Jove chords: Difference between revisions
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These are nine tetrads, one palindromic tetrad and four pairs in inverse relationship: | These are nine tetrads, one palindromic tetrad and four pairs in inverse relationship: | ||
* | * 1–11/9–10/7–7/4 with steps 11/9, 7/6, 11/9, 8/7; | ||
* | * 1–11/9–3/2–7/4 with steps 11/9, 11/9, 7/6, 8/7, and its inverse | ||
* | * 1–11/9–3/2–12/7 with steps 11/9, 11/9, 8/7, 7/6; | ||
* | * 1–9/8–11/9–7/4 with steps 9/8, 12/11, 10/7, 8/7, and its inverse | ||
* | * 1–10/7–14/9–7/4 with steps 10/7, 12/11, 9/8, 8/7; | ||
* 1–9/8–11/7–11/6 with steps 9/8, 7/5, 7/6, 12/11, and its inverse | |||
* 1–9/8–11/9–10/7 with steps 9/8, 12/11, 7/6, 7/5; | |||
* 1–9/7–7/5–11/7 with steps 9/7, 12/11, 9/8, 14/11, and its inverse | |||
* 1–9/7–18/11–11/6 with steps 9/7, 14/11, 9/8, 12/11. | |||
There are sixteen essentially jove pentads, consisting of eight inverse pairs. These are | There are sixteen essentially jove pentads, consisting of eight inverse pairs. These are | ||
* | * 1–11/9–10/7–11/7–7/4 with steps 11/9, 7/6, 11/10, 10/9, 8/7, and its inverse | ||
* | * 1–7/6–10/7–18/11–20/11 with steps 7/6, 11/9, 8/7, 10/9, 11/10; | ||
* | * 1–7/6–3/2–18/11–11/6 with steps 7/6, 9/7, 12/11, 9/8, 12/11, and its inverse | ||
* | * 1–9/7–3/2–18/11–11/6 with steps 9/7, 7/6, 12/11, 9/8, 12/11; | ||
* | * 1–11/9–11/8–3/2–7/4 with steps 11/9, 9/8, 12/11, 7/6, 8/7, and its inverse | ||
* | * 1–12/11–11/9–3/2–12/7 with steps 12/11, 9/8, 11/9, 8/7, 7/6; | ||
* | * 1–9/8–11/9–3/2–7/4 with steps 9/8, 12/11, 11/9, 7/6, 8/7, and its inverse | ||
* | * 1–9/8–9/7–3/2–11/6 with steps 9/8, 8/7, 7/6, 11/9, 12/11; | ||
* 1–9/8–11/9–10/7–7/4 with steps 9/8, 12/11, 7/6, 11/9, 8/7, and its inverse | |||
* 1–11/9–10/7–14/9–7/4 with steps 11/9, 7/6, 12/11, 9/8, 8/7; | |||
* 1–9/8–11/9–10/7–11/7 with steps 9/8, 12/11, 7/6, 11/10, 14/11, and its inverse | |||
* 1–9/8–10/7–11/7–11/6 with steps 9/8, 14/11, 11/10, 7/6, 12/11; | |||
* 1–9/8–11/9–11/8–7/4 with steps 9/8, 12/11, 9/8, 14/11, 8/7, and its inverse | |||
* 1–14/11–10/7–14/9–7/4 with steps 14/11, 9/8, 12/11, 9/8, 8/7; | |||
* 1–9/8–11/9–11/7–7/4 with steps 9/8, 12/11, 9/7, 10/9, 8/7, and its inverse | |||
* 1–9/7–7/5–11/7–9/5 with steps 9/7, 12/11, 9/8, 8/7, 10/9. | |||
Finally, there are six essentially jove hexads, two palindromic and two pairs of inversely related chords: | Finally, there are six essentially jove hexads, two palindromic and two pairs of inversely related chords: | ||
* | * 1–9/8–11/9–11/8–11/7–7/4 with steps 9/8, 12/11, 9/8, 8/7, 10/9, 8/7; | ||
* | * 1–7/6–9/7–3/2–18/11–11/6 with steps 7/6, 11/10, 7/6, 12/11, 9/8, 12/11; | ||
* | * 1–9/8–9/7–3/2–18/11–11/6 with steps 9/8, 8/7, 7/6, 12/11, 9/8, 12/11, and its inverse | ||
* | * 1–9/8–11/9–11/8–3/2–7/4 with steps 9/8, 12/11, 9/8, 12/11, 7/6, 8/7; | ||
* 1–9/8–9/7–10/7–11/7–11/6 with steps 9/8, 8/7, 10/9, 11/10, 7/6, 12/11, and its inverse | |||
* 1–9/8–11/9–10/7–11/7–7/4 with steps 9/8, 12/11, 7/6, 11/10, 10/9, 8/7. | |||
The essentially jove chords number tetrads: 9, pentads: 16, hexads: 6, for a total of 31. | The essentially jove chords number tetrads: 9, pentads: 16, hexads: 6, for a total of 31. | ||
Equal | [[Equal temperament]]s with jove tetrads include {{EDOs| 31, 41, 58, 72, 130, 161, 171 and 202 }}. | ||
[[Category:11-odd-limit]] | [[Category:11-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Tetrads]] | [[Category:Tetrads]] | ||