85/64: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
VisualWikitext
Aura (talk | contribs)
autopatrolled, emailconfirmed
5,920 edits
Created page with "{{Infobox Interval | JI glyph = | Ratio = 85/64 | Monzo = -6 0 1 0 0 0 1 | Cents = 491.26912 | Name = septendecimal fourth | Sound = | Color name = | FJS name = }} '''85/..."
 
TallKite (talk | contribs)
autopatrolled, Sysops
3,990 edits
added color name
 
(8 intermediate revisions by 3 users not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| JI glyph =
| Name = septendecimal harmonic fourth, archagall fourth
| Ratio = 85/64
| Color name = 17oy4, soyo 4th
| Monzo = -6 0 1 0 0 0 1
| Cents = 491.26912
| Name = septendecimal fourth
| Sound =
| Color name =  
| FJS name =
}}
}}


'''85/64''', the '''septendecimal fourth''', is a [[17-limit]] interval that closely approximates [[4/3]], from which it differs by [[256/255]].  Because it differs from [[15/8]] by [[24/17]], this interval is an easy substitute for 4/3 in scales where one desires to simultaneously maintain [[Rothenberg propriety]] and ensure that all notes in the scale suggest the Tonic as the virtual fundamental when played simultaneously.
'''85/64''', the '''septendecimal harmonic fourth''' or '''[[24576/24565#Archagall|archagall]] fourth''', is a [[17-limit]] [[rooted]] interval that comes rather close to [[4/3]], from which it differs by [[256/255]].  Notably, 85/64 is one of two intervals relatively simple intervals that can be used to generate a just version of something resembling a [[superpyth]] diatonic scale, the other being [[128/85]].
 
== See also ==
* [[128/85]] – its [[octave complement]]
* [[96/85]] – its [[fifth complement]]
* [[Gallery of just intervals]]

Latest revision as of 02:50, 29 December 2022

Interval information
Ratio 85/64
Factorization 2-6 × 5 × 17
Monzo [-6 0 1 0 0 0 1⟩
Size in cents 491.2691¢
Names septendecimal harmonic fourth,
archagall fourth
Color name 17oy4, soyo 4th
FJS name [math]\displaystyle{ \text{P4}^{5,17} }[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 12.4094
Weil height (log2 max(n, d)) 12.8188
Wilson height (sopfr(nd)) 34
Open this interval in xen-calc

85/64, the septendecimal harmonic fourth or archagall fourth, is a 17-limit rooted interval that comes rather close to 4/3, from which it differs by 256/255. Notably, 85/64 is one of two intervals relatively simple intervals that can be used to generate a just version of something resembling a superpyth diatonic scale, the other being 128/85.

See also

Retrieved from "https://en.xen.wiki/index.php?title=85/64&oldid=100588"