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"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]. | "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]. | ||
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 | 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. | ||
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]], which usually sound much more exotic. | ||
| Line 10: | Line 10: | ||
== List of Intervals in the 7-Prime Limit and 81-Odd Limit == | == List of Intervals in the 7-Prime Limit and 81-Odd Limit == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| colspan="2" |[[Kite's color notation|Interval]] | |||
| [[Ratio|Ratio]] | | [[Ratio|Ratio]] | ||
| [[monzo|Monzo]] | | [[monzo|Monzo]] | ||
| [[cents|Cents]] Value | | [[cents|Cents]] Value | ||
|- | |- | ||
|w1 | |||
|wa unison | |||
| 1/1 | | 1/1 | ||
| {{Monzo| 0 }} | | {{Monzo| 0 }} | ||
| 0.000 | | 0.000 | ||
|- | |- | ||
|g1 | |||
|gu comma | |||
| 81/80 | | 81/80 | ||
| {{Monzo| -4 4 -1 }} | | {{Monzo| -4 4 -1 }} | ||
| 21.506 | | 21.506 | ||
|- | |- | ||
|r1 | |||
|ru comma | |||
| 64/63 | | 64/63 | ||
| {{Monzo| 6 -2 0 -1 }} | | {{Monzo| 6 -2 0 -1 }} | ||
| 27.264 | | 27.264 | ||
|- | |- | ||
|rryy-2 | |||
|double ruyo comma | |||
| 50/49 | | 50/49 | ||
| {{Monzo| 1 0 2 -2 }} | | {{Monzo| 1 0 2 -2 }} | ||
| 34.976 | | 34.976 | ||
|- | |- | ||
|zz2 | |||
|zozo comma | |||
|49/48 | |||
|{{Monzo| 1 0 2 -2 }} | |||
|35.697 | |||
|- | |||
|rg1 | |||
|rugu comma | |||
| 36/35 | | 36/35 | ||
| {{Monzo| 2 2 -1 -1 }} | | {{Monzo| 2 2 -1 -1 }} | ||
| 48.770 | | 48.770 | ||
|- | |- | ||
|z2 | |||
|zo 2nd | |||
| 28/27 | | 28/27 | ||
| {{Monzo| 2 -3 0 1 }} | | {{Monzo| 2 -3 0 1 }} | ||
| 62.961 | | 62.961 | ||
|- | |- | ||
|yy1 | |||
|yoyo unison | |||
| 25/24 | | 25/24 | ||
| {{Monzo| -3 -1 2 }} | | {{Monzo| -3 -1 2 }} | ||
| 70.672 | | 70.672 | ||
|- | |- | ||
|zg2 | |||
|zogu 2nd | |||
| 21/20 | | 21/20 | ||
| {{Monzo| -2 1 -1 1 }} | | {{Monzo| -2 1 -1 1 }} | ||
| 84.467 | | 84.467 | ||
|- | |- | ||
|g2 | |||
|gu 2nd | |||
| 16/15 | | 16/15 | ||
| {{Monzo| 4 -1 -1 }} | | {{Monzo| 4 -1 -1 }} | ||
| 111.731 | | 111.731 | ||
|- | |- | ||
|ry1 | |||
|ruyo unison | |||
| 15/14 | | 15/14 | ||
| {{Monzo| -1 1 1 -1 }} | | {{Monzo| -1 1 1 -1 }} | ||
| 119.443 | | 119.443 | ||
|- | |- | ||
|gg2 | |||
|gugu 2nd | |||
| 27/25 | | 27/25 | ||
| | |0 3 -2> | | |<nowiki> |0 3 -2</nowiki>> | ||
| 133.238 | | 133.238 | ||
|- | |- | ||
|zzg3 | |||
|zozogu 3rd | |||
| 49/45 | | 49/45 | ||
| | |0 -2 -1 2> | | |<nowiki> |0 -2 -1 2</nowiki>> | ||
| 147.428 | | 147.428 | ||
|- | |- | ||
|zy2 | |||
|zoyo 2nd | |||
| 35/32 | | 35/32 | ||
| | |-5 0 1 1> | | |<nowiki> |-5 0 1 1</nowiki>> | ||
