12_Ruckus.mp3 Ruckus From the Quiet Zone] by Ralph Lewis
=== Modern renderings ===
* [http://micro.soonlabel.com/blue-tuning/blue-ji-excluded-by-peers.mp3 Excluded by Peers] by [[Chris Vaisvil]]
; {{W|Gustav Holst}}
* [http://micro.soonlabel.com/centaur_tuning/Prelude_For_Centaur_Tuned_Piano.mp3 Prelude for Centaur Tuned Piano] by Chris Vaisvil
* "Mars" from ''{{w|The Planets}}'' (1914–1917) – [http://chrisvaisvil.com/gustav-holsts-mars-arranged-for-7-limit-ji-orchestra/ blog] | [http://clones.soonlabel.com/public/classical-music/mars-7-limit-kontakt5.mp3 play] – arranged by [[Chris Vaisvil]] (2012)
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prelude%20%231%20for%207-limit%20JI.mp3 Prelude #1 in 7-limit JI] by [[Ivor_Darreg|Ivor Darreg]] &lt;-- are there any notations for it?
 
* [http://www.archive.org/details/ClintonVariations Clinton Variations] [http://www.archive.org/download/ClintonVariations/clinton.mp3 play] by [[Gene Ward Smith]]
; {{W|Scott Joplin}}
* [http://www.youtube.com/watch?v=HzQmaxDIxnc&feature=channel_video_title Pachelbel's Canon in D in 7-limit JI] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Pachelbel_s%20Canon%20in%20D%20-%20Relaxing%20music,%20with%20mountain%20views.mp3 play]
* ''{{w|Maple Leaf Rag}}'' (1899) – [http://web.archive.org/web/20190412163308/http://soonlabel.com/xenharmonic/archives/2127 play] – arranged by [[Claudi Meneghin]] (2014)
* [http://clones.soonlabel.com/public/classical-music/mars-7-limit-kontakt5.mp3 Mars in 7-Limit JI] from [http://en.wikipedia.org/wiki/The_Planets The Planets] the orchestral suite by Gustav Holst arranged by [[Chris Vaisvil]] (Blog entry: [http://chrisvaisvil.com/gustav-holsts-mars-arranged-for-7-limit-ji-orchestra/ Gustav Holst’s Mars arranged for 7-limit JI Orchestra « Music &amp; Techniques by Chris Vaisvil])
 
* [http://micro.soonlabel.com/gene_ward_smith/Others/Kite/Consolation%20%233%20by%20Ken%20Stillwell%20retuned.mp3 Liszt Consolation #3] Ken Stillwell performance, retuned by Kite Giedraitis to the [[kite33]] 7-limit JI scale
; {{W|Franz Liszt}}
* [http://tallkite.com/music/IHearNumbers.html I Hear Numbers] by [[KiteGiedraitis|TallKite]]
* {{W|Consolations (Liszt)|"Consolation No. 3"}} (1850) – [https://soundcloud.com/tallkite/liszt-consolation-3-by-ken-1 play] – Ken Stillwell performance, retuned by [[Kite Giedraitis]] to the [[kite33]] 7-limit JI scale
 
; {{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 ===
; [[Ben Johnston]]
* ''String Quartet No. 4'' (1973) – [https://newworldrecords.bandcamp.com/track/crossings-the-ascent-string-quartet-no-4-amazing-grace Bandcamp] | [https://www.youtube.com/watch?v=ReHIe0WDvNs YouTube] – performed by Kepler Quartet
 
=== 21st century ===
; [[Abnormality]]
* [https://www.youtube.com/watch?v=WuW5COnfOlE ''Just Elevation''] (2023)
 
; [[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]]
* [http://web.archive.org/web/20201127014610/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prelude%20%231%20for%207-limit%20JI.mp3 ''Prelude #1 in 7-limit JI'']
 
; [[dotuXil]]
* [https://dotuxil.bandcamp.com/track/waterpad "waterpad"] from [https://dotuxil.bandcamp.com/album/collected-refractions ''Collected Refractions''] (2024)
 
; [[E8 Heterotic]]
* [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]]
* [https://www.youtube.com/watch?v=NANoBRyxll8 ''Too Happy For My Mood''] (2023)
* [https://www.youtube.com/watch?v=YcMcychEAoE ''The Bazillionth Party Track''] (2023)
* [https://www.youtube.com/watch?v=qDfIzd_Q-Hc ''Counting to Infinity''] (2025)
* "You Geese" from ''Holy Carp'' (2025) – [https://open.spotify.com/track/5xcKZqwgw2SXSZRf1NQsyT Spotify] | [https://francium223.bandcamp.com/track/you-geese Bandcamp] | [https://www.youtube.com/watch?v=jlLQYfHp69A YouTube]
 
; [[Kite Giedraitis]]
* [http://tallkite.com/music/IHearNumbers.html ''I Hear Numbers'']
 
; [[Ralph Lewis]]
* [http://micro.soonlabel.com/0-praxis/audio/August/august_12_Ruckus.mp3 ''Ruckus From the Quiet Zone'']
 
; [[Kaiveran Lugheidh]]
* [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]]
* [https://www.youtube.com/watch?v=6IBM_JX52ck ''Cloudy Dreams''] (2022)
 
; [[Juhani Nuorvala]]
* [https://www.youtube.com/watch?v=0bXhY83asUo ''The tap dance scene from Flash Flash''] (2019)
 
; [[Gene Ward Smith]]
* ''Clinton Variations'' (2010) – [http://www.archive.org/details/ClintonVariations detail] | [http://www.archive.org/download/ClintonVariations/clinton.mp3 play]
 
; [[Chris Vaisvil]]
* [http://micro.soonlabel.com/blue-tuning/blue-ji-excluded-by-peers.mp3 ''Excluded by Peers'']
* [http://micro.soonlabel.com/centaur_tuning/Prelude_For_Centaur_Tuned_Piano.mp3 ''Prelude for Centaur Tuned Piano'']
 
; [[Randy Wells]]
* [https://www.youtube.com/watch?v=rTvMMwkH2Z8 ''The Antidote for Entropy''] (2022)


== See also ==
[[Category:7-limit| ]] <!-- main page -->
* [[Harmonic Limit]]
[[Category:Rank-4 temperaments]]
* [https://en.wikipedia.org/wiki/7-limit 7-limit - Wikipedia]
[[Category:Lists of intervals]]
* [https://en.wikipedia.org/wiki/Highly_composite_number Highly composite number - Wikipedia]    [[Category:7-limit| ]] <!-- main page -->
[[Category:Lattice]]
[[Category:example]]
[[Category:Listen]]
[[Category:interval]]
[[Category:lattice]]
[[Category:limit]]
[[Category:listen]]
[[Category:prime_limit]]
[[Category:rank_4]]
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