Biyatismic chords: Difference between revisions
Prefer voicing with the perfect fifth and sometimes other harmonics; one line each chord for readability |
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The two biyatismic triads are in inverse relationship: | 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. | ||
For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are | 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. | ||
The inversely related pairs of chords are | 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. | ||
For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is | 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. | ||
The inversely related pairs of chords are | 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 | ||
* | * 1–6/5–3/2–11/8–11/6 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. | ||
Finally, there is a palindromic hexad, | 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. | ||
Equal | [[Equal temperament]]s with biyatismic chords include {{Optimal ET sequence| 7, 9, 15, 16, 22, 24, 29, 31, 38, 46 and 53 }}. | ||
== See also == | == See also == | ||
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* [[Chords of porcupine]] | * [[Chords of porcupine]] | ||
[[Category:11-odd-limit]] | [[Category:11-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||