45:54:64:81

Chord information

Harmonics	45:54:64:81
Subharmonics	1/(576:480:405:320)
Intervals from root	1/1–6/5–64/45–9/5
Cents from root	0¢–316¢–610¢–1018¢
Step intervals	6/5, 32/27, 81/64
Step cents	316¢, 294¢, 408¢
Color name	gu-7 gu-5 or g7(g5)
Prime limit	5
Genus	34⋅5 (405)
Intervallic odd limit	81
Otonal odd limit	81
Utonal odd limit	405
Consistent edos (d ≥ 2)	12edo*, 41edo*, 53edo**, 65edo**
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

45:54:64:81 is a half-diminished seventh chord.

Although it has a relatively high odd limit for such a chord, this particular tuning of the chord is notable for being both a preimage of the half-diminished seventh chord in meantone temperaments (including 12edo and quarter-comma meantone), and tempered together with the vastly simpler 5:6:7:9 in archytas temperament (also supported by 12edo).

Edo approximations for 45:54:64:81 ▶
intervals: 6/5, 64/45, 9/5 · ≤ 60edo, RMS rel. error ≤ 15%

	Edo	Steps	Cents (¢)	Absolute errors (¢)	RMS (¢)	RMS (%)
▶	8	0  2  4  7	0.00 300.00 600.00 1050.00	0.00 -15.64  -9.78 +32.40	18.56	12.37
▶	12	0  3  6 10	0.00 300.00 600.00 1000.00	0.00 -15.64  -9.78 -17.60	6.84	6.84
▶	20	0  5 10 17	0.00 300.00 600.00 1020.00	0.00 -15.64  -9.78  +2.40	7.31	12.18
▶	24	0  6 12 20	0.00 300.00 600.00 1000.00	0.00 -15.64  -9.78 -17.60	6.84	13.69
▶	26	0  7 13 22	0.00 323.08 600.00 1015.38	0.00  +7.44  -9.78  -2.21	6.14	13.29
▶	27	0  7 14 23	0.00 311.11 622.22 1022.22	0.00  -4.53 +12.45  +4.63	6.27	14.12
▶	33	0  9 17 28	0.00 327.27 618.18 1018.18	0.00 +11.63  +8.41  +0.59	5.00	13.75
▶	38	0 10 19 32	0.00 315.79 600.00 1010.53	0.00  +0.15  -9.78  -7.07	4.36	13.79
▶	41	0 11 21 35	0.00 321.95 614.63 1024.39	0.00  +6.31  +4.86  +6.79	2.69	9.19
▶	45	0 12 23 38	0.00 320.00 613.33 1013.33	0.00  +4.36  +3.56  -4.26	3.41	12.78
▶	53	0 14 27 45	0.00 316.98 611.32 1018.87	0.00  +1.34  +1.54  +1.27	0.61	2.69