| 155.140 | | 155.140 | ||
|- | |- | ||
|rr1 | |||
|ruru unison | |||
| 54/49 | | 54/49 | ||
| | |1 3 0 -2> | | |<nowiki> |1 3 0 -2</nowiki>> | ||
| 168.213 | | 168.213 | ||
|- | |- | ||
|y2 | |||
|yo 2nd | |||
|10/9 | |||
|{{Monzo| 1 0 2 -2 }} | |||
|182.404 | |||
|- | |||
|zgg3 | |||
|zogugu 3rd | |||
| 28/25 | | 28/25 | ||
| | |2 0 -2 1> | | |<nowiki> |2 0 -2 1</nowiki>> | ||
| 196.198 | | 196.198 | ||
|- | |- | ||
|w2 | |||
|wa 2nd | |||
| 9/8 | | 9/8 | ||
| | |-3 2> | | |<nowiki> |-3 2</nowiki>> | ||
| 203.910 | | 203.910 | ||
|- | |- | ||
|r2 | |||
|ru 2nd | |||
| 8/7 | | 8/7 | ||
| | |3 0 0 -1> | | |<nowiki> |3 0 0 -1</nowiki>> | ||
| 231.174 | | 231.174 | ||
|- | |- | ||
|rg2 | |||
|rugu 2nd | |||
| 81/70 | | 81/70 | ||
| | |-1 4 -1 -1> | | |<nowiki> |-1 4 -1 -1</nowiki>> | ||
| 252.68 | | 252.68 | ||
|- | |- | ||
|z3 | |||
|zo 3rd | |||
| 7/6 | | 7/6 | ||
| | |-1 -1 0 1> | | |<nowiki> |-1 -1 0 1</nowiki>> | ||
| 266.871 | | 266.871 | ||
|- | |- | ||
|yy2 | |||
|yoyo 2nd | |||
| 75/64 | | 75/64 | ||
| | |-6 1 2> | | |<nowiki> |-6 1 2</nowiki>> | ||
| 274.582 | | 274.582 | ||
|- | |- | ||
|w3 | |||
|wa 3rd | |||
| 32/27 | | 32/27 | ||
| | |5 -3> | | |<nowiki> |5 -3</nowiki>> | ||
| 294.135 | | 294.135 | ||
|- | |- | ||
|ryy2 | |||
|ruyoyo 2nd | |||
| 25/21 | | 25/21 | ||
| | |0 -1 2 -1> | | |<nowiki> |0 -1 2 -1</nowiki>> | ||
| 301.847 | | 301.847 | ||
|- | |- | ||
|g3 | |||
|gu 3rd | |||
| 6/5 | | 6/5 | ||
| | |1 1 -1> | | |<nowiki> |1 1 -1</nowiki>> | ||
| 315.641 | | 315.641 | ||
|- | |- | ||
|zz4 | |||
|zozo 4th | |||
| 98/81 | | 98/81 | ||
| | |1 -4 0 2> | | |<nowiki> |1 -4 0 2</nowiki>> | ||
| 329.832 | | 329.832 | ||
|- | |- | ||
|rry2 | |||
|ruruyo 2nd | |||
| 60/49 | | 60/49 | ||
| | |2 1 1 -2> | | |<nowiki> |2 1 1 -2</nowiki>> | ||
| 350.617 | | 350.617 | ||
|- | |- | ||
|zzg4 | |||
|zozogu 4th | |||
| | 49/40 | | | 49/40 | ||
| | |-3 0 -1 2> | | |<nowiki> |-3 0 -1 2</nowiki>> | ||
| | 351.338 | | | 351.338 | ||
|- | |- | ||
|yy3 | |||
|yoyo 3rd | |||
| | 100/81 | | | 100/81 | ||
| | |2 -4 2> | | |<nowiki> |2 -4 2</nowiki>> | ||
| | 364.807 | | | 364.807 | ||
|- | |- | ||
|zg4 | |||
|zogu 4th | |||
| | 56/45 | | | 56/45 | ||
| | |3 -2 -1 1> | | |<nowiki> |3 -2 -1 1</nowiki>> | ||
| | 378.602 | | | 378.602 | ||
|- | |- | ||
|zgg4 | |||
|zogugu 4th | |||
| | 63/50 | | | 63/50 | ||
| | |-1 2 -2 1> | | |<nowiki> |-1 2 -2 1</nowiki>> | ||
| | 400.108 | | | 400.108 | ||
|- | |- | ||
|Lw3 | |||
|large wa 3rd | |||
| | 81/64 | | | 81/64 | ||
| | |-6 4> | | |<nowiki> |-6 4</nowiki>> | ||
| | 407.820 | | | 407.820 | ||
|- | |- | ||
|ry3 | |||
|ruyo 3rd | |||
| | 80/63 | | | 80/63 | ||
| | |4 -2 1 -1> | | |<nowiki> |4 -2 1 -1</nowiki>> | ||
