# 302edo

 ← 301edo 302edo 303edo →
Prime factorization 2 × 151
Step size 3.97351¢
Fifth 177\302 (703.311¢)
Semitones (A1:m2) 31:21 (123.2¢ : 83.44¢)
Dual sharp fifth 177\302 (703.311¢)
Dual flat fifth 176\302 (699.338¢) (→88\151)
Dual major 2nd 51\302 (202.649¢)
Consistency limit 3
Distinct consistency limit 3

302 equal divisions of the octave (302edo), or 302-tone equal temperament (302tet), 302 equal temperament (302et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 302 equal parts of about 3.97 ¢ each.

## Theory

Approximation of odd harmonics in 302edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) +1.36 -0.88 +0.71 -1.26 +1.00 +1.86 +0.47 -1.64 +0.50 -1.91 -0.46
relative (%) +34 -22 +18 -32 +25 +47 +12 -41 +13 -48 -12
Steps
(reduced)
479
(177)
701
(97)
848
(244)
957
(51)
1045
(139)
1118
(212)
1180
(274)
1234
(26)
1283
(75)
1326
(118)
1366
(158)

### Subsets and supersets

302 factors into 2 x 151, with subset edos 2, and 151. 906edo, which triples it, gives a good correction to the harmonic 3.

## Interval table

Steps Cents Ups and downs notation
(dual flat fifth 176\302)
Ups and downs notation
(dual sharp fifth 177\302)
Approximate ratios
0 0 D D 1/1
1 3.97351 ^D, vEbb ^D, v20Eb
2 7.94702 ^^D, Ebb ^^D, v19Eb
3 11.9205 ^3D, v23Eb ^3D, v18Eb
4 15.894 ^4D, v22Eb ^4D, v17Eb
5 19.8675 ^5D, v21Eb ^5D, v16Eb
6 23.8411 ^6D, v20Eb ^6D, v15Eb 64/63, 78/77
7 27.8146 ^7D, v19Eb ^7D, v14Eb 55/54, 65/64, 66/65, 81/80
8 31.7881 ^8D, v18Eb ^8D, v13Eb 50/49, 56/55
9 35.7616 ^9D, v17Eb ^9D, v12Eb 49/48
10 39.7351 ^10D, v16Eb ^10D, v11Eb 40/39, 45/44
11 43.7086 ^11D, v15Eb ^11D, v10Eb
12 47.6821 ^12D, v14Eb ^12D, v9Eb 77/75
13 51.6556 ^13D, v13Eb ^13D, v8Eb 36/35, 65/63
14 55.6291 ^14D, v12Eb ^14D, v7Eb 33/32
15 59.6026 ^15D, v11Eb ^15D, v6Eb 28/27
16 63.5762 ^16D, v10Eb ^16D, v5Eb 80/77
17 67.5497 ^17D, v9Eb ^17D, v4Eb 25/24, 27/26
18 71.5232 ^18D, v8Eb ^18D, v3Eb 26/25
19 75.4967 ^19D, v7Eb ^19D, vvEb
20 79.4702 ^20D, v6Eb ^20D, vEb 22/21
21 83.4437 ^21D, v5Eb ^21D, Eb
22 87.4172 ^22D, v4Eb ^22D, v30E 21/20
23 91.3907 ^23D, v3Eb ^23D, v29E 81/77
24 95.3642 D#, vvEb ^24D, v28E 55/52
25 99.3377 ^D#, vEb ^25D, v27E 35/33
26 103.311 ^^D#, Eb ^26D, v26E 52/49
27 107.285 ^3D#, v23E ^27D, v25E
28 111.258 ^4D#, v22E ^28D, v24E 16/15
29 115.232 ^5D#, v21E ^29D, v23E 77/72
30 119.205 ^6D#, v20E ^30D, v22E 15/14
31 123.179 ^7D#, v19E D#, v21E
32 127.152 ^8D#, v18E ^D#, v20E 14/13
33 131.126 ^9D#, v17E ^^D#, v19E
