Ramanujanismic chords: Difference between revisions
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* 1-7/6-24/13 with steps 7/6-19/12-13/12. | * 1-7/6-24/13 with steps 7/6-19/12-13/12. | ||
These chords feature the 19th harmonic: | These chords feature the [[19/16|octave-reduced 19th harmonic]]: | ||
* 1-19/16-9/7 with steps 19/16-13/12-14/9, and its inverse | * 1-19/16-9/7 with steps 19/16-13/12-14/9, and its inverse | ||
* 1-19/16-24/13 with steps 19/16-14/9-13/12; | * 1-19/16-24/13 with steps 19/16-14/9-13/12; | ||
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* 1-19/16-12/7 with steps 19/16-13/9-7/6. | * 1-19/16-12/7 with steps 19/16-13/9-7/6. | ||
These chords feature the 7th harmonic: | These chords feature the [[7/4|octave-reduced 7th harmonic]]: | ||
* 1-7/4-36/19 with steps 7/4-13/12-19/18, and its inverse | * 1-7/4-36/19 with steps 7/4-13/12-19/18, and its inverse | ||
* 1-7/4-24/13 with steps 7/4-19/18-13/12; | * 1-7/4-24/13 with steps 7/4-19/18-13/12; | ||
| Line 17: | Line 17: | ||
* 1-24/19-7/4 with steps 24/19-18/13-8/7. | * 1-24/19-7/4 with steps 24/19-18/13-8/7. | ||
These chords feature the 13th harmonic: | These chords feature the [[13/8|octave-reduced 13th harmonic]]: | ||
* 1-13/8-36/19 with steps 13/8-7/6-19/18, and its inverse | * 1-13/8-36/19 with steps 13/8-7/6-19/18, and its inverse | ||
* 1-13/8-12/7 with steps 13/8-19/18-7/6; | * 1-13/8-12/7 with steps 13/8-19/18-7/6; | ||
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* 1-21/16-18/13 with steps 21/16-19/18-13/9. | * 1-21/16-18/13 with steps 21/16-19/18-13/9. | ||
All the triads listed above work well with a perfect fifth, so we have the following tetrads: | All the triads listed above work well with a perfect fifth, so we have the following tetrads. | ||
These chords put an otonal 19 against a utonal 7, or the other way around: | |||
* 1-19/16-9/7-3/2 with steps 19/16-13/12-7/6-4/3, and its inverse | * 1-19/16-9/7-3/2 with steps 19/16-13/12-7/6-4/3, and its inverse | ||
* 1-7/6-24/19-3/2 with steps 7/6-13/12-19/16-4/3; | * 1-7/6-24/19-3/2 with steps 7/6-13/12-19/16-4/3; | ||
* 1-3/2-7/4-36/19 with steps 3/2-7/6-13/12-19/18, and its inverse | |||
* 1-3/2-19/12-12/7 with steps 3/2-19/18-13/12-7/6; | |||
* 1-24/19-3/2-7/4 with steps 24/19-19/16-7/6-8/7, and its inverse | |||
* 1-19/16-3/2-12/7 with steps 19/16-24/19-8/7-7/6; | |||
* 1-9/7-3/2-19/12 with steps 9/7-7/6-19/18-24/19, and its inverse | |||
* 1-7/6-3/2-36/19 with steps 7/6-9/7-24/19-19/18; | |||
These chords put an otonal 19 against a utonal 13, or the other way around: | |||
* 1-19/16-18/13-3/2 with steps 19/16-7/6-13/12-4/3, and its inverse | * 1-19/16-18/13-3/2 with steps 19/16-7/6-13/12-4/3, and its inverse | ||
* 1-13/12-24/19-3/2 with steps 13/12-7/6-19/16-4/3; | * 1-13/12-24/19-3/2 with steps 13/12-7/6-19/16-4/3; | ||
* 1- | * 1-3/2-13/8-36/19 with steps 3/2-13/12-7/6-19/18, and its inverse | ||
* 1- | * 1-3/2-19/12-24/13 with steps 3/2-19/18-7/6-13/12; | ||
* 1-3/2- | * 1-24/19-3/2-13/8 with steps 24/19-19/16-13/12-16/13, and its inverse | ||
* 1-3/2-19/12-12 | * 1-19/16-3/2-24/13 with steps 19/16-24/19-16/13-13/12. | ||
* 1-18/13-3/2-19/12 with steps 18/13-13/12-19/18-24/19, and its inverse | |||
* 1-13/12-3/2-36/19 with steps 13/12-18/13-24/19-19/18; | |||
These chords put an otonal 7 against a utonal 13, or the other way around: | |||
* 1-3/2-7/4-24/13 with steps 3/2-7/6-19/18-13/12, and its inverse | * 1-3/2-7/4-24/13 with steps 3/2-7/6-19/18-13/12, and its inverse | ||
* 1-3/2-13/8-12/7 with steps 3/2-13/12-19/18-7/6; | * 1-3/2-13/8-12/7 with steps 3/2-13/12-19/18-7/6; | ||
* 1-3/2- | * 1-18/13-3/2-7/4 with steps 18/13-13/12-7/6-8/7, and its inverse | ||
* 1-3/2- | * 1-13/12-3/2-12/7 with steps 13/12-18/13-8/7-7/6; | ||
* 1-9/7-3/2-13/8 with steps 9/7-7/6-13/12-16/13, and its inverse | * 1-9/7-3/2-13/8 with steps 9/7-7/6-13/12-16/13, and its inverse | ||
