Ramanujanismic chords: Difference between revisions

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Ramanujanismic chords are numerous. A basic ramanujanismic triad in the 2.3.7.13.19 [[subgroup]] [[19-odd-limit]] consists of [[7/6]], [[13/12]], and [[19/12]] closing at the [[octave]]:  
Ramanujanismic chords are numerous. A basic ramanujanismic triad in the 2.3.7.13.19 [[subgroup]] [[19-odd-limit]] consists of [[7/6]], [[13/12]], and [[19/12]] closing at the [[octave]]:  
* 1-7/6-24/19 with steps 7/6-13/12-19/12, and its inverse
* 1-7/6-24/19 with steps 7/6-13/12-19/12, and its inverse
* 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.


Other ramanujanismic triads are
These chords feature the 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;  
* 1-19/16-18/13 with steps 19/16-7/6-13/9, and its inverse
* 1-19/16-18/13 with steps 19/16-7/6-13/9, and its inverse
* 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:
* 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;  
* 1-18/13-7/4 with steps 18/13-24/19-8/7, and its inverse
* 1-24/19-7/4 with steps 24/19-18/13-8/7.
These chords feature the 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;  
* 1-18/13-7/4 with steps 18/13-24/19-8/7, and its inverse
* 1-24/19-7/4 with steps 24/19-18/13-8/7;
* 1-9/7-13/8 with steps 9/7-24/19-16/13, and its inverse
* 1-9/7-13/8 with steps 9/7-24/19-16/13, and its inverse
* 1-24/19-13/8 with steps 24/19-9/7-16/13;
* 1-24/19-13/8 with steps 24/19-9/7-16/13.


If we allow the [[21-odd-limit]], we have these additional triads:  
If we allow the [[21-odd-limit]], we have these additional triads:  
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* 1-9/8-21/16-36/19 with steps 9/8-7/6-13/9-19/18, and its inverse
* 1-9/8-21/16-36/19 with steps 9/8-7/6-13/9-19/18, and its inverse
* 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:
* 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;
* 1-3/2-13/8-7/4-36/19 with steps 3/2-13/12-14/13-13/12-19/18, and its inverse
* 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:
* 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;
* 1-24/19-3/2-7/4-24/13 with steps 24/19-19/16-7/6-19/18-13/12, and its inverse
* 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:
* 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;
* 1-24/19-3/2-13/8-12/7 with steps 24/19-19/16-13/12-19/18-7/6, and its inverse
* 1-19/16-3/2-7/4-24/13 with steps 19/16-24/19-7/6-19/18-13/12.
For hexads, the known ones are
* 1-9/8-19/16-9/7-18/13-3/2 with steps 9/8-19/18-13/12-14/13-13/12-4/3, and its inverse
* 1-13/12-7/6-24/19-4/3-3/2 with steps 13/12-14/13-13/12-19/18-9/8-4/3;
* 1-19/16-9/7-3/2-13/8-12/7 with steps 19/16-13/12-7/6-13/12-19/18-7/6, and its inverse
* 1-7/6-24/19-3/2-7/4-24/13 with steps 7/6-13/12-19/16-7/6-19/18-13/12;


[[Category:21-odd-limit]]
[[Category:21-odd-limit]]
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[[Category:Triads]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Ramanujanismic]]
[[Category:Ramanujanismic]]