Biyatismic chords: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
No edit summary
Tags: Mobile edit Mobile web edit
m Fix a ratio
 
(25 intermediate revisions by 3 users not shown)
Line 1: Line 1:
'''Biyatismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the biyatisma, [[121/120]].
'''Biyatismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the biyatisma, [[121/120]].


The biyatismic triad is the 121/120 tempering of 1-[[11/8]]-[[15/8]] chord, with steps of 11/8-11/8-[[16/15]].
There are two triads, nine tetrads, seven pentads and one hexad as 2.3.5.11 subgroup [[11-odd-limit]] essentially tempered chords. In this article, voicing with the [[perfect fifth]] is prioritized.  


The biyatismic pentads consist of two palindromic chords and two pairs of chords in an inverse relationship. The palindromic chords are 1-5/4-11/8-16/11-8/5 with steps 5/4-11/10-16/15-11/10-5/4 and 1-11/10-11/8-16/11-20/11 with steps 11/10-5/4-16/15-5/4-11/10. The inversely related pairs of chords are 1-5/4-11/8-16/11-20/11 with steps 5/4-11/10-16/15-5/4-11/10 and 1-11/10-11/8-16/11-8/5 with steps 11/10-5/4-16/15-11/10-5/4; and 1-11/10-6/5-3/2-15/8 with steps 11/10-11/10-5/4-5/4-16/15 and 1-16/15-4/3-5/3-11/6 with steps 16/15-5/4-5/4-11/10-11/10.
The two biyatismic triads are in inverse relationship:
* 1–11/8–5/3 with steps 11/8, 11/9, 6/5;
* 1–11/8–18/11 with steps 11/8, 6/5, 11/9.


Equal temperaments with biyatismic chords include 7, 9, 15, 16, 22, 24, 29, 31, 38, 46, and 53 [[EDO]]s.
For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are
* 1–9/8–11/8–18/11 with steps 9/8, 11/9, 6/5, 11/9;
* 1–11/10–11/8–3/2 with steps 11/10, 5/4, 11/10, 4/3;
* 1–3/2–18/11–11/6 with steps 3/2, 11/10, 10/9, 11/10.  


==Zeus chords==
The inversely related pairs of chords are
'''Zeus chords''' are essentially tempered dyadic chords of the [[Porwell family|Zeus temperament]]. Aside from the biyatismic, valinorsmic, and keenanismic chords, there are ten further essentially Zeus hexads. The two palindromic hexads are 1-11/10-5/4-11/8-11/7-12/7 with steps 11/10-8/7-11/10-8/7-11/10-7/6 and 1-8/7-5/4-15/11-3/2-12/7 with steps 8/7-11/10-11/10-11/10-8/7-7/6. The four inversely related pairs of hexads are 1-8/7-5/4-11/8-3/2-7/4 with steps 8/7-11/10-11/10-11/10-7/6-8/7 and 1-8/7-4/3-16/11-8/5-7/4 with steps 8/7-7/6-11/10-11/10-11/10-8/7; 1-8/7-5/4-10/7-11/7-12/7 with steps 8/7-11/10-8/7-11/10-11/10-7/6 and 1-7/6-14/11-7/5-8/5-7/4 with steps 7/6-11/10-11/10-8/7-11/10-8/7; 1-7/6-14/11-16/11-8/5-7/4 with steps 7/6-11/10-8/7-11/10-11/10-8/7 and 1-8/7-5/4-11/8-11/7-12/7 with steps 8/7-11/10-11/10-8/7-11/10-7/6; and 1-8/7-5/4-16/11-8/5-7/4 with steps 8/7-11/10-7/6-11/10-11/10-8/7 and 1-8/7-5/4-11/8-8/5-7/4 with steps 8/7-11/10-11/10-7/6-11/10-8/7.
* 1–11/8–3/2–18/11 with steps 11/8, 11/10, 11/10, 11/9, and its inverse
* 1–11/10–3/2–11/6 with steps 11/10, 11/8, 11/9, 11/10;
* 1–5/4–3/2–11/6 with steps 5/4, 6/5, 11/9, 11/10, and its inverse
* 1–6/5–3/2–18/11 with steps 6/5, 5/4, 11/10, 11/9;  
* 1–11/8–3/2–5/3 with steps 11/8, 11/10, 10/9, 6/5, and its inverse
* 1–11/10–3/2–9/5 with steps 11/10, 11/8, 6/5, 10/9.  