| | 413.578 | | | 413.578 | ||
|- | |- | ||
|gg4 | |||
|gugu 4th | |||
| | 32/25 | | | 32/25 | ||
| | |5 0 -2> | | |<nowiki> |5 0 -2</nowiki>> | ||
| | 427.373 | | | 427.373 | ||
|- | |- | ||
|r3 | |||
|ru 3rd | |||
| | 9/7 | | | 9/7 | ||
| | |0 2 0 -1> | | |<nowiki> |0 2 0 -1</nowiki>> | ||
| | 435.084 | | | 435.084 | ||
|- | |- | ||
|zy4 | |||
|zoyo 4th | |||
| | 35/27 | | | 35/27 | ||
| | |0 -3 1 1> | | |<nowiki> |0 -3 1 1</nowiki>> | ||
| | 449.275 | | | 449.275 | ||
|- | |- | ||
|rr3 | |||
|ruru 3rd | |||
| | 64/49 | | | 64/49 | ||
| | |6 0 0 -2> | | |<nowiki> |6 0 0 -2</nowiki>> | ||
| | 462.348 | | | 462.348 | ||
|- | |- | ||
|zzgg5 | |||
|double zogu 5th | |||
| | 98/75 | | | 98/75 | ||
| | |1 -1 -2 2> | | |<nowiki> |1 -1 -2 2</nowiki>> | ||
| | 463.069 | | | 463.069 | ||
|- | |- | ||
|z4 | |||
|zo 4th | |||
| | 21/16 | | | 21/16 | ||
| | |-4 1 0 1> | | |<nowiki> |-4 1 0 1</nowiki>> | ||
| | 470.781 | | | 470.781 | ||
|- | |- | ||
|w4 | |||
|wa 4th | |||
| | 4/3 | | | 4/3 | ||
| | |2 -1> | | |<nowiki> |2 -1</nowiki>> | ||
| | 498.045 | | | 498.045 | ||
|- | |- | ||
|ryy3 | |||
|ruyoyo 3rd | |||
| | 75/56 | | | 75/56 | ||
| | |-3 1 2 -1> | | |<nowiki> |-3 1 2 -1</nowiki>> | ||
| | 505.757 | | | 505.757 | ||
|- | |- | ||
|g4 | |||
|gu 4th | |||
| | 27/20 | | | 27/20 | ||
| | |-2 3 -1> | | |<nowiki> |-2 3 -1</nowiki>> | ||
| | 519.551 | | | 519.551 | ||
|- | |- | ||
|zz5 | |||
|zozo 5th | |||
| | 49/36 | | | 49/36 | ||
| | |-2 -2 0 2> | | |<nowiki> |-2 -2 0 2</nowiki>> | ||
| | 533.742 | | | 533.742 | ||
|- | |- | ||
|rg4 | |||
|rugu 4th | |||
| | 48/35 | | | 48/35 | ||
| | |4 1 -1 -1> | | |<nowiki> |4 1 -1 -1</nowiki>> | ||
| | 546.815 | | | 546.815 | ||
|- | |- | ||
|z5 | |||
|zo 5th | |||
| | 112/81 | | | 112/81 | ||
| | |4 -4 0 1> | | |<nowiki> |4 -4 0 1</nowiki>> | ||
| | 561.006 | | | 561.006 | ||
|- | |- | ||
|zg5 | |||
|zogu 5th | |||
| | 7/5 | | | 7/5 | ||
| | |0 0 -1 1> | | |<nowiki> |0 0 -1 1</nowiki>> | ||
| | 582.512 | | | 582.512 | ||
|- | |- | ||
|y4 | |||
|yo 4th | |||
| | 45/32 | | | 45/32 | ||
| | |-5 2 1> | | |<nowiki> |-5 2 1</nowiki>> | ||
| | 590.224 | | | 590.224 | ||
|- | |- | ||
|g5 | |||
|gu 5th | |||
| | 64/45 | | | 64/45 | ||
| | |6 -2 -1> | | |<nowiki> |6 -2 -1</nowiki>> | ||
| | 609.776 | | | 609.776 | ||
|- | |- | ||
|ry4 | |||
|ruyo 4th | |||
| | 10/7 | | | 10/7 | ||
| | |1 0 1 -1> | | |<nowiki> |1 0 1 -1</nowiki>> | ||
| | 617.488 | | | 617.488 | ||
|- | |- | ||
|r4 | |||
|ru 4th | |||
| | 81/56 | | | 81/56 | ||
| | |-3 4 0 -1> | | |<nowiki> |-3 4 0 -1</nowiki>> | ||
| | 638.994 | | | 638.994 | ||
|- | |- | ||
|zy5 | |||
|zoyo 5th | |||
| | 35/24 | | | 35/24 | ||
| | |-3 -1 1 1> | | |<nowiki> |-3 -1 1 1</nowiki>> | ||
