Ragismic chords

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

The ragismic temperament has 4 triads, 11 tetrads, 9 pentads and 2 hexads as essentially tempered chords.

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

• 1-27/25-7/6 chord with steps of 27/25-27/25-12/7;
• 1-25/18-27/14 chord with steps of 25/18-25/18-28/27.

The inversely related pair of chords is

• 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.

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

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

The inversely related pairs of chords are

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

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

• 1-27/25-7/6-3/2-14/9 chord with steps of 27/25-27/25-9/7-28/27-9/7.

The inversely related pairs of chords are

• 1-27/25-25/18-3/2-27/14 with steps of 27/25-9/7-27/25-9/7-28/27 and its inverse 1-9/7-25/18-25/14-27/14 with steps of 9/7-27/25-9/7-27/25-28/27;
• 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;
• 1-27/25-7/6-25/18-14/9 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;
• 1-25/18-3/2-25/14-27/14 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.

They can be extended to hexads as

• 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.

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.