34 135.099 ^10D#, v16E ^3D#, v18E
35 139.073 ^11D#, v15E ^4D#, v17E 13/12, 27/25
36 143.046 ^12D#, v14E ^5D#, v16E
37 147.02 ^13D#, v13E ^6D#, v15E 49/45
38 150.993 ^14D#, v12E ^7D#, v14E 12/11
39 154.967 ^15D#, v11E ^8D#, v13E 35/32
40 158.94 ^16D#, v10E ^9D#, v12E
41 162.914 ^17D#, v9E ^10D#, v11E
42 166.887 ^18D#, v8E ^11D#, v10E 11/10
43 170.861 ^19D#, v7E ^12D#, v9E 54/49
44 174.834 ^20D#, v6E ^13D#, v8E
45 178.808 ^21D#, v5E ^14D#, v7E 10/9, 72/65
46 182.781 ^22D#, v4E ^15D#, v6E
47 186.755 ^23D#, v3E ^16D#, v5E 49/44
48 190.728 Dx, vvE ^17D#, v4E 39/35
49 194.702 ^Dx, vE ^18D#, v3E
50 198.675 E ^19D#, vvE 28/25, 55/49
51 202.649 ^E, vFb ^20D#, vE
52 206.623 ^^E, Fb E 9/8, 44/39
53 210.596 ^3E, v23F ^E, v20F
54 214.57 ^4E, v22F ^^E, v19F
55 218.543 ^5E, v21F ^3E, v18F 25/22
56 222.517 ^6E, v20F ^4E, v17F
57 226.49 ^7E, v19F ^5E, v16F
58 230.464 ^8E, v18F ^6E, v15F 8/7
59 234.437 ^9E, v17F ^7E, v14F 55/48
60 238.411 ^10E, v16F ^8E, v13F 63/55
61 242.384 ^11E, v15F ^9E, v12F
62 246.358 ^12E, v14F ^10E, v11F 15/13
63 250.331 ^13E, v13F ^11E, v10F 52/45
64 254.305 ^14E, v12F ^12E, v9F
65 258.278 ^15E, v11F ^13E, v8F 65/56, 81/70
66 262.252 ^16E, v10F ^14E, v7F 64/55
67 266.225 ^17E, v9F ^15E, v6F 7/6
68 270.199 ^18E, v8F ^16E, v5F
69 274.172 ^19E, v7F ^17E, v4F 75/64
70 278.146 ^20E, v6F ^18E, v3F
71 282.119 ^21E, v5F ^19E, vvF
72 286.093 ^22E, v4F ^20E, vF 33/28
73 290.066 ^23E, v3F F 13/11, 32/27
74 294.04 E#, vvF ^F, v20Gb 77/65
75 298.013 ^E#, vF ^^F, v19Gb 25/21
76 301.987 F ^3F, v18Gb
77 305.96 ^F, vGbb ^4F, v17Gb
78 309.934 ^^F, Gbb ^5F, v16Gb
79 313.907 ^3F, v23Gb ^6F, v15Gb
80 317.881 ^4F, v22Gb ^7F, v14Gb 6/5, 65/54
81 321.854 ^5F, v21Gb ^8F, v13Gb 77/64
82 325.828 ^6F, v20Gb ^9F, v12Gb
83 329.801 ^7F, v19Gb ^10F, v11Gb 40/33
84 333.775 ^8F, v18Gb ^11F, v10Gb 63/52
85 337.748 ^9F, v17Gb ^12F, v9Gb
86 341.722 ^10F, v16Gb ^13F, v8Gb
87 345.695 ^11F, v15Gb ^14F, v7Gb 11/9, 39/32
88 349.669 ^12F, v14Gb ^15F, v6Gb 60/49
89 353.642 ^13F, v13Gb ^16F, v5Gb 49/40
90 357.616 ^14F, v12Gb ^17F, v4Gb 16/13, 27/22
91 361.589 ^15F, v11Gb ^18F, v3Gb
92 365.563 ^16F, v10Gb ^19F, vvGb
93 369.536 ^17F, v9Gb ^20F, vGb 26/21
94 373.51 ^18F, v8Gb ^21F, Gb
95 377.483 ^19F, v7Gb ^22F, v30G 56/45
96 381.457 ^20F, v6Gb ^23F, v29G
97 385.43 ^21F, v5Gb ^24F, v28G 5/4, 81/65
98 389.404 ^22F, v4Gb ^25F, v27G
99 393.377 ^23F, v3Gb ^26F, v26G 49/39
100 397.351 F#, vvGb ^27F, v25G 44/35
101 401.325 ^F#, vGb ^28F, v24G
102 405.298 ^^F#, Gb ^29F, v23G 63/50
