Ragismic chords: Difference between revisions

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Since the temperament is complex, even the simplest ragismic chords are [[27-odd-limit]], although they contain only [[7-limit|7-prime-limit]] intervals. There are 6 triads, 21 tetrads, 22 pentads and 7 hexads as essentially tempered chords.
Since the temperament is complex, even the simplest ragismic chords are [[27-odd-limit]], although they contain only [[7-limit|7-prime-limit]] intervals. There are 6 triads, 21 tetrads, 22 pentads and 7 hexads as essentially tempered chords.


For triads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
For triads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are  
* 1-27/25-7/6 chord with steps of 27/25-27/25-12/7;
* 1-25/18-36/25 with steps of 25/18-28/27-25/18;
* 1-25/18-27/14 chord with steps of 25/18-25/18-28/27.
* 1-27/25-7/6 with steps of 27/25-27/25-12/7.


The inversely related pairs of chords are
The inversely related pairs of chords are  
* 1-9/7-25/18 with steps of 9/7-27/25-36/25 and its inverse 1-27/25-25/18 with steps of 27/25-9/7-36/25;
* 1-9/7-25/18 with steps of 9/7-27/25-36/25, and its inverse  
* 1-25/24-27/25 with steps of 25/24-28/27-50/27 and its inverse 1-25/24-27/14 with steps of 25/24-50/27-28/27.
* 1-27/25-25/18 with steps of 27/25-9/7-36/25;
* 1-25/24-27/25 with steps of 25/24-28/27-50/27, and its inverse  
* 1-28/27-27/25 with steps of 28/27-25/24-50/27.


For tetrads, there are five palindromic chords and eight pairs of chords in inverse relationship. The palindromic chords are
For tetrads, there are five palindromic chords and eight pairs of chords in inverse relationship. The palindromic chords are  
* 1-27/25-25/18-14/9 chord with steps of 27/25-9/7-28/25-9/7;
* 1-28/25-36/25-14/9 with steps of 28/25-9/7-27/25-9/7;
* 1-27/25-25/18-3/2 chord with steps of 27/25-9/7-27/25-4/3;
* 1-27/25-25/18-3/2 with steps of 27/25-9/7-27/25-4/3;
* 1-27/25-9/7-25/18 chord with steps of 27/25-25/21-27/25-36/25;
* 1-27/25-9/7-25/18 with steps of 27/25-25/21-27/25-36/25;
* 1-25/24-27/25-9/8 chord with steps of 25/24-28/27-25/24-16/9;
* 1-25/24-27/25-9/8 with steps of 25/24-28/27-25/24-16/9;
* 1-25/24-27/25-27/14 chord with steps of 25/24-28/27-25/14-28/27.
* 1-28/27-27/25-28/25 with steps of 28/27-25/24-28/27-25/14.


