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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. | 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 [[ | 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. | ||
== See also == | == See also == | ||
* [[Starling family]] | |||
* [[Starling temperaments]] | |||
* [[Starling chords]] | |||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [ | * [[List of superparticular intervals]] | ||
* [[Wikipedia: Septimal semicomma]] | |||
[[Category:7-limit]] | [[Category:7-limit]] | ||
Revision as of 06:41, 14 January 2021
| Interval information |
septimal semicomma
reduced
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.