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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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|9/7]], [[14/9|14/9]], [[15/14|15/14]], [[28/15|28/15]], [[21/16|21/16]], [[32/21|32/21]], [[25/14|25/14]], [[28/25|28/25]], [[25/21|25/21]], [[42/25|42/25]], [[28/27|28/27]], [[27/14|27/14]], [[35/27|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.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:PiotrGrochowski|PiotrGrochowski]] and made on <tt>2016-08-24 12:29:21 UTC</tt>.<br>
: The original revision id was <tt>590065746</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The //7-limit// or "7 prime-limit" refers to a constraint on rational intervals such that 7 is the highest allowable [[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|9/7]], [[14_9|14/9]], [[15_14|15/14]], [[28_15|28/15]], [[21_16|21/16]], [[32_21|32/21]], [[25_14|25/14]], [[28_25|28/25]], [[25_21|25/21]], [[42_25|42/25]], [[28_27|28/27]], [[27_14|27/14]], [[35_27|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.


"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|6/5]], [[5_4|5/4]], [[4_3|4/3]], [[7_5|7/5]], [[10_7|10/7]], [[3_2|3/2]], [[8_5|8/5]], [[5_3|5/3]], [[12_7|12/7]], [[7_4|7/4]], [[2_1|2/1]], which is known as the 7-limit [[http://en.wikipedia.org/wiki/Tonality_diamond|tonality diamond]].
"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|6/5]], [[5/4|5/4]], [[4/3|4/3]], [[7/5|7/5]], [[10/7|10/7]], [[3/2|3/2]], [[8/5|8/5]], [[5/3|5/3]], [[12/7|12/7]], [[7/4|7/4]], [[2/1|2/1]], which is known as the 7-limit [http://en.wikipedia.org/wiki/Tonality_diamond 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 a pitch class representing that interval in every possible octave. 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 a pitch class representing that interval in every possible octave. 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.


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


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


==List of Intervals in the 7-Prime Limit and 81-Odd Limit==  
==List of Intervals in the 7-Prime Limit and 81-Odd Limit==


