User:BudjarnLambeth/Sooty fox scale: Difference between revisions

← 2ed343/338 3ed343/338 4ed343/338 →
Prime factorization	3 (prime)
Step size	8.47413 ¢
Octave	142\3ed343/338 (1203.33 ¢)
Twelfth	224\3ed343/338 (1898.21 ¢); (semiconvergent)
Consistency limit	2
Distinct consistency limit	2

← 1ed343/338 2ed343/338 3ed343/338 →
Prime factorization	2 (prime) (highly composite)
Step size	12.7112 ¢
Octave	94\2ed343/338 (1194.85 ¢) (→ 47\1ed343/338)
Twelfth	150\2ed343/338 (1906.68 ¢) (→ 75\1ed343/338)
Consistency limit	2
Distinct consistency limit	2

← 0ed343/338 1ed343/338 2ed343/338 →
Prime factorization	n/a
Step size	25.4224 ¢
Octave	47\1ed343/338 (1194.85 ¢)
Twelfth	75\1ed343/338 (1906.68 ¢)
Consistency limit	3
Distinct consistency limit	3

← Older edit Newer edit →

VisualWikitext

Revision as of 20:41, 26 October 2024

This page presents a novelty topic.

It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex.

Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks.

A sooty fox scale^{[idiosyncratic term]} (ed343/338 or syfx^{[idiosyncratic term]}) is an equal-step tuning in which 343/338 is justly tuned and is divided in a given number of equal steps.

This type of scale is named after the Aleutian sooty fox sparrow, taxa #343388 on iNaturalist.

A quick overview of the sooty fox scales:

1syfx = An okay no-7s 17-limit tuning
2syfx = (poor JI approximation)
3syfx = (poor JI approximation)
4syfx = A pretty good no-5s 29-limit tuning
5syfx = An excellent 5-limit tuning, can be extended to 2.3.5.13.17
6syfx = An excellent full 89-limit tuning!
7syfx = (poor JI approximation)
8syfx = An okay no-3s 13-limit tuning
9syfx = An okay full 13-limit tuning
10syfx = An excellent full 47-limit tuning!
11syfx = An okay full 41-limit tuning

The first sooty fox scale

1ed343/338 or 1syfx for short.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	25.4
2	50.8	31/30
3	76.3
4	101.7	18/17
5	127.1	14/13
6	152.5	12/11, 23/21
7	178	10/9, 21/19, 31/28
8	203.4
9	228.8
10	254.2
11	279.6	20/17, 27/23
12	305.1	25/21, 31/26
13	330.5	17/14, 23/19, 29/24
14	355.9
15	381.3
16	406.7	19/15
17	432.2	9/7
18	457.6	13/10, 30/23
19	483	29/22
20	508.4
21	533.9	19/14
22	559.3	18/13
23	584.7	7/5
24	610.1	27/19
25	635.5	13/9
26	661	19/13
27	686.4
28	711.8
29	737.2	23/15, 26/17
30	762.6	14/9, 31/20
31	788.1	30/19
32	813.5
33	838.9
34	864.3	23/14, 28/17
35	889.8	5/3
36	915.2	17/10
37	940.6	31/18
38	966
39	991.4	23/13
40	1016.9	9/5
41	1042.3	31/17
42	1067.7	13/7
43	1093.1
44	1118.5
45	1144
46	1169.4
47	1194.8	2/1

Harmonics

Approximation of harmonics in 1syfx
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-5.1	+4.7	+10.1	+12.4	-7.5	+8.4	+1.6	+12.4	+12.1	-7.8	+3.8
Error	Relative (%)	-20.2	+18.6	+39.9	+48.6	-29.4	+33.0	+6.2	+48.7	+47.7	-30.9	+15.0
Step		47	75	110	133	163	175	193	201	214	229	234

1syfx contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+2.6	+2.8	-3.4	-4.8	-9.5	+8.3	+1.4	-8.5	-7.2	-4.4	+11.3
Error	Relative (%)	+10.1	+11.0	-13.3	-19.0	-37.2	+32.5	+5.5	-33.4	-28.3	-17.5	+44.6
Step		246	253	256	262	270	278	280	286	290	292	298

47edo, 75edt, 28edf for comparison:

Approximation of prime harmonics in 47edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0	-12.6	-3.3	+1.4	+10.4	+2.0	-2.8	+8.9	+10.0	-8.3	+3.9
Error	Relative (%)	+0.0	-49.3	-13.1	+5.4	+40.7	+7.9	-11.1	+34.7	+39.3	-32.5	+15.3
Steps (reduced)		47 (0)	74 (27)	109 (15)	132 (38)	163 (22)	174 (33)	192 (4)	200 (12)	213 (25)	228 (40)	233 (45)

47edo contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+4.0	+5.0	-0.9	-1.7	-5.4	-12.4	+6.5	-2.7	-1.0	+2.0	-7.1
Error	Relative (%)	+15.6	+19.5	-3.4	-6.6	-21.2	-48.4	+25.5	-10.6	-3.8	+7.8	-27.8
Steps (reduced)		245 (10)	252 (17)	255 (20)	261 (26)	269 (34)	276 (41)	279 (44)	285 (3)	289 (7)	291 (9)	296 (14)

Approximation of prime harmonics in 75edt
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-8.1	+0.0	+3.2	+4.0	+7.6	-2.6	-10.6	-0.3	-1.4	+3.1	-10.9
Error	Relative (%)	-32.0	+0.0	+12.7	+15.7	+30.1	-10.4	-41.8	-1.1	-5.4	+12.2	-43.1
Steps (reduced)		47 (47)	75 (0)	110 (35)	133 (58)	164 (14)	175 (25)	193 (43)	201 (51)	214 (64)	230 (5)	234 (9)

75edt contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+12.4	+12.2	+5.8	+4.0	-1.1	-9.3	+9.1	-1.2	-0.1	+2.5	-7.4
Error	Relative (%)	+49.0	+48.2	+23.1	+15.8	-4.4	-36.5	+35.9	-4.6	-0.4	+9.9	-29.3
Steps (reduced)		247 (22)	254 (29)	257 (32)	263 (38)	271 (46)	278 (53)	281 (56)	287 (62)	291 (66)	293 (68)	298 (73)

Approximation of prime harmonics in 28edf
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.4	+3.4	-3.6	-9.5	+10.3	-3.2	+8.7	-8.3	+11.9	+11.7	-3.5
Error	Relative (%)	+13.4	+13.4	-14.2	-37.8	+41.0	-12.6	+34.8	-33.3	+47.4	+46.6	-13.9
Steps (reduced)		48 (20)	76 (20)	111 (27)	134 (22)	166 (26)	177 (9)	196 (0)	203 (7)	217 (21)	233 (9)	237 (13)

