Biyatismic chords: Difference between revisions
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'''Biyatismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the biyatisma, [[121/120]]. | '''Biyatismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the biyatisma, [[121/120]]. | ||
Biyatismic temperament contains many possibilities for essentially tempered dyadic chords including five triad in the 2.3.5.11 subgroup. | |||
The biyatismic pentads consist of two palindromic chords and two pairs of chords in 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. | The biyatismic triads consist of a palindromic chord and two paird of chords in inverse relationship. The palindromic chord is 1-[[11/8]]-[[16/11]] chord with steps of 11/8-[[16/15]]-11/8. The inversely related pairs of chords are 1-11/8-[[11/6]] chord with steps of 11/8-[[4/3]]-[[11/10]] and 1-11/10-16/11 chord with steps of 11/10-4/3-11/8; and 1-11/8-[[5/3]] chord with steps of 11/8-[[11/9]]-[[6/5]] and 1-6/5-16/11 chord with steps of 6/5-11/9-11/8. | ||
<!-- The biyatismic pentads consist of two palindromic chords and two pairs of chords in 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 == | ||
'''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. | '''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. | ||
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[[Category:Dyadic]] | [[Category:Dyadic]] | ||
[[Category:Triad]] | [[Category:Triad]] | ||