|| [[Ratio]] || [[Monzo]] || [[Cents]] Value ||
{| class="wikitable"
|| 1/1 || |0&gt; || 0.000 ||
|-
|| 81/80 || |-4 4 -1&gt; || 21.506 ||
| | [[Ratio|Ratio]]
|| 64/63 || |6 -2 0 -1&gt; || 27.264 ||
| | [[monzo|Monzo]]
|| 50/49 || |1 0 2 -2&gt; || 34.976 ||
| | [[cents|Cents]] Value
|| 36/35 || |2 2 -1 -1&gt; || 48.770 ||
|-
|| 28/27 || |2 -3 0 1&gt; || 62.961 ||
| | 1/1
|| 25/24 || |-3 -1 2&gt; || 70.672 ||
| | |0&gt;
|| 21/20 || |-2 1 -1 1&gt; || 84.467 ||
| | 0.000
|| 16/15 || |4 -1 -1&gt; || 111.731 ||
|-
|| 15/14 || |-1 1 1 -1&gt; || 119.443 ||
| | 81/80
|| 27/25 || |0 3 -2&gt; || 133.238 ||
| | |-4 4 -1&gt;
|| 49/45 || |0 -2 -1 2&gt; || 147.428 ||
| | 21.506
|| 35/32 || |-5 0 1 1&gt; || 155.140 ||
|-
|| 54/49 || |1 3 0 -2&gt; || 168.213 ||
| | 64/63
|| 28/25 || |2 0 -2 1&gt; || 196.198 ||
| | |6 -2 0 -1&gt;
|| 9/8 || |-3 2&gt; || 203.910 ||
| | 27.264
|| 8/7 || |3 0 0 -1&gt; || 231.174 ||
|-
|| 81/70 || |-1 4 -1 -1&gt; || 252.68 ||
| | 50/49
|| 7/6 || |-1 -1 0 1&gt; || 266.871 ||
| | |1 0 2 -2&gt;
|| 75/64 || |-6 1 2&gt; || 274.582 ||
| | 34.976
|| 32/27 || |5 -3&gt; || 294.135 ||
|-
|| 25/21 || |0 -1 2 -1&gt; || 301.847 ||
| | 36/35
|| 6/5 || |1 1 -1&gt; || 315.641 ||
| | |2 2 -1 -1&gt;
|| 98/81 || |1 -4 0 2&gt; || 329.832 ||
| | 48.770
|| 60/49 || |2 1 1 -2&gt; || 350.617 ||
|-
|| 49/40 || |-3 0 -1 2&gt; || 351.338 ||
| | 28/27
|| 100/81 || |2 -4 2&gt; || 364.807 ||
| | |2 -3 0 1&gt;
|| 56/45 || |3 -2 -1 1&gt; || 378.602 ||
| | 62.961
|| 63/50 || |-1 2 -2 1&gt; || 400.108 ||
|-
|| 81/64 || |-6 4&gt; || 407.820 ||
| | 25/24
|| 80/63 || |4 -2 1 -1&gt; || 413.578 ||
| | |-3 -1 2&gt;
|| 32/25 || |5 0 -2&gt; || 427.373 ||
| | 70.672
|| 9/7 || |0 2 0 -1&gt; || 435.084 ||
|-
|| 35/27 || |0 -3 1 1&gt; || 449.275 ||
| | 21/20
|| 64/49 || |6 0 0 -2&gt; || 462.348 ||
| | |-2 1 -1 1&gt;
|| 98/75 || |1 -1 -2 2&gt; || 463.069 ||
| | 84.467
|| 21/16 || |-4 1 0 1&gt; || 470.781 ||
|-
|| 4/3 || |2 -1&gt; || 498.045 ||
| | 16/15
|| 75/56 || |-3 1 2 -1&gt; || 505.757 ||
| | |4 -1 -1&gt;
|| 27/20 || |-2 3 -1&gt; || 519.551 ||
| | 111.731
|| 49/36 || |-2 -2 0 2&gt; || 533.742 ||
|-
|| 48/35 || |4 1 -1 -1&gt; || 546.815 ||
| | 15/14
|| 112/81 || |4 -4 0 1&gt; || 561.006 ||
| | |-1 1 1 -1&gt;
|| 7/5 || |0 0 -1 1&gt; || 582.512 ||
| | 119.443
|| 45/32 || |-5 2 1&gt; || 590.224 ||
|-
|| 64/45 || |6 -2 -1&gt; || 609.776 ||
| | 27/25
|| 10/7 || |1 0 1 -1&gt; || 617.488 ||
| | |0 3 -2&gt;
|| 81/56 || |-3 4 0 -1&gt; || 638.994 ||
| | 133.238
|| 35/24 || |-3 -1 1 1&gt; || 653.185 ||
