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. 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 (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.

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.

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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 (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.
 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.