Jove chords: Difference between revisions

Xenwolf (talk | contribs)
m recat
m Improve readability; recategorize
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
A ''jove chord'' is an 11 odd limit [[essentially tempered chord]] in [[Breed_family#Jove, aka Wonder|jove temperament]]. Since 243/242 is tempered out, [[rastmic_chords|rastmic chords]] are also jove chords; since 441/440 is tempered out, [[werckismic_chords|werckismic chords]] are also jove chords; and since 540/539 is tempered out, [[swetismic_chords|swetismic chords]] are also jove chords. Aside from these, there are also essentially jove tempered chords.  
A '''jove chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in [[jove]] temperament. Since [[243/242]] is tempered out, [[rastmic chords]] are also jove chords; since [[441/440]] is tempered out, [[werckismic chords]] are also jove chords; and since [[540/539]] is tempered out, [[swetismic chords]] are also jove chords. Aside from these, there are also essentially jove tempered chords.  


These are nine tetrads, one palindromic tetrad and four pairs in inverse relationship: 1-11/9-10/7-7/4 with steps 11/9-7/6-11/9-8/7; 1-11/9-3/2-7/4 with steps 11/9-11/9-7/6-8/7 and 1-11/9-3/2-12/7 with steps 11/9-11/9-8/7-7/6; 1-9/8-11/9-7/4 with steps 9/8-12/11-10/7-8/7 and 1-10/7-14/9-7/4 with steps 10/7-12/11-9/8-8/7; 1-9/8-11/7-11/6 with steps 9/8-7/5-7/6-12/11 and 1-9/8-11/9-10/7 and with steps 9/8-12/11-7/6-7/5; 1-9/7-7/5-11/7 with steps 9/7-12/11-9/8-14/11 and 1-9/7-18/11-11/6 with steps 9/7-14/11-9/8-12/11.
These are nine tetrads, one palindromic tetrad and four pairs in inverse relationship:  
* 1–11/9–10/7–7/4 with steps 11/9, 7/6, 11/9, 8/7;  
* 1–11/9–3/2–7/4 with steps 11/9, 11/9, 7/6, 8/7, and its inverse
* 1–11/9–3/2–12/7 with steps 11/9, 11/9, 8/7, 7/6;  
* 1–9/8–11/9–7/4 with steps 9/8, 12/11, 10/7, 8/7, and its inverse
* 1–10/7–14/9–7/4 with steps 10/7, 12/11, 9/8, 8/7;  
* 1–9/8–11/7–11/6 with steps 9/8, 7/5, 7/6, 12/11, and its inverse
* 1–9/8–11/9–10/7 with steps 9/8, 12/11, 7/6, 7/5;  
* 1–9/7–7/5–11/7 with steps 9/7, 12/11, 9/8, 14/11, and its inverse
* 1–9/7–18/11–11/6 with steps 9/7, 14/11, 9/8, 12/11.


