User:Hotcrystal0/Sandbox

← 1ed16/15 2ed16/15 3ed16/15 →
Prime factorization	2 (prime) (highly composite)
Step size	55.8656 ¢
Octave	21\2ed16/15 (1173.18 ¢); (semiconvergent)
Twelfth	34\2ed16/15 (1899.43 ¢) (→ 17\1ed16/15)
Consistency limit	3
Distinct consistency limit	3

← 53ed9/4 55ed9/4 57ed9/4 →
Prime factorization	5 × 11
Step size	25.5256 ¢
Octave	47\55ed9/4 (1199.7 ¢); (convergent)
Twelfth	75\55ed9/4 (1914.42 ¢) (→ 15\11ed9/4)
Consistency limit	3
Distinct consistency limit	3

← 27ed22/7 28ed22/7 29ed22/7 →
Prime factorization	22 × 7
Step size	70.8033 ¢
Octave	17\28ed22/7 (1203.66 ¢); (semiconvergent)
Twelfth	27\28ed22/7 (1911.69 ¢)
Consistency limit	5
Distinct consistency limit	5

{{Infobox Interval|355/113|debug=1 | Name = N/A }} {{Infobox Interval|2187/1250|debug=1 | Name = N/A }} {{Infobox Interval|442/295|debug=1 | Name = N/A }}

~~someone tell me how to insert the infobox without having to add the categories~~
nevermind I figured it out

2187/1250

Edo approximations for Hotcrystal0/Sandbox (968.43 ¢)
*≤ 80edo, relative error ≤ 10%*
Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
5	4\5	960.00	-8.43	-3.51
10	8\10	960.00	-8.43	-7.03
16	13\16	975.00	+6.57	+8.76
21	17\21	971.43	+3.00	+5.25
26	21\26	969.23	+0.80	+1.73
31	25\31	967.74	-0.69	-1.78
36	29\36	966.67	-1.76	-5.29
41	33\41	965.85	-2.58	-8.80
47	38\47	970.21	+1.78	+6.98
52	42\52	969.23	+0.80	+3.47
57	46\57	968.42	-0.01	-0.04
62	50\62	967.74	-0.69	-3.56
67	54\67	967.16	-1.27	-7.07
73	59\73	969.86	+1.43	+8.72
78	63\78	969.23	+0.80	+5.20

140/99

Edo approximations for Hotcrystal0/Sandbox (599.91 ¢)
*≤ 80edo, relative error ≤ 10%*
Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
2	1\2	600.00	+0.09	+0.01
4	2\4	600.00	+0.09	+0.03
6	3\6	600.00	+0.09	+0.04
8	4\8	600.00	+0.09	+0.06
10	5\10	600.00	+0.09	+0.07
12	6\12	600.00	+0.09	+0.09
14	7\14	600.00	+0.09	+0.10
16	8\16	600.00	+0.09	+0.12
18	9\18	600.00	+0.09	+0.13
20	10\20	600.00	+0.09	+0.15
22	11\22	600.00	+0.09	+0.16
24	12\24	600.00	+0.09	+0.18
26	13\26	600.00	+0.09	+0.19
28	14\28	600.00	+0.09	+0.21
30	15\30	600.00	+0.09	+0.22
32	16\32	600.00	+0.09	+0.24
34	17\34	600.00	+0.09	+0.25
36	18\36	600.00	+0.09	+0.26
38	19\38	600.00	+0.09	+0.28
40	20\40	600.00	+0.09	+0.29
42	21\42	600.00	+0.09	+0.31
44	22\44	600.00	+0.09	+0.32
46	23\46	600.00	+0.09	+0.34
48	24\48	600.00	+0.09	+0.35
50	25\50	600.00	+0.09	+0.37
52	26\52	600.00	+0.09	+0.38
54	27\54	600.00	+0.09	+0.40
56	28\56	600.00	+0.09	+0.41
58	29\58	600.00	+0.09	+0.43
60	30\60	600.00	+0.09	+0.44
62	31\62	600.00	+0.09	+0.46
64	32\64	600.00	+0.09	+0.47
66	33\66	600.00	+0.09	+0.49
68	34\68	600.00	+0.09	+0.50
70	35\70	600.00	+0.09	+0.52
72	36\72	600.00	+0.09	+0.53
74	37\74	600.00	+0.09	+0.54
76	38\76	600.00	+0.09	+0.56
78	39\78	600.00	+0.09	+0.57
80	40\80	600.00	+0.09	+0.59

55 equal divisions of 9/4 (abbreviated 55ed9/4) is a nonoctave tuning system that divides the interval of 9/4 into 55 equal parts of about 25.5 ¢ each. Each step represents a frequency ratio of (9/4)^1/55, or the 55th root of 9/4.

Approximation of prime harmonics in 17945edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0000	-0.0102	+0.0000	+0.0011	+0.0334	-0.0261	+0.0321	-0.0040	-0.0214	-0.0314	-0.0035
Error	Relative (%)	+0.0	-15.2	+0.0	+1.6	+50.0	-39.1	+47.9	-5.9	-31.9	-46.9	-5.3
Steps (reduced)		17945 (0)	28442 (10497)	41667 (5777)	50378 (14488)	62080 (8245)	66404 (12569)	73350 (1570)	76229 (4449)	81175 (9395)	87176 (15396)	88903 (17123)

ed16/15 testing

2 equal divisions of 16/15 (abbreviated 2ed16/15) is a nonoctave tuning system that divides the interval of 16/15 into 2 equal parts of about 55.9 ¢ each. Each step represents a frequency ratio of (16/15)^1/2, or the square root of 16/15.

.

← 2ed16/15

3ed16/15

4ed16/15 →

Prime factorization

3 (prime)

Step size

37.2438 ¢

Octave

32\3ed16/15 (1191.8 ¢)
(convergent)

Twelfth

51\3ed16/15 (1899.43 ¢) (→ 17\1ed16/15)

Consistency limit

4

Distinct consistency limit

4

3 equal divisions of 16/15 (abbreviated 3ed16/15) is a nonoctave tuning system that divides the interval of 16/15 into 3 equal parts of about 37.2 ¢ each. Each step represents a frequency ratio of (16/15)^1/3, or the cube root of 16/15.

.

← 3ed16/15

4ed16/15

5ed16/15 →

Prime factorization

2² (highly composite)

Step size

27.9328 ¢

Octave

43\4ed16/15 (1201.11 ¢)
(convergent)

Twelfth

68\4ed16/15 (1899.43 ¢) (→ 17\1ed16/15)

Consistency limit

8

Distinct consistency limit

8

4 equal divisions of 16/15 (abbreviated 4ed16/15) is a nonoctave tuning system that divides the interval of 16/15 into 4 equal parts of about 27.9 ¢ each. Each step represents a frequency ratio of (16/15)^1/4, or the 4th root of 16/15.

.

← 4ed16/15

5ed16/15

6ed16/15 →

Prime factorization

5 (prime)

Step size

22.3463 ¢

Octave

54\5ed16/15 (1206.7 ¢)

Twelfth

85\5ed16/15 (1899.43 ¢) (→ 17\1ed16/15)

Consistency limit

3

Distinct consistency limit

3

5 equal divisions of 16/15 (abbreviated 5ed16/15) is a nonoctave tuning system that divides the interval of 16/15 into 5 equal parts of about 22.3 ¢ each. Each step represents a frequency ratio of (16/15)^1/5, or the 5th root of 16/15.

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