28edf contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-9.0	-11.2	+6.6	+3.1	-4.4	+10.5	+2.9	-9.1	-9.2	-7.1	+6.5
Error	Relative (%)	-35.7	-44.6	+26.5	+12.2	-17.4	+42.0	+11.7	-36.1	-36.6	-28.4	+26.1
Steps (reduced)		249 (25)	256 (4)	260 (8)	266 (14)	274 (22)	282 (2)	284 (4)	290 (10)	294 (14)	296 (16)	302 (22)

The second sooty fox scale

2ed343/338 or 2syfx for short.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	12.7
2	25.4
3	38.1	43/42
4	50.8	35/34, 36/35
5	63.6
6	76.3	23/22
7	89	39/37, 41/39
8	101.7
9	114.4	31/29
10	127.1	14/13
11	139.8	13/12, 38/35
12	152.5
13	165.2
14	178	41/37
15	190.7	19/17
16	203.4
17	216.1	17/15, 43/38
18	228.8
19	241.5
20	254.2	22/19
21	266.9	7/6
22	279.6
23	292.3
24	305.1	37/31, 43/36
25	317.8	6/5
26	330.5	23/19
27	343.2
28	355.9	43/35
29	368.6
30	381.3
31	394
32	406.7	19/15, 43/34
33	419.5	37/29
34	432.2
35	444.9	22/17
36	457.6	30/23
37	470.3
38	483	41/31
39	495.7
40	508.4
41	521.1	23/17
42	533.9	34/25
43	546.6
44	559.3	29/21
45	572
46	584.7	7/5
47	597.4	41/29
48	610.1
49	622.8	43/30
50	635.5
51	648.3
52	661	22/15
53	673.7	31/21
54	686.4
55	699.1
56	711.8
57	724.5	35/23, 38/25
58	737.2
59	749.9
60	762.6
61	775.4	36/23
62	788.1
63	800.8
64	813.5
65	826.2	29/18
66	838.9
67	851.6	18/11
68	864.3
69	877
70	889.8
71	902.5	37/22
72	915.2	39/23
73	927.9
74	940.6	31/18, 43/25
75	953.3
76	966
77	978.7	37/21
78	991.4	39/22
79	1004.2	25/14
80	1016.9
81	1029.6
82	1042.3	31/17, 42/23
83	1055	35/19
84	1067.7
85	1080.4
86	1093.1
87	1105.8	36/19
88	1118.5	21/11
89	1131.3	25/13
90	1144	29/15
91	1156.7	41/21
92	1169.4
93	1182.1
94	1194.8

Harmonics

Approximation of harmonics in 2syfx
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-5.15	+4.72	-2.56	-0.36	+5.24	-4.32	+1.57	-0.32	-0.59	+4.86	+3.81
Error	Relative (%)	-40.5	+37.2	-20.2	-2.8	+41.3	-34.0	+12.3	-2.5	-4.7	+38.3	+29.9
Steps (reduced)		94 (0)	150 (0)	219 (1)	265 (1)	327 (1)	349 (1)	386 (0)	401 (1)	427 (1)	459 (1)	468 (0)

2syfx contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+2.57	+2.80	-3.38	-4.84	+3.25	-4.46	+1.39	+4.21	+5.51	-4.45	-1.37
Error	Relative (%)	+20.2	+22.1	-26.6	-38.1	+25.6	-35.1	+10.9	+33.1	+43.3	-35.0	-10.8
Steps (reduced)		492 (0)	506 (0)	512 (0)	524 (0)	541 (1)	555 (1)	560 (0)	573 (1)	581 (1)	584 (0)	595 (1)

94edo, 150edt, 55edf, for comparison:

Approximation of prime harmonics in 94edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.17	-3.33	+1.39	-2.38	+2.03	-2.83	-3.90	-2.74	+4.47	+3.90
Error	Relative (%)	+0.0	+1.4	-26.1	+10.9	-18.7	+15.9	-22.2	-30.5	-21.5	+35.0	+30.6
Steps (reduced)		94 (0)	149 (55)	218 (30)	264 (76)	325 (43)	348 (66)	384 (8)	399 (23)	425 (49)	457 (81)	466 (90)

94edo contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+3.98	+4.98	-0.88	-1.68	-5.42	+0.40	-6.25	-2.71	-0.97	+2.00	+5.68
Error	Relative (%)	+31.1	+39.0	-6.9	-13.1	-42.5	+3.2	-48.9	-21.2	-7.6	+15.6	+44.5
Steps (reduced)		490 (20)	504 (34)	510 (40)	522 (52)	538 (68)	553 (83)	557 (87)	570 (6)	578 (14)	582 (18)	593 (29)

Approximation of prime harmonics in 150edt
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+4.57	+0.00	+3.22	+3.97	-5.06	-2.63	+2.09	-0.27	-1.36	+3.08	+1.74
Error	Relative (%)	+36.1	+0.0	+25.4	+31.3	-39.9	-20.8	+16.5	-2.2	-10.7	+24.3	+13.8
Steps (reduced)		95 (95)	150 (0)	220 (70)	266 (116)	327 (27)	350 (50)	387 (87)	402 (102)	428 (128)	460 (10)	469 (19)

150edt contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.25	-0.45	+5.85	+4.02	-1.11	+3.42	-3.57	-1.16	-0.11	+2.51	+5.24
Error	Relative (%)	-2.0	-3.6	+46.1	+31.7	-8.7	+27.0	-28.2	-9.1	-0.9	+19.8	+41.4
Steps (reduced)		493 (43)	507 (57)	514 (64)	526 (76)	542 (92)	557 (107)	561 (111)	574 (124)	582 (132)	586 (136)	597 (147)

Approximation of prime harmonics in 55edf
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.30	-0.30	-4.02	+0.56	-3.40	+0.93	-4.03	-5.15	-4.08	+3.03	+2.44
Error	Relative (%)	-2.3	-2.3	-31.5	+4.4	-26.7	+7.3	-31.6	-40.3	-31.9	+23.7	+19.1
Steps (reduced)		94 (39)	149 (39)	218 (53)	264 (44)	325 (50)	348 (18)	384 (54)	399 (14)	425 (40)	457 (17)	466 (26)

55edf contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+2.44	+3.40	-2.48	-3.32	+5.65	-1.33	+4.77	-4.50	-2.79	+0.17	+3.81
Error	Relative (%)	+19.1	+26.6	-19.4	-26.0	+44.3	-10.4	+37.4	-35.3	-21.8	+1.3	+29.9
Steps (reduced)		490 (50)	504 (9)	510 (15)	522 (27)	539 (44)	553 (3)	558 (8)	570 (20)	578 (28)	582 (32)	593 (43)

