Escapade comma

Interval information

Ratio	4294967296/4271484375
Factorization	232 × 3-7 × 5-9
Monzo	[32 -7 -9⟩
Size in cents	9.491569¢
Name	escapade comma
Color name	ssp94, sasa-tritrigu 4th
FJS name	[math]\text{6d4}_{5,5,5,5,5,5,5,5,5}[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	63.9921
Weil height (log2 max(n, d))	64
Wilson height (sopfr(nd))	130
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.9972 bits
Comma size	small
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The escapade comma (monzo: [32 -7 -9⟩) is a small 5-limit comma with a size of 9.492 cents. It is the difference between nine just major thirds and seven just perfect fourths, that is, (4/3)⁷/(5/4)⁹. This can also be written as (5/3)/(16/15)⁸, that is, the difference between a stack of eight classic diatonic semitones and a classic major sixth. In terms of commas, it is equal to two lesser dieses minus three syntonic commas and one kleisma, that is, (128/125)²/((15625/15552)(81/80)³).

Temperaments

Temperaments in the escapade family tempers out this comma.

Etymology

The escapade comma seems to have been named by Paul Erlich in 2002, referring to the fact that this comma "escaped" a 5-limit comma search by Carl Lumma.