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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 triads and 33 tetrads 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 pairs 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: |
| | * 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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| The biyatismic tetrads consist of three palindromic chords and fifteen pairs of chords in inverse relationship. The palindromic chords are 1-9/8-11/8-18/11 chord with steps of 9/8-11/9-6/5-11/9, 1-5/4-11/8-11/6 chord with steps of 5/4-11/10-4/3-11/10, and 1-11/10-3/2-18/11 chord with steps of 11/10-11/8-11/10-11/9. The inversely related pairs of chords are 1-4/3-5/3-11/6 chord with steps of 4/3-5/4-11/10-11/10 and 1-11/10-6/5-3/2 chord with steps of 11/10-11/10-5/4-4/3; 1-11/9-11/8-18/11 chord with steps of 11/9-9/8-6/5-11/9 and 1-11/9-16/11-18/11 chord with steps of 11/9-6/5-9/8-11/9; 1-11/8-5/3-11/6 chord with steps of 11/8-11/9-11/10-11/10 and 1-11/10-6/5-16/11 chord with steps of 11/10-11/10-11/9-11/8; 1-4/3-3/2-11/6 chord with steps of 4/3-9/8-11/9-11/10 and 1-11/10-4/3-3/2 chord with steps of 11/10-11/9-9/8-4/3; 1-9/8-11/8-11/6 chord with steps of 9/8-11/9-4/3-11/10 and 1-11/10-16/11-16/9 chord with steps of 11/10-4/3-11/9-9/8; 1-4/3-3/2-18/11 chord with steps of 4/3-9/8-11/10-11/9 and 1-11/9-4/3-3/2 chord with steps of 11/9-11/10-9/8-4/3; 1-5/4-3/2-11/6 chord with steps of 5/4-6/5-11/9-11/10 and 1-11/10-4/3-8/5 chord with steps of 11/10-11/9-6/5-5/4; 1-6/5-3/2-11/6 chord with steps of 6/5-5/4-11/9-11/10 and 1-11/10-4/3-5/3 chord with steps of 11/10-11/9-5/4-6/5; 1-6/5-16/11-11/6 chord with steps of 6/5-11/9-5/4-11/10 and 1-11/10-11/8-5/3 chord with steps of 11/10-5/4-11/9-6/5; 1-5/4-11/8-16/11 chord with steps of 5/4-11/10-16/15-11/8 and 1-11/8-16/11-8/5 chord with steps of 11/8-16/15-11/10-5/4; 1-5/4-4/3-16/11 chord with steps of 5/4-16/15-11/10-11/8 and 1-11/8-3/2-8/5 chord with steps of 11/8-11/10-16/15-5/4; 1-5/4-4/3-11/6 chord with steps of 5/4-16/15-11/8-11/10 and 1-11/10-3/2-8/5 chord with steps of 11/10-11/8-16/15-5/4; 1-11/9-11/8-16/11 chord with steps of 11/9-9/8-16/15-11/8 and 1-11/8-16/11-18/11 chord with steps of 11/8-16/15-9/8-11/9; 1-11/8-5/3-16/9 chord with steps of 11/8-11/9-16/15-9/8 and 1-9/8-6/5-16/11 chord with steps of 9/8-16/15-11/9-11/8; and 1-11/8-16/11-16/9 chord with steps of 11/8-16/15-11/9-9/8 and 1-9/8-11/8-16/11 chord with steps of 9/8-11/9-16/15-11/8.
| | 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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| Equal temperaments with biyatismic chords include 7, 9, 15, 16, 22, 24, 29, 31, 38, 46, and 53 [[EDO]]s.
| | The inversely related pairs of chords are |
| | * 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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| [[Category:Chords]] | | For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is |
| [[Category:Dyadic]] | | * 1–9/8–11/8–3/2–18/11 chord with steps of 9/8, 11/9, 11/10, 11/10, 11/9. |
| [[Category:Triad]] | | |
| [[Category:Tetrad]] | | 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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| | 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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| | [[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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| | == See also == |
| | * [[Chords of orwell]] |
| | * [[Chords of valentine]] |
| | * [[Chords of porcupine]] |
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| | [[Category:11-odd-limit chords]] |
| | [[Category:Essentially tempered chords]] |
| | [[Category:Triads]] |
| | [[Category:Tetrads]] |
| | [[Category:Pentads]] |
| | [[Category:Hexads]] |
| | [[Category:Biyatismic]] |