The third sooty fox scale

3ed343/338 or 3syfx for short.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	8.5
2	16.9
3	25.4
4	33.9	50/49
5	42.4	42/41
6	50.8	35/34
7	59.3	30/29
8	67.8	26/25
9	76.3	23/22
10	84.7
11	93.2
12	101.7	52/49
13	110.2	49/46
14	118.6
15	127.1
16	135.6
17	144.1	25/23
18	152.5
19	161	34/31
20	169.5	43/39
21	178	41/37
22	186.4	49/44
23	194.9	47/42
24	203.4
25	211.9	26/23
26	220.3	25/22, 42/37
27	228.8
28	237.3	47/41
29	245.8
30	254.2	22/19
31	262.7
32	271.2	55/47
33	279.7
34	288.1	13/11
35	296.6	51/43
36	305.1	31/26, 37/31
37	313.6
38	322
39	330.5	23/19
40	339
41	347.4
42	355.9
43	364.4	21/17, 37/30
44	372.9	31/25, 36/29
45	381.3
46	389.8
47	398.3
48	406.8
49	415.2	47/37
50	423.7
51	432.2
52	440.7	49/38
53	449.1
54	457.6	43/33
55	466.1	55/42
56	474.6	25/19, 46/35
57	483	41/31
58	491.5
59	500
60	508.5	55/41
61	516.9	31/23
62	525.4	42/31
63	533.9	34/25
64	542.4	26/19, 41/30
65	550.8
66	559.3	29/21, 47/34
67	567.8
68	576.3
69	584.7
70	593.2	31/22
71	601.7	17/12
72	610.2	37/26
73	618.6	10/7
74	627.1
75	635.6
76	644.1
77	652.5	35/24
78	661
79	669.5
80	677.9	34/23, 37/25
81	686.4	52/35, 55/37
82	694.9
83	703.4
84	711.8
85	720.3	47/31
86	728.8
87	737.3
88	745.7
89	754.2	17/11
90	762.7
91	771.2
92	779.6
93	788.1	41/26
94	796.6	19/12
95	805.1	35/22
96	813.5
97	822	37/23
98	830.5	21/13
99	839
100	847.4	31/19
101	855.9	41/25
102	864.4
103	872.9
104	881.3
105	889.8
106	898.3	42/25
107	906.8
108	915.2
109	923.7	29/17
110	932.2	12/7
111	940.7
112	949.1
113	957.6
114	966.1
115	974.6
116	983	30/17
117	991.5	55/31
118	1000	41/23
119	1008.4	34/19
120	1016.9
121	1025.4	47/26
122	1033.9
123	1042.3	42/23
124	1050.8	11/6
125	1059.3
126	1067.8
127	1076.2	41/22
128	1084.7
129	1093.2	47/25
130	1101.7
131	1110.1	19/10
132	1118.6	21/11
133	1127.1	23/12
134	1135.6
135	1144
136	1152.5	37/19
137	1161
138	1169.5
139	1177.9
140	1186.4
141	1194.9
142	1203.4

Harmonics

Approximation of harmonics in 3syfx
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.33	-3.75	+1.68	+3.88	+1.01	-0.08	+1.57	+3.91	+3.64	+0.63	+3.81
Error	Relative (%)	+39.3	-44.2	+19.8	+45.8	+11.9	-1.0	+18.5	+46.2	+43.0	+7.4	+44.9
Steps (reduced)		142 (1)	224 (2)	329 (2)	398 (2)	490 (1)	524 (2)	579 (0)	602 (2)	641 (2)	688 (1)	702 (0)

3syfx contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+2.57	+2.80	-3.38	+3.64	-0.98	-0.22	+1.39	-0.03	+1.27	+4.02	+2.86
Error	Relative (%)	+30.3	+33.1	-39.9	+42.9	-11.6	-2.6	+16.4	-0.3	+15.0	+47.5	+33.8
Steps (reduced)		738 (0)	759 (0)	768 (0)	787 (1)	811 (1)	833 (2)	840 (0)	859 (1)	871 (1)	877 (1)	893 (2)

142edo, 224edt, 83edf for comparison:

Approximation of prime harmonics in 142edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.55	+2.42	+3.01	-2.02	-3.91	-3.55	-1.74	-2.92	+1.41	-4.19
Error	Relative (%)	+0.0	-6.5	+28.6	+35.6	-23.9	-46.2	-42.0	-20.6	-34.6	+16.7	-49.6
Steps (reduced)		142 (0)	225 (83)	330 (46)	399 (115)	491 (65)	525 (99)	580 (12)	603 (35)	642 (74)	690 (122)	703 (135)

142edo contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+2.18	+1.92	+3.98	+2.10	-3.08	-2.83	-1.39	-3.25	-2.23	+0.38	-1.16
Error	Relative (%)	+25.8	+22.8	+47.0	+24.8	-36.5	-33.5	-16.5	-38.5	-26.4	+4.5	-13.7
Steps (reduced)		740 (30)	761 (51)	771 (61)	789 (79)	813 (103)	835 (125)	842 (132)	861 (9)	873 (21)	879 (27)	895 (43)

Approximation of prime harmonics in 224edt
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-2.79	+0.00	-1.31	+2.05	+0.72	+0.20	+2.77	-2.99	-2.61	+3.65	-1.43
Error	Relative (%)	-32.8	+0.0	-15.4	+24.1	+8.5	+2.3	+32.6	-35.2	-30.7	+43.0	-16.8
Steps (reduced)		141 (141)	224 (0)	328 (104)	397 (173)	489 (41)	523 (75)	578 (130)	600 (152)	639 (191)	687 (15)	700 (28)

224edt contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-2.06	-1.47	+0.98	-0.17	+4.10	-3.26	-1.54	-2.63	-1.13	+1.72	+0.83
Error	Relative (%)	-24.3	-17.4	+11.5	-2.0	+48.3	-38.4	-18.1	-31.0	-13.3	+20.3	+9.8
Steps (reduced)		736 (64)	757 (85)	767 (95)	785 (113)	810 (138)	831 (159)	838 (166)	857 (185)	869 (197)	875 (203)	891 (219)

Approximation of prime harmonics in 83edf
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.94	+0.94	-3.87	-2.82	+1.21	-0.45	+0.27	+2.23	+1.31	-2.50	+0.44
Error	Relative (%)	+11.1	+11.1	-45.7	-33.4	+14.3	-5.3	+3.2	+26.4	+15.4	-29.6	+5.2
Steps (reduced)		142 (59)	225 (59)	329 (80)	398 (66)	491 (76)	525 (27)	580 (82)	603 (22)	642 (61)	689 (25)	703 (39)

83edf contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-1.41	-1.52	+0.59	-1.16	+2.27	+2.66	+4.15	+2.42	+3.52	-2.29	-3.72
Error	Relative (%)	-16.6	-18.0	+7.0	-13.7	+26.9	+31.5	+49.1	+28.6	+41.6	-27.1	-44.0
Steps (reduced)		739 (75)	760 (13)	770 (23)	788 (41)	813 (66)	835 (5)	842 (12)	861 (31)	873 (43)	878 (48)	894 (64)

The fourth sooty fox scale

← 3ed343/338

4ed343/338

5ed343/338 →

Prime factorization

2² (highly composite)

Step size

6.3556 ¢

Octave

189\4ed343/338 (1201.21 ¢)
(convergent)

Twelfth

299\4ed343/338 (1900.32 ¢)
(semiconvergent)

Consistency limit

3

Distinct consistency limit

3

4ed343/338 or 4syfx for short.

