39edf: Difference between revisions

Revision as of 05:08, 18 December 2024

39EDF is the equal division of the just perfect fifth into 39 parts of 17.9988 cents each, corresponding to 66.6709 edo. It is nearly identical to every third step of 200edo.

Approximation of harmonics in 39edf
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+5.92	+5.92	-6.15	+3.51	-6.15	-3.04	-0.23	-6.15	-8.57	+6.42	-0.23
Error	Relative (%)	+32.9	+32.9	-34.2	+19.5	-34.2	-16.9	-1.3	-34.2	-47.6	+35.6	-1.3
Steps (reduced)		67 (28)	106 (28)	133 (16)	155 (38)	172 (16)	187 (31)	200 (5)	211 (16)	221 (26)	231 (36)	239 (5)

Approximation of harmonics in 39edf
Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.19	+2.88	-8.57	+5.69	+8.73	-0.23	-3.84	-2.65	+2.88	-5.66	+7.38
Error	Relative (%)	+28.8	+16.0	-47.6	+31.6	+48.5	-1.3	-21.3	-14.7	+16.0	-31.4	+41.0
Steps (reduced)		247 (13)	254 (20)	260 (26)	267 (33)	273 (0)	278 (5)	283 (10)	288 (15)	293 (20)	297 (24)	302 (29)

Intervals of 39edf
degree	cents value	corresponding JI intervals	comments
0		exact 1/1
1	17.9988	100/99, 99/98, 96/95
2	35.9977	50/49, 49/48
3	53.9965	33/32
4	71.9954	(25/24), (24/23)
5	89.9942
6	107.9931	16/15
7	125.9919
8	143.9908	25/23
9	161.9896
10	179.9885	10/9
11	197.9873
12	215.9862	17/15
13	233.985	8/7
14	251.9838
15	269.9827	7/6
16	287.9815	13/11
17	305.9804	68/57
18	323.9792	6/5
19	341.9781	39/32
20	359.9769	16/13
21	377.9758		lower pseudo-5/4
22	395.9746		upper pseudo-5/4
23	413.9735	33/26
24	431.9723	9/7
25	449.9712
26	467.97
27	485.9688	45/34
28	503.9677	4/3
29	521.9665	27/20
30	539.9654
31	557.9642
32	575.9631
33	593.9619
34	611.9608	64/45
35	629.9596	(23/16), (36/25)
36	647.9585	16/11	pseudo-36/25
37	665.9573	72/49
38	683.9562	95/64, 49/33, 297/200, 40/27
39	701.955	exact 3/2	just perfect fifth
40	720.9388	50/33, 297/196, 144/95
41	737.9527	75/49, 49/32
42	755.9515	99/64
43	773.9504	25/16, 36/23
44	791.9492
45	809.9481	8/5
46	827.9469
47	845.9458	75/46
48	863.9446
49	881.9435	5/3
50	899.9423
51	917.9412	17/10
52	935.94	12/7
53	954.9388
54	971.9377	7/4
55	989.9365	39/22
56	1007.9354	34/19
57	1025.9342	9/5
58	1043.9331	117/64
59	1061.9319	24/13
60	1079.9308		lower pseudo-15/8
61	1097.9296		upper pseudo-15/8
62	1115.9285	99/52
63	1134.9273	27/14
64	1151.9261
65	1169.925	49/25
66	1187.9238	135/68
67	1205.9227	2/1
68	1223.9215	81/40
69	1241.9204
70	1259.9192
71	1277.9181
72	1295.9169
73	1313.9158	32/15
74	1331.9146	69/32, 54/25
75	1349.9135	24/11	pseudo-54/25
76	1367.9123	108/49
77	1385.9112	285/128, 49/22, 891/400, 20/9
78	1403.91	exact 9/4

@@ Line 4: / Line 4: @@
 == Harmonics ==
 {{Harmonics in equal|39|3|2}}
+{{Harmonics in equal|39|3|2|start=12|collapsed=1}}
 ==Intervals==
-{| class="wikitable"
+{| class="wikitable mw-collapsible"
+|+ Intervals of 39edf
 |-
 ! | degree
@@ Line 408: / Line 410: @@
 |}
+{{todo|expand}}
 [[Category:Edf]]
 [[Category:Edonoi]]