| | 653.185 | | | 653.185 | ||
|- | |- | ||
|rr4 | |||
|ruru 4th | |||
| | 72/49 | | | 72/49 | ||
| | |3 2 0 -2> | | |<nowiki> |3 2 0 -2</nowiki>> | ||
| | 666.258 | | | 666.258 | ||
|- | |- | ||
|y5 | |||
|yo 5th | |||
| | 40/27 | | | 40/27 | ||
| | |3 -3 1> | | |<nowiki> |3 -3 1</nowiki>> | ||
| | 680.449 | | | 680.449 | ||
|- | |- | ||
|zgg6 | |||
|zogugu 6th | |||
| | 112/75 | | | 112/75 | ||
| | |4 -1 -2 1> | | |<nowiki> |4 -1 -2 1</nowiki>> | ||
| | 694.243 | | | 694.243 | ||
|- | |- | ||
|w5 | |||
|wa 5th | |||
| | 3/2 | | | 3/2 | ||
| | |-1 1> | | |<nowiki> |-1 1</nowiki>> | ||
| | 701.955 | | | 701.955 | ||
|- | |- | ||
|r5 | |||
|ru 5th | |||
| | 32/21 | | | 32/21 | ||
| | |5 -1 0 -1> | | |<nowiki> |5 -1 0 -1</nowiki>> | ||
| | 729.219 | | | 729.219 | ||
|- | |- | ||
|rryy4 | |||
|double ruyo 4th | |||
| | 75/49 | | | 75/49 | ||
| | |0 1 2 -2> | | |<nowiki> |0 1 2 -2</nowiki>> | ||
| | 736.931 | | | 736.931 | ||
|- | |- | ||
|zz6 | |||
|zozo 6th | |||
| | 49/32 | | | 49/32 | ||
| | |-5 0 0 2> | | |<nowiki> |-5 0 0 2</nowiki>> | ||
| | 737.652 | | | 737.652 | ||
|- | |- | ||
|rg5 | |||
|rugu 5th | |||
| | 54/35 | | | 54/35 | ||
| | |1 3 -1 -1> | | |<nowiki> |1 3 -1 -1</nowiki>> | ||
| | 750.725 | | | 750.725 | ||
|- | |- | ||
|z6 | |||
|zo 6th | |||
| | 14/9 | | | 14/9 | ||
| | |1 -2 0 1> | | |<nowiki> |1 -2 0 1</nowiki>> | ||
| | 764.916 | | | 764.916 | ||
|- | |- | ||
|yy5 | |||
|yoyo 5th | |||
| | 25/16 | | | 25/16 | ||
| | |-4 0 2> | | |<nowiki> |-4 0 2</nowiki>> | ||
| | 772.627 | | | 772.627 | ||
|- | |- | ||
|zg6 | |||
|zogu 6th | |||
| | 63/40 | | | 63/40 | ||
| | |-3 2 -1 1> | | |<nowiki> |-3 2 -1 1</nowiki>> | ||
| | 786.422 | | | 786.422 | ||
|- | |- | ||
|sw6 | |||
|small wa 6th | |||
| | 128/81 | | | 128/81 | ||
| | |7 -4> | | |<nowiki> |7 -4</nowiki>> | ||
| | 792.180 | | | 792.180 | ||
|- | |- | ||
|ryy5 | |||
|ruyoyo 5th | |||
| | 100/63 | | | 100/63 | ||
| | |2 -2 2 -1> | | |<nowiki> |2 -2 2 -1</nowiki>> | ||
| | 799.892 | | | 799.892 | ||
|- | |- | ||
|ry5 | |||
|ruyo 5th | |||
| | 45/28 | | | 45/28 | ||
| | |-2 2 1 -1> | | |<nowiki> |-2 2 1 -1</nowiki>> | ||
| | 821.398 | | | 821.398 | ||
|- | |- | ||
|gg6 | |||
|gugu 6th | |||
| | 81/50 | | | 81/50 | ||
| | |-1 4 -2> | | |<nowiki> |-1 4 -2</nowiki>> | ||
| | 835.193 | | | 835.193 | ||
|- | |- | ||
|rry5 | |||
|ruruyo 5th | |||
| | 80/49 | | | 80/49 | ||
| | |4 0 1 -2> | | |<nowiki> |4 0 1 -2</nowiki>> | ||
| | 848.662 | | | 848.662 | ||
|- | |- | ||
|zzg7 | |||
|zozogu 7th | |||
| | 49/30 | | | 49/30 | ||
| | |-1 -1 -1 2> | | |<nowiki> |-1 -1 -1 2</nowiki>> | ||
| | 849.383 | | | 849.383 | ||
|- | |- | ||
|rr5 | |||
|ruru 5th | |||
