Biyatismic chords: Difference between revisions

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==Zeus chords==

'''Zeus chords''' are essentially tempered dyadic chords of the [[Porwell family|Zeus temperament]]. Aside from the biyatismic, valinorsmic, and keenanismic chords, there are 25 further essentially Zeus chords - ten hexads and fifteen heptads.

'''Zeus chords''' are essentially tempered dyadic chords of the [[Porwell family|Zeus temperament]]. Aside from the biyatismic, valinorsmic, and keenanismic chords, there are 43 further essentially Zeus chords - eighteen pentads, ten hexads, and fifteen heptads.

The Zeus ~~hexads~~ consist of two palindromic chords and ~~four~~ pairs of chords in inverse relationship. The two palindromic hexads are 1-11/10-5/4-11/8-11/7-12/7 with steps 11/10-8/7-11/10-8/7-11/10-7/6 and 1-8/7-5/4-11/8-3/2-12/7 with steps 8/7-11/10-11/10-11/10-8/7-7/6. The four inversely related pairs of hexads are 1-8/7-5/4-11/8-3/2-7/4 with steps 8/7-11/10-11/10-11/10-7/6-8/7 and 1-8/7-4/3-16/11-8/5-7/4 with steps 8/7-7/6-11/10-11/10-11/10-8/7; 1-8/7-5/4-10/7-11/7-12/7 with steps 8/7-11/10-8/7-11/10-11/10-7/6 and 1-7/6-14/11-7/5-8/5-7/4 with steps 7/6-11/10-11/10-8/7-11/10-8/7; 1-7/6-14/11-16/11-8/5-7/4 with steps 7/6-11/10-8/7-11/10-11/10-8/7 and 1-8/7-5/4-11/8-11/7-12/7 with steps 8/7-11/10-11/10-8/7-11/10-7/6; and 1-8/7-5/4-16/11-8/5-7/4 with steps 8/7-11/10-7/6-11/10-11/10-8/7 and 1-8/7-5/4-11/8-8/5-7/4 with steps 8/7-11/10-11/10-7/6-11/10-8/7.

The Zeus pentads consist of two palindromic chords and eight pairs of chords in inverse relationship.

The Zeus heptads consist of three palindromic chords and six pairs of chords in inverse relationship. The three palindromic heptads are 1-11/10-6/5-11/8-16/11-5/3-11/6 with steps 11/10-11/10-8/7-16/15-8/7-11/10-11/10, 1-11/10-5/4-11/8-16/11-8/5-11/6 with steps 11/10-8/7-11/10-16/15-11/10-8/7-11/10, and 1-8/7-5/4-11/8-16/11-8/5-7/4 with steps 8/7-11/10-11/10-16/15-11/10-11/10-8/7. The six inversely related pairs of heptads are 1-11/10-6/5-11/8-16/11-8/5-7/4 with steps 11/10-11/10-8/7-16/15-11/10-11/10-8/7 and 1-8/7-5/4-11/8-16/11-5/3-11/6 with steps 8/7-11/10-11/10-16/15-8/7-11/10-11/10; 1-11/10-6/5-11/8-16/11-8/5-11/6 with steps 11/10-11/10-8/7-16/15-11/10-8/7-11/10 and 1-11/10-5/4-11/8-16/11-5/3-11/6 with steps 11/10-8/7-11/10-16/15-8/7-11/10-11/10; 1-11/10-5/4-11/8-16/11-8/5-7/4 with steps 11/10-8/7-11/10-16/15-11/10-11/10-8/7 and 1-8/7-5/4-11/8-16/11-8/5-11/6 with steps 8/7-11/10-11/10-16/15-11/10-8/7-11/10; 1-11/10-6/5-14/11-16/11-5/3-11/6 with steps 11/10-11/10-16/15-8/7-8/7-11/10-11/10 and 1-11/10-6/5-11/8-11/7-5/3-11/6 with steps 11/10-11/10-8/7-8/7-16/15-11/10-11/10; 1-11/10-6/5-14/11-16/11-8/5-11/6 with steps 11/10-11/10-16/15-8/7-11/10-8/7-11/10 and 1-11/10-5/4-11/8-11/7-5/3-11/6 with steps 11/10-8/7-11/10-8/7-16/15-11/10-11/10; and 1-8/7-5/4-4/3-16/11-8/5-7/4 with steps 8/7-11/10-16/15-11/10-11/10-11/10-8/7 and 1-8/7-5/4-11/8-3/2-8/5-7/4 with steps 8/7-11/10-11/10-11/10-16/15-11/10-8/7.

