Xenharmonic Wiki

Biyatismic chords: Difference between revisions

← Older edit
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
Tags: Mobile edit Mobile web edit
m Fix a ratio
 
(21 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 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 43 further essentially Zeus chords - eighteen pentads, ten hexads, and fifteen heptads.
* 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.  


The Zeus pentads consist of two palindromic chords and eight pairs of chords in inverse relationship.
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 two palindromic pentads are: 1-6/5-11/8-16/11-5/3 with steps 6/5-8/7-16/15-8/7-6/5 and 1-8/7-11/8-16/11-7/4 with steps 8/7-6/5-16/15-6/5-8/7.
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.  


The eight inversely related pairs of pentads are: 1-8/7-11/8-16/11-5/3 with steps 8/7-6/5-16/15-8/7-6/5 and 1-6/5-11/8-16/11-7/4 with steps 6/5-8/7-16/15-6/5-8/7; 1-8/7-11/9-16/11-7/4 with steps 8/7-16/15-6/5-6/5-8/7 and 1-8/7-11/8-18/11-7/4 with steps 8/7-6/5-6/5-16/15-8/7; 1-8/7-11/8-16/11-8/5 with steps 8/7-6/5-16/15-11/10-5/4 and 1-5/4-11/8-16/11-7/4 with steps 5/4-11/10-16/15-6/5-8/7; 1-8/7-11/8-16/11-11/6 with steps 8/7-6/5-16/15-5/4-11/10 and 1-11/10-11/8-16/11-7/4 with steps 11/10-5/4-16/15-6/5-8/7; 1-5/4-11/8-16/11-5/3 with steps 5/4-11/10-16/15-8/7-6/5 and 1-6/5-11/8-16/11-8/5 with steps 6/5-8/7-16/15-11/10-5/4; 1-11/10-11/8-16/11-5/3 with steps 11/10-5/4-16/15-8/7-6/5 and 1-6/5-11/8-16/11-11/6 with steps 6/5-8/7-16/15-5/4-11/10; 1-5/4-3/2-8/5-11/6 with steps 5/4-6/5-16/15-8/7-11/10 and 1-11/10-5/4-4/3-8/5 with steps 11/10-8/7-16/15-6/5-5/4; and 1-5/4-11/8-18/11-7/4 with steps 5/4-11/10-6/5-16/15-8/7 and 1-8/7-11/9-16/11-8/5 with steps 8/7-16/15-6/5-11/10-5/4.
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.  


The Zeus hexads consist of two palindromic chords and four pairs of chords in inverse relationship.
[[Equal temperament]]s with biyatismic chords include {{Optimal ET sequence| 7, 9, 15, 16, 22, 24, 29, 31, 38, 46 and 53 }}.


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 1-8/7-5/4-11/8-3/2-12/7 with steps 8/7-11/10-11/10-11/10-8/7-7/6.
== See also ==
* [[Chords of orwell]]
* [[Chords of valentine]]
* [[Chords of porcupine]]


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.
[[Category:11-odd-limit chords]]
 
[[Category:Essentially tempered chords]]
The Zeus heptads consist of three palindromic chords and six pairs of chords in inverse relationship.
[[Category:Triads]]
 
[[Category:Tetrads]]
The three palindromic heptads are: 1-11/10-6/5-11/8-16/11-5/3-11/6 with steps 11/10-11/10-8/7-16/15-8/7-11/10-11/10, 1-11/10-5/4-11/8-16/11-8/5-11/6 with steps 11/10-8/7-11/10-16/15-11/10-8/7-11/10, and 1-8/7-5/4-11/8-16/11-8/5-7/4 with steps 8/7-11/10-11/10-16/15-11/10-11/10-8/7.
[[Category:Pentads]]
 
[[Category:Hexads]]
The six inversely related pairs of heptads are: 1-11/10-6/5-11/8-16/11-8/5-7/4 with steps 11/10-11/10-8/7-16/15-11/10-11/10-8/7 and 1-8/7-5/4-11/8-16/11-5/3-11/6 with steps 8/7-11/10-11/10-16/15-8/7-11/10-11/10; 1-11/10-6/5-11/8-16/11-8/5-11/6 with steps 11/10-11/10-8/7-16/15-11/10-8/7-11/10 and 1-11/10-5/4-11/8-16/11-5/3-11/6 with steps 11/10-8/7-11/10-16/15-8/7-11/10-11/10; 1-11/10-5/4-11/8-16/11-8/5-7/4 with steps 11/10-8/7-11/10-16/15-11/10-11/10-8/7 and 1-8/7-5/4-11/8-16/11-8/5-11/6 with steps 8/7-11/10-11/10-16/15-11/10-8/7-11/10; 1-11/10-6/5-14/11-16/11-5/3-11/6 with steps 11/10-11/10-16/15-8/7-8/7-11/10-11/10 and 1-11/10-6/5-11/8-11/7-5/3-11/6 with steps 11/10-11/10-8/7-8/7-16/15-11/10-11/10; 1-11/10-6/5-14/11-16/11-8/5-11/6 with steps 11/10-11/10-16/15-8/7-11/10-8/7-11/10 and 1-11/10-5/4-11/8-11/7-5/3-11/6 with steps 11/10-8/7-11/10-8/7-16/15-11/10-11/10; and 1-8/7-5/4-4/3-16/11-8/5-7/4 with steps 8/7-11/10-16/15-11/10-11/10-11/10-8/7 and 1-8/7-5/4-11/8-3/2-8/5-7/4 with steps 8/7-11/10-11/10-11/10-16/15-11/10-8/7.
[[Category:Biyatismic]]
 
[[Category:Chord]]
[[Category:Dyadic]]
[[Category:Triad]]
[[Category:Pentad]]
Retrieved from "https://en.xen.wiki/w/Biyatismic_chords"