30edf: Difference between revisions

Latest revision as of 19:21, 1 August 2025

Prime factorization

2 × 3 × 5

Step size

23.3985 ¢

Octave

51\30edf (1193.32 ¢) (→ 17\10edf)

Twelfth

81\30edf (1895.28 ¢) (→ 27\10edf)

Consistency limit

3

Distinct consistency limit

3

30EDF is the equal division of the just perfect fifth into 30 parts of 23.3985 cents each, corresponding to 51.2853 edo (practically identical to every seventh step of 359edo).

Approximation of prime harmonics in 30edf
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-6.7	-6.7	-1.9	+0.6	-9.8	+5.2	+8.7	+3.4	+0.2	-3.4	-1.8
Error	Relative (%)	-28.5	-28.5	-8.1	+2.4	-41.8	+22.2	+37.3	+14.4	+0.8	-14.3	-7.8
Steps (reduced)		51 (21)	81 (21)	119 (29)	144 (24)	177 (27)	190 (10)	210 (0)	218 (8)	232 (22)	249 (9)	254 (14)

Approximation of prime harmonics in 30edf
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-3.9	+5.5	-6.7	+3.1	+5.7	+7.2	-3.7	-2.4	-9.2	-10.5	-6.8
Error	Relative (%)	-16.9	+23.6	-28.8	+13.1	+24.2	+30.7	-16.0	-10.1	-39.2	-44.7	-29.2
Steps (reduced)		267 (27)	275 (5)	278 (8)	285 (15)	294 (24)	302 (2)	304 (4)	311 (11)	315 (15)	317 (17)	323 (23)

Intervals of 30edf
degree	cents value	corresponding JI intervals	comments
0		exact 1/1
1	23.3985	76/75
2	46.797	77/75
3	70.1955	25/24
4	93.594	19/18
5	116.9925	15/14
6	140.391	13/12
7	163.7895	11/10
8	187.188	39/35
9	210.5865	35/31
10	233.985	8/7
11	257.3835	29/25
12	280.782	20/17
13	304.1805	31/26
14	327.579	29/24
15	350.9775	60/49, 49/40
16	374.376	36/29
17	397.7745	39/31
18	421.173	51/40
19	444.5715
20	467.97	21/16
21	491.3685
22	514.767	35/26
23	538.1655	15/11
24	561.564	18/13
25	584.9625	7/5
26	608.361	27/19
27	631.7595	36/25
28	655.158
29	678.5565	40/27
30	701.955	exact 3/2	just perfect fifth
31	725.3535	38/25
32	748.752	77/50
33	772.1505	25/16
34	795.549	19/12
35	818.9475	45/28
36	842.346	13/8
37	865.7445	33/20
38	889.143	117/70
39	912.8415	105/62
40	935.94	12/7
41	959.3385	87/50
42	982.737	30/17
43	1006.1355	93/52
44	1028.534	29/16
45	1052.9325	90/49, 147/80
46	1076.331	48/29
47	1099.6995	117/62
48	1123.128	153/80
49	1146.5165
50	1169.925	63/32
51	1193.3435
52	1215.722	105/52
53	1240.1205	45/22
54	1263.519	27/13
55	1286.9175	21/10
56	1310.316	81/38
57	1333.7145	54/25
58	1357.113
59	1380.5115	20/9
60	1403.91	exact 9/4

@@ Line 1: / Line 1: @@
+{{Infobox ET}}
+{{todo|improve synopsis|text=Make the synopsis longer, add a couple paragraphs about the practical music making properties of the tuning}}
 '''30EDF''' is the [[EDF|equal division of the just perfect fifth]] into 30 parts of 23.3985 [[cent|cents]] each, corresponding to 51.2853 [[edo]] (practically identical to every seventh step of [[359edo]]).
+==Harmonics==
+{{Harmonics in equal|30|3|2|intervals=prime}}
+{{Harmonics in equal|30|3|2|intervals=prime|start=12|collapsed=1}}
 ==Intervals==
-{| class="wikitable"
+{| class="wikitable mw-collapsible"
+|+ Intervals of 30edf
 |-
 ! | degree
@@ Line 313: / Line 320: @@
 |
 |}
-[[Category:Edf]]
-[[Category:Edonoi]]