126/125: Difference between revisions
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== Temperaments == | == Temperaments == | ||
Tempering it out alone in the 7-limit leads to the [[starling]] temperament, and enables [[starling chords]]. See [[Starling family]] for the rank-3 temperament family where it is tempered out. See [[starling temperaments]] for a collection of rank-2 temperaments where it is tempered out. | Tempering it out alone in the 7-limit leads to the [[starling]] temperament, and enables [[starling chords]]. See [[Starling family]] for the rank-3 temperament family where it is tempered out. See [[starling temperaments]] for a collection of rank-2 temperaments where it is tempered out. | ||
== Approximation == | |||
When treated as an interval in its own right, 126/125 is extremely close to one step of [[87edo]], and it is a relationship that is represented with extremely high precision, with less than 0.001{{c}} of [[WE]] error (See [[87th-octave temperaments]]). Notably, 87edo itself does the mapping consistently. | |||
== See also == | == See also == | ||
Latest revision as of 23:08, 2 September 2026
| Interval information |
septimal semicomma
Zotrigu comma
reduced
The starling comma or septimal semicomma, 126/125 (about 13.8 cents), is the superparticular 7-limit comma which is the difference between 36/35 (septimal quartertone) and 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, 25/18) fall short of the 7/5 tritone, and the amount by which three 5/3's (octave-reduced) fall short of the 7/6 septimal minor third. It equates the 7th harmonic with (5/3)3(3/2). It can also be found when comparing the conventional 5-limit minor third and major tenth to the nearest Bohlen–Pierce intervals.
Temperaments
Tempering it out alone in the 7-limit leads to the starling temperament, and enables starling chords. See Starling family for the rank-3 temperament family where it is tempered out. See starling temperaments for a collection of rank-2 temperaments where it is tempered out.
Approximation
When treated as an interval in its own right, 126/125 is extremely close to one step of 87edo, and it is a relationship that is represented with extremely high precision, with less than 0.001 ¢ of WE error (See 87th-octave temperaments). Notably, 87edo itself does the mapping consistently.