174edo

← 173edo

174edo

175edo →

Prime factorization	2 × 3 × 29
Step size	6.89655 ¢
Fifth	102\174 (703.448 ¢) (→ 17\29)
Semitones (A1:m2)	18:12 (124.1 ¢ : 82.76 ¢)
Consistency limit	5
Distinct consistency limit	5

174 equal divisions of the octave (abbreviated 174edo or 174ed2), also called 174-tone equal temperament (174tet) or 174 equal temperament (174et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 174 equal parts of about 6.9 ¢ each. Each step represents a frequency ratio of 2^1/174, or the 174th root of 2.

174edo is closely related to 87edo, but the patent vals differ on the mapping for 17 and some higher primes. It is contorted in the 13-limit, tempering out 196/195, 245/243, 352/351, 364/363, and 625/624. Using the patent val, it tempers out 289/288 in the 17-limit; 361/360, 476/475, and 665/663 in the 19-limit; 391/390, 392/391, 460/459, 529/528, and 760/759 in the 23-limit; 1309/1305, 1450/1449, and 4147/4140 in the 29-limit; 496/495 and 1365/1364 in the 31-limit.

Odd harmonics

Approximation of prime harmonics in 174edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+1.49	-0.11	-3.31	+0.41	+0.85	-1.51	-0.96	-0.69	-1.99	-0.21
	Relative (%)	+0.0	+21.7	-1.5	-48.0	+5.9	+12.3	-21.9	-13.9	-10.0	-28.9	-3.0
Steps (reduced)		174 (0)	276 (102)	404 (56)	488 (140)	602 (80)	644 (122)	711 (15)	739 (43)	787 (91)	845 (149)	862 (166)

Subsets and supersets

Since 174 factors into 2 × 3 × 29, 174edo has subset edos 2, 3, 6, 29, 58, and 87.

