40/39
Jump to navigation
Jump to search
Ratio | 40/39 |
Factorization | 2^{3} × 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 (log_{2} nd) | 10.6073 |
Weil height (log_{2} 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 ⋅ 2^{3}) 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.