45:54:64:80

Chord information

Harmonics	45:54:64:80
Subharmonics	1/(192:160:135:108)
Intervals from root	1/1–6/5–64/45–16/9
Cents from root	0¢–316¢–610¢–996¢
Step intervals	6/5, 32/27, 5/4
Step cents	316¢, 294¢, 386¢
Color name	gu add-7 gu-5 or g,7(g5)
Prime limit	5
Genus	33⋅5 (135)
Intervallic odd limit	45
Otonal odd limit	45
Utonal odd limit	135
Consistent edos (d ≥ 2)	12edo*, 41edo*, 53edo**, 65edo*
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

45:54:64:80 is a half-diminished seventh chord found on vii^ø7 (15⁄8) in Ptolemy's intense diatonic scale (Zarlino), perhaps the most common 5-limit diatonic. It is also found on V^ø7 (3⁄2) in the duodene.

Edo approximations for 45:54:64:80 ▶
intervals: 6/5, 64/45, 16/9 · ≤ 60edo, RMS rel. error ≤ 15%

	Edo	Steps	Cents (¢)	Absolute errors (¢)	RMS (¢)	RMS (%)
▶	12	0  3  6 10	0.00 300.00 600.00 1000.00	0.00 -15.64  -9.78  +3.91	7.74	7.74
▶	16	0  4  8 13	0.00 300.00 600.00  975.00	0.00 -15.64  -9.78 -21.09	7.81	10.42
▶	18	0  5  9 15	0.00 333.33 600.00 1000.00	0.00 +17.69  -9.78  +3.91	9.86	14.79
▶	19	0  5 10 16	0.00 315.79 631.58 1010.53	0.00  +0.15 +21.80 +14.44	9.39	14.87
▶	28	0  7 14 23	0.00 300.00 600.00  985.71	0.00 -15.64  -9.78 -10.38	5.65	13.18
▶	30	0  8 15 25	0.00 320.00 600.00 1000.00	0.00  +4.36  -9.78  +3.91	5.69	14.21
▶	34	0  9 17 28	0.00 317.65 600.00  988.24	0.00  +2.01  -9.78  -7.85	5.01	14.18
▶	37	0 10 19 31	0.00 324.32 616.22 1005.41	0.00  +8.68  +6.44  +9.32	3.69	11.36
▶	41	0 11 21 34	0.00 321.95 614.63  995.12	0.00  +6.31  +4.86  -0.97	3.10	10.58
▶	46	0 12 23 38	0.00 313.04 600.00  991.30	0.00  -2.60  -9.78  -4.79	3.59	13.77
▶	49	0 13 25 41	0.00 318.37 612.24 1004.08	0.00  +2.73  +2.47  +7.99	2.91	11.89
▶	53	0 14 27 44	0.00 316.98 611.32  996.23	0.00  +1.34  +1.54  +0.14	0.69	3.06
▶	57	0 15 29 47	0.00 315.79 610.53  989.47	0.00  +0.15  +0.75  -6.62	3.01	14.29