392/375

392/375, the prograde comma, is a medium 7-limit comma measuring about 76.75 cents. It is the amount by which two septimal narrow tritones ((7/5)²) exceed a classical major seventh (15/8), as well as the amount by which two aberschismic chromatic semitones ((15/14)²) fall short of a classical minor third (6/5).

Interval information

Ratio	392/375
Factorization	23 × 3-1 × 5-3 × 72
Monzo	[3 -1 -3 2⟩
Size in cents	76.75567 ¢
Name	prograde comma
Color name	zzg33, Zozotrigu comma, zozotrigu 3rd
FJS name	[math]\displaystyle{ \text{dd3}^{7,7}_{5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	17.1655
Weil norm (log2 max(n, d))	17.2294
Wilson norm (sopfr(nd))	38
Comma size	medium
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In terms of other commas, it is the difference between an aberschismic diatonic semitone (21/20) and a marvel comma (225/224). It factors into (49/48)⋅(128/125) and (28/27)⋅(126/125). In the 11-limit, it factors into (56/55)⋅(77/75) and (56/55)²⋅(121/120).

Temperaments

Tempering out this comma results in the rank-3 prograde temperament. Rank-2 temperaments that temper it out include progress, progression and mohamaq.

Etymology

This comma was named by OffsuitKnave in 2022, likely as a variation of progress or progression.