Palingenetic chords: Difference between revisions
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A '''palingenetic chord''' is an [[Dyadic chord|essentially tempered dyadic chord]] tempered by [[1701/1700]], the palingenetic comma. | A '''palingenetic chord''' is an [[Dyadic chord|essentially tempered dyadic chord]] tempered by [[1701/1700]], the palingenetic comma. Currently, there are only a handful of palingenetic chords known. | ||
The known palingenetic triads are: | There is a 21-odd-limit palingenetic triad: | ||
* 1-10/9-9/5 with steps 10/9-34/21-10/9. | |||
Assuming we stick to the 27-odd-limit, we have two known triads and one known tetrad. | |||
The known 27-odd-limit palingenetic triads are: | |||
* 1-34/27-3/2 with steps 34/27-25/21-4/3, and its inversions; dubbed the "palingenetic major triad" | * 1-34/27-3/2 with steps 34/27-25/21-4/3, and its inversions; dubbed the "palingenetic major triad" | ||
* 1-25/21-3/2 with steps 25/21-34/27-4/3, and its inversions; dubbed the "palingenetic minor triad" | * 1-25/21-3/2 with steps 25/21-34/27-4/3, and its inversions; dubbed the "palingenetic minor triad" | ||
The known palingenetic tetrads are: | The known 27-odd-limit palingenetic tetrads are: | ||
* 1-18/17-32/27-5/4 with steps 18/17-28/25-135/128-8/5, and its inversions | * 1-18/17-32/27-5/4 with steps 18/17-28/25-135/128-8/5, and its inversions | ||
Revision as of 16:14, 15 February 2021
A palingenetic chord is an essentially tempered dyadic chord tempered by 1701/1700, the palingenetic comma. Currently, there are only a handful of palingenetic chords known.
There is a 21-odd-limit palingenetic triad:
- 1-10/9-9/5 with steps 10/9-34/21-10/9.
Assuming we stick to the 27-odd-limit, we have two known triads and one known tetrad.
The known 27-odd-limit palingenetic triads are:
- 1-34/27-3/2 with steps 34/27-25/21-4/3, and its inversions; dubbed the "palingenetic major triad"
- 1-25/21-3/2 with steps 25/21-34/27-4/3, and its inversions; dubbed the "palingenetic minor triad"
The known 27-odd-limit palingenetic tetrads are:
- 1-18/17-32/27-5/4 with steps 18/17-28/25-135/128-8/5, and its inversions