| | 81/49 | | | 81/49 | ||
| | |0 4 0 -2> | | |<nowiki> |0 4 0 -2</nowiki>> | ||
| | 870.168 | | | 870.168 | ||
|- | |- | ||
|y6 | |||
|yo 6th | |||
| | 5/3 | | | 5/3 | ||
| | |0 -1 1> | | |<nowiki> |0 -1 1</nowiki>> | ||
| | 884.359 | | | 884.359 | ||
|- | |- | ||
|zgg7 | |||
|zogugu 7th | |||
| | 42/25 | | | 42/25 | ||
| | |1 1 -2 1> | | |<nowiki> |1 1 -2 1</nowiki>> | ||
| | 898.153 | | | 898.153 | ||
|- | |- | ||
|w6 | |||
|wa 6th | |||
| | 27/16 | | | 27/16 | ||
| | |-4 3> | | |<nowiki> |-4 3</nowiki>> | ||
| | 905.865 | | | 905.865 | ||
|- | |- | ||
|gg7 | |||
|gugu 7th | |||
| | 128/75 | | | 128/75 | ||
| | |7 -1 -2> | | |<nowiki> |7 -1 -2</nowiki>> | ||
| | 925.418 | | | 925.418 | ||
|- | |- | ||
|r6 | |||
|ru 6th | |||
| | 12/7 | | | 12/7 | ||
| | |2 1 0 -1> | | |<nowiki> |2 1 0 -1</nowiki>> | ||
| | 933.129 | | | 933.129 | ||
|- | |- | ||
|zy7 | |||
|zoyo 7th | |||
| | 140/81 | | | 140/81 | ||
| | |2 -4 1 1> | | |<nowiki> |2 -4 1 1</nowiki>> | ||
| | 947.320 | | | 947.320 | ||
|- | |- | ||
|z7 | |||
|zo 7th | |||
| | 7/4 | | | 7/4 | ||
| | |-2 0 0 1> | | |<nowiki> |-2 0 0 1</nowiki>> | ||
| | 968.826 | | | 968.826 | ||
|- | |- | ||
|w7 | |||
|wa 7th | |||
| | 16/9 | | | 16/9 | ||
| | |4 -2> | | |<nowiki> |4 -2</nowiki>> | ||
| | 996.090 | | | 996.090 | ||
|- | |- | ||
|ryy6 | |||
|ruyoyo 6th | |||
| | 25/14 | | | 25/14 | ||
| | |-1 0 2 -1> | | |<nowiki> |-1 0 2 -1</nowiki>> | ||
| | 1003.802 | | | 1003.802 | ||
|- | |- | ||
|g7 | |||
|gu 7th | |||
|9/5 | |||
|{{Monzo| 1 0 2 -2 }} | |||
|1017.596 | |||
|- | |||
|zz8 | |||
|zozo 8ve | |||
| | 49/27 | | | 49/27 | ||
| | |0 -3 0 2> | | |<nowiki> |0 -3 0 2</nowiki>> | ||
| | 1031.787 | | | 1031.787 | ||
|- | |- | ||
|rg7 | |||
|rugu 7th | |||
| | 64/35 | | | 64/35 | ||
| | |6 0 -1 -1> | | |<nowiki> |6 0 -1 -1</nowiki>> | ||
| | 1044.860 | | | 1044.860 | ||
|- | |- | ||
|rry6 | |||
|ruruyo 6th | |||
| | 90/49 | | | 90/49 | ||
| | |1 2 1 -2> | | |<nowiki> |1 2 1 -2</nowiki>> | ||
| | 1052.572 | | | 1052.572 | ||
|- | |- | ||
|yy7 | |||
|yoyo 7th | |||
| | 50/27 | | | 50/27 | ||
| | |1 -3 2> | | |<nowiki> |1 -3 2</nowiki>> | ||
| | 1066.762 | | | 1066.762 | ||
|- | |- | ||
|zg8 | |||
|zogu 8ve | |||
| | 28/15 | | | 28/15 | ||
| | |2 -1 -1 1> | | |<nowiki> |2 -1 -1 1</nowiki>> | ||
| | 1080.557 | | | 1080.557 | ||
|- | |- | ||
|y7 | |||
|yo 7th | |||
| | 15/8 | | | 15/8 | ||
| | |-3 1 1> | | |<nowiki> |-3 1 1</nowiki>> | ||
| | 1088.269 | | | 1088.269 | ||
|- | |- | ||
|ry7 | |||
|ruyo 7th | |||
| | 40/21 | | | 40/21 | ||
| | |3 -1 1 -1> | | |<nowiki> |3 -1 1 -1</nowiki>> | ||
| | 1115.533 | | | 1115.533 | ||
|- | |- | ||
|gg8 | |||
|gugu 8ve | |||
| | 48/25 | | | 48/25 | ||