|-
|| 72/49 || |3 2 0 -2&gt; || 666.258 ||
| | 49/45
|| 40/27 || |3 -3 1&gt; || 680.449 ||
| | |0 -2 -1 2&gt;
|| 112/75 || |4 -1 -2 1&gt; || 694.243 ||
| | 147.428
|| 3/2 || |-1 1&gt; || 701.955 ||
|-
|| 32/21 || |5 -1 0 -1&gt; || 729.219 ||
| | 35/32
|| 75/49 || |0 1 2 -2&gt; || 736.931 ||
| | |-5 0 1 1&gt;
|| 49/32 || |-5 0 0 2&gt; || 737.652 ||
| | 155.140
|| 54/35 || |1 3 -1 -1&gt; || 750.725 ||
|-
|| 14/9 || |1 -2 0 1&gt; || 764.916 ||
| | 54/49
|| 25/16 || |-4 0 2&gt; || 772.627 ||
| | |1 3 0 -2&gt;
|| 63/40 || |-3 2 -1 1&gt; || 786.422 ||
| | 168.213
|| 128/81 || |7 -4&gt; || 792.180 ||
|-
|| 100/63 || |2 -2 2 -1&gt; || 799.892 ||
| | 28/25
|| 45/28 || |-2 2 1 -1&gt; || 821.398 ||
| | |2 0 -2 1&gt;
|| 81/50 || |-1 4 -2&gt; || 835.193 ||
| | 196.198
|| 80/49 || |4 0 1 -2&gt; || 848.662 ||
|-
|| 49/30 || |-1 -1 -1 2&gt; || 849.383 ||
| | 9/8
|| 81/49 || |0 4 0 -2&gt; || 870.168 ||
| | |-3 2&gt;
|| 5/3 || |0 -1 1&gt; || 884.359 ||
| | 203.910
|| 42/25 || |1 1 -2 1&gt; || 898.153 ||
|-
|| 27/16 || |-4 3&gt; || 905.865 ||
| | 8/7
|| 128/75 || |7 -1 -2&gt; || 925.418 ||
| | |3 0 0 -1&gt;
|| 12/7 || |2 1 0 -1&gt; || 933.129 ||
| | 231.174
|| 140/81 || |2 -4 1 1&gt; || 947.320 ||
|-
|| 7/4 || |-2 0 0 1&gt; || 968.826 ||
| | 81/70
|| 16/9 || |4 -2&gt; || 996.090 ||
| | |-1 4 -1 -1&gt;
|| 25/14 || |-1 0 2 -1&gt; || 1003.802 ||
| | 252.68
|| 49/27 || |0 -3 0 2&gt; || 1031.787 ||
|-
|| 64/35 || |6 0 -1 -1&gt; || 1044.860 ||
| | 7/6
|| 90/49 || |1 2 1 -2&gt; || 1052.572 ||
| | |-1 -1 0 1&gt;
|| 50/27 || |1 -3 2&gt; || 1066.762 ||
| | 266.871
|| 28/15 || |2 -1 -1 1&gt; || 1080.557 ||
|-
|| 15/8 || |-3 1 1&gt; || 1088.269 ||
| | 75/64
|| 40/21 || |3 -1 1 -1&gt; || 1115.533 ||
| | |-6 1 2&gt;
|| 48/25 || |4 1 -2&gt; || 1129.328 ||
| | 274.582
|| 27/14 || |-1 3 0 -1&gt; || 1137.039 ||
|-
|| 35/18 || |-1 -2 1 1&gt; || 1151.230 ||
| | 32/27
|| 49/25 || |0 0 -2 2&gt; || 1165.024 ||
| | |5 -3&gt;
|| 63/32 || |-5 2 0 1&gt; || 1172.736 ||
| | 294.135
|| 160/81 || |5 -4 1&gt; || 1178.494 ||
|-
|| 2/1 || |1&gt; || 1200.000 ||
| | 25/21
| | |0 -1 2 -1&gt;
| | 301.847
|-
| | 6/5
| | |1 1 -1&gt;
| | 315.641
|-
| | 98/81
| | |1 -4 0 2&gt;
| | 329.832
|-
| | 60/49
| | |2 1 1 -2&gt;
| | 350.617
|-
| | 49/40
| | |-3 0 -1 2&gt;
| | 351.338
|-
| | 100/81
| | |2 -4 2&gt;
| | 364.807
|-
| | 56/45
| | |3 -2 -1 1&gt;
| | 378.602
|-
| | 63/50
| | |-1 2 -2 1&gt;
| | 400.108
|-
| | 81/64
| | |-6 4&gt;
| | 407.820
|-
| | 80/63
| | |4 -2 1 -1&gt;
| | 413.578
|-
| | 32/25
