32edf: Difference between revisions

Revision as of 07:52, 18 December 2024

Prime factorization

2⁵

Step size

21.9361 ¢

Octave

55\32edf (1206.49 ¢)

Twelfth

87\32edf (1908.44 ¢)

Consistency limit

3

Distinct consistency limit

3

32EDF is the equal division of the just perfect fifth into 32 parts of 21.9361 cents each, corresponding to 54.7044 edo (similar to every seventh step of 383edo).

It is related to the regular temperament which tempers out |127 -127 32> in the 5-limit, which is supported by 164, 383, 547, 711, 875, and 1258 EDOs.

Lookalikes: 55edo, 87edt

Approximation of harmonics in 32edf
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+6.49	+6.49	-8.97	-0.43	-8.97	+9.33	-2.48	-8.97	+6.06	-5.40	-2.48
Error	Relative (%)	+29.6	+29.6	-40.9	-2.0	-40.9	+42.5	-11.3	-40.9	+27.6	-24.6	-11.3
Steps (reduced)		55 (23)	87 (23)	109 (13)	127 (31)	141 (13)	154 (26)	164 (4)	173 (13)	182 (22)	189 (29)	196 (4)

Approximation of harmonics in 32edf
Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-9.44	-6.12	+6.06	+4.00	+8.73	-2.48	-8.34	-9.40	-6.12	+1.09	-10.06
Error	Relative (%)	-43.0	-27.9	+27.6	+18.3	+39.8	-11.3	-38.0	-42.8	-27.9	+5.0	-45.9
Steps (reduced)		202 (10)	208 (16)	214 (22)	219 (27)	224 (0)	228 (4)	232 (8)	236 (12)	240 (16)	244 (20)	247 (23)

Intervals of 32edf
degree	cents value	corresponding JI intervals	comments
0		exact 1/1
1	21.9361	81/80
2	43.8722	40/39
3	65.8083	27/26, 28/27
4	87.7444
5	109.6805	49/46, 16/15
6	131.6166	41/38
7	153.5527	59/54, 18/11
8	175.4888
9	197.4248	65/58
10	219.3609	42/37
11	241.297	(23/20)
12	263.2331	7/6
13	285.1692
14	307.1053	117/98
15	329.0414	52/43
16	350.9775	60/49, 49/40
17	372.9136	129/104
18	394.8497	49/39
19	416.7858	14/11
20	438.7219	9/7
21	460.6580	(30/23)
22	482.5941	37/28
23	504.5302	87/65	pseudo-4/3
24	526.4663	61/45
25	548.4023	81/59
26	570.3384	57/41
27	592.2745	69/49
28	614.2106	10/7
29	636.1467	13/9
30	658.0828	117/80
31	680.0189	40/27
32	701.9550	exact 3/2	just perfect fifth
33	723.8911	243/160
34	745.8372	20/13
35	766.7633	81/52, 14/9
36	790.6994
37	811.6355	147/92, 8/5
38	833.5716	123/76
39	855.5077	59/36, 18/11
40	877.4438
41	899.3798	195/116
42	922.3159	63/37
43	943.252	69/40
44	965.1881	7/4
45	987.1242
46	1009.0603	351/196
47	1030.9964	78/43
48	1052.9325	90/49, 147/80
49	1076.8686	387/208
50	1096.847	147/78
51	1118.7408	21/11
52	1140.6769	27/14
53	1162.613	45/23
54	1184.5451	111/56
55	1206.4852	261/130	pseudo-2/1
56	1228.4213	61/30
57	1250.3575	243/118
58	1272.2934	171/82
59	1294.2395	207/98
60	1316.1656	15/7
61	1338.1017	13/6
62	1360.0378	351/160
63	1381.9739	20/9
64	1403.91	exact 9/4

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''32EDF''' is the [[EDF|equal division of the just perfect fifth]] into 32 parts of 21.9361 [[cent|cents]] each, corresponding to 54.7044 [[edo]] (similar to every seventh step of [[383edo]]). It is related to the regular temperament which tempers out |127 -127 32&gt; in the 5-limit, which is supported by 164, 383, 547, 711, 875, and 1258 EDOs.
+'''32EDF''' is the [[EDF|equal division of the just perfect fifth]] into 32 parts of 21.9361 [[cent|cents]] each, corresponding to 54.7044 [[edo]] (similar to every seventh step of [[383edo]]).
+It is related to the [[regular temperament]] which [[tempers out]] |127 -127 32&gt; in the [[5-limit]], which is supported by {{EDOs|164, 383, 547, 711, 875, and 1258}} EDOs.
 Lookalikes: [[55edo]], [[87edt]]
+==Harmonics==
+{{Harmonics in equal|32|3|2}}
+{{Harmonics in equal|32|3|2|start=12|collapsed=1}}
 ==Intervals==
-{| class="wikitable"
+{| class="wikitable mw-collapsible"
+|+ Intervals of 32edf
 |-
 ! | degree
@@ Line 337: / Line 344: @@
 |}
+{{todo|expand}}
 [[Category:Edf]]
 [[Category:Edonoi]]