40/39
Jump to navigation
Jump to search
| 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{n\cdot d}[/math]) |
~4.76657 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.