103 409.272 ^3F#, v23G ^30F, v22G 80/63
104 413.245 ^4F#, v22G F#, v21G 33/26, 81/64
105 417.219 ^5F#, v21G ^F#, v20G 14/11
106 421.192 ^6F#, v20G ^^F#, v19G
107 425.166 ^7F#, v19G ^3F#, v18G 50/39
108 429.139 ^8F#, v18G ^4F#, v17G 32/25
109 433.113 ^9F#, v17G ^5F#, v16G 77/60
110 437.086 ^10F#, v16G ^6F#, v15G 9/7
111 441.06 ^11F#, v15G ^7F#, v14G
112 445.033 ^12F#, v14G ^8F#, v13G 35/27
113 449.007 ^13F#, v13G ^9F#, v12G
114 452.98 ^14F#, v12G ^10F#, v11G
115 456.954 ^15F#, v11G ^11F#, v10G 13/10
116 460.927 ^16F#, v10G ^12F#, v9G 64/49
117 464.901 ^17F#, v9G ^13F#, v8G 55/42
118 468.874 ^18F#, v8G ^14F#, v7G 72/55
119 472.848 ^19F#, v7G ^15F#, v6G 21/16
120 476.821 ^20F#, v6G ^16F#, v5G
121 480.795 ^21F#, v5G ^17F#, v4G
122 484.768 ^22F#, v4G ^18F#, v3G 33/25
123 488.742 ^23F#, v3G ^19F#, vvG 65/49
124 492.715 Fx, vvG ^20F#, vG
125 496.689 ^Fx, vG G 4/3
126 500.662 G ^G, v20Ab
127 504.636 ^G, vAbb ^^G, v19Ab 75/56
128 508.609 ^^G, Abb ^3G, v18Ab
129 512.583 ^3G, v23Ab ^4G, v17Ab 35/26
130 516.556 ^4G, v22Ab ^5G, v16Ab 66/49
131 520.53 ^5G, v21Ab ^6G, v15Ab
132 524.503 ^6G, v20Ab ^7G, v14Ab 27/20, 65/48
133 528.477 ^7G, v19Ab ^8G, v13Ab
134 532.45 ^8G, v18Ab ^9G, v12Ab 49/36
135 536.424 ^9G, v17Ab ^10G, v11Ab 15/11
136 540.397 ^10G, v16Ab ^11G, v10Ab
137 544.371 ^11G, v15Ab ^12G, v9Ab
138 548.344 ^12G, v14Ab ^13G, v8Ab 48/35
139 552.318 ^13G, v13Ab ^14G, v7Ab 11/8
140 556.291 ^14G, v12Ab ^15G, v6Ab
141 560.265 ^15G, v11Ab ^16G, v5Ab
142 564.238 ^16G, v10Ab ^17G, v4Ab 18/13, 25/18
143 568.212 ^17G, v9Ab ^18G, v3Ab
144 572.185 ^18G, v8Ab ^19G, vvAb
145 576.159 ^19G, v7Ab ^20G, vAb 39/28
146 580.132 ^20G, v6Ab ^21G, Ab
147 584.106 ^21G, v5Ab ^22G, v30A 7/5
148 588.079 ^22G, v4Ab ^23G, v29A
149 592.053 ^23G, v3Ab ^24G, v28A 45/32, 55/39
150 596.026 G#, vvAb ^25G, v27A
151 600 ^G#, vAb ^26G, v26A
152 603.974 ^^G#, Ab ^27G, v25A
153 607.947 ^3G#, v23A ^28G, v24A 64/45, 78/55
154 611.921 ^4G#, v22A ^29G, v23A 77/54
155 615.894 ^5G#, v21A ^30G, v22A 10/7
156 619.868 ^6G#, v20A G#, v21A
157 623.841 ^7G#, v19A ^G#, v20A 56/39, 63/44
158 627.815 ^8G#, v18A ^^G#, v19A
159 631.788 ^9G#, v17A ^3G#, v18A 75/52
160 635.762 ^10G#, v16A ^4G#, v17A 13/9, 36/25
161 639.735 ^11G#, v15A ^5G#, v16A
162 643.709 ^12G#, v14A ^6G#, v15A 81/56
163 647.682 ^13G#, v13A ^7G#, v14A 16/11
164 651.656 ^14G#, v12A ^8G#, v13A 35/24
165 655.629 ^15G#, v11A ^9G#, v12A
166 659.603 ^16G#, v10A ^10G#, v11A
167 663.576 ^17G#, v9A ^11G#, v10A 22/15
