Harmonics 20–40

The harmonic segment 20::40 (also harmonics 20–40) consists of harmonics 20 through 40 (20:21:…:40) and spans one octave above the root. Used as a scale, it is also called mode 20 of the harmonic series.

Harmonics 20–40

Prime factorization	22 × 5
Fifth	30/20 (701.955c)

Intervals

otone	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40
freq. ratio	1/1	21/20	11/10	23/20	6/5	5/4	13/10	27/20	7/5	29/20	3/2	31/20	8/5	33/20	17/10	7/4	9/5	37/20	19/10	39/20	2/1
cents	0	84	165	242	316	386	454	520	583	643	702	759	814	867	919	969	1018	1065	1111	1156	1200

Internal intervals

A reference chart to find cents values for every interval available in this scale:

	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39
20	0	84	165	242	316	386	454	520	583	643	702	759	814	867	919	969	1018	1065	1111	1156
21	1116	0	81	157	231	302	370	435	498	559	617	674	729	782	834	884	933	981	1027	1072
22	1035	1119	0	77	151	221	289	355	418	478	537	594	649	702	754	804	853	900	946	991
23	958	1043	1123	0	74	144	212	278	341	401	460	517	572	625	677	727	776	823	869	914
24	884	969	1049	1126	0	71	139	204	267	328	386	443	498	551	603	653	702	749	796	841
25	814	583	979	1056	1129	0	68	133	196	257	316	372	427	481	532	583	631	679	725	770
26	746	830	911	988	1061	1132	0
27
28
29
30
31
32
33
34
35
36
37
38
39

Scales

• 3-5-7-9 hexany
• 20:21:24:28:30:35:40 Rotated Ternessbabdec