126/125: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Mike Battaglia (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, emailconfirmed, Interface administrators, Sysops
1,399 edits
m Text replacement - "(\[\[\:(dev|es|purdal|de|en):[^[:space:]\|]*) (.*])" to "$1|$3"
ArrowHead294 (talk | contribs)
14,512 edits
mNo edit summary
 
(20 intermediate revisions by 11 users not shown)
Line 1: Line 1:
<span style="display: block; text-align: right;">[[:de:126/125|Deutsch]]</span>
{{interwiki
| de = 126/125
| en = 126/125
| es =
| ja =
}}
{{Infobox Interval
| Name = starling comma, septimal semicomma
| Color name = zg<sup>3</sup>2, zotrigu 2nd,<br>Zotrigu comma
| Comma = yes
}}
{{Wikipedia|Septimal semicomma}}


The '''starling comma''' or '''septimal semicomma''', 126/125 (about 13.8 cents), is the only superparticular [[7-limit|7-limit]] [[Comma|comma]] which is not the difference between two 7-limit superparticular ratios. Instead, it is the amount by which [[12/7|12/7]] falls short of three [[6/5|6/5]] minor thirds. It is also the amount by which two [[5/3|5/3 major sixths]] (octave-reduced) exceed the [[7/5|7/5 tritone]], and the amount by which three 5/3s (octave-reduced) fall short of the [[7/6|7/6 septimal minor third]]. It can also be found when comparing the conventional 5-limit minor third and major tenth to the nearest Bohlen–Pierce intervals.
The '''starling comma''' or '''septimal semicomma''', '''126/125''' (about 13.8 [[cent]]s), is the [[superparticular]] [[7-limit]] [[comma]] which is the difference between [[36/35]] (septimal quartertone) and [[50/49]] (jubilisma). In terms of just intervals, it is the amount by which [[12/7]] falls short of three [[6/5]] minor thirds. It is also the amount by which two [[5/3]] major sixths (octave-reduced, [[25/18]]) fall short of the [[7/5]] [[tritone]], and the amount by which three 5/3's (octave-reduced) fall short of the [[7/6]] septimal minor third. It can also be found when comparing the conventional 5-limit minor third and major tenth to the nearest [[Bohlen–Pierce]] intervals.


Tempering it out leads to [[Starling_temperaments#Starling comma|starling temperament]], and three minor thirds plus a [[7/6|7/6]] subminor third, when 126/125 is tempered out, gives the [[starling_tetrad|starling tetrad]] or septimal semicomma diminished seventh chord.
== Temperaments ==
Tempering it out alone in the 7-limit leads to the [[starling]] temperament, and enables [[starling chords]]. See [[Starling family]] for the rank-3 temperament family where it is tempered out. See [[starling temperaments]] for a collection of rank-2 temperaments where it is tempered out.  


[http://en.wikipedia.org/wiki/Septimal_semicomma http://en.wikipedia.org/wiki/Septimal_semicomma]      [[Category:7-limit]]
== See also ==
[[Category:comma]]
* [[Small comma]]
[[Category:interval]]
* [[Gallery of just intervals]]
[[Category:septimal]]
* [[List of superparticular intervals]]
[[Category:starling]]
 
[[Category:Starling]]
[[Category:Commas named after musical traditions]]

Latest revision as of 18:20, 13 March 2025

Interval information
Ratio 126/125
Factorization 2 × 32 × 5-3 × 7
Monzo [1 2 -3 1⟩
Size in cents 13.79477¢
Names starling comma,
septimal semicomma
Color name zg32, zotrigu 2nd,
Zotrigu comma
FJS name [math]\displaystyle{ \text{d2}^{7}_{5,5,5} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 13.9431
Weil norm (log2 max(n, d)) 13.9546
Wilson norm (sopfr(nd)) 30
Comma size small
Open this interval in xen-calc
English Wikipedia has an article on:

The starling comma or septimal semicomma, 126/125 (about 13.8 cents), is the superparticular 7-limit comma which is the difference between 36/35 (septimal quartertone) and 50/49 (jubilisma). In terms of just intervals, it is the amount by which 12/7 falls short of three 6/5 minor thirds. It is also the amount by which two 5/3 major sixths (octave-reduced, 25/18) fall short of the 7/5 tritone, and the amount by which three 5/3's (octave-reduced) fall short of the 7/6 septimal minor third. It can also be found when comparing the conventional 5-limit minor third and major tenth to the nearest Bohlen–Pierce intervals.

Temperaments

Tempering it out alone in the 7-limit leads to the starling temperament, and enables starling chords. See Starling family for the rank-3 temperament family where it is tempered out. See starling temperaments for a collection of rank-2 temperaments where it is tempered out.

See also

Retrieved from "https://en.xen.wiki/index.php?title=126/125&oldid=185727"