| | |4 1 -2> | | |<nowiki> |4 1 -2</nowiki>> | ||
| | 1129.328 | | | 1129.328 | ||
|- | |- | ||
|r7 | |||
|ru 7th | |||
| | 27/14 | | | 27/14 | ||
| | |-1 3 0 -1> | | |<nowiki> |-1 3 0 -1</nowiki>> | ||
| | 1137.039 | | | 1137.039 | ||
|- | |- | ||
|zy8 | |||
|zoyo 8ve | |||
| | 35/18 | | | 35/18 | ||
| | |-1 -2 1 1> | | |<nowiki> |-1 -2 1 1</nowiki>> | ||
| | 1151.230 | | | 1151.230 | ||
|- | |- | ||
|zzgg9 | |||
|bizogu 9th | |||
| | 49/25 | | | 49/25 | ||
| | |0 0 -2 2> | | |<nowiki> |0 0 -2 2</nowiki>> | ||
| | 1165.024 | | | 1165.024 | ||
|- | |- | ||
|z8 | |||
|zo 8ve | |||
| | 63/32 | | | 63/32 | ||
| | |-5 2 0 1> | | |<nowiki> |-5 2 0 1</nowiki>> | ||
| | 1172.736 | | | 1172.736 | ||
|- | |- | ||
|y8 | |||
|yo 8ve | |||
| | 160/81 | | | 160/81 | ||
| | |5 -4 1> | | |<nowiki> |5 -4 1</nowiki>> | ||
| | 1178.494 | | | 1178.494 | ||
|- | |- | ||
|w8 | |||
|wa 8ve | |||
| | 2/1 | | | 2/1 | ||
| | |1> | | |<nowiki> |1</nowiki>> | ||
| | 1200.000 | | | 1200.000 | ||
|} | |} | ||
| Line 387: | Line 584: | ||
* [http://www.archive.org/details/ClintonVariations Clinton Variations] [http://www.archive.org/download/ClintonVariations/clinton.mp3 play] by [[Gene Ward Smith]] | * [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&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://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] | ||
* [http://clones.soonlabel.com/public/classical-music/mars-7-limit-kontakt5.mp3 | * [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 & 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 | * [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 | ||
* [http://tallkite.com/music/IHearNumbers.html I Hear Numbers] by [[KiteGiedraitis|TallKite]] | |||
== See also == | == See also == | ||
* [[Harmonic Limit]] | * [[Harmonic Limit]] | ||
* [https://en.wikipedia.org/wiki/7-limit 7-limit - Wikipedia] | * [https://en.wikipedia.org/wiki/7-limit 7-limit - Wikipedia] | ||
* [https://en.wikipedia.org/wiki/Highly_composite_number Highly composite number - Wikipedia] | * [https://en.wikipedia.org/wiki/Highly_composite_number Highly composite number - Wikipedia] [[Category:7-limit| ]] <!-- main page --> | ||
[[Category:7-limit| ]] <!-- main page --> | |||
[[Category:example]] | [[Category:example]] | ||
[[Category:interval]] | [[Category:interval]] | ||
Revision as of 18:34, 31 October 2018
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, 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.
"7 odd-limit" refers to 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-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 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.
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.