Harmonics

Approximation of harmonics in 4syfx
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+1.21	-1.63	-2.56	-0.36	-1.11	+2.04	+1.57	-0.32	-0.59	-1.49	-2.55
Error	Relative (%)	+19.0	-25.7	-40.3	-5.6	-17.5	+32.0	+24.7	-5.1	-9.3	-23.5	-40.1
Steps (reduced)		189 (1)	299 (3)	438 (2)	530 (2)	653 (1)	699 (3)	772 (0)	802 (2)	854 (2)	917 (1)	935 (3)

4syfx contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+2.57	+2.80	+2.97	+1.52	-3.10	+1.90	+1.39	-2.15	-0.85	+1.91	-1.37
Error	Relative (%)	+40.4	+44.1	+46.7	+23.9	-48.8	+29.9	+21.8	-33.8	-13.3	+30.0	-21.6
Steps (reduced)		984 (0)	1012 (0)	1025 (1)	1049 (1)	1081 (1)	1111 (3)	1120 (0)	1145 (1)	1161 (1)	1169 (1)	1190 (2)

189edo, 299edt, 110edf for comparison:

Approximation of prime harmonics in 189edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+2.81	+0.99	+2.60	+1.06	-2.43	+2.98	+0.90	+0.30	-1.01	-2.18
Error	Relative (%)	+0.0	+44.2	+15.6	+41.0	+16.7	-38.3	+47.0	+14.2	+4.7	-15.8	-34.3
Steps (reduced)		189 (0)	300 (111)	439 (61)	531 (153)	654 (87)	699 (132)	773 (17)	803 (47)	855 (99)	918 (162)	936 (180)

189edo contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+2.62	+2.68	+2.77	+1.16	+2.69	+1.15	+0.58	-3.12	-1.92	+0.78	-2.63
Error	Relative (%)	+41.3	+42.3	+43.6	+18.3	+42.3	+18.0	+9.1	-49.1	-30.2	+12.3	-41.5
Steps (reduced)		985 (40)	1013 (68)	1026 (81)	1050 (105)	1083 (138)	1112 (167)	1121 (176)	1146 (12)	1162 (28)	1170 (36)	1191 (57)

Approximation of prime harmonics in 299edt
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+2.24	+0.00	-0.17	+2.53	+2.45	-0.51	-0.58	-2.31	-2.30	-2.85	+2.55
Error	Relative (%)	+35.2	+0.0	-2.7	+39.8	+38.5	-8.1	-9.2	-36.3	-36.1	-44.8	+40.1
Steps (reduced)		189 (189)	299 (0)	438 (139)	530 (231)	653 (55)	698 (100)	771 (173)	801 (203)	853 (255)	916 (19)	935 (38)

299edt contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+1.57	+1.96	+2.20	+0.88	+2.79	+1.60	+1.13	-2.26	-0.87	+1.92	-1.24
Error	Relative (%)	+24.7	+30.9	+34.6	+13.8	+43.9	+25.1	+17.8	-35.6	-13.7	+30.2	-19.6
Steps (reduced)		983 (86)	1011 (114)	1024 (127)	1048 (151)	1081 (184)	1110 (213)	1119 (222)	1144 (247)	1160 (263)	1168 (271)	1189 (292)

Approximation of prime harmonics in 110edf
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.30	-0.30	+2.36	+0.56	+2.98	+0.93	+2.35	+1.23	+2.30	+3.03	+2.44
Error	Relative (%)	-4.6	-4.6	+37.0	+8.7	+46.7	+14.6	+36.8	+19.3	+36.1	+47.5	+38.2
Steps (reduced)		188 (78)	298 (78)	437 (107)	528 (88)	651 (101)	696 (36)	769 (109)	799 (29)	851 (81)	914 (34)	932 (52)

110edf contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+2.44	-2.98	-2.48	+3.07	-0.73	-1.33	-1.61	+1.88	-2.79	+0.17	-2.57
Error	Relative (%)	+38.2	-46.8	-38.9	+48.0	-11.4	-20.9	-25.3	+29.5	-43.7	+2.7	-40.2
Steps (reduced)		980 (100)	1007 (17)	1020 (30)	1045 (55)	1077 (87)	1106 (6)	1115 (15)	1141 (41)	1156 (56)	1164 (64)	1185 (85)

The fifth sooty fox scale

← 4ed343/338

5ed343/338

6ed343/338 →

Prime factorization

5 (prime)

Step size

5.08448 ¢

Octave

236\5ed343/338 (1199.94 ¢)
(convergent)

Twelfth

374\5ed343/338 (1901.6 ¢)
(convergent)

Consistency limit

6

Distinct consistency limit

6

5ed343/338 or 5syfx for short.

Harmonics

Approximation of harmonics in 5syfx
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.06	-0.36	-0.02	+2.18	-2.38	-1.78	+1.57	+2.22	+1.95	+2.32	-1.28
Error	Relative (%)	-1.2	-7.1	-0.4	+43.0	-46.9	-35.0	+30.8	+43.7	+38.3	+45.6	-25.2
Steps (reduced)		236 (1)	374 (4)	548 (3)	663 (3)	816 (1)	873 (3)	965 (0)	1003 (3)	1068 (3)	1147 (2)	1169 (4)

5syfx contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-2.52	-2.28	+1.70	+0.25	+0.71	-1.91	+1.39	+1.67	-2.12	+0.63	+1.17
Error	Relative (%)	-49.5	-44.9	+33.4	+4.8	+14.0	-37.7	+27.3	+32.8	-41.6	+12.5	+23.0
Steps (reduced)		1229 (4)	1264 (4)	1281 (1)	1311 (1)	1352 (2)	1388 (3)	1400 (0)	1432 (2)	1451 (1)	1461 (1)	1488 (3)

236edo, 374edt, 138edf for comparison:

Approximation of prime harmonics in 236edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.26	+0.13	+2.36	-2.17	-1.54	+1.82	+2.49	+2.23	-2.46	-0.97
Error	Relative (%)	+0.0	-5.1	+2.5	+46.4	-42.6	-30.4	+35.9	+48.9	+43.9	-48.4	-19.0
Steps (reduced)		236 (0)	374 (138)	548 (76)	663 (191)	816 (108)	873 (165)	965 (21)	1003 (59)	1068 (124)	1146 (202)	1169 (225)

