Escapade comma
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Ratio | 4294967296/4271484375 |
Factorization | 2^{32} × 3^{-7} × 5^{-9} |
Monzo | [32 -7 -9⟩ |
Size in cents | 9.4915692¢ |
Name | escapade comma |
Color name | ssp^{9}4, 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 (log_{2} nd) | 63.9921 |
Weil height (log_{2} max(n, d)) | 64 |
Wilson height (sopfr (nd)) | 130 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.9972 bits |
Comma size | small |
open this interval in xen-calc |
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^{[1]}.