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Charismic chords

(Redirected from Diasemismic chords)

Charismic chords (formerly diasemismic chords) are essentially tempered dyadic chords tempered by the charisma, 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 charismic 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 charismic chords include 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111.

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