The two palindromic pentads are: 1-6/5-11/8-16/11-5/3 with steps 6/5-8/7-16/15-8/7-6/5 and 1-8/7-11/8-16/11-7/4 with steps 8/7-6/5-16/15-6/5-8/7.

The eight inversely related pairs of pentads are: 1-8/7-11/8-16/11-5/3 with steps 8/7-6/5-16/15-8/7-6/5 and 1-6/5-11/8-16/11-7/4 with steps 6/5-8/7-16/15-6/5-8/7; 1-8/7-11/9-16/11-7/4 with steps 8/7-16/15-6/5-6/5-8/7 and 1-8/7-11/8-18/11-7/4 with steps 8/7-6/5-6/5-16/15-8/7; 1-8/7-11/8-16/11-8/5 with steps 8/7-6/5-16/15-11/10-5/4 and 1-5/4-11/8-16/11-7/4 with steps 5/4-11/10-16/15-6/5-8/7; 1-8/7-11/8-16/11-11/6 with steps 8/7-6/5-16/15-5/4-11/10 and 1-11/10-11/8-16/11-7/4 with steps 11/10-5/4-16/15-6/5-8/7; 1-5/4-11/8-16/11-5/3 with steps 5/4-11/10-16/15-8/7-6/5 and 1-6/5-11/8-16/11-8/5 with steps 6/5-8/7-16/15-11/10-5/4; 1-11/10-11/8-16/11-5/3 with steps 11/10-5/4-16/15-8/7-6/5 and 1-6/5-11/8-16/11-11/6 with steps 6/5-8/7-16/15-5/4-11/10; 1-5/4-3/2-8/5-11/6 with steps 5/4-6/5-16/15-8/7-11/10 and 1-11/10-5/4-4/3-8/5 with steps 11/10-8/7-16/15-6/5-5/4; and 1-5/4-11/8-18/11-7/4 with steps 5/4-11/10-6/5-16/15-8/7 and 1-8/7-11/9-16/11-8/5 with steps 8/7-16/15-6/5-11/10-5/4.

The Zeus hexads consist of two palindromic chords and four pairs of chords in inverse relationship.

The two palindromic hexads are: 1-11/10-5/4-11/8-11/7-12/7 with steps 11/10-8/7-11/10-8/7-11/10-7/6 and 1-8/7-5/4-11/8-3/2-12/7 with steps 8/7-11/10-11/10-11/10-8/7-7/6.

The four inversely related pairs of hexads are: 1-8/7-5/4-11/8-3/2-7/4 with steps 8/7-11/10-11/10-11/10-7/6-8/7 and 1-8/7-4/3-16/11-8/5-7/4 with steps 8/7-7/6-11/10-11/10-11/10-8/7; 1-8/7-5/4-10/7-11/7-12/7 with steps 8/7-11/10-8/7-11/10-11/10-7/6 and 1-7/6-14/11-7/5-8/5-7/4 with steps 7/6-11/10-11/10-8/7-11/10-8/7; 1-7/6-14/11-16/11-8/5-7/4 with steps 7/6-11/10-8/7-11/10-11/10-8/7 and 1-8/7-5/4-11/8-11/7-12/7 with steps 8/7-11/10-11/10-8/7-11/10-7/6; and 1-8/7-5/4-16/11-8/5-7/4 with steps 8/7-11/10-7/6-11/10-11/10-8/7 and 1-8/7-5/4-11/8-8/5-7/4 with steps 8/7-11/10-11/10-7/6-11/10-8/7.

The Zeus heptads consist of three palindromic chords and six pairs of chords in inverse relationship.

The three palindromic heptads are: 1-11/10-6/5-11/8-16/11-5/3-11/6 with steps 11/10-11/10-8/7-16/15-8/7-11/10-11/10, 1-11/10-5/4-11/8-16/11-8/5-11/6 with steps 11/10-8/7-11/10-16/15-11/10-8/7-11/10, and 1-8/7-5/4-11/8-16/11-8/5-7/4 with steps 8/7-11/10-11/10-16/15-11/10-11/10-8/7.