Intervals

Steps	Cents	Approximate ratios	Ups and downs notation
0	0	1/1	D
1	6.9		^D, ^7E♭♭
2	13.79		^^D, ^8E♭♭
3	20.69		^3D, v9E♭
4	27.59	63/62	^4D, v8E♭
5	34.48	51/50, 52/51	^5D, v7E♭
6	41.38	42/41, 43/42	^6D, v6E♭
7	48.28		^7D, v5E♭
8	55.17	32/31	^8D, v4E♭
9	62.07	57/55	^9D, v3E♭
10	68.97	26/25	v8D♯, vvE♭
11	75.86	23/22	v7D♯, vE♭
12	82.76	43/41	v6D♯, E♭
13	89.66	20/19	v5D♯, ^E♭
14	96.55	37/35, 55/52	v4D♯, ^^E♭
15	103.45		v3D♯, ^3E♭
16	110.34		vvD♯, ^4E♭
17	117.24	46/43	vD♯, ^5E♭
18	124.14	43/40	D♯, ^6E♭
19	131.03	41/38, 55/51	^D♯, ^7E♭
20	137.93	13/12	^^D♯, ^8E♭
21	144.83	25/23, 62/57	^3D♯, v9E
22	151.72	12/11	^4D♯, v8E
23	158.62	23/21, 34/31, 57/52	^5D♯, v7E
24	165.52	11/10	^6D♯, v6E
25	172.41	21/19	^7D♯, v5E
26	179.31	51/46	^8D♯, v4E
27	186.21		^9D♯, v3E
28	193.1	19/17	v8D𝄪, vvE
29	200	46/41	v7D𝄪, vE
30	206.9	62/55	E
31	213.79	43/38	^E, ^7F♭
32	220.69	25/22, 42/37	^^E, ^8F♭
33	227.59	57/50	^3E, v9F
34	234.48	55/48, 63/55	^4E, v8F
35	241.38	23/20	^5E, v7F
36	248.28	15/13	^6E, v6F
37	255.17	51/44	^7E, v5F
38	262.07	50/43	^8E, v4F
39	268.97		^9E, v3F
40	275.86	34/29	v8E♯, vvF
41	282.76		v7E♯, vF
42	289.66	13/11	F
43	296.55	19/16, 51/43	^F, ^7G♭♭
44	303.45	31/26, 56/47	^^F, ^8G♭♭
45	310.34	55/46	^3F, v9G♭
46	317.24		^4F, v8G♭
47	324.14	41/34	^5F, v7G♭
48	331.03	23/19, 63/52	^6F, v6G♭
49	337.93	62/51	^7F, v5G♭
50	344.83	50/41	^8F, v4G♭
51	351.72	38/31	^9F, v3G♭
52	358.62	16/13	v8F♯, vvG♭
53	365.52	21/17	v7F♯, vG♭
54	372.41	31/25, 57/46	v6F♯, G♭
55	379.31		v5F♯, ^G♭
56	386.21	5/4	v4F♯, ^^G♭
57	393.1		v3F♯, ^3G♭
58	400	63/50	vvF♯, ^4G♭
59	406.9	43/34	vF♯, ^5G♭
60	413.79	33/26, 47/37	F♯, ^6G♭
61	420.69	37/29, 51/40	^F♯, ^7G♭
62	427.59	32/25	^^F♯, ^8G♭
63	434.48		^3F♯, v9G
64	441.38	40/31	^4F♯, v8G
65	448.28	57/44	^5F♯, v7G
66	455.17	13/10	^6F♯, v6G
67	462.07		^7F♯, v5G
68	468.97	38/29	^8F♯, v4G
69	475.86	25/19	^9F♯, v3G
70	482.76	37/28, 41/31	v8F𝄪, vvG
71	489.66		v7F𝄪, vG
72	496.55		G
73	503.45		^G, ^7A♭♭
74	510.34	43/32, 47/35, 51/38	^^G, ^8A♭♭
75	517.24	31/23, 58/43	^3G, v9A♭
76	524.14	23/17	^4G, v8A♭
77	531.03	34/25	^5G, v7A♭
78	537.93	15/11	^6G, v6A♭
79	544.83	63/46	^7G, v5A♭
80	551.72	11/8	^8G, v4A♭
81	558.62	29/21	^9G, v3A♭
82	565.52	43/31	v8G♯, vvA♭
83	572.41	32/23	v7G♯, vA♭
84	579.31		v6G♯, A♭
85	586.21		v5G♯, ^A♭
86	593.1	31/22	v4G♯, ^^A♭
87	600	41/29, 58/41	v3G♯, ^3A♭
88	606.9	44/31	vvG♯, ^4A♭
89	613.79	57/40	vG♯, ^5A♭
90	620.69	63/44	G♯, ^6A♭
91	627.59	23/16	^G♯, ^7A♭
92	634.48	62/43	^^G♯, ^8A♭
93	641.38	42/29, 55/38	^3G♯, v9A
94	648.28	16/11	^4G♯, v8A
95	655.17		^5G♯, v7A
96	662.07	22/15, 63/43	^6G♯, v6A
97	668.97	25/17	^7G♯, v5A
98	675.86	34/23	^8G♯, v4A
99	682.76	43/29, 46/31	^9G♯, v3A
100	689.66		v8G𝄪, vvA
101	696.55		v7G𝄪, vA
102	703.45		A
103	710.34		^A, ^7B♭♭
104	717.24	56/37, 62/41	^^A, ^8B♭♭
105	724.14	38/25	^3A, v9B♭
106	731.03	29/19	^4A, v8B♭
107	737.93		^5A, v7B♭
108	744.83	20/13, 63/41	^6A, v6B♭
109	751.72		^7A, v5B♭
110	758.62	31/20	^8A, v4B♭
111	765.52		^9A, v3B♭
112	772.41	25/16	v8A♯, vvB♭
113	779.31	58/37	v7A♯, vB♭
114	786.21	52/33, 63/40	v6A♯, B♭
115	793.1		v5A♯, ^B♭
116	800		v4A♯, ^^B♭
117	806.9	51/32	v3A♯, ^3B♭
118	813.79	8/5	vvA♯, ^4B♭
119	820.69		vA♯, ^5B♭
120	827.59	50/31	A♯, ^6B♭
121	834.48	34/21	^A♯, ^7B♭
122	841.38	13/8	^^A♯, ^8B♭
123	848.28	31/19	^3A♯, v9B
124	855.17	41/25	^4A♯, v8B
125	862.07	51/31	^5A♯, v7B
126	868.97	38/23	^6A♯, v6B
127	875.86	63/38	^7A♯, v5B
128	882.76		^8A♯, v4B
129	889.66		^9A♯, v3B
130	896.55	47/28, 52/31	v8A𝄪, vvB
131	903.45	32/19	v7A𝄪, vB
132	910.34	22/13	B
133	917.24		^B, ^7C♭
134	924.14	29/17	^^B, ^8C♭
135	931.03		^3B, v9C
136	937.93	43/25, 55/32	^4B, v8C
137	944.83		^5B, v7C
138	951.72	26/15	^6B, v6C
139	958.62	40/23	^7B, v5C
140	965.52		^8B, v4C
141	972.41		^9B, v3C
142	979.31	37/21, 44/25	v8B♯, vvC
143	986.21		v7B♯, vC
144	993.1	55/31	C
145	1000	41/23, 57/32	^C, ^7D♭♭
146	1006.9	34/19	^^C, ^8D♭♭
147	1013.79		^3C, v9D♭
148	1020.69		^4C, v8D♭
149	1027.59	38/21	^5C, v7D♭
150	1034.48	20/11	^6C, v6D♭
151	1041.38	31/17, 42/23	^7C, v5D♭
152	1048.28	11/6	^8C, v4D♭
153	1055.17	46/25, 57/31	^9C, v3D♭
154	1062.07	24/13	v8C♯, vvD♭
155	1068.97	63/34	v7C♯, vD♭
156	1075.86		v6C♯, D♭
157	1082.76	43/23	v5C♯, ^D♭
158	1089.66		v4C♯, ^^D♭
159	1096.55		v3C♯, ^3D♭
160	1103.45		vvC♯, ^4D♭
161	1110.34	19/10	vC♯, ^5D♭
162	1117.24		C♯, ^6D♭
163	1124.14	44/23	^C♯, ^7D♭
164	1131.03	25/13	^^C♯, ^8D♭
165	1137.93		^3C♯, v9D
166	1144.83	31/16	^4C♯, v8D
167	1151.72		^5C♯, v7D
168	1158.62	41/21	^6C♯, v6D
169	1165.52	51/26	^7C♯, v5D
170	1172.41	63/32	^8C♯, v4D
171	1179.31		^9C♯, v3D
172	1186.21		v8C𝄪, vvD
173	1193.1		v7C𝄪, vD
174	1200	2/1	D