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.