List of octave-reduced harmonics
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This is a list of harmonics up to 255, sorted by ascending pitch of their octave-reduced equivalent (except the octave, which is not reduced). Prime harmonics are in bold.
Harmonic | Size (¢)^{[1]} | Factorization | Name | Remarks |
---|---|---|---|---|
1 | 0 | 1 | unison | present in all tunings and tonal systems |
129 | 13.473 | 3 x 43 | ||
65 | 26.841 | 5 x 13 | 13-limit | |
131 | 40.108 | prime | close to square root of 67 | |
33 | 53.273 | 3 x 11 | undecimal comma | 11-limit / close to quarter-tone (1 degree of 24edo), square root of 17 |
133 | 66.339 | 7 x 19 | close to 1 degree of 18edo / 19edo, square root of 69 | |
67 | 79.307 | prime | close to 1 degree of 15edo | |
135 | 92.179 | 3 x 3 x 3 x 5 | 5-limit, close to 1 degree of 13edo / square root of 71 | |
17 | 104.955 | prime | harmonic half-step | close to 1 degree of 11edo / 2 degrees of 23edo |
137 | 117.6385 | prime | harmonic secor | close to 3 degrees of 31edo, square root of 73 |
69 | 130.229 | 3 x 23 | close to 1 degree of 9edo | |
139 | 142.729 | prime | close to 2 degrees of 17edo | |
35 | 155.140 | 5 x 7 | 7-limit / close to 3 degrees of 24edo | |
141 | 167.462 | 3 x 47 | ||
71 | 179.697 | prime | close to 3 degrees of 20edo, square root of 79 | |
143 | 191.846 | 11 x 13 | 11-13 meantone | 13-limit / close to square root of 5 (a.k.a. 5 degrees of 31edo) |
9 | 203.910 | 3 x 3 | major whole-tone / Pythagorean whole tone | 3-limit |
145 | 215.891 | 5 x 29 | 5-29 eventone | close to 2 degrees of 11edo |
73 | 227.789 | prime | close to 3 degrees of 16edo / 4 degrees of 21edo | |
147 | 239.607 | 3 x 7 x 7 | 7-limit / close to 1 degree of 5edo, square root of 21 | |
37 | 251.344 | prime | harmonic hemifourth | close to 5 degrees of 24edo |
149 | 263.002 | prime | harmonic subminor third | |
75 | 274.582 | 3 x 5 x 5 | augmented second | 5-limit / close to 5 degrees of 22edo, 3 degrees of 13edo, square root of 11 |
151 | 286.086 | prime | harmonic gentle minor third | close to 4 degrees of 17edo |
19 | 297.513 | prime | harmonic minor third | close to 3 degrees of 12edo (a.k.a. 1 degree of 4edo) |
153 | 308.865 | 3 x 3 x 17 | close to 8 degrees of 31edo | |
77 | 320.144 | 7 x 11 | ||
155 | 331.349 | 5 x 31 | ||
39 | 342.483 | 3 x 13 | 13-limit / close to 2 degrees of 7edo | |
157 | 353.545 | prime | harmonic hemififth | close to 5 degrees of 17edo |
79 | 364.537 | prime | close to 7 degrees of 23edo | |
159 | 375.4595 | 3 x 53 | close to 5 degrees of 16edo | |
5 | 386.314 | prime | 5-limit major third | 5-limit / close to 10 degrees of 31edo |
161 | 397.100 | prime | close to 4 degrees of 12edo (a.k.a. 1 degree of 3edo) | |
81 | 407.820 | 3 x 3 × 3 × 3 | Pythagorean major third | 3-limit |
163 | 418.474 | prime | overtone gentle major third | close to 8 degrees of 23edo / square root of phi |
41 | 429.062 | prime | close to 5 degrees of 14edo | |
165 | 439.587 | 3 x 5 x 11 | ||
167 | 460.445 | prime | ||
