126/125: Difference between revisions

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<span style="display: block; text-align: right;">[[:de:126/125|Deutsch]]</span>
{{interwiki
| de = 126/125
| en = 126/125
| es =
| ja =
}}
{{Infobox Interval
| Icon =
| Ratio = 126/125
| Monzo = 2 3 -3 1
| Cents = 13.79477
| Name = Starling comma, <br> septimal semicomma
| Color name =
| Sound =
}}


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 cents), is the only superparticular [[7-limit]] [[comma]] which is not the difference between two 7-limit superparticular ratios. Instead, 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) exceed the [[7/5]] [[tritone]], and the amount by which three 5/3s (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.
Tempering it out leads to [[Starling_temperaments#Starling comma|starling temperament]], and three minor thirds plus a [[7/6]] subminor third, when 126/125 is tempered out, gives the [[starling tetrad]] or septimal semicomma diminished seventh chord.


[http://en.wikipedia.org/wiki/Septimal_semicomma http://en.wikipedia.org/wiki/Septimal_semicomma]     [[Category:7-limit]]
[http://en.wikipedia.org/wiki/Septimal_semicomma http://en.wikipedia.org/wiki/Septimal_semicomma]
[[Category:comma]]
 
[[Category:interval]]
[[Category:7-limit]]
[[Category:septimal]]
[[Category:Comma]]
[[Category:starling]]
[[Category:Interval]]
[[Category:Septimal]]
[[Category:Starling]]
[[Category:Superparticular]]

Revision as of 08:48, 14 July 2020

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
FJS name [math]\displaystyle{ \text{d2}^{7}_{5,5,5} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 13.9431
Weil height (log2 max(n, d)) 13.9546
Wilson height (sopfr(nd)) 30
Open this interval in xen-calc

The starling comma or septimal semicomma, 126/125 (about 13.8 cents), is the only superparticular 7-limit comma which is not the difference between two 7-limit superparticular ratios. Instead, 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) exceed the 7/5 tritone, and the amount by which three 5/3s (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 temperament, and three minor thirds plus a 7/6 subminor third, when 126/125 is tempered out, gives the starling tetrad or septimal semicomma diminished seventh chord.

http://en.wikipedia.org/wiki/Septimal_semicomma

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