15/8
| Ratio | 15/8 |
| Factorization | 2-3 × 3 × 5 |
| Monzo | [-3 1 1⟩ |
| Size in cents | 1088.2687¢ |
| Names | just major seventh, classic(al) major seventh, ptolemaic major seventh |
| Color name | y7, yo 7th |
| FJS name | [math]\text{M7}^{5}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 6.90689 |
| Weil height (log2 max(n, d)) | 7.81378 |
| Wilson height (sopfr (nd)) | 14 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.58244 bits |
[sound info] | |
| open this interval in xen-calc | |
In 5-limit just intonation, 15/8 is the just major seventh, classic(al) major seventh, or ptolemaic major seventh[1] of about 1088.3¢. It is also the 15th harmonic (octave-reduced), and appears as a complex consonance in chords such as 8:10:12:15, a just version of a major seventh chord. Since 15 is 3×5, it can be seen as a perfect fifth above a major third or vice versa, and this understanding is compatible with the 1100¢ interval of 12edo.
Since 15 is a perfect fifth above 10 (15/10 = 3/2), seventh chords can be formed with the 10th harmonic as major third and 15th harmonic as major seventh. The simplest and most familiar example is the classical major seventh chord 8:10:12:15 with steps 5/4, 6/5 and 5/4. Another example replaces the 12 with 13, as 8:10:13:15 with steps 5/4, 13/10 and 15/13. A particularly uncommon but mentionable example is a 23-limit seventh chord 16:20:23:30.