Chord cubes: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 151546173 - Original comment: ** |
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Revision as of 03:17, 5 July 2010
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- This revision was by author genewardsmith and made on 2010-07-05 03:17:43 UTC.
- The original revision id was 151546173.
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Original Wikitext content:
A cube scale is a 7-limit scale (we might also consider the 9 odd limit) whose notes are derived from a cube in the [[The Seven Limit Symmetrical Lattices|7-limit lattice of chords]]. For odd n, we will call the octave-reduced set of notes deriving from all chords of the form [i, j, k], (1-n)/2 <= i, j, k <= (n-1)/2, Cube[n]. If n is even, we will use Cube[n] to refer to the notes of [i, j, k] with 1-n/2 <= i, j, k < n/2. If n is odd, Cube[n] has (n+1)^3/2 notes to it; if n is even, its growth is more complicated but still approximately cubic. For odd n, the inversion of the scale gives another scale, centered around a minor rather than a major tetrad. Here are the first three cube scales: **Cube[2] -- the stellated hexany, 14 notes** [21/20, 15/14, 35/32, 9/8, 5/4, 21/16, 35/24, 3/2, 49/32, 25/16, 105/64, 7/4, 15/8, 2] **Cube[3] 32 notes** [49/48, 25/24, 21/20, 15/14, 35/32, 9/8, 8/7, 7/6, 6/5, 60/49, 49/40, 5/4, 9/7, 21/16, 4/3, 7/5, 10/7, 35/24, 3/2, 49/32, 25/16, 8/5, 105/64, 5/3, 42/25, 12/7, 7/4, 25/14, 9/5, 15/8, 35/18, 2] **Cube[4] 63 notes** [50/49, 49/48, 36/35, 25/24, 21/20, 16/15, 15/14, 35/32, 10/9, 28/25, 9/8, 8/7, 7/6, 25/21, 6/5, 128/105, 60/49, 49/40, 5/4, 32/25, 9/7, 35/27, 64/49, 21/16, 4/3, 168/125, 49/36, 48/35, 25/18, 480/343, 7/5, 10/7, 343/240, 36/25, 35/24, 72/49, 125/84, 3/2, 32/21, 49/32, 54/35, 14/9, 25/16, 8/5, 80/49, 49/30, 105/64, 5/3, 42/25, 12/7, 7/4, 16/9, 25/14, 9/5, 64/35, 28/15, 15/8, 40/21, 48/25, 35/18, 96/49, 49/25, 2]
Original HTML content:
<html><head><title>Chord cubes</title></head><body><br /> A cube scale is a 7-limit scale (we might also consider the 9 odd limit) whose notes are derived from a cube in the <a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices">7-limit lattice of chords</a>. For odd n, we will call the octave-reduced set of notes deriving from all chords of the form [i, j, k], (1-n)/2 <= i, j, k <= (n-1)/2, Cube[n]. If n is even, we will use Cube[n] to refer to the notes of [i, j, k] with 1-n/2 <= i, j, k < n/2. If n is odd, Cube[n] has (n+1)^3/2 notes to it; if n is even, its growth is more complicated but still approximately cubic. For odd n, the inversion of the scale gives another scale, centered around a minor rather than a major tetrad. Here are the first three cube scales:<br /> <br /> <strong>Cube[2] -- the stellated hexany, 14 notes</strong><br /> [21/20, 15/14, 35/32, 9/8, 5/4, 21/16, 35/24, 3/2, 49/32, 25/16, 105/64, 7/4, 15/8, 2]<br /> <br /> <strong>Cube[3] 32 notes</strong><br /> [49/48, 25/24, 21/20, 15/14, 35/32, 9/8, 8/7, 7/6, 6/5, 60/49, 49/40, 5/4, 9/7, 21/16, 4/3, 7/5, 10/7, 35/24, 3/2, 49/32, 25/16, 8/5, 105/64, 5/3, 42/25, 12/7, 7/4, 25/14, 9/5, 15/8, 35/18, 2]<br /> <br /> <strong>Cube[4] 63 notes</strong><br /> [50/49, 49/48, 36/35, 25/24, 21/20, 16/15, 15/14, 35/32, 10/9, 28/25, 9/8, 8/7, 7/6, 25/21, 6/5, 128/105, 60/49, 49/40, 5/4, 32/25, 9/7, 35/27, 64/49, 21/16, 4/3, 168/125, 49/36, 48/35, 25/18, 480/343, 7/5, 10/7, 343/240, 36/25, 35/24, 72/49, 125/84, 3/2, 32/21, 49/32, 54/35, 14/9, 25/16, 8/5, 80/49, 49/30, 105/64, 5/3, 42/25, 12/7, 7/4, 16/9, 25/14, 9/5, 64/35, 28/15, 15/8, 40/21, 48/25, 35/18, 96/49, 49/25, 2]</body></html>