Miracle chords

A miracle chord is an essentially tempered chord of the miracle temperament; they are included among those listed as chords of miracle. Aside from the swetismic, werckismic, keenanismic, rastmic, marvel, unimarvel, jove and prodigy chords listed there, there are ten further essentially miracle chords. These are the inversely related pair of tetrads:

• 1–10/7–8/5–7/4 with steps 10/7, 9/8, 12/11, 8/7, and its inverse
• 1–9/8–8/5–11/6 with steps 9/8, 10/7, 8/7, 12/11;

The three pairs of pentads:

• 1–5/4–10/7–8/5–7/4 with steps 5/4, 8/7, 9/8, 12/11, 8/7, and its inverse
• 1–5/4–10/7–14/9–7/4 with steps 5/4, 8/7, 12/11, 9/8, 8/7;
• 1–11/9–11/8–3/2–12/7 with steps 11/9, 9/8, 12/11, 8/7, 7/6, and its inverse
• 1–12/11–11/9–3/2–7/4 with steps 12/11, 9/8, 11/9, 7/6, 8/7;
• 1–9/8–10/7–8/5–7/4 with steps 9/8, 14/11, 9/8, 12/11, 8/7, and its inverse
• 1–9/8–10/7–8/5–11/6 with steps 9/8, 14/11, 9/8, 8/7, 12/11;

And the pair of hexads:

• 1–9/8–5/4–10/7–8/5–7/4 with steps 9/8, 10/9, 8/7, 9/8, 12/11, 8/7, and its inverse
• 1–10/9–5/4–10/7–14/9–7/4 with steps 10/9, 9/8, 8/7, 12/11, 9/8, 8/7.

The count of miracle chords is therefore tetrads: 2, pentads: 6, and hexads: 2.

Equal temperaments allowing miracle chords include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde and 463bcde.