Palingenetic chords: Difference between revisions

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

* 1-18/17-10/9 with steps 18/17-21/20-9/5 and its inverse 1-21/20-10/9 with steps 21/20-18/17-9/5.

* 1-18/17-10/9 with steps 18/17-21/20-9/5 and its inverse

* 1-21/20-10/9 with steps 21/20-18/17-9/5.

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

* 1-10/9-20/17-21/17 with steps 10/9-18/17-21/20-34/21 and its inverse 1-21/20-10/9-21/17 with steps 21/20-18/17-10/9-34/21;

* 1-10/9-20/17-21/17 with steps 10/9-18/17-21/20-34/21 and its inverse

* 1-10/9-7/6-21/17 with steps 10/9-21/20-18/17-34/21 and its inverse 1-18/17-10/9-21/17 with steps 18/17-21/20-10/9-34/21.

* 1-21/20-10/9-21/17 with steps 21/20-18/17-10/9-34/21;

* 1-10/9-7/6-21/17 with steps 10/9-21/20-18/17-34/21 and its inverse

* 1-18/17-10/9-21/17 with steps 18/17-21/20-10/9-34/21.

Then there are two inversely related pentads:

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* 1-28/25-32/27-40/27 with steps 28/25-18/17-5/4-27/20

Equal temperaments with palingenetic chords include {{Optimal ET sequence|12, 46, 53, 58, 60, 72, 99, 111, 118, 171, 183, 243, 270, 289, 354, 400, 472 and 571}}.

Equal temperaments with palingenetic chords include {{Optimal ET sequence| 12, 46, 53, 58, 60, 72, 99, 111, 118, 171, 183, 243, 270, 289, 354, 400, 472 and 571 }}.

[[Category:21-odd-limit]]

@@ Line 5: / Line 5: @@
 There is an inversely related pair which is even more squeezed:
-* 1-18/17-10/9 with steps 18/17-21/20-9/5 and its inverse 1-21/20-10/9 with steps 21/20-18/17-9/5.
+* 1-18/17-10/9 with steps 18/17-21/20-9/5 and its inverse
+* 1-21/20-10/9 with steps 21/20-18/17-9/5.
 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
-* 1-10/9-20/17-21/17 with steps 10/9-18/17-21/20-34/21 and its inverse 1-21/20-10/9-21/17 with steps 21/20-18/17-10/9-34/21;
+* 1-10/9-20/17-21/17 with steps 10/9-18/17-21/20-34/21 and its inverse
-* 1-10/9-7/6-21/17 with steps 10/9-21/20-18/17-34/21 and its inverse 1-18/17-10/9-21/17 with steps 18/17-21/20-10/9-34/21.
+* 1-21/20-10/9-21/17 with steps 21/20-18/17-10/9-34/21;
+* 1-10/9-7/6-21/17 with steps 10/9-21/20-18/17-34/21 and its inverse
+* 1-18/17-10/9-21/17 with steps 18/17-21/20-10/9-34/21.
 Then there are two inversely related pentads:
@@ Line 31: / Line 34: @@
 * 1-28/25-32/27-40/27 with steps 28/25-18/17-5/4-27/20
-Equal temperaments with palingenetic chords include {{Optimal ET sequence|12, 46, 53, 58, 60, 72, 99, 111, 118, 171, 183, 243, 270, 289, 354, 400, 472 and 571}}.
+Equal temperaments with palingenetic chords include {{Optimal ET sequence| 12, 46, 53, 58, 60, 72, 99, 111, 118, 171, 183, 243, 270, 289, 354, 400, 472 and 571 }}.
 [[Category:21-odd-limit]]