236edo contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-2.19	-1.94	+2.04	+0.60	+1.07	-1.54	+1.76	+2.05	-1.73	+1.02	+1.56
Error	Relative (%)	-43.1	-38.2	+40.2	+11.7	+21.1	-30.4	+34.6	+40.3	-34.0	+20.1	+30.8
Steps (reduced)		1229 (49)	1264 (84)	1281 (101)	1311 (131)	1352 (172)	1388 (208)	1400 (220)	1432 (16)	1451 (35)	1461 (45)	1488 (72)

Approximation of prime harmonics in 374edt
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.16	+0.00	+0.51	-2.26	-1.60	-0.94	+2.50	-1.90	-2.11	-1.66	-0.15
Error	Relative (%)	+3.2	+0.0	+10.0	-44.5	-31.4	-18.4	+49.1	-37.4	-41.5	-32.7	-3.0
Steps (reduced)		236 (236)	374 (0)	548 (174)	662 (288)	816 (68)	873 (125)	965 (217)	1002 (254)	1067 (319)	1146 (24)	1169 (47)

374edt contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-1.34	-1.06	-2.15	+1.51	+2.01	-0.58	-2.35	-2.04	-0.72	+2.04	-2.49
Error	Relative (%)	-26.3	-20.9	-42.3	+29.6	+39.6	-11.4	-46.3	-40.1	-14.2	+40.1	-48.9
Steps (reduced)		1229 (107)	1264 (142)	1280 (158)	1311 (189)	1352 (230)	1388 (266)	1399 (277)	1431 (309)	1451 (329)	1461 (339)	1487 (365)

Approximation of prime harmonics in 138edf
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.44	+0.44	+1.16	-1.48	-0.63	+0.10	-1.44	-0.71	-0.84	-0.30	+1.24
Error	Relative (%)	+8.7	+8.7	+22.8	-29.0	-12.3	+2.0	-28.4	-13.9	-16.5	-5.9	+24.3
Steps (reduced)		236 (98)	374 (98)	548 (134)	662 (110)	816 (126)	873 (45)	964 (136)	1002 (36)	1067 (101)	1146 (42)	1169 (65)

138edf contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.12	+0.44	-0.63	-2.02	-1.47	+1.07	-0.69	-0.34	+1.00	-1.31	-0.72
Error	Relative (%)	+2.5	+8.6	-12.4	-39.7	-28.8	+21.1	-13.5	-6.7	+19.7	-25.7	-14.1
Steps (reduced)		1229 (125)	1264 (22)	1280 (38)	1310 (68)	1351 (109)	1388 (8)	1399 (19)	1431 (51)	1451 (71)	1460 (80)	1487 (107)

The sixth sooty fox scale

← 5ed343/338

6ed343/338

7ed343/338 →

Prime factorization

2 × 3 (highly composite)

Step size

4.23707 ¢

Octave

283\6ed343/338 (1199.09 ¢)

Twelfth

449\6ed343/338 (1902.44 ¢)
(semiconvergent)

Consistency limit

3

Distinct consistency limit

3

6ed343/338 or 6syfx for short.

Harmonics

Approximation of harmonics in 6syfx
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.91	+0.49	+1.68	-0.36	+1.01	-0.08	+1.57	-0.32	-0.59	+0.63	-0.43
Error	Relative (%)	-21.5	+11.5	+39.5	-8.5	+23.8	-1.9	+37.0	-7.6	-14.0	+14.8	-10.2
Steps (reduced)		283 (1)	449 (5)	658 (4)	795 (3)	980 (2)	1048 (4)	1158 (0)	1203 (3)	1281 (3)	1376 (2)	1403 (5)

6syfx contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-1.67	-1.43	+0.85	-0.60	-0.98	-0.22	+1.39	-0.03	+1.27	-0.21	-1.37
Error	Relative (%)	-39.5	-33.8	+20.1	-14.2	-23.2	-5.2	+32.7	-0.7	+30.0	-5.0	-32.4
Steps (reduced)		1475 (5)	1517 (5)	1537 (1)	1573 (1)	1622 (2)	1666 (4)	1680 (0)	1718 (2)	1742 (2)	1753 (1)	1785 (3)

283edo, 449edt, 166edf for comparison:

Approximation of prime harmonics in 283edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+1.93	-0.45	-2.04	-0.08	-0.95	+1.05	-0.69	-0.71	+0.81	-0.16
Error	Relative (%)	+0.0	+45.6	-10.6	-48.1	-1.9	-22.4	+24.8	-16.3	-16.8	+19.1	-3.8
Steps (reduced)		283 (0)	449 (166)	657 (91)	794 (228)	979 (130)	1047 (198)	1157 (25)	1202 (70)	1280 (148)	1375 (243)	1402 (270)

283edo contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-1.17	-0.79	+1.56	+0.22	-0.01	+0.90	-1.69	+1.26	-1.60	+1.19	+0.13
Error	Relative (%)	-27.5	-18.7	+36.7	+5.1	-0.1	+21.2	-39.9	+29.7	-37.8	+28.0	+3.0
Steps (reduced)		1474 (59)	1516 (101)	1536 (121)	1572 (157)	1621 (206)	1665 (250)	1678 (263)	1717 (19)	1740 (42)	1752 (54)	1784 (86)

Approximation of prime harmonics in 449edt
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.22	+0.00	+0.96	-1.22	-0.06	-1.22	+0.31	-1.63	-1.98	-0.87	-1.96
Error	Relative (%)	-28.7	+0.0	+22.7	-28.8	-1.4	-28.8	+7.3	-38.5	-46.8	-20.5	-46.2
Steps (reduced)		283 (283)	449 (0)	658 (209)	795 (346)	980 (82)	1048 (150)	1158 (260)	1203 (305)	1281 (383)	1376 (29)	1403 (56)

449edt contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.96	+1.16	-0.82	+1.93	+1.49	-2.03	-0.44	-1.89	-0.62	-2.12	+0.92
Error	Relative (%)	+22.7	+27.3	-19.3	+45.5	+35.2	-47.9	-10.4	-44.7	-14.6	-50.0	+21.8
Steps (reduced)		1476 (129)	1518 (171)	1537 (190)	1574 (227)	1623 (276)	1666 (319)	1680 (333)	1718 (371)	1742 (395)	1753 (406)	1786 (439)

Approximation of prime harmonics in 166edf
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.94	+0.94	+0.36	+1.40	+1.21	-0.45	+0.27	-2.00	+1.31	+1.72	+0.44
Error	Relative (%)	+22.1	+22.1	+8.6	+33.2	+28.6	-10.7	+6.4	-47.2	+30.9	+40.8	+10.4
Steps (reduced)		284 (118)	450 (118)	659 (161)	797 (133)	982 (152)	1050 (54)	1160 (164)	1205 (43)	1284 (122)	1379 (51)	1406 (78)

166edf contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-1.41	-1.52	+0.59	-1.16	-1.96	-1.56	-0.08	-1.81	-0.71	+1.94	+0.51
Error	Relative (%)	-33.3	-36.0	+14.1	-27.5	-46.3	-37.0	-1.8	-42.8	-16.8	+45.9	+12.0
Steps (reduced)		1478 (150)	1520 (26)	1540 (46)	1576 (82)	1625 (131)	1669 (9)	1683 (23)	1721 (61)	1745 (85)	1757 (97)	1789 (129)

The seventh sooty fox scale

← 6ed343/338

7ed343/338

8ed343/338 →

Prime factorization

7 (prime)

Step size

3.63177 ¢

Octave

330\7ed343/338 (1198.48 ¢)

Twelfth

524\7ed343/338 (1903.05 ¢)

Consistency limit

2

Distinct consistency limit

2

7ed343/338 or 7syfx for short.

