Charismic chords: Difference between revisions

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'''Diasemismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the diasemisma, [[256/255]].
'''Charsmic chords''' (or '''diasemismic chords''') are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the charsma (or diasemisma), [[256/255]].


There are 2 triads, 13 tetrads, 17 pentads and 6 hexads as 2.3.5.17 subgroup [[17-odd-limit]] essentially tempered chords.
There are 2 triads, 13 tetrads, 17 pentads and 6 hexads as 2.3.5.17 subgroup [[17-odd-limit]] essentially tempered chords.


The two diasemismic triads are in inverse relationship:  
The two charsmic triads are in inverse relationship:  
* 1-5/4-24/17 with steps of 5/4-9/8-17/12;
* 1-5/4-24/17 with steps of 5/4-9/8-17/12;
* 1-9/8-24/17 with steps of 9/8-5/4-17/12.
* 1-9/8-24/17 with steps of 9/8-5/4-17/12.
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* 1-16/15-5/4-4/3-3/2-15/8 with steps of 16/15-20/17-16/15-9/8-5/4-16/15.
* 1-16/15-5/4-4/3-3/2-15/8 with steps of 16/15-20/17-16/15-9/8-5/4-16/15.


Equal temperaments with diasemismic chords include {{Optimal ET sequence|9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.
Equal temperaments with charsmic chords include {{Optimal ET sequence|9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.


[[Category:17-odd-limit]]
[[Category:17-odd-limit]]
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[[Category:Pentads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Hexads]]
[[Category:Diasemismic]]
[[Category:Charsmic]]

Revision as of 23:50, 6 January 2024

Charsmic chords (or diasemismic chords) are essentially tempered dyadic chords tempered by the charsma (or diasemisma), 256/255.

There are 2 triads, 13 tetrads, 17 pentads and 6 hexads as 2.3.5.17 subgroup 17-odd-limit essentially tempered chords.

The two charsmic triads are in inverse relationship:

  • 1-5/4-24/17 with steps of 5/4-9/8-17/12;
  • 1-9/8-24/17 with steps of 9/8-5/4-17/12.

For tetrads, there are five palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are

  • 1-5/4-24/17-30/17 with steps of 5/4-9/8-5/4-17/15;
  • 1-9/8-5/4-24/17 with steps of 9/8-10/9-9/8-17/12;
  • 1-16/15-4/3-17/12 with steps of 16/15-5/4-16/15-24/17;
  • 1-16/15-5/4-4/3 with steps of 16/15-20/17-16/15-3/2;
  • 1-16/15-9/8-6/5 with steps of 16/15-18/17-16/15-5/3.

The inversely related pairs of chords are

  • 1-5/4-24/17-15/8 with steps of 5/4-9/8-4/3-16/15, and its inverse
  • 1-4/3-3/2-15/8 with steps of 4/3-9/8-5/4-16/15;
  • 1-5/4-24/17-3/2 with steps of 5/4-9/8-16/15-4/3, and its inverse
  • 1-16/15-6/5-3/2 with steps of 16/15-9/8-5/4-4/3;
  • 1-5/4-4/3-24/17 with steps of 5/4-16/15-18/17-17/12, and its inverse
  • 1-18/17-9/8-24/17 with steps of 18/17-16/15-5/4-17/12;
  • 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12, and its inverse
  • 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12.

For pentads, there are one palindromic chord and eight pairs of chords in inverse relationship. The palindromic chord is

  • 1-5/4-24/17-30/17-15/8 with steps of 5/4-9/8-5/4-16/15-16/15.

The inversely related pairs of chords are

  • 1-9/8-5/4-24/17-3/2 with steps of 9/8-10/9-9/8-16/15-4/3, and its inverse
  • 1-9/8-5/4-24/17-15/8 with steps of 9/8-10/9-9/8-4/3-16/15;
  • 1-5/4-24/17-3/2-15/8 with steps of 5/4-9/8-16/15-5/4-16/15, and its inverse
  • 1-5/4-4/3-5/3-16/9 with steps of 5/4-16/15-5/4-16/15-9/8;
  • 1-5/4-4/3-24/17-15/8 with steps of 5/4-16/15-18/17-4/3-16/15, and its inverse
  • 1-5/4-4/3-16/9-15/8 with steps of 5/4-16/15-4/3-18/17-16/15;
  • 1-5/4-4/3-24/17-3/2 with steps of 5/4-16/15-18/17-16/15-4/3, and its inverse
  • 1-16/15-9/8-6/5-3/2 with steps of 16/15-18/17-16/15-5/4-4/3;
  • 1-20/17-5/4-4/3-15/8 with steps of 20/17-16/15-16/15-24/17-16/15, and its inverse
  • 1-20/17-5/4-30/17-15/8 with steps of 20/17-16/15-24/17-16/15-16/15;
  • 1-16/15-5/4-4/3-3/2 with steps of 16/15-20/17-16/15-9/8-4/3, and its inverse
  • 1-9/8-6/5-24/17-3/2 with steps of 9/8-16/15-20/17-16/15-4/3;
  • 1-20/17-5/4-4/3-24/17 with steps of 20/17-16/15-16/15-18/17-17/12, and its inverse
  • 1-18/17-9/8-6/5-24/17 with steps of 18/17-16/15-16/15-20/17-17/12;
  • 1-5/4-24/17-3/2-30/17 with steps of 5/4-9/8-16/15-20/17-17/15, and its inverse
  • 1-16/15-6/5-3/2-17/10 with steps of 16/15-9/8-5/4-17/15-20/17.

For hexads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are

  • 1-9/8-5/4-24/17-3/2-15/8 with steps of 9/8-10/9-9/8-16/15-5/4-16/15;
  • 1-5/4-4/3-24/17-3/2-15/8 with steps of 5/4-16/15-18/17-16/15-5/4-16/15.

The inversely related pairs of chords are

  • 1-16/15-5/4-4/3-17/12-3/2 with steps of 16/15-20/17-16/15-16/15-18/17-4/3, and its inverse
  • 1-18/17-9/8-6/5-24/17-3/2 with steps of 18/17-16/15-16/15-20/17-16/15-4/3;
  • 1-5/4-24/17-3/2-30/17-15/8 with steps of 5/4-9/8-16/15-20/17-16/15-16/15, and its inverse
  • 1-16/15-5/4-4/3-3/2-15/8 with steps of 16/15-20/17-16/15-9/8-5/4-16/15.

Equal temperaments with charsmic chords include 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111.

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