73edo

← 72edo

73edo

74edo →

Prime factorization	73 (prime)
Step size	16.4384¢
Fifth	43\73 (706.849¢)
Semitones (A1:m2)	9:4 (147.9¢ : 65.75¢)
Consistency limit	7
Distinct consistency limit	7

73 equal divisions of the octave (abbreviated 73edo or 73ed2), also called 73-tone equal temperament (73tet) or 73 equal temperament (73et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 73 equal parts of about 16.4 ¢ each. Each step represents a frequency ratio of 2^1/73, or the 73rd root of 2.

Theory

73edo has a very sharp tendency, with the approximations of 3, 5, 7, 11 all sharp. The equal temperament tempers out 78732/78125 and 262144/253125 in the 5-limit; 126/125 and 245/243 in the 7-limit; 176/175, 441/440 and 4000/3993 in the 11-limit; 91/90, 169/168, 196/195, 325/324, 351/350 and 352/351 in the 13-limit. It provides the optimal patent val for the marrakesh temperament, though 104edo and 135edo tunes it better.

73edo fits in mavila scale, by the 9;5 relation in the superdiatonic scheme.

Prime harmonics

Approximation of prime harmonics in 73edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	absolute (¢)	+0.00	+4.89	+8.21	+1.04	+7.59	-2.17	-6.33	-1.62	-3.62	+6.04	+5.65
	relative (%)	+0	+30	+50	+6	+46	-13	-38	-10	-22	+37	+34
Steps (reduced)		73 (0)	116 (43)	170 (24)	205 (59)	253 (34)	270 (51)	298 (6)	310 (18)	330 (38)	355 (63)	362 (70)

Subsets and supersets

73edo is the 21st prime edo, past 71edo and before 79edo.

Intervals

Steps	Cents	Ups and downs notation	Approximate ratios
0	0	D	1/1
1	16.4384	^D, v3Eb	78/77
2	32.8767	^^D, vvEb	49/48, 55/54, 65/64, 66/65
3	49.3151	^3D, vEb	36/35, 40/39, 65/63
4	65.7534	^4D, Eb	80/77
5	82.1918	^5D, v8E	21/20, 22/21
6	98.6301	^6D, v7E	35/33, 52/49
7	115.068	^7D, v6E	77/72
8	131.507	^8D, v5E	14/13, 27/25
9	147.945	D#, v4E	12/11
10	164.384	^D#, v3E	11/10
11	180.822	^^D#, vvE	10/9, 39/35, 49/44, 72/65
12	197.26	^3D#, vE
13	213.699	E	44/39
14	230.137	^E, v3F	8/7, 63/55
15	246.575	^^E, vvF
16	263.014	^3E, vF	7/6, 65/56
17	279.452	F
18	295.89	^F, v3Gb	77/65
19	312.329	^^F, vvGb	6/5
20	328.767	^3F, vGb	40/33
21	345.205	^4F, Gb	11/9, 39/32, 49/40
22	361.644	^5F, v8G	16/13
23	378.082	^6F, v7G
24	394.521	^7F, v6G	44/35, 49/39, 63/50
25	410.959	^8F, v5G	14/11, 80/63
26	427.397	F#, v4G	77/60
27	443.836	^F#, v3G	35/27
28	460.274	^^F#, vvG	64/49, 72/55
29	476.712	^3F#, vG	21/16, 33/25
30	493.151	G	4/3, 65/49
31	509.589	^G, v3Ab
32	526.027	^^G, vvAb	27/20, 65/48
33	542.466	^3G, vAb	15/11, 48/35
34	558.904	^4G, Ab
35	575.342	^5G, v8A	39/28
36	591.781	^6G, v7A
37	608.219	^7G, v6A	77/54
38	624.658	^8G, v5A	56/39, 63/44
39	641.096	G#, v4A
40	657.534	^G#, v3A	22/15, 35/24
41	673.973	^^G#, vvA	40/27, 65/44, 81/55
42	690.411	^3G#, vA
43	706.849	A	3/2
44	723.288	^A, v3Bb	32/21, 50/33
45	739.726	^^A, vvBb	49/32, 55/36
46	756.164	^3A, vBb	54/35, 65/42
47	772.603	^4A, Bb
48	789.041	^5A, v8B	11/7, 63/40
49	805.479	^6A, v7B	35/22, 78/49
50	821.918	^7A, v6B	77/48
51	838.356	^8A, v5B	13/8, 81/50
52	854.795	A#, v4B	18/11, 64/39, 80/49
53	871.233	^A#, v3B	33/20
54	887.671	^^A#, vvB	5/3
55	904.11	^3A#, vB
56	920.548	B
57	936.986	^B, v3C	12/7
58	953.425	^^B, vvC
59	969.863	^3B, vC	7/4
60	986.301	C	39/22
61	1002.74	^C, v3Db
62	1019.18	^^C, vvDb	9/5, 65/36, 70/39
63	1035.62	^3C, vDb	20/11
64	1052.05	^4C, Db	11/6
65	1068.49	^5C, v8D	13/7, 50/27
66	1084.93	^6C, v7D
67	1101.37	^7C, v6D	49/26, 66/35
68	1117.81	^8C, v5D	21/11, 40/21
69	1134.25	C#, v4D	77/40
70	1150.68	^C#, v3D	35/18, 39/20
71	1167.12	^^C#, vvD	65/33
72	1183.56	^3C#, vD	77/39
73	1200	D	2/1

Scales

Palace (subset of Porky[15])

• 164.384
• 328.767
• 493.151
• 706.849
• 871.233
• 1035.616
• 1200.000

Music

Claudi Meneghin

• Little Fugue on Happy Birthday