4394/4375: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Eliora (talk | contribs)
autopatrolled
3,351 edits
No edit summary
BudjarnLambeth (talk | contribs)
autopatrolled
18,215 edits
mNo edit summary
 
(7 intermediate revisions by 6 users not shown)
Line 1: Line 1:
{{Infobox Interval|Ratio=4394/4375|Cents=7.502|Monzo=1 0 -4 -1 0 3|Name=rectified Hebrew comma}}
{{Infobox Interval
| Name = hebrewsma
| Color name = 3o<sup>3</sup>rg<sup>4</sup>2, tritho-aruquadgu 2nd
| Comma = yes
}}


'''4394/4375''', the '''rectified Hebrew comma''', is a small 13-limit comma of about 7.5 cents.
'''4394/4375''', the '''hebrewsma''', is a small 13-limit comma of about 7.5 cents. When octave-reduced, 4394/4375 represents the difference between a stack of three [[13/10]]'s against [[35/32]].  


When octave-reduced, 4394/4375 represents a difference between a stack of three [[13/10]] against one [[35/32]].
== Temperaments ==
Tempering out this comma in the 13-limit results in the rank-5 '''hebrewsmic temperament'''. Tempering it out in the 2.5.7.13 subgroup results in the rank-3 '''hebrew temperament'''. In either case [[14/13]] is split in two parts, each corresponding to [[26/25]].


== Theory ==
Tempering it out alongside with [[3136/3125]] sets the rectified hebrew temperament, which is a 2.5.7.13 subgroup extension of [[didacus]]. The presence of 4394/4375 being tempered out is the defining factor which specifies the temperament as rectified hebrew.  
Tempering out 4394/4375 alongside with [[3136/3125]] sets the rectified Hebrew temperament, which is a 13-limit extension of [[didacus]]. The presence of 4394/4375 being tempered out is the defining factor which specifies the temperament as Rectified Hebrew.  


The comma is tempered out by the following vals: {{EDOs|72, 58, 53, 130, 111, 19p, 34d, 19e, 77, 38df}}. In addition, it is tempered out by [[353edo]], where it is connected to a proposal to reform the Hebrew calendar, and where it takes its name from.
The comma is tempered out in the {{Optimal ET sequence|legend=1| 19(e), 34d, 38df, 53, 58, 72, 77, 111, 130, 19e}}. In addition, it is tempered out by [[353edo]], where it is connected to a proposal to reform the Hebrew calendar, hence its name.
 
[[Category:Hebrewsmic]]
[[Category:Commas referencing a famous use of a number]]

Latest revision as of 23:59, 15 November 2024

Interval information
Ratio 4394/4375
Factorization 2 × 5-4 × 7-1 × 133
Monzo [1 0 -4 -1 0 3⟩
Size in cents 7.502223¢
Name hebrewsma
Color name 3o3rg42, tritho-aruquadgu 2nd
FJS name [math]\displaystyle{ \text{ddd2}^{13,13,13}_{5,5,5,5,7} }[/math]
Special properties reduced
Tenney height (log2 nd) 24.1964
Weil height (log2 max(n, d)) 24.2026
Wilson height (sopfr(nd)) 68
Comma size small
S-expression S262 × S27
Open this interval in xen-calc

4394/4375, the hebrewsma, is a small 13-limit comma of about 7.5 cents. When octave-reduced, 4394/4375 represents the difference between a stack of three 13/10's against 35/32.

Temperaments

Tempering out this comma in the 13-limit results in the rank-5 hebrewsmic temperament. Tempering it out in the 2.5.7.13 subgroup results in the rank-3 hebrew temperament. In either case 14/13 is split in two parts, each corresponding to 26/25.

Tempering it out alongside with 3136/3125 sets the rectified hebrew temperament, which is a 2.5.7.13 subgroup extension of didacus. The presence of 4394/4375 being tempered out is the defining factor which specifies the temperament as rectified hebrew.

The comma is tempered out in the Optimal ET sequence: 19(e), 34d, 38df, 53, 58, 72, 77, 111, 130, 19e. In addition, it is tempered out by 353edo, where it is connected to a proposal to reform the Hebrew calendar, hence its name.

Retrieved from "https://en.xen.wiki/index.php?title=4394/4375&oldid=165507"