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Ainismic chords: Difference between revisions

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An '''ainic chord''' is an [[Dyadic chord|essentially tempered dyadic chord]] tempered by [[936/935]], the ainos comma.  So far, only ainic triads are known, however, there are also likely to be tetrads, pentads and so forth.  The known ainic triads are 1-17/16-13/11 with steps 17/16-10/9-22/13, and its inversions; 1-10/9-13/11 with steps 10/9-17/16-22/13, and its inversions; 1-13/11-24/17 with steps 13/11-6/5-24/17, and its inversions; 1-6/5-24/17 with steps 6/5-13/11-24/17, and its inversions; 1-18/17-5/4 with steps 18/17-13/11-8/5, and its inversions; and 1-13/11-5/4 with steps 13/11-18/17-8/5, and its inversions.
'''Ainismic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by [[936/935]], the ainisma.  


[[Category:17-limit]]
Ainismic chords are numerous, including 22 triads and 99 tetrads as 2.3.5.11.13.17 subgroup [[17-odd-limit]] essentially tempered chords.
[[Category:Chords]]
 
[[Category:Dyadic]]
For triads, there are eleven pairs of chords in inverse relationship:
[[Category:Ainic]]
* 1–5/4–26/17 with steps of 5/4, 11/9, 17/13 (ainismic major triad), and its inverse
* 1–11/9–26/17 with steps of 11/9, 5/4, 17/13 (ainismic neutral triad);
* 1–11/8–26/17 with steps of 11/8, 10/9, 17/13 (ainismic suspended demisharp four), and its inverse
* 1–10/9–26/17 with steps of 10/9, 11/8, 17/13 (ainismic suspended two);
* 1–6/5–17/12 with steps of 6/5, 13/11, 24/17, and its inverse
* 1–13/11–17/12 with steps of 13/11, 6/5, 24/17;
* 1–13/10–17/12 with steps of 13/10, 12/11, 24/17, and its inverse
* 1–12/11–17/12 with steps of 12/11, 13/10, 24/17;
* 1–11/9–24/17 with steps of 11/9, 15/13, 17/12, and its inverse
* 1–15/13–24/17 with steps of 15/13, 11/9, 17/12;
* 1–13/10–11/8 with steps of 13/10, 18/17, 16/11, and its inverse
* 1–18/17–11/8 with steps of 18/17, 13/10, 16/11;
* 1–6/5–17/13 with steps of 6/5, 12/11, 26/17, and its inverse
* 1–12/11–17/13 with steps of 12/11, 6/5, 26/17;
* 1–11/9–13/10 with steps of 11/9, 17/16, 20/13, and its inverse
* 1–17/16–13/10 with steps of 17/16, 11/9, 20/13;
* 1–13/11–5/4 with steps of 13/11, 18/17, 8/5, and its inverse
* 1–18/17–5/4 with steps of 18/17, 13/11, 8/5;
* 1–10/9–13/11 with steps of 10/9, 17/16, 22/13, and its inverse
* 1–17/16–13/11 with steps of 17/16, 10/9, 22/13;
* 1–12/11–15/13 with steps of 12/11, 18/17, 26/15, and its inverse
* 1–18/17–15/13 with steps of 18/17, 12/11, 26/15.
 
For tetrads, there are three palindromic chords and forty-eight pairs of chords in inverse relationship. The palindromic chords are:
* 1–12/11–6/5–17/13 with steps of 12/11, 11/10, 12/11, 26/17;
* 1–13/11–17/12–5/3 with steps of 13/11, 6/5, 20/17, 6/5;
* 1–12/11–17/12–17/11 with steps of 12/11, 13/10, 12/11, 22/17.
 
Some of the inversely related pairs of tetrads include:
* 1–12/11–17/12–3/2 with steps of 12/11, 13/10, 18/17, 4/3, and its inverse
* 1–12/11–15/13–3/2 with steps of 12/11, 18/17, 13/10, 4/3;
* 1–13/10–17/12–3/2 with steps of 13/10, 12/11, 18/17, 4/3, and its inverse
* 1–13/10–11/8–3/2 with steps of 13/10, 18/17, 12/11, 4/3;
* 1–18/17–11/8–3/2 with steps of 18/17, 13/10, 12/11, 4/3, and its inverse
* 1–18/17–15/13–3/2 with steps of 18/17, 12/11, 13/10, 4/3;
* 1–15/13–24/17–3/2 with steps of 15/13, 11/9, 17/16, 4/3, and its inverse
* 1–17/16–13/10–3/2 with steps of 17/16, 11/9, 15/13, 4/3.
 
Equal temperaments with ainismic chords include {{Optimal ET sequence| 22, 24, 26, 31, 34, 46, 53, 65, 72, 87, 96, 111, 137, 145, 159, 183, 217 and 270 }}.
 
[[Category:17-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Ainismic]]
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