15/8

Interval information

Ratio	15/8
Factorization	2-3 × 3 × 5
Monzo	[-3 1 1⟩
Size in cents	1088.269¢
Names	just major seventh, classic(al) major seventh, ptolemaic major seventh
Color name	y7, yo 7th
FJS name	[math]\displaystyle{ \text{M7}^{5} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	6.90689
Weil norm (log2 max(n, d))	7.81378
Wilson norm (sopfr(nd))	14
[sound info]
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Major seventh

In 5-limit just intonation, 15/8 is the just major seventh, classic(al) major seventh, or ptolemaic major seventh 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.

See also

• 16/15 – its octave complement
• 8/5 – its twelfth complement
• Ed15/8
• Gallery of just intervals