168 667.55 ^18G#, v8A ^12G#, v9A 72/49
169 671.523 ^19G#, v7A ^13G#, v8A
170 675.497 ^20G#, v6A ^14G#, v7A 40/27, 65/44, 81/55
171 679.47 ^21G#, v5A ^15G#, v6A 77/52
172 683.444 ^22G#, v4A ^16G#, v5A 49/33
173 687.417 ^23G#, v3A ^17G#, v4A 52/35
174 691.391 Gx, vvA ^18G#, v3A
175 695.364 ^Gx, vA ^19G#, vvA
176 699.338 A ^20G#, vA
177 703.311 ^A, vBbb A 3/2
178 707.285 ^^A, Bbb ^A, v20Bb
179 711.258 ^3A, v23Bb ^^A, v19Bb
180 715.232 ^4A, v22Bb ^3A, v18Bb 50/33
181 719.205 ^5A, v21Bb ^4A, v17Bb
182 723.179 ^6A, v20Bb ^5A, v16Bb
183 727.152 ^7A, v19Bb ^6A, v15Bb 32/21
184 731.126 ^8A, v18Bb ^7A, v14Bb 55/36
185 735.099 ^9A, v17Bb ^8A, v13Bb 75/49
186 739.073 ^10A, v16Bb ^9A, v12Bb 49/32
187 743.046 ^11A, v15Bb ^10A, v11Bb 20/13
188 747.02 ^12A, v14Bb ^11A, v10Bb
189 750.993 ^13A, v13Bb ^12A, v9Bb 77/50
190 754.967 ^14A, v12Bb ^13A, v8Bb 54/35, 65/42
191 758.94 ^15A, v11Bb ^14A, v7Bb
192 762.914 ^16A, v10Bb ^15A, v6Bb 14/9
193 766.887 ^17A, v9Bb ^16A, v5Bb
194 770.861 ^18A, v8Bb ^17A, v4Bb 25/16, 81/52
195 774.834 ^19A, v7Bb ^18A, v3Bb 39/25
196 778.808 ^20A, v6Bb ^19A, vvBb
197 782.781 ^21A, v5Bb ^20A, vBb 11/7
198 786.755 ^22A, v4Bb ^21A, Bb 52/33
199 790.728 ^23A, v3Bb ^22A, v30B 63/40
200 794.702 A#, vvBb ^23A, v29B
201 798.675 ^A#, vBb ^24A, v28B
202 802.649 ^^A#, Bb ^25A, v27B 35/22
203 806.623 ^3A#, v23B ^26A, v26B 78/49
204 810.596 ^4A#, v22B ^27A, v25B
205 814.57 ^5A#, v21B ^28A, v24B 8/5
206 818.543 ^6A#, v20B ^29A, v23B 77/48
207 822.517 ^7A#, v19B ^30A, v22B 45/28
208 826.49 ^8A#, v18B A#, v21B
209 830.464 ^9A#, v17B ^A#, v20B 21/13
210 834.437 ^10A#, v16B ^^A#, v19B
211 838.411 ^11A#, v15B ^3A#, v18B
212 842.384 ^12A#, v14B ^4A#, v17B 13/8, 44/27, 81/50
213 846.358 ^13A#, v13B ^5A#, v16B 80/49
214 850.331 ^14A#, v12B ^6A#, v15B 49/30
215 854.305 ^15A#, v11B ^7A#, v14B 18/11, 64/39
216 858.278 ^16A#, v10B ^8A#, v13B
217 862.252 ^17A#, v9B ^9A#, v12B
218 866.225 ^18A#, v8B ^10A#, v11B
219 870.199 ^19A#, v7B ^11A#, v10B 33/20
220 874.172 ^20A#, v6B ^12A#, v9B 81/49
221 878.146 ^21A#, v5B ^13A#, v8B
222 882.119 ^22A#, v4B ^14A#, v7B 5/3
223 886.093 ^23A#, v3B ^15A#, v6B
224 890.066 Ax, vvB ^16A#, v5B
225 894.04 ^Ax, vB ^17A#, v4B
226 898.013 B ^18A#, v3B
227 901.987 ^B, vCb ^19A#, vvB 42/25
228 905.96 ^^B, Cb ^20A#, vB
229 909.934 ^3B, v23C B 22/13, 27/16
230 913.907 ^4B, v22C ^B, v20C 56/33
231 917.881 ^5B, v21C ^^B, v19C
232 921.854 ^6B, v20C ^3B, v18C 75/44
233 925.828 ^7B, v19C ^4B, v17C
234 929.801 ^8B, v18C ^5B, v16C 77/45