Harmonics

Approximation of harmonics in 7syfx
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.52	+1.09	-0.75	+1.46	-0.20	+1.13	+1.57	+1.49	+1.22	-0.58	+0.17
Error	Relative (%)	-41.7	+30.1	-20.5	+40.1	-5.6	+31.1	+43.1	+41.1	+33.7	-16.1	+4.8
Steps (reduced)		330 (1)	524 (6)	767 (4)	928 (4)	1143 (2)	1223 (5)	1351 (0)	1404 (4)	1495 (4)	1605 (2)	1637 (6)

7syfx contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-1.07	-0.83	+0.25	-1.21	+1.44	+0.99	+1.39	-1.24	+0.06	-0.82	+0.44
Error	Relative (%)	-29.4	-22.8	+6.8	-33.2	+39.6	+27.3	+38.2	-34.1	+1.7	-22.5	+12.2
Steps (reduced)		1721 (6)	1770 (6)	1793 (1)	1835 (1)	1893 (3)	1944 (5)	1960 (0)	2004 (2)	2032 (2)	2045 (1)	2083 (4)

320edo, 524edt, 187edf for comparison:

Approximation of prime harmonics in 320edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.71	-0.06	-1.33	-0.07	-0.53	+0.04	-1.26	+1.73	+1.67	-1.29
Error	Relative (%)	+0.0	-18.8	-1.7	-35.4	-1.8	-14.1	+1.2	-33.7	+46.0	+44.6	-34.3
Steps (reduced)		320 (0)	507 (187)	743 (103)	898 (258)	1107 (147)	1184 (224)	1308 (28)	1359 (79)	1448 (168)	1555 (275)	1585 (305)

320edo contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.09	-1.56	-1.52	-1.76	+0.25	-1.67	+0.62	-0.56	+0.30	+0.96	-0.79
Error	Relative (%)	-2.5	-41.7	-40.5	-46.8	+6.5	-44.6	+16.4	-14.9	+8.1	+25.6	-21.0
Steps (reduced)		1667 (67)	1714 (114)	1736 (136)	1777 (177)	1833 (233)	1882 (282)	1898 (298)	1941 (21)	1968 (48)	1981 (61)	2017 (97)

Approximation of prime harmonics in 524edt
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+1.43	+0.00	+1.28	-0.48	+1.04	-1.42	-1.25	-1.44	+1.73	-0.30	+0.39
Error	Relative (%)	+39.3	+0.0	+35.4	-13.2	+28.7	-39.2	-34.5	-39.5	+47.8	-8.3	+10.7
Steps (reduced)		331 (331)	524 (0)	768 (244)	928 (404)	1144 (96)	1223 (175)	1351 (303)	1404 (356)	1496 (448)	1606 (34)	1638 (66)

524edt contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-1.03	-0.89	+0.14	-1.40	+1.12	+0.57	+0.93	-1.79	-0.55	-1.45	-0.27
Error	Relative (%)	-28.3	-24.5	+3.8	-38.7	+30.8	+15.6	+25.6	-49.3	-15.1	-40.1	-7.5
Steps (reduced)		1722 (150)	1771 (199)	1794 (222)	1836 (264)	1894 (322)	1945 (373)	1961 (389)	2005 (433)	2033 (461)	2046 (474)	2084 (512)

Approximation of prime harmonics in 187edf
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+1.21	+1.21	-1.02	-1.69	+0.35	+0.18	+1.22	+0.11	-0.32	+0.03	+0.94
Error	Relative (%)	+32.1	+32.1	-27.1	-45.1	+9.4	+4.9	+32.6	+2.8	-8.6	+0.7	+24.9
Steps (reduced)		320 (133)	507 (133)	742 (181)	897 (149)	1106 (171)	1183 (61)	1307 (185)	1358 (49)	1446 (137)	1553 (57)	1584 (88)

187edf contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-1.32	+1.15	+1.27	+1.19	-0.35	+1.67	+0.26	-0.75	+0.22	+0.92	-0.69
Error	Relative (%)	-35.1	+30.5	+33.9	+31.7	-9.4	+44.5	+7.0	-19.9	+5.7	+24.5	-18.4
Steps (reduced)		1665 (169)	1713 (30)	1735 (52)	1776 (93)	1831 (148)	1881 (11)	1896 (26)	1939 (69)	1966 (96)	1979 (109)	2015 (145)

The eighth sooty fox scale

← 7ed343/338

8ed343/338

9ed343/338 →

Prime factorization

2³

Step size

3.1778 ¢

Octave

378\8ed343/338 (1201.21 ¢) (→ 189\4ed343/338)

Twelfth

599\8ed343/338 (1903.5 ¢)

Consistency limit

3

Distinct consistency limit

3

8ed343/338 or 8syfx for short.

Harmonics

Approximation of harmonics in 8syfx
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+1.21	+1.55	+0.62	-0.36	-1.11	-1.14	+1.57	-0.32	-0.59	-1.49	+0.63
Error	Relative (%)	+38.0	+48.7	+19.4	-11.3	-35.0	-35.9	+49.3	-10.2	-18.7	-47.0	+19.7
Steps (reduced)		378 (2)	599 (7)	877 (5)	1060 (4)	1306 (2)	1397 (5)	1544 (0)	1604 (4)	1708 (4)	1834 (2)	1871 (7)

8syfx contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.61	-0.37	-0.21	+1.52	+0.08	-1.28	+1.39	+1.03	-0.85	-1.27	-1.37
Error	Relative (%)	-19.3	-11.8	-6.5	+47.7	+2.4	-40.2	+43.6	+32.5	-26.6	-40.0	-43.2
Steps (reduced)		1967 (7)	2023 (7)	2049 (1)	2098 (2)	2163 (3)	2221 (5)	2240 (0)	2291 (3)	2322 (2)	2337 (1)	2380 (4)

378edo, 599edt, 221edf for comparison:

