Valinorsmic chords: Difference between revisions

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A ''valinorsmic chord'' is a valinorsma (176/175) tempered [[Dyadic_chord|essentially tempered chord]] in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.

A '''valinorsmic chord''' is a [[valinorsma]] (176/175) tempered [[Dyadic_chord|essentially tempered chord]] in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.

The count is triads: 3, tetrads: 6, pentads: 2; 11 in total.

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Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.

[[Category:Valinorsmic]]

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-A ''valinorsmic chord'' is a valinorsma (176/175) tempered [[Dyadic_chord|essentially tempered chord]] in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.
+A '''valinorsmic chord''' is a [[valinorsma]] (176/175) tempered [[Dyadic_chord|essentially tempered chord]] in the 2.5.7.11 subgroup in the 11 odd limit. There are three valinorsmic triads: the valinorsmic version of the augmented triad, 1-5/4-8/5 with steps 5/4-14/11-5/4, and an inversely related pair, 1-8/5-7/4 with steps 8/5-11/10-8/7 and 1-8/7-5/4 with steps 8/7-11/10-8/5. Valinorsmic tetrads are six in number, consisting of two palindromic chords and a pair of pairs of inversely related chords. The palindromes are 1-11/10-5/4-7/4 with steps 11/10-8/7-7/5-8/7 and 1-11/10-5/4-11/8 with steps 11/10-8/7-11/10-16/11. The rest are 1-5/4-8/5-7/4 with steps 5/4-14/11-11/10-8/7 and 1-5/4-10/7-11/7 with steps 5/4-8/7-11/10-14/11, plus 1-5/4-11/8-11/7 with steps 5/4-11/10-8/7-14/11 and 1-11/10-11/8-7/4 with steps 11/10-5/4-14/11-8/7. Finally, there are the two inversely related pentads, 1-11/10-5/4-8/5-7/4 with steps 11/10-8/7-14/11-11/10-8/7 and 1-11/10-5/4-11/8-7/4 with steps 11/10-8/7-11/10-14/11-8/7.
 The count is triads: 3, tetrads: 6, pentads: 2; 11 in total.
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 Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.
+[[Category:Valinorsmic]]