Ragismic chords

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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;
  • 1-4/3-25/18-36/25-3/2 with steps of 4/3-25/24-28/27-25/24-4/3.

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;
  • 1-36/25-3/2-14/9-42/25 with steps of 36/25-25/24-28/27-27/25-25/21, and its inverse
  • 1-25/24-3/2-25/14-27/14 with steps of 25/24-36/25-25/21-27/25-28/27;
  • 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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