View source for 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 [[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 ([[didymus chords #Septimal meantone chords|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.

[[Category:9-odd-limit chords]]
[[Category:11-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Hexads]]
[[Category:Tutone]]