The six inversely related pairs of heptads are: 1-11/10-6/5-11/8-16/11-8/5-7/4 with steps 11/10-11/10-8/7-16/15-11/10-11/10-8/7 and 1-8/7-5/4-11/8-16/11-5/3-11/6 with steps 8/7-11/10-11/10-16/15-8/7-11/10-11/10; 1-11/10-6/5-11/8-16/11-8/5-11/6 with steps 11/10-11/10-8/7-16/15-11/10-8/7-11/10 and 1-11/10-5/4-11/8-16/11-5/3-11/6 with steps 11/10-8/7-11/10-16/15-8/7-11/10-11/10; 1-11/10-5/4-11/8-16/11-8/5-7/4 with steps 11/10-8/7-11/10-16/15-11/10-11/10-8/7 and 1-8/7-5/4-11/8-16/11-8/5-11/6 with steps 8/7-11/10-11/10-16/15-11/10-8/7-11/10; 1-11/10-6/5-14/11-16/11-5/3-11/6 with steps 11/10-11/10-16/15-8/7-8/7-11/10-11/10 and 1-11/10-6/5-11/8-11/7-5/3-11/6 with steps 11/10-11/10-8/7-8/7-16/15-11/10-11/10; 1-11/10-6/5-14/11-16/11-8/5-11/6 with steps 11/10-11/10-16/15-8/7-11/10-8/7-11/10 and 1-11/10-5/4-11/8-11/7-5/3-11/6 with steps 11/10-8/7-11/10-8/7-16/15-11/10-11/10; and 1-8/7-5/4-4/3-16/11-8/5-7/4 with steps 8/7-11/10-16/15-11/10-11/10-11/10-8/7 and 1-8/7-5/4-11/8-3/2-8/5-7/4 with steps 8/7-11/10-11/10-11/10-16/15-11/10-8/7.

[[Category:Chord]]

