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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]]. |
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| Biyatismic temperament contains many possibilities for essentially tempered dyadic chords including five triad in the 2.3.5.11 subgroup.
| | There are two triads, nine tetrads, seven pentads and one hexad as 2.3.5.11 subgroup [[11-odd-limit]] essentially tempered chords. In this article, voicing with the [[perfect fifth]] is prioritized. |
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| 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 two biyatismic triads are in inverse relationship: |
| <!-- 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. -->
| | * 1–11/8–5/3 with steps 11/8, 11/9, 6/5; |
| | * 1–11/8–18/11 with steps 11/8, 6/5, 11/9. |
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| Equal temperaments with biyatismic chords include 7, 9, 15, 16, 22, 24, 29, 31, 38, 46, and 53 [[EDO]]s.
| | For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are |
| | * 1–9/8–11/8–18/11 with steps 9/8, 11/9, 6/5, 11/9; |
| | * 1–11/10–11/8–3/2 with steps 11/10, 5/4, 11/10, 4/3; |
| | * 1–3/2–18/11–11/6 with steps 3/2, 11/10, 10/9, 11/10. |
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| == Zeus chords ==
| | The inversely related pairs of chords are |
| '''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.
| | * 1–11/8–3/2–18/11 with steps 11/8, 11/10, 11/10, 11/9, and its inverse |
| | * 1–11/10–3/2–11/6 with steps 11/10, 11/8, 11/9, 11/10; |
| | * 1–5/4–3/2–11/6 with steps 5/4, 6/5, 11/9, 11/10, and its inverse |
| | * 1–6/5–3/2–18/11 with steps 6/5, 5/4, 11/10, 11/9; |
| | * 1–11/8–3/2–5/3 with steps 11/8, 11/10, 10/9, 6/5, and its inverse |
| | * 1–11/10–3/2–9/5 with steps 11/10, 11/8, 6/5, 10/9. |
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| The Zeus pentads consist of two palindromic chords and eight pairs of chords in inverse relationship.
| | For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is |
| | * 1–9/8–11/8–3/2–18/11 chord with steps of 9/8, 11/9, 11/10, 11/10, 11/9. |
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| 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 inversely related pairs of chords are |
| | * 1–11/8–3/2–5/3–11/6 with steps 11/8, 11/10, 10/9, 11/10, 11/10 and its inverse |
| | * 1–11/10–3/2–18/11–9/5 with steps 11/10, 11/8, 11/10, 11/10, 10/9; |
| | * 1–5/4–3/2–5/3–11/6 with steps 5/4, 6/5, 10/9, 11/10, 11/10 and its inverse |
| | * 1–6/5–3/2–18/11–11/6 with steps 6/5, 5/4, 11/10, 11/10, 10/9; |
| | * 1–5/4–11/8–3/2–11/6 with steps 5/4, 11/10, 11/10, 11/9, 11/10 and its inverse |
| | * 1–11/10–6/5–3/2–18/11 with steps 11/10, 11/10, 5/4, 11/10, 11/9. |
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| 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.
| | Finally, there is a palindromic hexad, |
| | * 1–5/4–11/8–3/2–5/3–11/6 with steps 5/4, 11/10, 11/10, 10/9, 11/10, 11/10. |
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| The Zeus hexads consist of two palindromic chords and four pairs of chords in inverse relationship.
| | [[Equal temperament]]s with biyatismic chords include {{Optimal ET sequence| 7, 9, 15, 16, 22, 24, 29, 31, 38, 46 and 53 }}. |
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| 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.
| | == See also == |
| | * [[Chords of orwell]] |
| | * [[Chords of valentine]] |
| | * [[Chords of porcupine]] |
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| 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:11-odd-limit chords]] |
| | | [[Category:Essentially tempered chords]] |
| The Zeus heptads consist of three palindromic chords and six pairs of chords in inverse relationship.
| | [[Category:Triads]] |
| | | [[Category:Tetrads]] |
| 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.
| | [[Category:Pentads]] |
| | | [[Category:Hexads]] |
| 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:Biyatismic]] |
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| [[Category:Chords]] | |
| [[Category:Dyadic]] | |
| [[Category:Triad]] | |