151263/151250: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
The full history is in the Small comma page
Squib (talk | contribs)
condense and clarify relationship to 6th-octave temperaments
Tags: Mobile edit Mobile web edit Advanced mobile edit
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
|Comma=yes
| Name = odiheim comma
|Name=odiheim comma, odiheim
| Color name = luluquinzo-aquadgu 4th, 1uuz^5g^44
|Color name = luluquinzo-aquadgu 4th, 1uuz^5g^44
| Comma = yes
}}
}}
 
'''151263/151250''', the '''odiheim comma''', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] [[comma]]. It is expressible as ([[2401/2400]])/([[3025/3024]]), and is also the difference between [[63/50]] and a stack of two [[55/49]]'s. 55/49 is very close to [[6edo|1\6]], and 63/50 to [[3edo|1\3]], so this comma  is tempered out in a number of [[6th-octave temperaments]] (although it does not define such temperaments on its own).
'''151263/151250''', the '''odiheim comma''' or '''odiheim''', is an [[11-limit]] unnoticeable comma. It is expressible as ([[2401/2400]])/([[3025/3024]]), and also represents the difference between [[63/50]] and a stack of two [[55/49]]s, which is notable due to 55/49 being a very good approximation of one step of [[6edo]], and 63/50 being the same for [[3edo]]; therefore this comma  is tempered out in a number of [[6th-octave temperaments]].


== Temperaments ==
== Temperaments ==

Latest revision as of 18:22, 4 July 2026

Interval information
Ratio 151263/151250
Factorization 2-1 × 32 × 5-4 × 75 × 11-2
Monzo [-1 2 -4 5 -2
Size in cents 0.1487939¢
Name odiheim comma
Color name luluquinzo-aquadgu 4th, 1uuz^5g^44
FJS name [math]\displaystyle{ \text{ddd4}^{7,7,7,7,7}_{5,5,5,5,11,11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 34.4133
Weil norm (log2 max(n, d)) 34.4134
Wilson norm (sopfr(nd)) 85
Comma size unnoticeable
Open this interval in xen-calc

151263/151250, the odiheim comma, is an unnoticeable 11-limit comma. It is expressible as (2401/2400)/(3025/3024), and is also the difference between 63/50 and a stack of two 55/49's. 55/49 is very close to 1\6, and 63/50 to 1\3, so this comma is tempered out in a number of 6th-octave temperaments (although it does not define such temperaments on its own).

Temperaments

It is tempered out by notable edos like 270edo, 342edo, 1578edo and 1848edo.

Etymology

This comma was presumably named by Gene Ward Smith in 2011 since it seems this wiki was the place where it made its first appearance[1]. The name is a contraction of odin and heimdall, the two notable rank-3 temperaments where the comma is tempered out.

Notes