@@ Line 8: / Line 8: @@
 ==Zeus chords==
-'''Zeus chords''' are essentially tempered dyadic chords of the [[Porwell family|Zeus temperament]]. Aside from the biyatismic, valinorsmic, and keenanismic chords, there are 25 further essentially Zeus chords - ten hexads and fifteen heptads.
+'''Zeus chords''' are essentially tempered dyadic chords of the [[Porwell family|Zeus temperament]]. Aside from the biyatismic, valinorsmic, and keenanismic chords, there are 43 further essentially Zeus chords - eighteen pentads, ten hexads, and fifteen heptads.
-The Zeus hexads consist of two palindromic chords and four pairs of chords in inverse relationship. The two palindromic hexads are 1-11/10-5/4-11/8-11/7-12/7 with steps 11/10-8/7-11/10-8/7-11/10-7/6 and 1-8/7-5/4-11/8-3/2-12/7 with steps 8/7-11/10-11/10-11/10-8/7-7/6. The four inversely related pairs of hexads are 1-8/7-5/4-11/8-3/2-7/4 with steps 8/7-11/10-11/10-11/10-7/6-8/7 and 1-8/7-4/3-16/11-8/5-7/4 with steps 8/7-7/6-11/10-11/10-11/10-8/7; 1-8/7-5/4-10/7-11/7-12/7 with steps 8/7-11/10-8/7-11/10-11/10-7/6 and 1-7/6-14/11-7/5-8/5-7/4 with steps 7/6-11/10-11/10-8/7-11/10-8/7; 1-7/6-14/11-16/11-8/5-7/4 with steps 7/6-11/10-8/7-11/10-11/10-8/7 and 1-8/7-5/4-11/8-11/7-12/7 with steps 8/7-11/10-11/10-8/7-11/10-7/6; and 1-8/7-5/4-16/11-8/5-7/4 with steps 8/7-11/10-7/6-11/10-11/10-8/7 and 1-8/7-5/4-11/8-8/5-7/4 with steps 8/7-11/10-11/10-7/6-11/10-8/7.
+The Zeus pentads consist of two palindromic chords and eight pairs of chords in inverse relationship.
-The Zeus heptads consist of three palindromic chords and six pairs of chords in inverse relationship. The three palindromic heptads are 1-11/10-6/5-11/8-16/11-5/3-11/6 with steps 11/10-11/10-8/7-16/15-8/7-11/10-11/10, 1-11/10-5/4-11/8-16/11-8/5-11/6 with steps 11/10-8/7-11/10-16/15-11/10-8/7-11/10, and 1-8/7-5/4-11/8-16/11-8/5-7/4 with steps 8/7-11/10-11/10-16/15-11/10-11/10-8/7. The six inversely related pairs of heptads are 1-11/10-6/5-11/8-16/11-8/5-7/4 with steps 11/10-11/10-8/7-16/15-11/10-11/10-8/7 and 1-8/7-5/4-11/8-16/11-5/3-11/6 with steps 8/7-11/10-11/10-16/15-8/7-11/10-11/10; 1-11/10-6/5-11/8-16/11-8/5-11/6 with steps 11/10-11/10-8/7-16/15-11/10-8/7-11/10 and 1-11/10-5/4-11/8-16/11-5/3-11/6 with steps 11/10-8/7-11/10-16/15-8/7-11/10-11/10; 1-11/10-5/4-11/8-16/11-8/5-7/4 with steps 11/10-8/7-11/10-16/15-11/10-11/10-8/7 and 1-8/7-5/4-11/8-16/11-8/5-11/6 with steps 8/7-11/10-11/10-16/15-11/10-8/7-11/10; 1-11/10-6/5-14/11-16/11-5/3-11/6 with steps 11/10-11/10-16/15-8/7-8/7-11/10-11/10 and 1-11/10-6/5-11/8-11/7-5/3-11/6 with steps 11/10-11/10-8/7-8/7-16/15-11/10-11/10; 1-11/10-6/5-14/11-16/11-8/5-11/6 with steps 11/10-11/10-16/15-8/7-11/10-8/7-11/10 and 1-11/10-5/4-11/8-11/7-5/3-11/6 with steps 11/10-8/7-11/10-8/7-16/15-11/10-11/10; and 1-8/7-5/4-4/3-16/11-8/5-7/4 with steps 8/7-11/10-16/15-11/10-11/10-11/10-8/7 and 1-8/7-5/4-11/8-3/2-8/5-7/4 with steps 8/7-11/10-11/10-11/10-16/15-11/10-8/7.
+The two palindromic pentads are: 1-6/5-11/8-16/11-5/3 with steps 6/5-8/7-16/15-8/7-6/5 and 1-8/7-11/8-16/11-7/4 with steps 8/7-6/5-16/15-6/5-8/7.
