Biyatismic chords: Difference between revisions
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Prefer voicing with the perfect fifth and sometimes other harmonics; one line each chord for readability |
m Fix a ratio |
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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 | ||
* | * 1–6/5–3/2–18/11–11/6 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. | ||
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 == | ||
| Line 41: | Line 41: | ||
* [[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]] | ||
Latest revision as of 10:25, 10 October 2024
Biyatismic chords are essentially tempered dyadic chords tempered by the biyatisma, 121/120.
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.
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
- 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
- 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
- 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
- 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.
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 temperaments with biyatismic chords include 7, 9, 15, 16, 22, 24, 29, 31, 38, 46 and 53.