Approximation of prime harmonics in 378edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.37	+0.99	-0.57	+1.06	+0.74	-0.19	+0.90	+0.30	-1.01	+1.00
Error	Relative (%)	+0.0	-11.6	+31.1	-18.0	+33.5	+23.4	-6.1	+28.3	+9.4	-31.7	+31.4
Steps (reduced)		378 (0)	599 (221)	878 (122)	1061 (305)	1308 (174)	1399 (265)	1545 (33)	1606 (94)	1710 (198)	1836 (324)	1873 (361)

378edo contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.55	-0.49	-0.41	+1.16	-0.49	+1.15	+0.58	+0.06	+1.26	+0.78	+0.54
Error	Relative (%)	-17.3	-15.5	-12.8	+36.5	-15.4	+36.1	+18.1	+1.8	+39.6	+24.6	+17.1
Steps (reduced)		1969 (79)	2025 (135)	2051 (161)	2100 (210)	2165 (275)	2224 (334)	2242 (352)	2293 (25)	2325 (57)	2340 (72)	2383 (115)

Approximation of prime harmonics in 599edt
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.23	+0.00	+1.53	+0.08	-1.31	-1.57	+0.75	-1.29	+1.35	+0.12	-1.03
Error	Relative (%)	+7.3	+0.0	+48.1	+2.5	-41.2	-49.6	+23.8	-40.6	+42.4	+3.8	-32.4
Steps (reduced)		378 (378)	599 (0)	878 (279)	1061 (462)	1307 (109)	1398 (200)	1545 (347)	1605 (407)	1710 (512)	1836 (39)	1872 (75)

599edt contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.66	+0.75	+0.85	-0.73	+0.84	-0.66	-1.22	+1.47	-0.49	-0.96	-1.17
Error	Relative (%)	+20.7	+23.7	+26.8	-22.9	+26.5	-20.9	-38.5	+46.2	-15.5	-30.1	-36.8
Steps (reduced)		1969 (172)	2025 (228)	2051 (254)	2099 (302)	2165 (368)	2223 (426)	2241 (444)	2293 (496)	2324 (527)	2339 (542)	2382 (585)

Approximation of prime harmonics in 221edf
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.63	+0.63	-0.73	+1.19	+0.06	-0.11	-0.80	+0.40	-0.03	-1.13	+0.94
Error	Relative (%)	+19.8	+19.8	-22.9	+37.6	+2.0	-3.4	-25.2	+12.5	-1.1	-35.5	+29.5
Steps (reduced)		378 (157)	599 (157)	877 (214)	1061 (177)	1307 (202)	1398 (72)	1544 (218)	1605 (58)	1709 (162)	1835 (67)	1872 (104)

221edf contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.45	-0.30	-0.17	+1.48	-0.06	-1.51	+1.13	+0.70	-1.23	+1.50	+1.33
Error	Relative (%)	-14.2	-9.4	-5.4	+46.5	-2.0	-47.4	+35.6	+21.9	-38.7	+47.2	+41.9
Steps (reduced)		1968 (200)	2024 (35)	2050 (61)	2099 (110)	2164 (175)	2222 (12)	2241 (31)	2292 (82)	2323 (113)	2339 (129)	2382 (172)

The ninth sooty fox scale

← 8ed343/338

9ed343/338

10ed343/338 →

Prime factorization

3²

Step size

2.82471 ¢

Octave

425\9ed343/338 (1200.5 ¢)
(semiconvergent)

Twelfth

673\9ed343/338 (1901.03 ¢)

Consistency limit

2

Distinct consistency limit

2

9ed343/338 or 9syfx for short.

Harmonics

Approximation of harmonics in 9syfx
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.50	-0.92	-1.15	+1.05	+1.01	-0.08	-1.26	+1.09	+0.82	+0.63	+0.98
Error	Relative (%)	+17.8	-32.7	-40.7	+37.3	+35.6	-2.9	-44.5	+38.6	+29.0	+22.1	+34.7
Steps (reduced)		425 (2)	673 (7)	986 (5)	1193 (5)	1470 (3)	1572 (6)	1736 (8)	1805 (5)	1922 (5)	2064 (3)	2105 (8)

9syfx contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.26	-0.02	-0.56	+0.81	-0.98	-0.22	+1.39	-0.03	+1.27	+1.20	+0.04
Error	Relative (%)	-9.2	-0.7	-19.8	+28.7	-34.8	-7.8	+49.1	-1.0	+45.0	+42.5	+1.4
Steps (reduced)		2213 (8)	2276 (8)	2305 (1)	2360 (2)	2433 (3)	2499 (6)	2520 (0)	2577 (3)	2613 (3)	2630 (2)	2678 (5)

425edo, 673edt, 249edf for comparison:

Approximation of prime harmonics in 425edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+1.10	+0.51	-0.36	-0.73	+0.88	-0.48	-1.04	+1.37	+1.01	+1.32
Error	Relative (%)	+0.0	+39.1	+18.1	-12.6	-25.8	+31.3	-17.2	-36.9	+48.6	+35.8	+46.7
Steps (reduced)		425 (0)	674 (249)	987 (137)	1193 (343)	1470 (195)	1573 (298)	1737 (37)	1805 (105)	1923 (223)	2065 (365)	2106 (406)

425edo contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.05	+0.11	-0.46	+0.85	-1.03	-0.35	+1.23	-0.25	+1.01	+0.92	-0.30
Error	Relative (%)	-1.8	+4.0	-16.3	+30.0	-36.6	-12.3	+43.7	-8.8	+35.7	+32.5	-10.7
Steps (reduced)		2214 (89)	2277 (152)	2306 (181)	2361 (236)	2434 (309)	2500 (375)	2521 (396)	2578 (28)	2614 (64)	2631 (81)	2679 (129)

Approximation of prime harmonics in 673edt
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+1.09	+0.00	+0.21	-0.13	+0.20	-0.75	+1.13	+0.74	+0.63	+0.64	+1.05
Error	Relative (%)	+38.4	+0.0	+7.3	-4.7	+7.1	-26.5	+39.9	+26.3	+22.4	+22.5	+37.0
Steps (reduced)		425 (425)	673 (0)	986 (313)	1192 (519)	1469 (123)	1571 (225)	1736 (390)	1804 (458)	1921 (575)	2063 (44)	2104 (85)

673edt contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.04	+0.28	-0.22	+1.23	-0.47	+0.39	-0.80	+0.69	-0.79	-0.84	+0.89
Error	Relative (%)	-1.6	+9.9	-7.7	+43.4	-16.5	+13.7	-28.4	+24.3	-27.9	-29.7	+31.6
Steps (reduced)		2212 (193)	2275 (256)	2304 (285)	2359 (340)	2432 (413)	2498 (479)	2518 (499)	2576 (557)	2611 (592)	2628 (609)	2677 (658)

