40/39

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Interval information
Ratio 40/39
Factorization 23 × 3-1 × 5 × 13-1
Monzo [3 -1 1 0 0 -1
Size in cents 43.831051¢
Names tridecimal 1/5-tone,
tridecimal minor diesis
Color name 3uy1, thuyo unison
FJS name [math]\text{A1}^{5}_{13}[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 10.6073
Weil height (log2 max(n, d)) 10.6439
Wilson height (sopfr (nd)) 27
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.50925 bits
open this interval in xen-calc

40/39 is the difference between the third octave of the third 5/4 (40 = 5 ⋅ 23) and the fifth of the thirteenth partial of the same root (39 = 13 ⋅ 3). If tempered out, it tempers together 5-limit and 13-limit] intervals. However, it does not assosciate major with greater neutral and minor with lesser neutral as one would expect (see 65/64), but the other way around. In particular 5/4~39/32 and 6/5~16/13 are temperings.