Aureusmic chords: Difference between revisions

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There is an inversely related pair which is even more squeezed:

* 1-17/16-19/17 with steps 17/16-20/19-34/19 and its inverse 1-20/19-19/17 with steps 20/19-17/16-34/19.

* 1-17/16-19/17 with steps 17/16-20/19-34/19, and its inverse

* 1-20/19-19/17 with steps 20/19-17/16-34/19.

They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are

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The inversely related pairs of chords are

* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5 and its inverse 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5;

* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse

* 1-19/17-20/17-5/4 with steps 19/17-20/19-17/16-8/5 and its inverse 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.

* 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5;

* 1-19/17-20/17-5/4 with steps 19/17-20/19-17/16-8/5, and its inverse

* 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.

Then there are two inversely related pentads:

* 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5 and its inverse 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.

* 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5 and its inverse,

* 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.

Equal temperaments with aureusmic chords include {{Optimal ET sequence|12, 13, 25, 31, 37, 43, 56, 68, 81, 93, 124, 137, 149, 205, 230 and 286}}.

Equal temperaments with aureusmic chords include {{Optimal ET sequence| 12, 13, 25, 31, 37, 43, 56, 68, 81, 93, 124, 137, 149, 205, 230 and 286 }}.

[[Category:19-odd-limit]]

@@ Line 5: / Line 5: @@
 There is an inversely related pair which is even more squeezed:
-* 1-17/16-19/17 with steps 17/16-20/19-34/19 and its inverse 1-20/19-19/17 with steps 20/19-17/16-34/19.
+* 1-17/16-19/17 with steps 17/16-20/19-34/19, and its inverse
+* 1-20/19-19/17 with steps 20/19-17/16-34/19.
 They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
@@ Line 12: / Line 13: @@
 The inversely related pairs of chords are
-* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5 and its inverse 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5;
+* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse
-* 1-19/17-20/17-5/4 with steps 19/17-20/19-17/16-8/5 and its inverse 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.
+* 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5;
+* 1-19/17-20/17-5/4 with steps 19/17-20/19-17/16-8/5, and its inverse
+* 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.
 Then there are two inversely related pentads:
-* 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5 and its inverse 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.
+* 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5 and its inverse,
+* 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.
-Equal temperaments with aureusmic chords include {{Optimal ET sequence|12, 13, 25, 31, 37, 43, 56, 68, 81, 93, 124, 137, 149, 205, 230 and 286}}.
+Equal temperaments with aureusmic chords include {{Optimal ET sequence| 12, 13, 25, 31, 37, 43, 56, 68, 81, 93, 124, 137, 149, 205, 230 and 286 }}.
 [[Category:19-odd-limit]]