| | |5 0 -2&gt;
| | 427.373
|-
| | 9/7
| | |0 2 0 -1&gt;
| | 435.084
|-
| | 35/27
| | |0 -3 1 1&gt;
| | 449.275
|-
| | 64/49
| | |6 0 0 -2&gt;
| | 462.348
|-
| | 98/75
| | |1 -1 -2 2&gt;
| | 463.069
|-
| | 21/16
| | |-4 1 0 1&gt;
| | 470.781
|-
| | 4/3
| | |2 -1&gt;
| | 498.045
|-
| | 75/56
| | |-3 1 2 -1&gt;
| | 505.757
|-
| | 27/20
| | |-2 3 -1&gt;
| | 519.551
|-
| | 49/36
| | |-2 -2 0 2&gt;
| | 533.742
|-
| | 48/35
| | |4 1 -1 -1&gt;
| | 546.815
|-
| | 112/81
| | |4 -4 0 1&gt;
| | 561.006
|-
| | 7/5
| | |0 0 -1 1&gt;
| | 582.512
|-
| | 45/32
| | |-5 2 1&gt;
| | 590.224
|-
| | 64/45
| | |6 -2 -1&gt;
| | 609.776
|-
| | 10/7
| | |1 0 1 -1&gt;
| | 617.488
|-
| | 81/56
| | |-3 4 0 -1&gt;
| | 638.994
|-
| | 35/24
| | |-3 -1 1 1&gt;
| | 653.185
|-
| | 72/49
| | |3 2 0 -2&gt;
| | 666.258
|-
| | 40/27
| | |3 -3 1&gt;
| | 680.449
|-
| | 112/75
| | |4 -1 -2 1&gt;
| | 694.243
|-
| | 3/2
| | |-1 1&gt;
| | 701.955
|-
| | 32/21
| | |5 -1 0 -1&gt;
| | 729.219
|-
| | 75/49
| | |0 1 2 -2&gt;
| | 736.931
|-
| | 49/32
| | |-5 0 0 2&gt;
| | 737.652
|-
| | 54/35
| | |1 3 -1 -1&gt;
| | 750.725
|-
| | 14/9
| | |1 -2 0 1&gt;
| | 764.916
|-
| | 25/16
| | |-4 0 2&gt;
| | 772.627
|-
| | 63/40
| | |-3 2 -1 1&gt;
| | 786.422
|-
| | 128/81
| | |7 -4&gt;
| | 792.180
|-
| | 100/63
| | |2 -2 2 -1&gt;
| | 799.892
|-
| | 45/28
| | |-2 2 1 -1&gt;
| | 821.398
|-
| | 81/50
| | |-1 4 -2&gt;
| | 835.193
|-
| | 80/49
| | |4 0 1 -2&gt;
| | 848.662
|-
| | 49/30
| | |-1 -1 -1 2&gt;
| | 849.383
|-
| | 81/49
| | |0 4 0 -2&gt;
| | 870.168
|-
| | 5/3
| | |0 -1 1&gt;
| | 884.359
|-
| | 42/25
| | |1 1 -2 1&gt;
| | 898.153
|-
| | 27/16
| | |-4 3&gt;
| | 905.865
|-
| | 128/75
| | |7 -1 -2&gt;
| | 925.418
|-
| | 12/7
| | |2 1 0 -1&gt;
| | 933.129
|-
| | 140/81
| | |2 -4 1 1&gt;
| | 947.320
|-
| | 7/4
| | |-2 0 0 1&gt;
| | 968.826
|-
| | 16/9
| | |4 -2&gt;
| | 996.090
|-
| | 25/14
| | |-1 0 2 -1&gt;
| | 1003.802
|-
| | 49/27
| | |0 -3 0 2&gt;
| | 1031.787
|-
| | 64/35
| | |6 0 -1 -1&gt;
| | 1044.860
|-
| | 90/49
| | |1 2 1 -2&gt;
| | 1052.572
|-
| | 50/27
| | |1 -3 2&gt;
| | 1066.762
|-
| | 28/15
| | |2 -1 -1 1&gt;
| | 1080.557
|-
| | 15/8
| | |-3 1 1&gt;
| | 1088.269
|-
| | 40/21
| | |3 -1 1 -1&gt;
| | 1115.533
|-
| | 48/25
| | |4 1 -2&gt;
| | 1129.328
|-
| | 27/14
| | |-1 3 0 -1&gt;
| | 1137.039
|-
| | 35/18
| | |-1 -2 1 1&gt;
| | 1151.230
|-
| | 49/25
| | |0 0 -2 2&gt;
| | 1165.024
|-
| | 63/32
| | |-5 2 0 1&gt;
| | 1172.736
|-
| | 160/81
| | |5 -4 1&gt;
| | 1178.494
|-
| | 2/1
| | |1&gt;
| | 1200.000
|}


