10:12:15:18

10:12:15:18, the just, classical, or ptolemaic minor seventh chord, is a minor seventh chord. It is an anomalous saturated suspension in the 9-odd-limit. It is found on the iii (5/4) and vi (5/3) of Ptolemy's intense diatonic scale (Zarlino), perhaps the most common 5-limit diatonic.

Chord information

Harmonics	10:12:15:18
Subharmonics	1/(18:15:12:10)
Intervals from root	1/1–6/5–3/2–9/5
Cents from root	0¢–316¢–702¢–1018¢
Step intervals	6/5, 5/4, 6/5
Step cents	316¢, 386¢, 316¢
Color name	gu-7 or g7
Prime limit	5
Genus	32⋅5 (45)
Intervallic odd limit	9
Otonal odd limit	15
Utonal odd limit	15
Consistent edos (d ≥ 2)	12edo*, 19edo**, 34edo*, 38edo*, …
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

Todo: expand, add sound example

See also

Chords below are 5-limit unless noted.

• Its homonym 12:15:18:20 (1–5/4–3/2–5/3), a major sixth chord.
• 12:14:18:21 (7-limit) - Another anomalous saturated suspension in the 9-odd-limit