Miracle chords: Difference between revisions
m Recategorize |
m Improve readability; recategorize |
||
| Line 1: | Line 1: | ||
A '''miracle chord''' is an [[essentially tempered chord]] of the [[miracle]] temperament; they are included among those listed as [[chords of miracle]]. Aside from the swetismic, werckismic, keenanismic, rastmic, marvel, unimarvel, jove and prodigy chords listed there, there are ten further essentially miracle chords. These are the inversely related pair of tetrads: | A '''miracle chord''' is an [[essentially tempered chord]] of the [[miracle]] temperament; they are included among those listed as [[chords of miracle]]. Aside from the [[swetismic chords|swetismic]], [[werckismic chords|werckismic]], [[keenanismic chords|keenanismic]], [[rastmic chords|rastmic]], [[marvel chords|marvel]], [[undecimal marvel chords|unimarvel]], [[jove chords|jove]] and [[prodigy chords|prodigy]] chords listed there, there are ten further essentially miracle chords. These are the inversely related pair of tetrads: | ||
* | * 1–10/7–8/5–7/4 with steps 10/7, 9/8, 12/11, 8/7, and its inverse | ||
* 1–9/8–8/5–11/6 with steps 9/8, 10/7, 8/7, 12/11; | |||
The three pairs of pentads: | |||
* | * 1–5/4–10/7–8/5–7/4 with steps 5/4, 8/7, 9/8, 12/11, 8/7, and its inverse | ||
* 1–5/4–10/7–14/9–7/4 with steps 5/4, 8/7, 12/11, 9/8, 8/7; | |||
* 1–11/9–11/8–3/2–12/7 with steps 11/9, 9/8, 12/11, 8/7, 7/6, and its inverse | |||
* 1–12/11–11/9–3/2–7/4 with steps 12/11, 9/8, 11/9, 7/6, 8/7; | |||
* 1–9/8–10/7–8/5–7/4 with steps 9/8, 14/11, 9/8, 12/11, 8/7, and its inverse | |||
* 1–9/8–10/7–8/5–11/6 with steps 9/8, 14/11, 9/8, 8/7, 12/11; | |||
And the pair of hexads: | |||
* | * 1–9/8–5/4–10/7–8/5–7/4 with steps 9/8, 10/9, 8/7, 9/8, 12/11, 8/7, and its inverse | ||
* 1–10/9–5/4–10/7–14/9–7/4 with steps 10/9, 9/8, 8/7, 12/11, 9/8, 8/7. | |||
The count of miracle chords is therefore tetrads: 2, pentads: 6, and hexads: 2. | The count of miracle chords is therefore tetrads: 2, pentads: 6, and hexads: 2. | ||
[[Equal temperament]]s allowing miracle chords include {{EDOs| 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde and 463bcde }}. | |||
[[Category:11-odd-limit]] | [[Category:11-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Tetrads]] | [[Category:Tetrads]] | ||