The inversely related pairs of chords are
The inversely related pairs of chords are  
* 1-27/25-7/6-3/2 with steps of 27/25-27/25-9/7-4/3 and its inverse 1-27/25-7/6-14/9 with steps of 27/25-27/25-4/3-9/7;
* 1-25/18-36/25-3/2 with steps of 25/18-28/27-25/24-4/3, and its inverse  
* 1-27/25-7/6-25/18 with steps of 27/25-27/25-25/21-36/25 and its inverse 1-25/21-9/7-25/18 with steps of 25/21-27/25-27/25-36/25;
* 1-25/24-27/25-3/2 with steps of 25/24-28/27-25/18-4/3;
* 1-27/25-3/2-14/9 with steps of 27/25-25/18-28/27-9/7 and its inverse 1-25/18-3/2-27/14 with steps of 25/18-27/25-9/7-28/27;
* 1-9/7-25/18-3/2 with steps of 9/7-27/25-27/25-4/3, and its inverse  
* 1-25/18-25/14-27/14 with steps of 25/18-9/7-27/25-28/27 and its inverse 1-27/25-25/18-27/14 with steps of 27/25-9/7-25/18-28/27;
* 1-27/25-7/6-3/2 with steps of 27/25-27/25-9/7-4/3;
* 1-25/24-27/25-3/2 with steps of 25/24-28/27-25/18-4/3 and its inverse 1-25/24-25/18-27/14 with steps of 25/24-4/3-25/18-28/27;
* 1-9/7-25/18-36/25 with steps of 9/7-27/25-28/27-25/18, and its inverse  
* 1-25/24-27/25-25/18 with steps of 25/24-28/27-9/7-36/25 and its inverse 1-25/24-3/2-27/14 with steps of 25/24-36/25-9/7-28/27;
* 1-28/27-28/25-36/25 with steps of 28/27-27/25-9/7-25/18;
* 1-27/25-9/8-7/6 with steps of 27/25-25/24-28/27-12/7 and its inverse 1-25/24-9/8-27/14 with steps of 25/24-27/25-12/7-28/27;
* 1-27/25-3/2-14/9 with steps of 27/25-25/18-28/27-9/7, and its inverse  
* 1-25/24-27/25-7/6 with steps of 25/24-28/27-27/25-12/7 and its inverse 1-25/24-25/14-27/14 with steps of 25/24-12/7-27/25-28/27.
* 1-25/18-3/2-27/14 with steps of 25/18-27/25-9/7-28/27;
* 1-36/25-3/2-14/9 with steps of 36/25-25/24-28/27-9/7, and its inverse  
* 1-25/24-3/2-27/14 with steps of 25/24-36/25-9/7-28/27;
* 1-25/21-9/7-25/18 with steps of 25/21-27/25-27/25-36/25, and its inverse  
* 1-27/25-7/6-25/18 with steps of 27/25-27/25-25/21-36/25;
* 1-27/25-9/8-7/6 with steps of 27/25-25/24-28/27-12/7, and its inverse  
* 1-28/27-27/25-7/6 with steps of 28/27-25/24-27/25-12/7;
* 1-27/25-28/25-7/6 with steps of 27/25-28/27-25/24-12/7, and its inverse  
* 1-25/24-27/25-7/6 with steps of 25/24-28/27-27/25-12/7.


For pentads, there are two palindromic chords and ten pairs of chords in inverse relationship. The palindromic chords are
For pentads, there are two palindromic chords and ten pairs of chords in inverse relationship. The palindromic chords are  
* 1-27/25-7/6-3/2-14/9 chord with steps of 27/25-27/25-9/7-28/27-9/7;
* 1-27/25-7/6-3/2-14/9 with steps of 27/25-27/25-9/7-28/27-9/7;
* 1-25/24-27/25-9/8-3/2 chord with steps of 25/24-28/27-25/24-4/3-4/3.
* 1-25/24-27/25-9/8-3/2 with steps of 25/24-28/27-25/24-4/3-4/3.