21 | 470.781 | 3 x 7 | narrow fourth / septimal fourth | 7-limit / close to 9 degrees of 23edo |
169 | 481.055 | 13 x 13 | 13-limit / close to 2 degrees of 5edo, square root of 7 | |
85 | 491.269 | 5 x 17 | near fourth | close to 9 degrees of 22edo |
171 | 501.423 | 3 x 3 x 19 | close to 5 degrees of 12edo | |
43 | 511.518 | prime | close to 3 degrees of 7edo / square root of 29 | |
173 | 521.554 | prime | close to 10 degrees of 23edo | |
87 | 531.532 | 3 x 29 | close to 4 degrees of 9edo | |
175 | 541.453 | 5 x 5 x 7 | close to 9 degrees of 20edo | |
11 | 551.318 | prime | undecimal semi-augmented fourth / undecimal tritone | 11-limit / close to 11 degrees of 24edo |
177 | 561.127 | 3 x 59 | close to 7 degrees of 15edo | |
89 | 570.880 | prime | close to 10 degrees of 21edo / 9 degrees of 19edo / square root of 31 | |
179 | 580.579 | prime | close to 15 degrees of 31edo | |
45 | 590.224 | 3 x 3 x 5 | high 5-limit tritone | 5-limit / close to square root of 15 |
181 | 599.815 | prime | close to square root of 2 | |
91 | 609.354 | 7 x 13 | 13-limit | |
183 | 618.840 | 3 x 61 | ||
23 | 628.274 | prime | close to 11 degrees of 21edo / 10 degrees of 19edo / square root of 33 | |
185 | 637.658 | 5 x 37 | ||
93 | 646.991 | 3 x 31 | close to 7 degrees of 13edo / 13 degrees of 24edo | |
187 | 656.273 | 11 x 17 | close to 11 degrees of 20edo | |
47 | 665.507 | prime | close to 5 degrees of 9edo | |
189 | 674.691 | 3 x 3 x 3 x 7 | 7-limit / close to 9 degrees of 16edo, square root of 35 | |
95 | 683.827 | 5 x 19 | close to 4 degrees of 7edo | |
191 | 692.9155 | prime | close to 11 degrees of 19edo | |
3 | 701.955 | prime | just perfect fifth | 3-limit / close to 7 degrees of 12edo |
193 | 710.948 | prime | close to 13 degrees of 22edo | |
97 | 719.895 | prime | close to 3 degrees of 5edo | |
195 | 728.796 | 3 x 5 x 13 | 13-limit / close to 19 degrees of 31edo, square root of 37 | |
49 | 737.652 | 7 x 7 | 7-limit / close to 8 degrees of 13edo | |
197 | 746.462 | prime | ||
99 | 755.228 | 3 x 3 x 11 | 11-limit / close to 5 degrees of 8edo / 12 degrees of 19edo | |
199 | 763.9495 | prime | close to 7 degrees of 11edo | |
25 | 772.627 | 5 x 5 | augmented fifth | 5-limit / close to 9 degrees of 14edo / 11 degrees of 17edo, square root of 39 |
201 | 781.262 | 3 x 67 | harmonic gentle minor sixth, circular sixth | close to 19 degrees of 23edo / pi |
101 | 789.854 | prime | ||
203 | 798.403 | 7 x 29 | close to 8 degrees of 12edo (a.k.a. 2 degrees of 3edo) | |
51 | 806.910 | 3 x 17 | ||
205 | 815.376 | 5 x 41 | close to 21 degrees of 31edo, square root of 41 , | |
103 | 823.801 | prime | close to 11 degrees of 16edo / 13 degrees of 19edo | |
207 | 832.143 | 3 x 3 x 23 | close to 17 degrees of 22edo, 10 degrees of 13edo | |
13 | 840.528 | prime | harmonic sixth, golden overtone | 13-limit / close to 7 degrees of 10edo, golden ratio |
209 | 848.831 | 11 x 19 | 11-19 hemieleventh | close to 12 degrees of 17edo |
105 | 857.095 | 3 x 5 x 7 | 7-limit / close to 5 degrees of 7edo, square root of 43 | |
