126/125

Interval information

Ratio	126/125
Factorization	2 × 32 × 5-3 × 7
Monzo	[1 2 -3 1⟩
Size in cents	13.794767¢
Names	starling comma, septimal semicomma
Color name	zg32, zotrigu 2nd, Zotrigu comma
FJS name	[math]\text{d2}^{7}_{5,5,5}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	13.9431
Weil height (log2 max(n, d))	13.9546
Wilson height (sopfr(nd))	30
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~2.74804 bits
Comma size	small
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Septimal semicomma

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 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.

See also

• Small comma
• Gallery of just intervals
• List of superparticular intervals