The inversely related pairs of chords are
The inversely related pairs of chords are  
* 1-27/25-7/6-25/18-14/9 with steps of 27/25-27/25-25/21-28/25-9/7 and its inverse 1-27/25-7/6-3/2-42/25 with steps of 27/25-27/25-9/7-28/25-25/21;
* 1-9/7-25/18-3/2-25/14 with steps of 9/7-27/25-27/25-25/21-28/25, and its inverse  
* 1-27/25-7/6-25/18-3/2 with steps of 27/25-27/25-25/21-27/25-4/3 and its inverse 1-27/25-7/6-14/9-42/25 with steps of 27/25-27/25-4/3-27/25-25/21;
* 1-27/25-7/6-3/2-42/25 with steps of 27/25-27/25-9/7-28/25-25/21;
* 1-9/7-25/18-25/14-27/14 with steps of 9/7-27/25-9/7-27/25-28/27 and its inverse 1-27/25-25/18-3/2-27/14 with steps of 27/25-9/7-27/25-9/7-28/27;
* 1-27/25-25/18-3/2-14/9 with steps of 27/25-9/7-27/25-28/27-9/7, and its inverse  
* 1-25/18-3/2-25/14-27/14 with steps of 25/18-27/25-25/21-27/25-28/27 and its inverse 1-27/25-3/2-14/9-42/25 with steps of 27/25-25/18-28/27-27/25-25/21;
* 1-27/25-25/18-3/2-27/14 with steps of 27/25-9/7-27/25-9/7-28/27;
* 1-27/25-9/8-7/6-3/2 with steps of 27/25-25/24-28/27-9/7-4/3 and its inverse 1-9/7-4/3-25/18-3/2 with steps of 9/7-28/27-25/24-27/25-4/3;
* 1-9/7-25/18-36/25-3/2 with steps of 9/7-27/25-28/27-25/24-4/3, and its inverse  
* 1-25/24-27/25-7/6-3/2 with steps of 25/24-28/27-27/25-9/7-4/3 and its inverse 1-9/7-25/18-36/25-3/2 with steps of 9/7-27/25-28/27-25/24-4/3;
* 1-25/24-27/25-7/6-3/2 with steps of 25/24-28/27-27/25-9/7-4/3;
* 1-25/24-27/25-25/18-3/2 with steps of 25/24-28/27-9/7-27/25-4/3 and its inverse 1-27/25-25/18-36/25-3/2 with steps of 27/25-9/7-28/27-25/24-4/3;
* 1-9/7-4/3-25/18-3/2 with steps of 9/7-28/27-25/24-27/25-4/3, and its inverse  
* 1-25/24-27/25-7/6-25/18 with steps of 25/24-28/27-27/25-25/21-36/25 and its inverse 1-25/21-9/7-4/3-25/18 with steps of 25/21-27/25-28/27-25/24-36/25.
* 1-27/25-9/8-7/6-3/2 with steps of 27/25-25/24-28/27-9/7-4/3;
* 1-25/24-27/25-25/18-27/14 with steps of 25/24-28/27-9/7-25/18-28/27 and its inverse 1-25/24-27/25-3/2-27/14 with steps of 25/24-28/27-25/18-9/7-28/27.
* 1-27/25-25/18-36/25-3/2 with steps of 27/25-9/7-28/27-25/24-4/3, and its inverse  
* 1-25/24-27/25-9/8-7/6 with steps of 25/24-28/27-25/24-28/27-12/7 and its inverse 1-25/24-27/25-9/8-27/14 with steps of 25/24-28/27-25/24-12/7-28/27.
* 1-25/24-27/25-25/18-3/2 with steps of 25/24-28/27-9/7-27/25-4/3;
* 1-27/25-9/7-25/18-3/2 with steps of 27/25-25/21-27/25-27/25-4/3, and its inverse  
* 1-27/25-7/6-25/18-3/2 with steps of 27/25-27/25-25/21-27/25-4/3;
* 1-25/18-36/25-3/2-14/9 with steps of 25/18-28/27-25/24-28/27-9/7, and its inverse  
* 1-25/24-27/25-3/2-27/14 with steps of 25/24-28/27-25/18-9/7-28/27;
* 1-25/18-3/2-25/14-27/14 with steps of 25/18-27/25-25/21-27/25-28/27, and its inverse  
* 1-27/25-3/2-14/9-42/25 with steps of 27/25-25/18-28/27-27/25-25/21;
* 1-25/21-9/7-4/3-25/18 with steps of 25/21-27/25-28/27-25/24-36/25, and its inverse  
* 1-25/24-27/25-7/6-25/18 with steps of 25/24-28/27-27/25-25/21-36/25;
* 1-25/24-27/25-9/8-7/6 with steps of 25/24-28/27-25/24-28/27-12/7, and its inverse  
* 1-28/27-27/25-28/25-7/6 with steps of 28/27-25/24-28/27-25/24-12/7.


For hexads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is
For hexads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is  
* 1-25/24-27/25-25/18-3/2-27/14 chord with steps of 25/24-28/27-9/7-27/25-9/7-28/27.
* 1-27/25-25/18-36/25-3/2-14/9 with steps of 27/25-9/7-28/27-25/24-28/27-9/7.


