Keenanismic chords: Difference between revisions
Readability; +categories |
Prefer voicing with the perfect fifth and sometimes other harmonics |
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* 1-5/4-12/7 with steps 5/4-11/8-7/6, and its inverse | * 1-5/4-12/7 with steps 5/4-11/8-7/6, and its inverse | ||
* 1- | * 1-5/4-16/11 with steps 5/4-7/6-11/8; | ||
* 1- | * 1-8/7-11/8 with steps 8/7-6/5-16/11, and its inverse | ||
* 1-6/5-11/8 with steps 6/5-8/7-16/11; | * 1-6/5-11/8 with steps 6/5-8/7-16/11; | ||
* 1-8/5-7/4 with steps 8/5-12/11-8/7, and its inverse | * 1-8/5-7/4 with steps 8/5-12/11-8/7, and its inverse | ||
* 1- | * 1-12/11-7/4 with steps 12/11-8/5-8/7. | ||
Keenanismic tetrads are especially interesting; there are fifteen in total. These include three palindromic tetrads: | Keenanismic tetrads are especially interesting; there are fifteen in total. These include three palindromic tetrads: | ||
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* 1-6/5-11/8-3/2 with steps 6/5-8/7-12/11-4/3, and its inverse | * 1-6/5-11/8-3/2 with steps 6/5-8/7-12/11-4/3, and its inverse | ||
* 1- | * 1-12/11-5/4-3/2 with steps 12/11-8/7-6/5-4/3. | ||
Finally, there is the pair | Finally, there is the pair | ||
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* 1-5/4-11/8-3/2-12/7 with steps 5/4-11/10-12/11-8/7-7/6, and its inverse | * 1-5/4-11/8-3/2-12/7 with steps 5/4-11/10-12/11-8/7-7/6, and its inverse | ||
* 1- | * 1-12/11-6/5-3/2-7/4 with steps 12/11-11/10-5/4-7/6-8/7; | ||
* 1-6/5-11/8-3/2-7/4 with steps 6/5-8/7-12/11-7/6-8/7, and its inverse | * 1-6/5-11/8-3/2-7/4 with steps 6/5-8/7-12/11-7/6-8/7, and its inverse | ||
* 1-12/11-5/4-3/2-12/7 with steps 12/11-8/7-6/5-8/7-7/6; | * 1-12/11-5/4-3/2-12/7 with steps 12/11-8/7-6/5-8/7-7/6; | ||
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The count of 11-limit chords is triads: 6, tetrads: 15, pentads: 6, for a total of 27. | The count of 11-limit chords is triads: 6, tetrads: 15, pentads: 6, for a total of 27. | ||
If we are willing to go as high as the 15-odd limit, there are many more keenanismic chords, all of which have a step of size 16/15. There are six additional keenanismic triads in the 15 limit, 32 additional keenanismic tetrads and 44 additional pentads. | If we are willing to go as high as the [[15-odd-limit]], there are many more keenanismic chords, all of which have a step of size [[16/15]]. There are six additional keenanismic triads in the 15-odd-limit, 32 additional keenanismic tetrads and 44 additional pentads. | ||
Equal temperaments with keenanismic tetrads include {{EDOs| 19, 22, 31, 41, 46, 53, 68, 72, 87, 94, 103, 118, 159, 190, 212, 284 and 402de }}. | Equal temperaments with keenanismic tetrads include {{EDOs| 19, 22, 31, 41, 46, 53, 68, 72, 87, 94, 103, 118, 159, 190, 212, 284 and 402de }}. | ||