Crystal ball: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-~~06 20~~:20:10 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-22 21:10:00 UTC</tt>.

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Crystal ball one can also be described as Cube[2], the 2x2x2 cube scale, which consists of the notes of the eight chords [i, j, k] with i, j, and k either -1 or 0. Crystal ball two consists of Cube[4], the 4x4x4 cube with i, j, and k from -2 to 1, minus the eight chords [-2 -2 1], [-2 1 -2], [-2 1 1], [1 -2 -2], [1 -2 1], [-2 -2 -2], [1 1 -2], [1 1 1].

The first two crystal balls can also equally well be described as Euclidean ball scales; they began to diverge with the third crystal ball. If we take everything within a radius of one of the unison, we get crystal ball one; if we take everything within a radius of two, we get crystal ball two. This means we also have two intermediate scales, Euclidean balls of radius ~~sqrt(2)~~ and ~~sqrt(3)~~.

The first two crystal balls can also equally well be described as Euclidean ball scales; they began to diverge with the third crystal ball. If we take everything within a radius of one of the unison, we get crystal ball one; if we take everything within a radius of two, we get crystal ball two. This means we also have two intermediate scales, Euclidean balls of radius √2 and √3.

**Euclid 2 19 notes**

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Crystal ball one can also be described as Cube[2], the 2x2x2 cube scale, which consists of the notes of the eight chords [i, j, k] with i, j, and k either -1 or 0. Crystal ball two consists of Cube[4], the 4x4x4 cube with i, j, and k from -2 to 1, minus the eight chords [-2 -2 1], [-2 1 -2], [-2 1 1], [1 -2 -2], [1 -2 1], [-2 -2 -2], [1 1 -2], [1 1 1].

The first two crystal balls can also equally well be described as Euclidean ball scales; they began to diverge with the third crystal ball. If we take everything within a radius of one of the unison, we get crystal ball one; if we take everything within a radius of two, we get crystal ball two. This means we also have two intermediate scales, Euclidean balls of radius ~~sqrt(2)~~ and ~~sqrt(3)~~.

The first two crystal balls can also equally well be described as Euclidean ball scales; they began to diverge with the third crystal ball. If we take everything within a radius of one of the unison, we get crystal ball one; if we take everything within a radius of two, we get crystal ball two. This means we also have two intermediate scales, Euclidean balls of radius √2 and √3.

Euclid 2 19 notes

@@ 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>2011-07-06 20:20:10 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-22 21:10:00 UTC</tt>.<br>
-: The original revision id was <tt>240282537</tt>.<br>
+: The original revision id was <tt>278346330</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>
@@ Line 47: / Line 47: @@
 Crystal ball one can also be described as Cube[2], the 2x2x2 cube scale, which consists of the notes of the eight chords [i, j, k] with i, j, and k either -1 or 0. Crystal ball two consists of Cube[4], the 4x4x4 cube with i, j, and k from -2 to 1, minus the eight chords [-2 -2 1], [-2 1 -2], [-2 1 1], [1 -2 -2], [1 -2 1], [-2 -2 -2], [1 1 -2], [1 1 1].
-The first two crystal balls can also equally well be described as Euclidean ball scales; they began to diverge with the third crystal ball. If we take everything within a radius of one of the unison, we get crystal ball one; if we take everything within a radius of two, we get crystal ball two. This means we also have two intermediate scales, Euclidean balls of radius sqrt(2) and sqrt(3).
+The first two crystal balls can also equally well be described as Euclidean ball scales; they began to diverge with the third crystal ball. If we take everything within a radius of one of the unison, we get crystal ball one; if we take everything within a radius of two, we get crystal ball two. This means we also have two intermediate scales, Euclidean balls of radius √2 and √3.
 **Euclid 2 19 notes**
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 Crystal ball one can also be described as Cube[2], the 2x2x2 cube scale, which consists of the notes of the eight chords [i, j, k] with i, j, and k either -1 or 0. Crystal ball two consists of Cube[4], the 4x4x4 cube with i, j, and k from -2 to 1, minus the eight chords [-2 -2 1], [-2 1 -2], [-2 1 1], [1 -2 -2], [1 -2 1], [-2 -2 -2], [1 1 -2], [1 1 1].&lt;br /&gt;
 &lt;br /&gt;
-The first two crystal balls can also equally well be described as Euclidean ball scales; they began to diverge with the third crystal ball. If we take everything within a radius of one of the unison, we get crystal ball one; if we take everything within a radius of two, we get crystal ball two. This means we also have two intermediate scales, Euclidean balls of radius sqrt(2) and sqrt(3).&lt;br /&gt;
+The first two crystal balls can also equally well be described as Euclidean ball scales; they began to diverge with the third crystal ball. If we take everything within a radius of one of the unison, we get crystal ball one; if we take everything within a radius of two, we get crystal ball two. This means we also have two intermediate scales, Euclidean balls of radius √2 and √3.&lt;br /&gt;
 &lt;br /&gt;
 &lt;strong&gt;Euclid 2 19 notes&lt;/strong&gt;&lt;br /&gt;