211 | 865.319 | prime | close to 13 degrees of 18edo | |
53 | 873.505 | prime | close to 8 degrees of 11edo | |
213 | 881.6515 | 3 x 71 | close to 11 degrees of 15edo / close to 14 degrees of 19edo | |
215 | 897.831 | 5 x 43 | close to 9 degrees of 12edo (a.k.a. 3 degrees of 4edo), square root of 45 | |
27 | 905.865 | 3 x 3 x 3 | Pythagorean major sixth | 3-limit |
217 | 913.8615 | 7 x 31 | harmonic gentle major third | close to 13 degrees of 17edo |
109 | 921.821 | prime | close to 10 degrees of 13edo | |
219 | 929.7445 | 3 x 73 | close to 24 degrees of 31edo, square root of 47 | |
55 | 937.632 | 5 x 11 | 11-limit / close to 18 degrees of 23edo | |
221 | 945.483 | 13 x 17 | close to 15 degrees of 19edo | |
111 | 953.299 | 3 x 37 | harmonic hemitwelfth | close to 19 degrees of 24edo / square root of 3 |
223 | 961.080 | prime | close to 4 degrees of 5edo | |
7 | 968.826 | prime | harmonic seventh / septimal minor seventh | 7-limit / close to 17 degrees of 21edo / 25 degrees of 31edo |
225 | 976.537 | 3 x 3 x 5 x 5 | 5-limit subminor seventh | 5-limit / close to 11 degrees of 16edo |
113 | 984.215 | prime | close to 9 degrees of 11edo | |
227 | 991.858 | prime | ||
57 | 999.468 | 3 x 19 | close to 10 degrees of 12edo (a.k.a. 5 degrees of 6edo), square root of 51 | |
229 | 1007.0445 | prime | ||
115 | 1014.588 | 5 x 23 | close to 11 degrees of 13edo | |
231 | 1022.099 | 3 x 7 x 11 | close to square root of 13 | |
29 | 1029.577 | prime | close to 6 degrees of 7edo | |
233 | 1037.023 | prime | close to square root of 53 | |
117 | 1044.438 | 3 x 3 x 13 | 13-limit / close to 13 degrees of 15edo / 20 degrees of 23edo | |
235 | 1051.820 | 5 x 47 | close to 21 degrees of 24edo | |
59 | 1059.172 | prime | close to 15 degrees of 17edo | |
237 | 1066.492 | 3 x 79 | close to 8 degrees of 9edo, square root of 55 | |
119 | 1073.781 | 7 x 17 | close to 17 degrees of 19edo | |
239 | 1081.040 | prime | close to 3 degrees of 31edo | |
15 | 1088.269 | 3 x 5 | 5-limit major seventh | 5-limit / close to 19 degrees of 21edo / 10 degrees of 11edo |
241 | 1095.467 | prime | ||
121 | 1102.636 | 11 x 11 | 11-limit / close to 11 degrees of 12edo, square root of 57 | |
243 | 1109.775 | 3 x 3 x 3 x 3 × 3 | Pythagorean major seventh | close to 12 degrees of 13edo |
61 | 1116.885 | prime | close to 13 degrees of 14edo | |
245 | 1123.9655 | 5 x 7 x 7 | close to 16 degrees of 17edo | |
123 | 1131.017 | 3 x 41 | close to 17 degrees of 18edo, 18 degrees of 19edo, square root of 59 | |
247 | 1138.041 | prime | close to 19 degrees of 20edo | |
31 | 1145.036 | prime | close to 21 degrees of 22edo | |
249 | 1152.002 | 3 x 83 | close to 24 degrees of 25edo | |
125 | 1158.941 | 5 x 5 x 5 | 5-limit, close to square root of 61 | |
251 | 1165.852 | prime | ||
63 | 1172.736 | 3 x 3 x 7 | 7-limit | |
253 | 1179.592 | 11 x 23 | ||
127 | 1186.422 | prime | close to square root of 63 | |
255 | 1193.224 | 3 x 5 x 17 | ||
2 | 1200 | prime | octave | 2-limit |
- ↑ cent values are given for the octave reduced equivalent