Werckismic chords: Difference between revisions
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A '''werckismic chord''' is an [[essentially tempered dyadic chord]] | A '''werckismic chord''' is an [[essentially tempered dyadic chord]] tempered by the werckisma, [[441/440]]. | ||
Werckismic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the [[11-odd-limit]], meaning that there are 6 [[triad]]s, 15 [[tetrad]]s and 6 [[pentad]]s, for a total of 27 distinct chord structures. | |||
The werckismic triads consist of three pairs of inversely related chords: | The werckismic triads consist of three pairs of inversely related chords: | ||
* | * 1–11/9–7/5 with steps 11/9, 8/7, 10/7, and its inverse | ||
* | * 1–11/9–7/4 with steps 11/9, 10/7, 8/7; | ||
* | * 1–11/7–7/4 with steps 11/7, 10/9, 8/7, and its inverse | ||
* 1–11/7–9/5 with steps 11/7, 8/7, 10/9; | |||
* 1–7/5–11/7 with steps 7/5, 9/8, 14/11, and its inverse | |||
* 1–14/11–10/7 with steps 14/11, 9/8, 7/5. | |||
The werckismic tetrads consist of three palindromic (self-inversive) chords and five pairs of chords in an inverse relationship. The palindromic chords are | The werckismic tetrads consist of three palindromic (self-inversive) chords and five pairs of chords in an inverse relationship. The palindromic chords are | ||
* | * 1–5/4–10/7–7/4 with steps 5/4, 8/7, 11/9, 8/7; | ||
* | * 1–9/8–10/7–11/7 with steps 9/8, 14/11, 11/10, 14/11; | ||
* | * 1–14/11–7/5–16/9 with steps 14/11, 11/10, 14/11, 9/8. | ||
The pairs of chords are | The pairs of chords are: | ||
* | * 1–11/9–11/7–7/4 with steps 11/9, 9/7, 10/9, 8/7, and its inverse | ||
* | * 1–9/7–11/7–9/5 with steps 9/7, 11/9, 8/7, 10/9; | ||
* | * 1–10/7–11/7–7/4 with steps 10/7, 11/10, 10/9, 8/7, and its inverse | ||
* | * 1–8/7–14/11–7/5 with steps 8/7, 10/9, 11/10, 10/7; | ||
* | * 1–9/8–10/7–7/4 with steps 9/8, 14/11, 11/9, 8/7, and its inverse | ||
* 1–11/9–14/9–7/4 with steps 11/9, 14/11, 9/8, 8/7; | |||
* 1–11/9–11/8–7/4 with steps 11/9, 9/8, 14/11, 8/7, and its inverse | |||
* 1–14/11–10/7–7/4 with steps 14/11, 9/8, 11/9, 8/7; | |||
* 1–9/8–5/4–10/7 with steps 9/8, 10/9, 8/7, 7/5, and its inverse | |||
* 1–10/9–5/4–7/4 with steps 10/9, 9/8, 7/5, 8/7; | |||
* 1–9/8–9/7–10/7 with steps 9/8, 8/7, 10/9, 7/5, and its inverse | |||
* 1–9/8–11/7–7/4 with steps 9/8, 7/5, 10/9, 8/7. | |||
The werckismic pentads consist of three pairs of chords in an inverse relationship: | The werckismic pentads consist of three pairs of chords in an inverse relationship: | ||
* | * 1–9/8–5/4–10/7–7/4 with steps 9/8, 10/9, 8/7, 11/9, 8/7, and its inverse | ||
* | * 1–11/9–7/5–14/9–7/4 with steps 11/9, 8/7, 10/9, 9/8, 8/7; | ||
* | * 1–11/9–11/8–11/7–7/4 with steps 11/9, 9/8, 8/7, 10/9, 8/7, and its inverse | ||
* 1–9/8–11/8–11/7–7/4 with steps 9/8, 11/9, 8/7, 10/9, 8/7; | |||
* 1–9/8–9/7–10/7–11/7 with steps 9/8, 8/7, 10/9, 11/10, 14/11, and its inverse | |||
* 1–9/8–10/7–11/7–7/4 with steps 9/8, 14/11, 11/10, 10/9, 8/7. | |||
[[Equal temperament]]s with werckismic chords include {{EDOs| 31, 41, 43, 46, 58, 72, 77, 84, 103, 118, 130, 159, 171, 190, 248, 289, and 320 }}, with [[320edo]] giving the [[optimal patent val]]. | |||
[[Category:11-odd-limit chords]] | |||
[[Category:11-odd-limit]] | |||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category: | [[Category:Triads]] | ||
[[Category: | [[Category:Tetrads]] | ||
[[Category: | [[Category:Pentads]] | ||
[[Category:Werckismic]] | [[Category:Werckismic]] | ||