The inversely related pairs of chords are
The inversely related pairs of chords are  
* 1-27/25-7/6-25/18-3/2-14/9 with steps of 27/25-27/25-25/21-27/25-28/27-9/7 and its inverse 1-27/25-7/6-3/2-14/9-42/25 with steps of 27/25-27/25-9/7-28/27-27/25-25/21;
* 1-27/25-7/6-25/18-3/2-14/9 with steps of 27/25-27/25-25/21-27/25-28/27-9/7, and its inverse  
* 1-25/24-27/25-7/6-25/18-3/2 with steps of 25/24-28/27-27/25-25/21-27/25-4/3 and its inverse 1-27/25-9/7-25/18-36/25-3/2 with steps of 27/25-25/21-27/25-28/27-25/24-4/3;
* 1-27/25-9/7-25/18-3/2-27/14 with steps of 27/25-25/21-27/25-27/25-9/7-28/27;
* 1-25/24-27/25-9/8-7/6-3/2 with steps of 25/24-28/27-25/24-28/27-9/7-4/3 and its inverse 1-25/24-27/25-9/8-3/2-27/14 with steps of 25/24-28/27-25/24-4/3-9/7-28/27.
* 1-9/7-4/3-25/18-36/25-3/2 with steps of 9/7-28/27-25/24-28/27-25/24-4/3, and its inverse  
* 1-25/24-27/25-9/8-7/6-3/2 with steps of 25/24-28/27-25/24-28/27-9/7-4/3;
* 1-27/25-9/7-25/18-36/25-3/2 with steps of 27/25-25/21-27/25-28/27-25/24-4/3, and its inverse  
* 1-25/24-27/25-7/6-25/18-3/2 with steps of 25/24-28/27-27/25-25/21-27/25-4/3.


Equal temperaments with ragismic chords include {{Optimal ET sequence|19, 53, 72, 99, 118, 152, 171, 224, 270, 323, 441, 494, 612, 665, 783, 935, 1106, 1277 and 1547}}.
Equal temperaments with ragismic chords include {{Optimal ET sequence|19, 53, 72, 99, 118, 152, 171, 224, 270, 323, 441, 494, 612, 665, 783, 935, 1106, 1277 and 1547}}.

Revision as of 02:31, 24 November 2023

Ragismic chords are essentially tempered chords tempered by the ragisma, 4375/4374.

Since the temperament is complex, even the simplest ragismic chords are 27-odd-limit, although they contain only 7-prime-limit intervals. There are 6 triads, 21 tetrads, 22 pentads and 7 hexads as essentially tempered chords.

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

  • 1-25/18-36/25 with steps of 25/18-28/27-25/18;
  • 1-27/25-7/6 with steps of 27/25-27/25-12/7.

The inversely related pairs of chords are

  • 1-9/7-25/18 with steps of 9/7-27/25-36/25, and its inverse
  • 1-27/25-25/18 with steps of 27/25-9/7-36/25;
  • 1-25/24-27/25 with steps of 25/24-28/27-50/27, and its inverse
  • 1-28/27-27/25 with steps of 28/27-25/24-50/27.

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

  • 1-28/25-36/25-14/9 with steps of 28/25-9/7-27/25-9/7;
  • 1-27/25-25/18-3/2 with steps of 27/25-9/7-27/25-4/3;
  • 1-27/25-9/7-25/18 with steps of 27/25-25/21-27/25-36/25;
  • 1-25/24-27/25-9/8 with steps of 25/24-28/27-25/24-16/9;
  • 1-28/27-27/25-28/25 with steps of 28/27-25/24-28/27-25/14.

The inversely related pairs of chords are

  • 1-25/18-36/25-3/2 with steps of 25/18-28/27-25/24-4/3, and its inverse
  • 1-25/24-27/25-3/2 with steps of 25/24-28/27-25/18-4/3;
  • 1-9/7-25/18-3/2 with steps of 9/7-27/25-27/25-4/3, and its inverse
  • 1-27/25-7/6-3/2 with steps of 27/25-27/25-9/7-4/3;
  • 1-9/7-25/18-36/25 with steps of 9/7-27/25-28/27-25/18, and its inverse
  • 1-28/27-28/25-36/25 with steps of 28/27-27/25-9/7-25/18;
  • 1-27/25-3/2-14/9 with steps of 27/25-25/18-28/27-9/7, and its inverse
  • 1-25/18-3/2-27/14 with steps of 25/18-27/25-9/7-28/27;
  • 1-36/25-3/2-14/9 with steps of 36/25-25/24-28/27-9/7, and its inverse
  • 1-25/24-3/2-27/14 with steps of 25/24-36/25-9/7-28/27;
  • 1-25/21-9/7-25/18 with steps of 25/21-27/25-27/25-36/25, and its inverse
  • 1-27/25-7/6-25/18 with steps of 27/25-27/25-25/21-36/25;
  • 1-27/25-9/8-7/6 with steps of 27/25-25/24-28/27-12/7, and its inverse
  • 1-28/27-27/25-7/6 with steps of 28/27-25/24-27/25-12/7;
  • 1-27/25-28/25-7/6 with steps of 27/25-28/27-25/24-12/7, and its inverse
  • 1-25/24-27/25-7/6 with steps of 25/24-28/27-27/25-12/7.