There are sixteen essentially jove pentads, consisting of eight inverse pairs. These are 1-11/9-10/7-11/7-7/4 with steps 11/9-7/6-11/10-10/9-8/7 and 1-7/6-10/7-18/11-20/11 with steps 7/6-11/9-8/7-10/9-11/10; 1-7/6-3/2-18/11-11/6 with steps 7/6-9/7-12/11-9/8-12/11 and 1-9/7-3/2-18/11-11/6 with steps 9/7-7/6-12/11-9/8-12/11; 1-11/9-11/8-3/2-7/4 with steps 11/9-9/8-12/11-7/6-8/7 and 1-12/11-11/9-3/2-12/7 with steps 12/11-9/8-11/9-8/7-7/6; 1-9/8-11/9-3/2-7/4 with steps 9/8-12/11-11/9-7/6-8/7 and 1-9/8-9/7-3/2-11/6 with steps 9/8-8/7-7/6-11/9-12/11; 1-9/8-11/9-10/7-7/4 with steps 9/8-12/11-7/6-11/9-8/7 and 1-11/9-10/7-14/9-7/4 with steps 11/9-7/6-12/11-9/8-8/7; 1-9/8-11/9-10/7-11/7 with steps 9/8-12/11-7/6-11/10-14/11 and 1-9/8-10/7-11/7-11/6 with steps 9/8-14/11-11/10-7/6-12/11; 1-9/8-11/9-11/8-7/4 with steps 9/8-12/11-9/8-14/11-8/7 and 1-14/11-10/7-14/9-7/4 with steps 14/11-9/8-12/11-9/8-8/7; and 1-9/8-11/9-11/7-7/4 with steps 9/8-12/11-9/7-10/9-8/7 and 1-9/7-7/5-11/7-9/5 with steps 9/7-12/11-9/8-8/7-10/9.
There are sixteen essentially jove pentads, consisting of eight inverse pairs. These are  
* 1–11/9–10/7–11/7–7/4 with steps 11/9, 7/6, 11/10, 10/9, 8/7, and its inverse
* 1–7/6–10/7–18/11–20/11 with steps 7/6, 11/9, 8/7, 10/9, 11/10;  
* 1–7/6–3/2–18/11–11/6 with steps 7/6, 9/7, 12/11, 9/8, 12/11, and its inverse
* 1–9/7–3/2–18/11–11/6 with steps 9/7, 7/6, 12/11, 9/8, 12/11;  
* 1–11/9–11/8–3/2–7/4 with steps 11/9, 9/8, 12/11, 7/6, 8/7, and its inverse
* 1–12/11–11/9–3/2–12/7 with steps 12/11, 9/8, 11/9, 8/7, 7/6;  
* 1–9/8–11/9–3/2–7/4 with steps 9/8, 12/11, 11/9, 7/6, 8/7, and its inverse
* 1–9/8–9/7–3/2–11/6 with steps 9/8, 8/7, 7/6, 11/9, 12/11;  
* 1–9/8–11/9–10/7–7/4 with steps 9/8, 12/11, 7/6, 11/9, 8/7, and its inverse
* 1–11/9–10/7–14/9–7/4 with steps 11/9, 7/6, 12/11, 9/8, 8/7;  
* 1–9/8–11/9–10/7–11/7 with steps 9/8, 12/11, 7/6, 11/10, 14/11, and its inverse
* 1–9/8–10/7–11/7–11/6 with steps 9/8, 14/11, 11/10, 7/6, 12/11;  
* 1–9/8–11/9–11/8–7/4 with steps 9/8, 12/11, 9/8, 14/11, 8/7, and its inverse
* 1–14/11–10/7–14/9–7/4 with steps 14/11, 9/8, 12/11, 9/8, 8/7;  
* 1–9/8–11/9–11/7–7/4 with steps 9/8, 12/11, 9/7, 10/9, 8/7, and its inverse
* 1–9/7–7/5–11/7–9/5 with steps 9/7, 12/11, 9/8, 8/7, 10/9.


Finally, there are six essentially jove hexads, two palindromic and two pairs of inversely related chords: 1-9/8-11/9-11/8-11/7-7/4 with steps 9/8-12/11-9/8-8/7-10/9-8/7; 1-7/6-9/7-3/2-18/11-11/6 with steps 7/6-11/10-7/6-12/11-9/8-12/11; 1-9/8-9/7-3/2-18/11-11/6 with steps 9/8-8/7-7/6-12/11-9/8-12/11 and 1-9/8-11/9-11/8-3/2-7/4 with steps 9/8-12/11-9/8-12/11-7/6-8/7; and a pair whose steps are permutations of the JI hexad--1-9/8-9/7-10/7-11/7-11/6 with steps 9/8-8/7-10/9-11/10-7/6-12/11 and 1-9/8-11/9-10/7-11/7-7/4 with steps 9/8-12/11-7/6-11/10-10/9-8/7.
Finally, there are six essentially jove hexads, two palindromic and two pairs of inversely related chords:  
* 1–9/8–11/9–11/8–11/7–7/4 with steps 9/8, 12/11, 9/8, 8/7, 10/9, 8/7;  
* 1–7/6–9/7–3/2–18/11–11/6 with steps 7/6, 11/10, 7/6, 12/11, 9/8, 12/11;  
* 1–9/8–9/7–3/2–18/11–11/6 with steps 9/8, 8/7, 7/6, 12/11, 9/8, 12/11, and its inverse
* 1–9/8–11/9–11/8–3/2–7/4 with steps 9/8, 12/11, 9/8, 12/11, 7/6, 8/7;  
* 1–9/8–9/7–10/7–11/7–11/6 with steps 9/8, 8/7, 10/9, 11/10, 7/6, 12/11, and its inverse
* 1–9/8–11/9–10/7–11/7–7/4 with steps 9/8, 12/11, 7/6, 11/10, 10/9, 8/7.


The essentially jove chords number tetrads: 9, pentads: 16, hexads: 6, for a total of 31.
The essentially jove chords number tetrads: 9, pentads: 16, hexads: 6, for a total of 31.


Equal divisions with jove tetrads include 31, 41, 58, 72, 130, 161, 171 and 202.
[[Equal temperament]]s with jove tetrads include {{EDOs| 31, 41, 58, 72, 130, 161, 171 and 202 }}.


[[Category:11-odd-limit]]
[[Category:11-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Jove]]
[[Category:Jove]]
[[Category:Tetrad]]
[[Category:Essentially tempered chords]]
{{Todo|add links}}