In 5-limit Just Intonation, 15/8 is a major seventh of about 1088.3¢. It is also the 15th overtone (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), root-3rd-P5 triads can be formed with the 10th harmonic as root and 15th harmonic as perfect fifth. The simplest and most familiar example is the classic minor triad 10:12:15 -- a 6/5 with a 5/4 stacked on top of it. Another is the Barbados triad, 10:13:15 -- a 13/10 on bottom and a 15/13 on top. And a particularly uncommon but mentionable example is the 23-limit inframinor triad 20:23:30.