Biyatismic chords: Difference between revisions
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The biyatismic triad is the 121/120 tempering of 1-[[11/8]]-[[15/8]] chord, with steps of 11/8-11/8-[[16/15]]. | The biyatismic triad is the 121/120 tempering of 1-[[11/8]]-[[15/8]] chord, with steps of 11/8-11/8-[[16/15]]. | ||
The biyatismic pentads consist of two palindromic chords and two pairs of chords in an inverse relationship. The palindromic chords are 1-5/4-11/8-16/11-8/5 with steps 5/4-11/10-16/15-11/10-5/4 and 1-11/10-11/8-16/11-20/11 with steps 11/10-5/4-16/15-5/4-11/10. The pairs of chords are 1-5/4-11/8-16/11-20/11 with steps 5/4-11/10-16/15-5/4-11/10 and 1-11/10-11/8-16/11-8/5 with steps 11/10-5/4-16/15-11/10-5/4; and 1-11/10-6/5-3/2-15/8 with steps 11/10-11/10-5/4-5/4-16/15 and 1-16/15-4/3-5/3-11/6 with steps 16/15-5/4-5/4-11/10-11/10. | The biyatismic pentads consist of two palindromic chords and two pairs of chords in an inverse relationship. The palindromic chords are 1-5/4-11/8-16/11-8/5 with steps 5/4-11/10-16/15-11/10-5/4 and 1-11/10-11/8-16/11-20/11 with steps 11/10-5/4-16/15-5/4-11/10. The inversely related pairs of chords are 1-5/4-11/8-16/11-20/11 with steps 5/4-11/10-16/15-5/4-11/10 and 1-11/10-11/8-16/11-8/5 with steps 11/10-5/4-16/15-11/10-5/4; and 1-11/10-6/5-3/2-15/8 with steps 11/10-11/10-5/4-5/4-16/15 and 1-16/15-4/3-5/3-11/6 with steps 16/15-5/4-5/4-11/10-11/10. | ||
Equal temperaments with biyatismic chords include 7, 9, 15, 16, 22, 24, 29, 31, 38, 46, and 53 [[EDO]]s. | Equal temperaments with biyatismic chords include 7, 9, 15, 16, 22, 24, 29, 31, 38, 46, and 53 [[EDO]]s. | ||
==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 ten further essentially Zeus hexads. 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 1-8/7-5/4-15/11-3/2-12/7 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. | |||
[[Category:Chord]] | [[Category:Chord]] | ||
Revision as of 04:28, 16 June 2019
Biyatismic chords are essentially tempered dyadic chords tempered by the biyatisma, 121/120.
The biyatismic triad is the 121/120 tempering of 1-11/8-15/8 chord, with steps of 11/8-11/8-16/15.
The biyatismic pentads consist of two palindromic chords and two pairs of chords in an inverse relationship. The palindromic chords are 1-5/4-11/8-16/11-8/5 with steps 5/4-11/10-16/15-11/10-5/4 and 1-11/10-11/8-16/11-20/11 with steps 11/10-5/4-16/15-5/4-11/10. The inversely related pairs of chords are 1-5/4-11/8-16/11-20/11 with steps 5/4-11/10-16/15-5/4-11/10 and 1-11/10-11/8-16/11-8/5 with steps 11/10-5/4-16/15-11/10-5/4; and 1-11/10-6/5-3/2-15/8 with steps 11/10-11/10-5/4-5/4-16/15 and 1-16/15-4/3-5/3-11/6 with steps 16/15-5/4-5/4-11/10-11/10.
Equal temperaments with biyatismic chords include 7, 9, 15, 16, 22, 24, 29, 31, 38, 46, and 53 EDOs.
Zeus chords
Zeus chords are essentially tempered dyadic chords of the Zeus temperament. Aside from the biyatismic, valinorsmic, and keenanismic chords, there are ten further essentially Zeus hexads. 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 1-8/7-5/4-15/11-3/2-12/7 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.