40/39

Interval information

Ratio

40/39

Factorization

2³ × 3^-1 × 5 × 13^-1

Monzo

[3 -1 1 0 0 -1⟩

Size in cents

43.83105¢

Names

tridecimal 1/5-tone,
tridecimal minor diesis

Color name

3uy1, thuyo unison

FJS name

[math]\displaystyle{ \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

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.