List of octave-reduced harmonics

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 (¢)	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

See also

• List of tritave reduced harmonics
• Pentave Reduced Harmonics