=Music=
[http://micro.soonlabel.com/0-praxis/audio/August/august_12_Ruckus.mp3 Ruckus From the Quiet Zone] by Ralph Lewis


=Music=
[http://micro.soonlabel.com/blue-tuning/blue-ji-excluded-by-peers.mp3 Excluded by Peers] by [[Chris_Vaisvil|Chris Vaisvil]]
[[http://micro.soonlabel.com/0-praxis/audio/August/august_12_Ruckus.mp3|Ruckus From the Quiet Zone]] by Ralph Lewis
[[http://micro.soonlabel.com/blue-tuning/blue-ji-excluded-by-peers.mp3|Excluded by Peers]] by [[Chris Vaisvil]]
[[http://micro.soonlabel.com/centaur_tuning/Prelude_For_Centaur_Tuned_Piano.mp3|Prelude for Centaur Tuned Piano]] by Chris Vaisvil
[[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]] &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]]
[[http://www.youtube.com/watch?v=HzQmaxDIxnc&amp;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]]
[[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


=see also=
[http://micro.soonlabel.com/centaur_tuning/Prelude_For_Centaur_Tuned_Piano.mp3 Prelude for Centaur Tuned Piano] by Chris Vaisvil
* [[Harmonic Limit]]
* [[http://en.wikipedia.org/wiki/7-limit|7-limit - Wikipedia]]
* [[http://en.wikipedia.org/wiki/Highly_composite_number|Highly composite number - Wikipedia]]


[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|Gene Ward Smith]]


[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]


[[media type="custom" key="23473462"]]</pre></div>
[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|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])
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;7-limit&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;7-limit&lt;/em&gt; or &amp;quot;7 prime-limit&amp;quot; refers to a constraint on rational intervals such that 7 is the highest allowable &lt;a class="wiki_link" href="/prime%20number"&gt;prime number&lt;/a&gt;, 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 &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;, &lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt;, &lt;a class="wiki_link" href="/15_14"&gt;15/14&lt;/a&gt;, &lt;a class="wiki_link" href="/28_15"&gt;28/15&lt;/a&gt;, &lt;a class="wiki_link" href="/21_16"&gt;21/16&lt;/a&gt;, &lt;a class="wiki_link" href="/32_21"&gt;32/21&lt;/a&gt;, &lt;a class="wiki_link" href="/25_14"&gt;25/14&lt;/a&gt;, &lt;a class="wiki_link" href="/28_25"&gt;28/25&lt;/a&gt;, &lt;a class="wiki_link" href="/25_21"&gt;25/21&lt;/a&gt;, &lt;a class="wiki_link" href="/42_25"&gt;42/25&lt;/a&gt;, &lt;a class="wiki_link" href="/28_27"&gt;28/27&lt;/a&gt;, &lt;a class="wiki_link" href="/27_14"&gt;27/14&lt;/a&gt;, &lt;a class="wiki_link" href="/35_27"&gt;35/27&lt;/a&gt;, 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.&lt;br /&gt;
&lt;br /&gt;
&amp;quot;7 odd-limit&amp;quot; refers to a constraint on the selection of &lt;a class="wiki_link" href="/JustIntonation"&gt;just&lt;/a&gt; &lt;a class="wiki_link" href="/Interval%20class"&gt;intervals&lt;/a&gt; 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 &lt;a class="wiki_link" href="/1_1"&gt;1/1&lt;/a&gt;, &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;, &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;, &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;, &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;, &lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;, &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;, &lt;a class="wiki_link" href="/10_7"&gt;10/7&lt;/a&gt;, &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;, &lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;, &lt;a class="wiki_link" href="/5_3"&gt;5/3&lt;/a&gt;, &lt;a class="wiki_link" href="/12_7"&gt;12/7&lt;/a&gt;, &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;, &lt;a class="wiki_link" href="/2_1"&gt;2/1&lt;/a&gt;, which is known as the 7-limit &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tonality_diamond" rel="nofollow"&gt;tonality diamond&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
The phrase &amp;quot;7-limit just intonation&amp;quot; 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 a pitch class representing that interval in every possible octave. This leaves primes 3, 5, and 7, which can be represented in &lt;a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices"&gt;3-dimensional lattice diagrams&lt;/a&gt;, 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.&lt;br /&gt;
&lt;br /&gt;
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 &lt;a class="wiki_link" href="/11-limit"&gt;11-&lt;/a&gt; or &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;, which usually sound much more exotic.&lt;br /&gt;
&lt;br /&gt;
Relative to their size, the equal divisions &lt;a class="wiki_link" href="/1edo"&gt;1edo&lt;/a&gt;, &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt;, &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt;, &lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt;, &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;, &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;, &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, &lt;a class="wiki_link" href="/21edo"&gt;21edo&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;, &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt;, &lt;a class="wiki_link" href="/87edo"&gt;87edo&lt;/a&gt;, &lt;a class="wiki_link" href="/94edo"&gt;94edo&lt;/a&gt;, &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118edo&lt;/a&gt;, &lt;a class="wiki_link" href="/130edo"&gt;130edo&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140edo&lt;/a&gt;, &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt;, &lt;a class="wiki_link" href="/270edo"&gt;270edo&lt;/a&gt;, &lt;a class="wiki_link" href="/410edo"&gt;410edo&lt;/a&gt;, &lt;a class="wiki_link" href="/441edo"&gt;441edo&lt;/a&gt; and &lt;a class="wiki_link" href="/612edo"&gt;612edo&lt;/a&gt; provide good approximations to the 7-limit.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-List of Intervals in the 7-Prime Limit and 81-Odd Limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;List of Intervals in the 7-Prime Limit and 81-Odd Limit&lt;/h2&gt;
&lt;br /&gt;


