Tutonic hexad: Difference between revisions
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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 | 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. | 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 | 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 | 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]] | [[Category:9-odd-limit chords]] | ||
[[Category:11-odd-limit]] | [[Category:11-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Hexads]] | [[Category:Hexads]] | ||
[[Category:Tutone]] | [[Category:Tutone]] | ||