Tutonic hexad

A tutonic hexad is an essentially tempered chord of the tutone temperament, which is every other member of the generator chain of 11-limit meantone (also called as Huygens, tempered by 81/80, 99/98 and 126/125).

There are eight hexads as 11-odd-limit essentially tempered chords of the 11-limit meantone, all of them are available in the tutone temperament; in other words, all of the essentially tempered hexads of the 11-limit meantone are tutonic hexads.

The palindromic hexads are

• 1–9/8–5/4–7/5–14/9–7/4 with steps of 9/8, 9/8, 9/8, 9/8, 9/8, 8/7 (erato hexad, tempered by 81/80 and 126/125);
• 1–9/8–9/7–10/7–11/7–7/4 with steps of 9/8, 8/7, 9/8, 11/10, 9/8, 8/7 (euterpe hexad, tempered by 81/80 and 99/98);
• 1–9/8–9/7–7/5–8/5–7/4 with steps of 9/8, 8/7, 11/10, 8/7, 11/10, 8/7 (minerva hexad, tempered by 99/98 and 176/175);
• 1–9/8–5/4–7/5–8/5–7/4 with steps of 9/8, 9/8, 9/8, 8/7, 11/10, 8/7 (minerva hexad, tempered by 99/98 and 176/175).

The inversely related pairs of hexads are

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