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

  • 1-27/25-7/6-3/2-14/9 with steps of 27/25-27/25-9/7-28/27-9/7;
  • 1-25/24-27/25-9/8-3/2 with steps of 25/24-28/27-25/24-4/3-4/3.

The inversely related pairs of chords are

  • 1-9/7-25/18-3/2-25/14 with steps of 9/7-27/25-27/25-25/21-28/25, and its inverse
  • 1-27/25-7/6-3/2-42/25 with steps of 27/25-27/25-9/7-28/25-25/21;
  • 1-27/25-25/18-3/2-14/9 with steps of 27/25-9/7-27/25-28/27-9/7, and its inverse
  • 1-27/25-25/18-3/2-27/14 with steps of 27/25-9/7-27/25-9/7-28/27;
  • 1-9/7-25/18-36/25-3/2 with steps of 9/7-27/25-28/27-25/24-4/3, and its inverse
  • 1-25/24-27/25-7/6-3/2 with steps of 25/24-28/27-27/25-9/7-4/3;
  • 1-9/7-4/3-25/18-3/2 with steps of 9/7-28/27-25/24-27/25-4/3, and its inverse
  • 1-27/25-9/8-7/6-3/2 with steps of 27/25-25/24-28/27-9/7-4/3;
  • 1-27/25-25/18-36/25-3/2 with steps of 27/25-9/7-28/27-25/24-4/3, and its inverse
  • 1-25/24-27/25-25/18-3/2 with steps of 25/24-28/27-9/7-27/25-4/3;
  • 1-27/25-9/7-25/18-3/2 with steps of 27/25-25/21-27/25-27/25-4/3, and its inverse
  • 1-27/25-7/6-25/18-3/2 with steps of 27/25-27/25-25/21-27/25-4/3;
  • 1-25/18-36/25-3/2-14/9 with steps of 25/18-28/27-25/24-28/27-9/7, and its inverse
  • 1-25/24-27/25-3/2-27/14 with steps of 25/24-28/27-25/18-9/7-28/27;
  • 1-25/18-3/2-25/14-27/14 with steps of 25/18-27/25-25/21-27/25-28/27, and its inverse
  • 1-27/25-3/2-14/9-42/25 with steps of 27/25-25/18-28/27-27/25-25/21;
  • 1-25/21-9/7-4/3-25/18 with steps of 25/21-27/25-28/27-25/24-36/25, and its inverse
  • 1-25/24-27/25-7/6-25/18 with steps of 25/24-28/27-27/25-25/21-36/25;
  • 1-25/24-27/25-9/8-7/6 with steps of 25/24-28/27-25/24-28/27-12/7, and its inverse
  • 1-28/27-27/25-28/25-7/6 with steps of 28/27-25/24-28/27-25/24-12/7.

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

  • 1-27/25-25/18-36/25-3/2-14/9 with steps of 27/25-9/7-28/27-25/24-28/27-9/7.

The inversely related pairs of chords are

  • 1-27/25-7/6-25/18-3/2-14/9 with steps of 27/25-27/25-25/21-27/25-28/27-9/7, and its inverse
  • 1-27/25-9/7-25/18-3/2-27/14 with steps of 27/25-25/21-27/25-27/25-9/7-28/27;
  • 1-9/7-4/3-25/18-36/25-3/2 with steps of 9/7-28/27-25/24-28/27-25/24-4/3, and its inverse
  • 1-25/24-27/25-9/8-7/6-3/2 with steps of 25/24-28/27-25/24-28/27-9/7-4/3;
  • 1-27/25-9/7-25/18-36/25-3/2 with steps of 27/25-25/21-27/25-28/27-25/24-4/3, and its inverse
  • 1-25/24-27/25-7/6-25/18-3/2 with steps of 25/24-28/27-27/25-25/21-27/25-4/3.

Equal temperaments with ragismic chords include 19, 53, 72, 99, 118, 152, 171, 224, 270, 323, 441, 494, 612, 665, 783, 935, 1106, 1277 and 1547.

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