Chord cubes: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-~~07 03~~:11:24 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-28 14:02:18 UTC</tt>.<br>

: The original revision id was <tt>~~240321807~~</tt>.<br>

: The original revision id was <tt>269661578</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>

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:

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, but an alternative cube is derived from -n/2 < i, j, k < n/2-1. 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. Note that in the case of even n, the two types of cubes are distinctly different; for instance the alternative 2x2x2 cube is the 7-limit [[tonality diamond]], which has only 13 notes. 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**

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<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"><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 &lt;= i, j, k &lt;= (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 &lt;= i, j, k &lt; 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 />

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 &lt;= i, j, k &lt;= (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 &lt;= i, j, k &lt; n/2, but an alternative cube is derived from -n/2 &lt; i, j, k &lt; n/2-1. 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. Note that in the case of even n, the two types of cubes are distinctly different; for instance the alternative 2x2x2 cube is the 7-limit <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a>, which has only 13 notes. For odd n, the inversion of the scale gives another scale, centered around a minor rather than a major tetrad. <br />

<br />

Here are the first three cube scales:<br />

<br />

<strong>Cube[2] -- the stellated hexany, 14 notes</strong><br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-07 03:11:24 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-28 14:02:18 UTC</tt>.<br>
-: The original revision id was <tt>240321807</tt>.<br>
+: The original revision id was <tt>269661578</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">
-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 &lt;= i, j, k &lt;= (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 &lt;= i, j, k &lt; 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:
+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 &lt;= i, j, k &lt;= (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 &lt;= i, j, k &lt; n/2, but an alternative cube is derived from -n/2 &lt; i, j, k &lt; n/2-1. 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. Note that in the case of even n, the two types of cubes are distinctly different; for instance the alternative 2x2x2 cube is the 7-limit [[tonality diamond]], which has only 13 notes. 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**
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 <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;Chord cubes&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;br /&gt;
-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 &lt;a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices"&gt;7-limit lattice of chords&lt;/a&gt;. 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 &amp;lt;= i, j, k &amp;lt;= (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 &amp;lt;= i, j, k &amp;lt; 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:&lt;br /&gt;
+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 &lt;a class="wiki_link" href="/The%20Seven%20Limit%20Symmetrical%20Lattices"&gt;7-limit lattice of chords&lt;/a&gt;. 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 &amp;lt;= i, j, k &amp;lt;= (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 &amp;lt;= i, j, k &amp;lt; n/2, but an alternative cube is derived from -n/2 &amp;lt; i, j, k &amp;lt; n/2-1. 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. Note that in the case of even n, the two types of cubes are distinctly different; for instance the alternative 2x2x2 cube is the 7-limit &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt;, which has only 13 notes. For odd n, the inversion of the scale gives another scale, centered around a minor rather than a major tetrad. &lt;br /&gt;
+&lt;br /&gt;
+Here are the first three cube scales:&lt;br /&gt;
 &lt;br /&gt;
 &lt;strong&gt;Cube[2] -- the stellated hexany, 14 notes&lt;/strong&gt;&lt;br /&gt;