List of Intervals in the 7-Prime Limit and 81-Odd Limit
| Interval | Ratio | Monzo | Cents Value | |
| w1 | wa unison | 1/1 | [0⟩ | 0.000 |
| g1 | gu comma | 81/80 | [-4 4 -1⟩ | 21.506 |
| r1 | ru comma | 64/63 | [6 -2 0 -1⟩ | 27.264 |
| rryy-2 | double ruyo comma | 50/49 | [1 0 2 -2⟩ | 34.976 |
| zz2 | zozo comma | 49/48 | [1 0 2 -2⟩ | 35.697 |
| rg1 | rugu comma | 36/35 | [2 2 -1 -1⟩ | 48.770 |
| z2 | zo 2nd | 28/27 | [2 -3 0 1⟩ | 62.961 |
| yy1 | yoyo unison | 25/24 | [-3 -1 2⟩ | 70.672 |
| zg2 | zogu 2nd | 21/20 | [-2 1 -1 1⟩ | 84.467 |
| g2 | gu 2nd | 16/15 | [4 -1 -1⟩ | 111.731 |
| ry1 | ruyo unison | 15/14 | [-1 1 1 -1⟩ | 119.443 |
| gg2 | gugu 2nd | 27/25 | |0 3 -2> | 133.238 |
| zzg3 | zozogu 3rd | 49/45 | |0 -2 -1 2> | 147.428 |
| zy2 | zoyo 2nd | 35/32 | |-5 0 1 1> | 155.140 |
| rr1 | ruru unison | 54/49 | |1 3 0 -2> | 168.213 |
| y2 | yo 2nd | 10/9 | [1 0 2 -2⟩ | 182.404 |
| zgg3 | zogugu 3rd | 28/25 | |2 0 -2 1> | 196.198 |
| w2 | wa 2nd | 9/8 | |-3 2> | 203.910 |
| r2 | ru 2nd | 8/7 | |3 0 0 -1> | 231.174 |
| rg2 | rugu 2nd | 81/70 | |-1 4 -1 -1> | 252.68 |
| z3 | zo 3rd | 7/6 | |-1 -1 0 1> | 266.871 |
| yy2 | yoyo 2nd | 75/64 | |-6 1 2> | 274.582 |
| w3 | wa 3rd | 32/27 | |5 -3> | 294.135 |
| ryy2 | ruyoyo 2nd | 25/21 | |0 -1 2 -1> | 301.847 |
| g3 | gu 3rd | 6/5 | |1 1 -1> | 315.641 |
| zz4 | zozo 4th | 98/81 | |1 -4 0 2> | 329.832 |
| rry2 | ruruyo 2nd | 60/49 | |2 1 1 -2> | 350.617 |
| zzg4 | zozogu 4th | 49/40 | |-3 0 -1 2> | 351.338 |
| yy3 | yoyo 3rd | 100/81 | |2 -4 2> | 364.807 |
| zg4 | zogu 4th | 56/45 | |3 -2 -1 1> | 378.602 |
| zgg4 | zogugu 4th | 63/50 | |-1 2 -2 1> | 400.108 |
| Lw3 | large wa 3rd | 81/64 | |-6 4> | 407.820 |
| ry3 | ruyo 3rd | 80/63 | |4 -2 1 -1> | 413.578 |
| gg4 | gugu 4th | 32/25 | |5 0 -2> | 427.373 |
| r3 | ru 3rd | 9/7 | |0 2 0 -1> | 435.084 |
| zy4 | zoyo 4th | 35/27 | |0 -3 1 1> | 449.275 |
| rr3 | ruru 3rd | 64/49 | |6 0 0 -2> | 462.348 |
| zzgg5 | double zogu 5th | 98/75 | |1 -1 -2 2> | 463.069 |
| z4 | zo 4th | 21/16 | |-4 1 0 1> | 470.781 |
| w4 | wa 4th | 4/3 | |2 -1> | 498.045 |
| ryy3 | ruyoyo 3rd | 75/56 | |-3 1 2 -1> | 505.757 |
| g4 | gu 4th | 27/20 | |-2 3 -1> | 519.551 |
| zz5 | zozo 5th | 49/36 | |-2 -2 0 2> | 533.742 |
| rg4 | rugu 4th | 48/35 | |4 1 -1 -1> | 546.815 |
| z5 | zo 5th | 112/81 | |4 -4 0 1> | 561.006 |
| zg5 | zogu 5th | 7/5 | |0 0 -1 1> | 582.512 |
| y4 | yo 4th | 45/32 | |-5 2 1> | 590.224 |
| g5 | gu 5th | 64/45 | |6 -2 -1> | 609.776 |
| ry4 | ruyo 4th | 10/7 | |1 0 1 -1> | 617.488 |
| r4 | ru 4th | 81/56 | |-3 4 0 -1> | 638.994 |
| zy5 | zoyo 5th | 35/24 | |-3 -1 1 1> | 653.185 |
| rr4 | ruru 4th | 72/49 | |3 2 0 -2> | 666.258 |