* 1-7/6-3/2-24/13 with steps 7/6-9/7-16/13-13/12; | * 1-7/6-3/2-24/13 with steps 7/6-9/7-16/13-13/12; | ||
* 1 | * 1-7/6-18/13-3/2 with steps 7/6-19/16-13/12-4/3, and its inverse | ||
* 1-13/12-9/7-3/2 with steps 13/12-19/16-7/6; | |||
* 1-13/12- | |||
Otherwise they work with a major second: | Otherwise they work with a major second: | ||
| Line 60: | Line 66: | ||
* 1-9/8-18/13-7/4 with steps 9/8-16/13-24/19-8/7, and its inverse | * 1-9/8-18/13-7/4 with steps 9/8-16/13-24/19-8/7, and its inverse | ||
* 1-9/8-9/7-13/8 with steps 9/8-8/7-24/19-16/13. | * 1-9/8-9/7-13/8 with steps 9/8-8/7-24/19-16/13. | ||
These chords put an otonal 19 against utonal 7 and 13, or the other way around, without the fifth: | |||
* 1-19/16-9/7-18/13 with steps 19/16-13/12-14/13-13/9, and its inverse | |||
* 1-19/16-12/7-24/13 with steps 19/16-13/9-14/13-13/12; | |||
* 1-13/8-7/4-36/19 with steps 13/8-14/13-13/12-19/18, and its inverse | |||
* 1-13/12-7/6-36/19 with steps 13/12-14/13-13/8-19/18; | |||
* 1-19/12-12/7-24/13 with steps 19/12-13/12-14/13-13/12. | |||
These chords put an otonal 7 against utonal 13 and 19, or the other way around, without the fifth: | |||
* 1-18/13-7/4-36/19 with steps 18/13-24/19-13/12-19/18, and its inverse | |||
* 1-24/19-7/4-24/13 with steps 24/19-18/13-19/18-13/12; | |||
* 1-19/16-13/8-12/7 with steps 19/16-26/19-19/18-7/6, and its inverse | |||
* 1-19/18-13/9-12/7 with steps 19/18-26/19-19/16-7/6; | |||
* 1-7/6-24/19-24/13 with steps 7/6-13/12-19/13-13/12. | |||
These chords put an otonal 13 against utonal 7 and 19, or the other way around, without the fifth: | |||
* 1-9/7-13/8-36/19 with steps 9/7-24/19-7/6-19/18, and its inverse | |||
* 1-24/19-13/8-12/7 with steps 24/19-9/7-19/18-7/6; | |||
* 1-19/16-7/4-24/13 with steps 19/16-28/19-19/18-13/12, and its inverse | |||
* 1-19/18-14/9-24/13 with steps 19/18-28/19-19/16-13/12; | |||
* 1-13/12-24/19-12/7 with steps 13/12-7/6-19/14-7/6. | |||
If we allow the 21-odd-limit, we have these additional tetrads: | If we allow the 21-odd-limit, we have these additional tetrads: | ||
| Line 71: | Line 98: | ||
* 1-9/8-19/16-12/7 with steps 9/8-19/18-13/9-7/6. | * 1-9/8-19/16-12/7 with steps 9/8-19/18-13/9-7/6. | ||
For pentads, the following chords put an otonal 19 against utonal 7 and 13: | For pentads, the following chords put an otonal 19 against utonal 7 and 13, or the other way around: | ||
* 1-19/16-9/7-18/13-3/2 with steps 19/16-13/12-14/13-13/12-4/3, and its inverse | * 1-19/16-9/7-18/13-3/2 with steps 19/16-13/12-14/13-13/12-4/3, and its inverse | ||
* 1-13/12-7/6-24/19-3/2 with steps 13/12-14/13-13/12-19/16-4/3; | * 1-13/12-7/6-24/19-3/2 with steps 13/12-14/13-13/12-19/16-4/3; | ||
| Line 77: | Line 104: | ||
* 1-3/2-19/12-12/7-24/13 with steps 3/2-19/18-13/12-14/13-13/12. | * 1-3/2-19/12-12/7-24/13 with steps 3/2-19/18-13/12-14/13-13/12. | ||
These chords put an otonal 7 against utonal 13 and 19: | These chords put an otonal 7 against utonal 13 and 19, or the other way around: | ||
* 1-18/13-3/2-7/4-36/19 with steps 18/13-13/12-7/6-13/12-19/18, and its inverse | * 1-18/13-3/2-7/4-36/19 with steps 18/13-13/12-7/6-13/12-19/18, and its inverse | ||
* 1-13/12-3/2-19/12-12/7 with steps 13/12-18/13-19/18-13/12-7/6; | * 1-13/12-3/2-19/12-12/7 with steps 13/12-18/13-19/18-13/12-7/6; | ||
| Line 83: | Line 110: | ||
* 1-19/16-3/2-13/8-12/7 with steps 19/16-24/19-13/12-19/18-7/6. | * 1-19/16-3/2-13/8-12/7 with steps 19/16-24/19-13/12-19/18-7/6. | ||
These chords put an otonal 13 against utonal 7 and 19: | These chords put an otonal 13 against utonal 7 and 19, or the other way around: | ||
* 1-9/7-3/2-13/8-36/19 with steps 9/7-7/6-13/12-7/6-19/18, and its inverse | * 1-9/7-3/2-13/8-36/19 with steps 9/7-7/6-13/12-7/6-19/18, and its inverse | ||
* 1-7/6-3/2-19/12-24/13 with steps 7/6-9/7-19/18-7/6-13/12; | * 1-7/6-3/2-19/12-24/13 with steps 7/6-9/7-19/18-7/6-13/12; | ||