[[Category:Chord]]
For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is
[[Category:Dyadic]]
* 1–9/8–11/8–3/2–18/11 chord with steps of 9/8, 11/9, 11/10, 11/10, 11/9.
[[Category:Triad]]
 
[[Category:Pentad]]
The inversely related pairs of chords are
* 1–11/8–3/2–5/3–11/6 with steps 11/8, 11/10, 10/9, 11/10, 11/10 and its inverse
* 1–11/10–3/2–18/11–9/5 with steps 11/10, 11/8, 11/10, 11/10, 10/9;
* 1–5/4–3/2–5/3–11/6 with steps 5/4, 6/5, 10/9, 11/10, 11/10 and its inverse
* 1–6/5–3/2–18/11–11/6 with steps 6/5, 5/4, 11/10, 11/10, 10/9;
* 1–5/4–11/8–3/2–11/6 with steps 5/4, 11/10, 11/10, 11/9, 11/10 and its inverse
* 1–11/10–6/5–3/2–18/11 with steps 11/10, 11/10, 5/4, 11/10, 11/9.
 
Finally, there is a palindromic hexad,
* 1–5/4–11/8–3/2–5/3–11/6 with steps 5/4, 11/10, 11/10, 10/9, 11/10, 11/10.
 
[[Equal temperament]]s with biyatismic chords include {{Optimal ET sequence| 7, 9, 15, 16, 22, 24, 29, 31, 38, 46 and 53 }}.
 
== See also ==
* [[Chords of orwell]]
* [[Chords of valentine]]
* [[Chords of porcupine]]
 
[[Category:11-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Biyatismic]]

Latest revision as of 10:25, 10 October 2024

Biyatismic chords are essentially tempered dyadic chords tempered by the biyatisma, 121/120.

There are two triads, nine tetrads, seven pentads and one hexad as 2.3.5.11 subgroup 11-odd-limit essentially tempered chords. In this article, voicing with the perfect fifth is prioritized.

The two biyatismic triads are in inverse relationship:

  • 1–11/8–5/3 with steps 11/8, 11/9, 6/5;
  • 1–11/8–18/11 with steps 11/8, 6/5, 11/9.

For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are

  • 1–9/8–11/8–18/11 with steps 9/8, 11/9, 6/5, 11/9;
  • 1–11/10–11/8–3/2 with steps 11/10, 5/4, 11/10, 4/3;
  • 1–3/2–18/11–11/6 with steps 3/2, 11/10, 10/9, 11/10.

The inversely related pairs of chords are

  • 1–11/8–3/2–18/11 with steps 11/8, 11/10, 11/10, 11/9, and its inverse
  • 1–11/10–3/2–11/6 with steps 11/10, 11/8, 11/9, 11/10;
  • 1–5/4–3/2–11/6 with steps 5/4, 6/5, 11/9, 11/10, and its inverse
  • 1–6/5–3/2–18/11 with steps 6/5, 5/4, 11/10, 11/9;
  • 1–11/8–3/2–5/3 with steps 11/8, 11/10, 10/9, 6/5, and its inverse
  • 1–11/10–3/2–9/5 with steps 11/10, 11/8, 6/5, 10/9.

For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is

  • 1–9/8–11/8–3/2–18/11 chord with steps of 9/8, 11/9, 11/10, 11/10, 11/9.

The inversely related pairs of chords are

  • 1–11/8–3/2–5/3–11/6 with steps 11/8, 11/10, 10/9, 11/10, 11/10 and its inverse
  • 1–11/10–3/2–18/11–9/5 with steps 11/10, 11/8, 11/10, 11/10, 10/9;
  • 1–5/4–3/2–5/3–11/6 with steps 5/4, 6/5, 10/9, 11/10, 11/10 and its inverse
  • 1–6/5–3/2–18/11–11/6 with steps 6/5, 5/4, 11/10, 11/10, 10/9;
  • 1–5/4–11/8–3/2–11/6 with steps 5/4, 11/10, 11/10, 11/9, 11/10 and its inverse
  • 1–11/10–6/5–3/2–18/11 with steps 11/10, 11/10, 5/4, 11/10, 11/9.

Finally, there is a palindromic hexad,

  • 1–5/4–11/8–3/2–5/3–11/6 with steps 5/4, 11/10, 11/10, 10/9, 11/10, 11/10.

Equal temperaments with biyatismic chords include 7, 9, 15, 16, 22, 24, 29, 31, 38, 46 and 53.

See also

Retrieved from "https://en.xen.wiki/index.php?title=Biyatismic_chords&oldid=159393"