15/8
| Interval information |
classic(al) major seventh,
ptolemaic major seventh
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
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.