Horizmic chords: Difference between revisions
mNo edit summary |
m Cleanup |
||
| Line 4: | Line 4: | ||
For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is | For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is | ||
* | * 1–8/7–17/13 with steps of 8/7, 8/7, 26/17. | ||
The inversely related pair of chords is | The inversely related pair of chords is | ||
* | * 1–14/13–8/7 with steps of 14/13, 17/16, 7/4, and its inverse | ||
* | * 1–17/16–8/7 with steps of 17/16, 14/13, 7/4. | ||
For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are | For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are | ||
* | * 1–14/13–8/7–16/13 with steps of 14/13, 17/16, 14/13, 13/8; | ||
* | * 1–17/16–8/7–17/14 with steps of 17/16, 14/13, 17/16, 28/17. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* | * 1–8/7–16/13–17/13 with steps of 8/7, 14/13, 17/16, 26/17, and its inverse | ||
* | * 1–17/16–8/7–17/13 with steps of 17/16, 14/13, 8/7, 26/17; | ||
* | * 1–8/7–17/14–17/13 with steps of 8/7, 17/16, 14/13, 26/17, and its inverse | ||
* | * 1–14/13–8/7–17/13 with steps of 14/13, 17/16, 8/7, 26/17. | ||
They can be extended to pentads: | They can be extended to pentads: | ||
* | * 1–14/13–8/7–16/13–17/13 with steps of 14/13, 17/16, 14/13, 17/16, 26/17, and its inverse | ||
* | * 1–17/16–8/7–17/14–17/13 with steps of 17/16, 14/13, 17/16, 14/13, 26/17. | ||
Equal temperaments with horizmic chords include {{Optimal ET sequence|10, 11, 21, 26, 31, 36, 46, 47, 57, 67, 83, 93, 103, 104 and 150}}. | Equal temperaments with horizmic chords include {{Optimal ET sequence| 10, 11, 21, 26, 31, 36, 46, 47, 57, 67, 83, 93, 103, 104 and 150 }}. | ||
[[Category:17-odd-limit]] | [[Category:17-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||