32:40:48:55

Chord information

Harmonics	32:40:48:55
Subharmonics	1/(165:132:110:96)
Intervals from root	1/1–5/4–3/2–55/32
Cents from root	0¢–386¢–702¢–938¢
Step intervals	5/4, 6/5, 55/48
Step cents	386¢, 316¢, 236¢
Color name	yo loyo-6
Prime limit	11
Genus	3⋅5⋅11 (165)
Intervallic odd limit	55
Otonal odd limit	55
Utonal odd limit	165
Consistent edos (d ≥ 2)	31edo*, 41edo*, 46edo*, 50edo*, …
* 2 ≤ d < 4; ** 4 ≤ d < 8; *** 8 ≤ d < 16; …

32:40:48:55 is an 11-limit tetrad that easily fits in what is otherwise a 5-limit context, especially when the root of the chord is a Ptolemaic minor sixth (8/5) above the Tonic.

Edo approximations for 32:40:48:55 ▶
intervals: 5/4, 3/2, 55/32 · ≤ 60edo, RMS rel. error ≤ 15%

	Edo	Steps	Cents (¢)	Absolute errors (¢)	RMS (¢)	RMS (%)
▶	9	0  3  5  7	0.00 400.00 666.67 933.33	0.00 +13.69 -35.29  -4.30	17.91	13.43
▶	15	0  5  9 12	0.00 400.00 720.00 960.00	0.00 +13.69 +18.04 +22.37	8.39	10.49
▶	19	0  6 11 15	0.00 378.95 694.74 947.37	0.00  -7.37  -7.22  +9.74	6.99	11.06
▶	22	0  7 13 17	0.00 381.82 709.09 927.27	0.00  -4.50  +7.14 -10.36	6.39	11.72
▶	24	0  8 14 19	0.00 400.00 700.00 950.00	0.00 +13.69  -1.96 +12.37	7.05	14.10
▶	26	0  8 15 20	0.00 369.23 692.31 923.08	0.00 -17.08  -9.65 -14.55	6.53	14.15
▶	31	0 10 18 24	0.00 387.10 696.77 929.03	0.00  +0.78  -5.18  -8.60	3.85	9.94
▶	37	0 12 22 29	0.00 389.19 713.51 940.54	0.00  +2.88 +11.56  +2.91	4.33	13.36
▶	41	0 13 24 32	0.00 380.49 702.44 936.59	0.00  -5.83  +0.48  -1.05	2.50	8.55
▶	46	0 15 27 36	0.00 391.30 704.35 939.13	0.00  +4.99  +2.39  +1.50	1.81	6.95
▶	50	0 16 29 39	0.00 384.00 696.00 936.00	0.00  -2.31  -5.96  -1.63	2.18	9.07
▶	56	0 18 33 44	0.00 385.71 707.14 942.86	0.00  -0.60  +5.19  +5.23	2.76	12.89

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