126/125: Difference between revisions
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<span style="display: block; text-align: right;">[[:de:126/125 Deutsch]]</span> | <span style="display: block; text-align: right;">[[:de:126/125|Deutsch]]</span> | ||
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|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. | ||
Revision as of 00:09, 17 September 2018
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.