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 [[essentially tempered chord]].  


The count is triads: 3, tetrads: 6, pentads: 2; 11 in total.
Valinorsmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.5.7.11 [[subgroup]] [[11-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.  


If we are willing to go to the 15 odd limit, we get four alternative, valinorsmic, temperings of the four [[keenanismic_chords|keenanismic tetrads]] which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9-6/5-8/7-6/5, leading to 1-11/9-22/15-5/3 chords.
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,


Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111, 268cd, 326cd and 437cd.
and an inversely related pair,
* 1–8/5–7/4 with steps 8/5, 11/10, 8/7, and its inverse
* 1–8/7–5/4 with steps 8/7, 11/10, 8/5.  


[[Category:Chords]]
Valinorsmic tetrads are six in number, consisting of two palindromic chords and two 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 its inverse
* 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 its inverse
* 1–5/4–10/7–11/7 with steps 5/4, 8/7, 11/10, 14/11;
* 1–5/4–11/8–11/7 with steps 5/4, 11/10, 8/7, 14/11, and its inverse
* 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 its inverse
* 1–11/10–5/4–11/8–7/4 with steps 11/10, 8/7, 11/10, 14/11, 8/7.
 
If we are willing to go to the [[15-odd-limit]], we get four alternative, valinorsmic, temperings of the four [[keenanismic chords|keenanismic tetrads]] which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9, 6/5, 8/7, 6/5, leading to 1–11/9–22/15–5/3 chords.
 
[[Equal temperament]]s with valinorsmic chords include {{EDOs| 22, 31, 43, 46, 53, 58, 68, 80, 89, 111 }} with 111edo giving the [[optimal patent val]].
 
[[Category:11-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Valinorsmic]]
[[Category:Valinorsmic]]

Latest revision as of 09:20, 10 October 2024

A valinorsmic chord is a valinorsma (176/175) tempered essentially tempered chord.

Valinorsmic chords are of pattern 1a in the 2.5.7.11 subgroup 11-odd-limit, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

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 its inverse
  • 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 two 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 its inverse
  • 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 its inverse
  • 1–5/4–10/7–11/7 with steps 5/4, 8/7, 11/10, 14/11;
  • 1–5/4–11/8–11/7 with steps 5/4, 11/10, 8/7, 14/11, and its inverse
  • 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 its inverse
  • 1–11/10–5/4–11/8–7/4 with steps 11/10, 8/7, 11/10, 14/11, 8/7.

If we are willing to go to the 15-odd-limit, we get four alternative, valinorsmic, temperings of the four keenanismic tetrads which have steps which are permutations of the otonal/utonal 7-limit tetrads. The reason for the similarity between valinorsmic and keenanismic tetrads is that they both temper 48/35, valinorsmic to 15/11 and keenanismic to 11/8. Another valinorsmic tetrad has steps 11/9, 6/5, 8/7, 6/5, leading to 1–11/9–22/15–5/3 chords.

Equal temperaments with valinorsmic chords include 22, 31, 43, 46, 53, 58, 68, 80, 89, 111 with 111edo giving the optimal patent val.

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