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 × 43
65	26.841	5 × 13		13-limit
131	40.108	prime		close to square root of 67
33	53.273	3 × 11	undecimal comma	11-limit / close to quarter-tone (1 degree of 24edo), square root of 17
133	66.339	7 × 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 × 3 × 3 × 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 × 23		close to 1 degree of 9edo
139	142.729	prime		close to 2 degrees of 17edo
35	155.140	5 × 7		7-limit / close to 3 degrees of 24edo
141	167.462	3 × 47
71	179.697	prime		close to 3 degrees of 20edo, square root of 79
143	191.846	11 × 13	11-13 meantone	13-limit / close to square root of 5 (a.k.a. 5 degrees of 31edo)
9	203.910	3 × 3	major whole-tone / Pythagorean whole tone	3-limit
145	215.891	5 × 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 × 7 × 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 × 5 × 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 × 3 × 17		close to 8 degrees of 31edo
77	320.144	7 × 11		close to 4 degrees of 15edo
155	331.349	5 × 31
39	342.483	3 × 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 × 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	7 × 23		close to 4 degrees of 12edo (a.k.a. 1 degree of 3edo)
81	407.820	3 × 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 × 5 × 11
83	450.047	prime		close to 3 degrees of 8edo
167	460.445	prime
21	470.781	3 × 7	narrow fourth / septimal fourth	7-limit / close to 9 degrees of 23edo
169	481.055	13 × 13		13-limit / close to 2 degrees of 5edo, square root of 7
85	491.269	5 × 17	near fourth	close to 9 degrees of 22edo
171	501.423	3 × 3 × 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 × 29		close to 4 degrees of 9edo
175	541.453	5 × 5 × 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 × 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 × 3 × 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 × 13		13-limit
183	618.840	3 × 61
23	628.274	prime		close to 11 degrees of 21edo / 10 degrees of 19edo / square root of 33
185	637.658	5 × 37
93	646.991	3 × 31		close to 7 degrees of 13edo / 13 degrees of 24edo
187	656.273	11 × 17		close to 11 degrees of 20edo
47	665.507	prime		close to 5 degrees of 9edo
189	674.691	3 × 3 × 3 × 7		7-limit / close to 9 degrees of 16edo, square root of 35
95	683.827	5 × 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 × 5 × 13		13-limit / close to 19 degrees of 31edo, square root of 37
49	737.652	7 × 7		7-limit / close to 8 degrees of 13edo
197	746.462	prime
99	755.228	3 × 3 × 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 × 5	augmented fifth	5-limit / close to 9 degrees of 14edo / 11 degrees of 17edo, square root of 39
201	781.262	3 × 67	harmonic gentle minor sixth, circular sixth	close to 19 degrees of 23edo / pi
101	789.854	prime
203	798.403	7 × 29		close to 8 degrees of 12edo (a.k.a. 2 degrees of 3edo)
51	806.910	3 × 17
205	815.376	5 × 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 × 3 × 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 × 19	11-19 hemieleventh	close to 12 degrees of 17edo
105	857.095	3 × 5 × 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	881.652	3 × 71		close to 11 degrees of 15edo / close to 14 degrees of 19edo
107	889.760	prime
215	897.831	5 × 43		close to 9 degrees of 12edo (a.k.a. 3 degrees of 4edo), square root of 45
27	905.865	3 × 3 × 3	Pythagorean major sixth	3-limit
217	913.8615	7 × 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 × 73		close to 24 degrees of 31edo, square root of 47
55	937.632	5 × 11		11-limit / close to 18 degrees of 23edo
221	945.483	13 × 17		close to 15 degrees of 19edo
111	953.299	3 × 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 × 3 × 5 × 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 × 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 × 23		close to 11 degrees of 13edo
231	1022.099	3 × 7 × 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 × 3 × 13		13-limit / close to 13 degrees of 15edo / 20 degrees of 23edo
235	1051.820	5 × 47		close to 21 degrees of 24edo
59	1059.172	prime		close to 15 degrees of 17edo
237	1066.492	3 × 79		close to 8 degrees of 9edo, square root of 55
119	1073.781	7 × 17		close to 17 degrees of 19edo
239	1081.040	prime		close to 3 degrees of 31edo
15	1088.269	3 × 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 × 11		11-limit / close to 11 degrees of 12edo, square root of 57
243	1109.775	3 × 3 × 3 × 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 × 7 × 7		close to 16 degrees of 17edo
123	1131.017	3 × 41		close to 17 degrees of 18edo, 18 degrees of 19edo, square root of 59
247	1138.041	13 × 19		close to 19 degrees of 20edo
31	1145.036	prime		close to 21 degrees of 22edo
249	1152.002	3 × 83		close to 24 degrees of 25edo
125	1158.941	5 × 5 × 5		5-limit, close to square root of 61
251	1165.852	prime
63	1172.736	3 × 3 × 7		7-limit
253	1179.592	11 × 23
127	1186.422	prime		close to square root of 63
255	1193.224	3 × 5 × 17
2	1200	prime	octave	2-limit

See also

• List of tritave reduced harmonics
• Pentave Reduced Harmonics