+The eight inversely related pairs of pentads are: 1-8/7-11/8-16/11-5/3 with steps 8/7-6/5-16/15-8/7-6/5 and 1-6/5-11/8-16/11-7/4 with steps 6/5-8/7-16/15-6/5-8/7; 1-8/7-11/9-16/11-7/4 with steps 8/7-16/15-6/5-6/5-8/7 and 1-8/7-11/8-18/11-7/4 with steps 8/7-6/5-6/5-16/15-8/7; 1-8/7-11/8-16/11-8/5 with steps 8/7-6/5-16/15-11/10-5/4 and 1-5/4-11/8-16/11-7/4 with steps 5/4-11/10-16/15-6/5-8/7; 1-8/7-11/8-16/11-11/6 with steps 8/7-6/5-16/15-5/4-11/10 and 1-11/10-11/8-16/11-7/4 with steps 11/10-5/4-16/15-6/5-8/7; 1-5/4-11/8-16/11-5/3 with steps 5/4-11/10-16/15-8/7-6/5 and 1-6/5-11/8-16/11-8/5 with steps 6/5-8/7-16/15-11/10-5/4; 1-11/10-11/8-16/11-5/3 with steps 11/10-5/4-16/15-8/7-6/5 and 1-6/5-11/8-16/11-11/6 with steps 6/5-8/7-16/15-5/4-11/10; 1-5/4-3/2-8/5-11/6 with steps 5/4-6/5-16/15-8/7-11/10 and 1-11/10-5/4-4/3-8/5 with steps 11/10-8/7-16/15-6/5-5/4; and 1-5/4-11/8-18/11-7/4 with steps 5/4-11/10-6/5-16/15-8/7 and 1-8/7-11/9-16/11-8/5 with steps 8/7-16/15-6/5-11/10-5/4.
+The Zeus hexads consist of two palindromic chords and four pairs of chords in inverse relationship.
+The two palindromic hexads are: 1-11/10-5/4-11/8-11/7-12/7 with steps 11/10-8/7-11/10-8/7-11/10-7/6 and 1-8/7-5/4-11/8-3/2-12/7 with steps 8/7-11/10-11/10-11/10-8/7-7/6.
+The four inversely related pairs of hexads are: 1-8/7-5/4-11/8-3/2-7/4 with steps 8/7-11/10-11/10-11/10-7/6-8/7 and 1-8/7-4/3-16/11-8/5-7/4 with steps 8/7-7/6-11/10-11/10-11/10-8/7; 1-8/7-5/4-10/7-11/7-12/7 with steps 8/7-11/10-8/7-11/10-11/10-7/6 and 1-7/6-14/11-7/5-8/5-7/4 with steps 7/6-11/10-11/10-8/7-11/10-8/7; 1-7/6-14/11-16/11-8/5-7/4 with steps 7/6-11/10-8/7-11/10-11/10-8/7 and 1-8/7-5/4-11/8-11/7-12/7 with steps 8/7-11/10-11/10-8/7-11/10-7/6; and 1-8/7-5/4-16/11-8/5-7/4 with steps 8/7-11/10-7/6-11/10-11/10-8/7 and 1-8/7-5/4-11/8-8/5-7/4 with steps 8/7-11/10-11/10-7/6-11/10-8/7.
+The Zeus heptads consist of three palindromic chords and six pairs of chords in inverse relationship.
+The three palindromic heptads are: 1-11/10-6/5-11/8-16/11-5/3-11/6 with steps 11/10-11/10-8/7-16/15-8/7-11/10-11/10, 1-11/10-5/4-11/8-16/11-8/5-11/6 with steps 11/10-8/7-11/10-16/15-11/10-8/7-11/10, and 1-8/7-5/4-11/8-16/11-8/5-7/4 with steps 8/7-11/10-11/10-16/15-11/10-11/10-8/7.
+The six inversely related pairs of heptads are: 1-11/10-6/5-11/8-16/11-8/5-7/4 with steps 11/10-11/10-8/7-16/15-11/10-11/10-8/7 and 1-8/7-5/4-11/8-16/11-5/3-11/6 with steps 8/7-11/10-11/10-16/15-8/7-11/10-11/10; 1-11/10-6/5-11/8-16/11-8/5-11/6 with steps 11/10-11/10-8/7-16/15-11/10-8/7-11/10 and 1-11/10-5/4-11/8-16/11-5/3-11/6 with steps 11/10-8/7-11/10-16/15-8/7-11/10-11/10; 1-11/10-5/4-11/8-16/11-8/5-7/4 with steps 11/10-8/7-11/10-16/15-11/10-11/10-8/7 and 1-8/7-5/4-11/8-16/11-8/5-11/6 with steps 8/7-11/10-11/10-16/15-11/10-8/7-11/10; 1-11/10-6/5-14/11-16/11-5/3-11/6 with steps 11/10-11/10-16/15-8/7-8/7-11/10-11/10 and 1-11/10-6/5-11/8-11/7-5/3-11/6 with steps 11/10-11/10-8/7-8/7-16/15-11/10-11/10; 1-11/10-6/5-14/11-16/11-8/5-11/6 with steps 11/10-11/10-16/15-8/7-11/10-8/7-11/10 and 1-11/10-5/4-11/8-11/7-5/3-11/6 with steps 11/10-8/7-11/10-8/7-16/15-11/10-11/10; and 1-8/7-5/4-4/3-16/11-8/5-7/4 with steps 8/7-11/10-16/15-11/10-11/10-11/10-8/7 and 1-8/7-5/4-11/8-3/2-8/5-7/4 with steps 8/7-11/10-11/10-11/10-16/15-11/10-8/7.
 [[Category:Chord]]