235 933.775 ^9B, v17C ^6B, v15C 12/7
236 937.748 ^10B, v16C ^7B, v14C 55/32
237 941.722 ^11B, v15C ^8B, v13C
238 945.695 ^12B, v14C ^9B, v12C
239 949.669 ^13B, v13C ^10B, v11C 45/26
240 953.642 ^14B, v12C ^11B, v10C 26/15
241 957.616 ^15B, v11C ^12B, v9C
242 961.589 ^16B, v10C ^13B, v8C
243 965.563 ^17B, v9C ^14B, v7C
244 969.536 ^18B, v8C ^15B, v6C 7/4
245 973.51 ^19B, v7C ^16B, v5C
246 977.483 ^20B, v6C ^17B, v4C
247 981.457 ^21B, v5C ^18B, v3C 44/25
248 985.43 ^22B, v4C ^19B, vvC
249 989.404 ^23B, v3C ^20B, vC
250 993.377 B#, vvC C 16/9, 39/22
251 997.351 ^B#, vC ^C, v20Db
252 1001.32 C ^^C, v19Db 25/14
253 1005.3 ^C, vDbb ^3C, v18Db
254 1009.27 ^^C, Dbb ^4C, v17Db 70/39
255 1013.25 ^3C, v23Db ^5C, v16Db
256 1017.22 ^4C, v22Db ^6C, v15Db
257 1021.19 ^5C, v21Db ^7C, v14Db 9/5, 65/36
258 1025.17 ^6C, v20Db ^8C, v13Db
259 1029.14 ^7C, v19Db ^9C, v12Db 49/27
260 1033.11 ^8C, v18Db ^10C, v11Db 20/11
261 1037.09 ^9C, v17Db ^11C, v10Db
262 1041.06 ^10C, v16Db ^12C, v9Db
263 1045.03 ^11C, v15Db ^13C, v8Db 64/35
264 1049.01 ^12C, v14Db ^14C, v7Db 11/6
265 1052.98 ^13C, v13Db ^15C, v6Db
266 1056.95 ^14C, v12Db ^16C, v5Db
267 1060.93 ^15C, v11Db ^17C, v4Db 24/13, 50/27, 81/44
268 1064.9 ^16C, v10Db ^18C, v3Db
269 1068.87 ^17C, v9Db ^19C, vvDb
270 1072.85 ^18C, v8Db ^20C, vDb 13/7
271 1076.82 ^19C, v7Db ^21C, Db
272 1080.79 ^20C, v6Db ^22C, v30D 28/15
273 1084.77 ^21C, v5Db ^23C, v29D
274 1088.74 ^22C, v4Db ^24C, v28D 15/8
275 1092.72 ^23C, v3Db ^25C, v27D
276 1096.69 C#, vvDb ^26C, v26D 49/26
277 1100.66 ^C#, vDb ^27C, v25D 66/35
278 1104.64 ^^C#, Db ^28C, v24D
279 1108.61 ^3C#, v23D ^29C, v23D
280 1112.58 ^4C#, v22D ^30C, v22D 40/21
281 1116.56 ^5C#, v21D C#, v21D
282 1120.53 ^6C#, v20D ^C#, v20D 21/11
283 1124.5 ^7C#, v19D ^^C#, v19D
284 1128.48 ^8C#, v18D ^3C#, v18D 25/13
285 1132.45 ^9C#, v17D ^4C#, v17D 48/25, 52/27
286 1136.42 ^10C#, v16D ^5C#, v16D 77/40
287 1140.4 ^11C#, v15D ^6C#, v15D 27/14
288 1144.37 ^12C#, v14D ^7C#, v14D 64/33
289 1148.34 ^13C#, v13D ^8C#, v13D 35/18
290 1152.32 ^14C#, v12D ^9C#, v12D
291 1156.29 ^15C#, v11D ^10C#, v11D
292 1160.26 ^16C#, v10D ^11C#, v10D 39/20
293 1164.24 ^17C#, v9D ^12C#, v9D
294 1168.21 ^18C#, v8D ^13C#, v8D 49/25, 55/28
295 1172.19 ^19C#, v7D ^14C#, v7D 65/33
296 1176.16 ^20C#, v6D ^15C#, v6D 63/32, 77/39
297 1180.13 ^21C#, v5D ^16C#, v5D
298 1184.11 ^22C#, v4D ^17C#, v4D
299 1188.08 ^23C#, v3D ^18C#, v3D
300 1192.05 Cx, vvD ^19C#, vvD
301 1196.03 ^Cx, vD ^20C#, vD
302 1200 D D 2/1