126/125: Difference between revisions

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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 (actually it~~ is the difference between the [[36/35]] septimal quartertone and the [[50/49]] jubilisma~~, so this is not correct)~~. ~~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 superparticular [[7-limit]] [[comma]] which is the difference between the [[36/35]] septimal quartertone and the [[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) 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]] subminor third, when 126/125 is tempered out, gives the [[starling tetrad]] or septimal semicomma diminished seventh chord.

== Temperaments ==

Tempering it out leads to the [[Starling family #Starling|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 ==

* [[Starling family]]

* [[Starling family]], the rank-3 temperament family where it is tempered out

* [[Starling temperaments]]

* [[Starling temperaments]], a collection of rank-2 temperaments where it is tempered out

* [[Starling chords]]

* [[Small comma]]

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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 (actually it is the difference between the [[36/35]] septimal quartertone and the [[50/49]] jubilisma, so this is not correct). 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 superparticular [[7-limit]] [[comma]] which is the difference between the [[36/35]] septimal quartertone and the [[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) 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]] subminor third, when 126/125 is tempered out, gives the [[starling tetrad]] or septimal semicomma diminished seventh chord.
+== Temperaments ==
+Tempering it out leads to the [[Starling family #Starling|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 ==
-* [[Starling family]]
+* [[Starling family]], the rank-3 temperament family where it is tempered out
-* [[Starling temperaments]]
+* [[Starling temperaments]], a collection of rank-2 temperaments where it is tempered out
 * [[Starling chords]]
 * [[Small comma]]