[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|kite33]] 7-limit JI scale


&lt;table class="wiki_table"&gt;
=see also=
    &lt;tr&gt;
<ul><li>[[Harmonic_Limit|Harmonic Limit]]</li><li>[http://en.wikipedia.org/wiki/7-limit 7-limit - Wikipedia]</li><li>[http://en.wikipedia.org/wiki/Highly_composite_number Highly composite number - Wikipedia]</li></ul>
        &lt;td&gt;&lt;a class="wiki_link" href="/Ratio"&gt;Ratio&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Monzo"&gt;Monzo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Cents"&gt;Cents&lt;/a&gt; Value&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|0&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.000&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;81/80&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-4 4 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21.506&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;64/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|6 -2 0 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27.264&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;50/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|1 0 2 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;34.976&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;36/35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|2 2 -1 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;48.770&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|2 -3 0 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;62.961&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25/24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-3 -1 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;70.672&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21/20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-2 1 -1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;84.467&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|4 -1 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;111.731&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-1 1 1 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;119.443&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|0 3 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;133.238&lt;br /&gt;
&lt;/td&gt;
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    &lt;tr&gt;
        &lt;td&gt;49/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|0 -2 -1 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;147.428&lt;br /&gt;
&lt;/td&gt;
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    &lt;tr&gt;
        &lt;td&gt;35/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-5 0 1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;155.140&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;54/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|1 3 0 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;168.213&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|2 0 -2 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;196.198&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-3 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203.910&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|3 0 0 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;231.174&lt;br /&gt;
&lt;/td&gt;
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    &lt;tr&gt;
        &lt;td&gt;81/70&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-1 4 -1 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;252.68&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-1 -1 0 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;266.871&lt;br /&gt;
&lt;/td&gt;
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    &lt;tr&gt;
        &lt;td&gt;75/64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-6 1 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;274.582&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|5 -3&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;294.135&lt;br /&gt;
&lt;/td&gt;
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    &lt;tr&gt;
        &lt;td&gt;25/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|0 -1 2 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;301.847&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|1 1 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;315.641&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;98/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|1 -4 0 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;329.832&lt;br /&gt;
&lt;/td&gt;
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    &lt;tr&gt;
        &lt;td&gt;60/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|2 1 1 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;350.617&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;49/40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-3 0 -1 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;351.338&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;100/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|2 -4 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364.807&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;56/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|3 -2 -1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;378.602&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;63/50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-1 2 -2 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;400.108&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;81/64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-6 4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;407.820&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;80/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|4 -2 1 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;413.578&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;32/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|5 0 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;427.373&lt;br /&gt;
&lt;/td&gt;
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    &lt;tr&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|0 2 0 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;435.084&lt;br /&gt;
&lt;/td&gt;
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    &lt;tr&gt;
        &lt;td&gt;35/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|0 -3 1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;449.275&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;64/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|6 0 0 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;462.348&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;98/75&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|1 -1 -2 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;463.069&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;21/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-4 1 0 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;470.781&lt;br /&gt;
&lt;/td&gt;
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    &lt;tr&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|2 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498.045&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;75/56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-3 1 2 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;505.757&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27/20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-2 3 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;519.551&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49/36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-2 -2 0 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;533.742&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;48/35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|4 1 -1 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;546.815&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;112/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|4 -4 0 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;561.006&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|0 0 -1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;582.512&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;45/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-5 2 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;590.224&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;64/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|6 -2 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;609.776&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|1 0 1 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;617.488&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;81/56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-3 4 0 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;638.994&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35/24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-3 -1 1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;653.185&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;72/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|3 2 0 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;666.258&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;40/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|3 -3 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;680.449&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;112/75&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|4 -1 -2 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;694.243&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.955&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|5 -1 0 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;729.219&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;75/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|0 1 2 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;736.931&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-5 0 0 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;737.652&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;54/35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|1 3 -1 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;750.725&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|1 -2 0 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;764.916&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-4 0 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;772.627&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;63/40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-3 2 -1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;786.422&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;128/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|7 -4&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;792.180&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;100/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|2 -2 2 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;799.892&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;45/28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-2 2 1 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;821.398&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;81/50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-1 4 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;835.193&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;80/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|4 0 1 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;848.662&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49/30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-1 -1 -1 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;849.383&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;81/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|0 4 0 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;870.168&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|0 -1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;884.359&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;42/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|1 1 -2 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;898.153&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-4 3&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;905.865&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;128/75&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|7 -1 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;925.418&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|2 1 0 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;933.129&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;140/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|2 -4 1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;947.320&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-2 0 0 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;968.826&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|4 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;996.090&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-1 0 2 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1003.802&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|0 -3 0 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1031.787&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;64/35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|6 0 -1 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1044.860&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;90/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|1 2 1 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1052.572&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;50/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|1 -3 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1066.762&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|2 -1 -1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1080.557&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-3 1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1088.269&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;40/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|3 -1 1 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1115.533&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;48/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|4 1 -2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1129.328&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-1 3 0 -1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1137.039&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35/18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-1 -2 1 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1151.230&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|0 0 -2 2&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1165.024&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;63/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|-5 2 0 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1172.736&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;160/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|5 -4 1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1178.494&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;|1&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200.000&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
[[Category:7-limit]]
&lt;br /&gt;
[[Category:example]]
&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Music&lt;/h1&gt;
[[Category:interval]]
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/0-praxis/audio/August/august_12_Ruckus.mp3" rel="nofollow"&gt;Ruckus From the Quiet Zone&lt;/a&gt; by Ralph Lewis&lt;br /&gt;
[[Category:lattice]]
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/blue-tuning/blue-ji-excluded-by-peers.mp3" rel="nofollow"&gt;Excluded by Peers&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
[[Category:limit]]
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/centaur_tuning/Prelude_For_Centaur_Tuned_Piano.mp3" rel="nofollow"&gt;Prelude for Centaur Tuned Piano&lt;/a&gt; by Chris Vaisvil&lt;br /&gt;
[[Category:listen]]
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prelude%20%231%20for%207-limit%20JI.mp3" rel="nofollow"&gt;Prelude #1 in 7-limit JI&lt;/a&gt; by &lt;a class="wiki_link" href="/Ivor%20Darreg"&gt;Ivor Darreg&lt;/a&gt; &amp;lt;-- are there any notations for it?&lt;br /&gt;
[[Category:prime_limit]]
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/ClintonVariations" rel="nofollow"&gt;Clinton Variations&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.archive.org/download/ClintonVariations/clinton.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;br /&gt;
[[Category:rank_4]]
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=HzQmaxDIxnc&amp;amp;feature=channel_video_title" rel="nofollow"&gt;Pachelbel's Canon in D in 7-limit JI&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Pachelbel_s%20Canon%20in%20D%20-%20Relaxing%20music,%20with%20mountain%20views.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/classical-music/mars-7-limit-kontakt5.mp3" rel="nofollow"&gt; Mars in 7-Limit JI&lt;/a&gt; from &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/The_Planets" rel="nofollow" target="_blank"&gt;The Planets&lt;/a&gt; the orchestral suite by Gustav Holst arranged by &lt;a class="wiki_link" href="/Chris%20Vaisvil" target="_blank"&gt;Chris Vaisvil&lt;/a&gt; (Blog entry: &lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/gustav-holsts-mars-arranged-for-7-limit-ji-orchestra/" rel="nofollow"&gt;Gustav Holst’s Mars arranged for 7-limit JI Orchestra « Music &amp;amp; Techniques by Chris Vaisvil&lt;/a&gt;)&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Kite/Consolation%20%233%20by%20Ken%20Stillwell%20retuned.mp3" rel="nofollow"&gt;Liszt Consolation #3&lt;/a&gt; Ken Stillwell performance, retuned by Kite Giedraitis to the &lt;a class="wiki_link" href="/kite33"&gt;kite33&lt;/a&gt; 7-limit JI scale&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="see also"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;see also&lt;/h1&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;Harmonic Limit&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/7-limit" rel="nofollow"&gt;7-limit - Wikipedia&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Highly_composite_number" rel="nofollow"&gt;Highly composite number - Wikipedia&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
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