| y5 | yo 5th | 40/27 | |3 -3 1> | 680.449 |
| zgg6 | zogugu 6th | 112/75 | |4 -1 -2 1> | 694.243 |
| w5 | wa 5th | 3/2 | |-1 1> | 701.955 |
| r5 | ru 5th | 32/21 | |5 -1 0 -1> | 729.219 |
| rryy4 | double ruyo 4th | 75/49 | |0 1 2 -2> | 736.931 |
| zz6 | zozo 6th | 49/32 | |-5 0 0 2> | 737.652 |
| rg5 | rugu 5th | 54/35 | |1 3 -1 -1> | 750.725 |
| z6 | zo 6th | 14/9 | |1 -2 0 1> | 764.916 |
| yy5 | yoyo 5th | 25/16 | |-4 0 2> | 772.627 |
| zg6 | zogu 6th | 63/40 | |-3 2 -1 1> | 786.422 |
| sw6 | small wa 6th | 128/81 | |7 -4> | 792.180 |
| ryy5 | ruyoyo 5th | 100/63 | |2 -2 2 -1> | 799.892 |
| ry5 | ruyo 5th | 45/28 | |-2 2 1 -1> | 821.398 |
| gg6 | gugu 6th | 81/50 | |-1 4 -2> | 835.193 |
| rry5 | ruruyo 5th | 80/49 | |4 0 1 -2> | 848.662 |
| zzg7 | zozogu 7th | 49/30 | |-1 -1 -1 2> | 849.383 |
| rr5 | ruru 5th | 81/49 | |0 4 0 -2> | 870.168 |
| y6 | yo 6th | 5/3 | |0 -1 1> | 884.359 |
| zgg7 | zogugu 7th | 42/25 | |1 1 -2 1> | 898.153 |
| w6 | wa 6th | 27/16 | |-4 3> | 905.865 |
| gg7 | gugu 7th | 128/75 | |7 -1 -2> | 925.418 |
| r6 | ru 6th | 12/7 | |2 1 0 -1> | 933.129 |
| zy7 | zoyo 7th | 140/81 | |2 -4 1 1> | 947.320 |
| z7 | zo 7th | 7/4 | |-2 0 0 1> | 968.826 |
| w7 | wa 7th | 16/9 | |4 -2> | 996.090 |
| ryy6 | ruyoyo 6th | 25/14 | |-1 0 2 -1> | 1003.802 |
| g7 | gu 7th | 9/5 | [1 0 2 -2⟩ | 1017.596 |
| zz8 | zozo 8ve | 49/27 | |0 -3 0 2> | 1031.787 |
| rg7 | rugu 7th | 64/35 | |6 0 -1 -1> | 1044.860 |
| rry6 | ruruyo 6th | 90/49 | |1 2 1 -2> | 1052.572 |
| yy7 | yoyo 7th | 50/27 | |1 -3 2> | 1066.762 |
| zg8 | zogu 8ve | 28/15 | |2 -1 -1 1> | 1080.557 |
| y7 | yo 7th | 15/8 | |-3 1 1> | 1088.269 |
| ry7 | ruyo 7th | 40/21 | |3 -1 1 -1> | 1115.533 |
| gg8 | gugu 8ve | 48/25 | |4 1 -2> | 1129.328 |
| r7 | ru 7th | 27/14 | |-1 3 0 -1> | 1137.039 |
| zy8 | zoyo 8ve | 35/18 | |-1 -2 1 1> | 1151.230 |
| zzgg9 | bizogu 9th | 49/25 | |0 0 -2 2> | 1165.024 |
| z8 | zo 8ve | 63/32 | |-5 2 0 1> | 1172.736 |
| y8 | yo 8ve | 160/81 | |5 -4 1> | 1178.494 |
| w8 | wa 8ve | 2/1 | |1> | 1200.000 |
Music
- Ruckus From the Quiet Zone by Ralph Lewis
- Excluded by Peers by Chris Vaisvil
- Prelude for Centaur Tuned Piano by Chris Vaisvil
- Prelude #1 in 7-limit JI by Ivor Darreg <-- are there any notations for it?
- Clinton Variations play by Gene Ward Smith
- Pachelbel's Canon in D in 7-limit JI play
- Mars in 7-Limit JI from The Planets the orchestral suite by Gustav Holst arranged by Chris Vaisvil (Blog entry: Gustav Holst’s Mars arranged for 7-limit JI Orchestra « Music & Techniques by Chris Vaisvil)
- Liszt Consolation #3 Ken Stillwell performance, retuned by Kite Giedraitis to the kite33 7-limit JI scale
- I Hear Numbers by TallKite