Approximation of prime harmonics in 249edf
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.94	+0.94	-1.05	-0.01	+1.21	-0.45	+0.27	-0.59	+1.31	+0.31	+0.44
Error	Relative (%)	+33.2	+33.2	-37.1	-0.2	+43.0	-16.0	+9.7	-20.8	+46.3	+11.1	+15.6
Steps (reduced)		426 (177)	675 (177)	988 (241)	1195 (199)	1473 (228)	1575 (81)	1740 (246)	1808 (65)	1926 (183)	2068 (76)	2109 (117)

249edf contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-1.41	+1.30	+0.59	-1.16	-0.55	-0.15	+1.33	-0.40	+0.70	+0.53	-0.90
Error	Relative (%)	-49.9	+46.0	+21.1	-41.2	-19.4	-5.5	+47.3	-14.2	+24.8	+18.8	-32.0
Steps (reduced)		2217 (225)	2281 (40)	2310 (69)	2364 (123)	2438 (197)	2504 (14)	2525 (35)	2582 (92)	2618 (128)	2635 (145)	2683 (193)

The tenth sooty fox scale

← 9ed343/338

10ed343/338

11ed343/338 →

Prime factorization

2 × 5

Step size

2.54224 ¢

Octave

472\10ed343/338 (1199.94 ¢) (→ 236\5ed343/338)

Twelfth

748\10ed343/338 (1901.6 ¢) (→ 374\5ed343/338)

Consistency limit

12

Distinct consistency limit

12

10ed343/338 or 10syfx for short.

Harmonics

Approximation of harmonics in 10syfx
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.06	-0.36	-0.02	-0.36	+0.16	+0.76	-0.98	-0.32	-0.59	-0.22	+1.26
Error	Relative (%)	-2.5	-14.2	-0.8	-14.1	+6.3	+30.1	-38.4	-12.7	-23.3	-8.7	+49.7
Steps (reduced)		472 (2)	748 (8)	1096 (6)	1325 (5)	1633 (3)	1747 (7)	1929 (9)	2005 (5)	2135 (5)	2293 (3)	2339 (9)

10syfx contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.02	+0.26	-0.84	+0.25	+0.71	+0.63	-1.16	-0.88	+0.42	+0.63	+1.17
Error	Relative (%)	+0.9	+10.3	-33.1	+9.7	+28.0	+24.7	-45.5	-34.4	+16.7	+25.0	+45.9
Steps (reduced)		2459 (9)	2529 (9)	2561 (1)	2622 (2)	2704 (4)	2777 (7)	2799 (9)	2863 (3)	2903 (3)	2922 (2)	2976 (6)

472edo, 748edt, 276edf for comparison:

Approximation of prime harmonics in 472edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.26	+0.13	-0.18	+0.38	+1.00	-0.72	-0.06	-0.31	+0.08	-0.97
Error	Relative (%)	+0.0	-10.2	+5.0	-7.2	+14.8	+39.2	-28.2	-2.2	-12.1	+3.3	-38.1
Steps (reduced)		472 (0)	748 (276)	1096 (152)	1325 (381)	1633 (217)	1747 (331)	1929 (41)	2005 (117)	2135 (247)	2293 (405)	2338 (450)

472edo contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.35	+0.60	-0.50	+0.60	+1.07	+1.00	-0.78	-0.49	+0.81	+1.02	-0.98
Error	Relative (%)	+13.8	+23.5	-19.7	+23.4	+42.2	+39.2	-30.8	-19.4	+31.9	+40.3	-38.5
Steps (reduced)		2459 (99)	2529 (169)	2561 (201)	2622 (262)	2704 (344)	2777 (417)	2799 (439)	2863 (31)	2903 (71)	2922 (90)	2975 (143)

Approximation of prime harmonics in 748edt
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.16	+0.00	+0.51	+0.28	+0.94	-0.94	-0.05	+0.64	+0.43	+0.88	-0.15
Error	Relative (%)	+6.5	+0.0	+20.0	+11.0	+37.2	-36.9	-1.9	+25.2	+17.1	+34.7	-6.1
Steps (reduced)		472 (472)	748 (0)	1096 (348)	1325 (577)	1633 (137)	1746 (250)	1929 (433)	2005 (509)	2135 (639)	2293 (49)	2338 (94)

748edt contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+1.21	-1.06	+0.39	-1.04	-0.53	-0.58	+0.19	+0.50	-0.72	-0.50	+0.06
Error	Relative (%)	+47.4	-41.9	+15.3	-40.7	-20.9	-22.8	+7.5	+19.7	-28.4	-19.8	+2.2
Steps (reduced)		2459 (215)	2528 (284)	2561 (317)	2621 (377)	2703 (459)	2776 (532)	2799 (555)	2863 (619)	2902 (658)	2921 (677)	2975 (731)

Approximation of prime harmonics in 276edf
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.44	+0.44	+1.16	+1.07	-0.63	+0.10	+1.10	-0.71	-0.84	-0.30	+1.24
Error	Relative (%)	+17.5	+17.5	+45.6	+41.9	-24.7	+4.0	+43.2	-27.9	-33.0	-11.7	+48.6
Steps (reduced)		472 (196)	748 (196)	1096 (268)	1325 (221)	1632 (252)	1746 (90)	1929 (273)	2004 (72)	2134 (202)	2292 (84)	2338 (130)

276edf contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.12	+0.44	-0.63	+0.52	+1.08	+1.07	-0.69	-0.34	+1.00	+1.23	-0.72
Error	Relative (%)	+4.9	+17.2	-24.8	+20.5	+42.3	+42.1	-27.1	-13.3	+39.5	+48.5	-28.2
Steps (reduced)		2458 (250)	2528 (44)	2560 (76)	2621 (137)	2703 (219)	2776 (16)	2798 (38)	2862 (102)	2902 (142)	2921 (161)	2974 (214)

The eleventh sooty fox scale

← 10ed343/338

11ed343/338

12ed343/338 →

Prime factorization

11 (prime)

Step size

2.31113 ¢

Octave

519\11ed343/338 (1199.47 ¢)

Twelfth

823\11ed343/338 (1902.06 ¢)
(convergent)

Consistency limit

4

Distinct consistency limit

4

11ed343/338 or 11syfx for short.

Harmonics

Approximation of harmonics in 11syfx
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.53	+0.10	+0.91	+0.80	-0.53	-0.85	-0.74	+0.83	+0.56	-0.92	-0.82
Error	Relative (%)	-22.7	+4.4	+39.2	+34.5	-23.1	-36.9	-32.2	+36.0	+24.3	-39.6	-35.4
Steps (reduced)		519 (2)	823 (9)	1206 (7)	1458 (6)	1796 (3)	1921 (7)	2122 (10)	2206 (6)	2349 (6)	2522 (3)	2572 (9)

11syfx contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.25	+0.49	-1.07	-0.22	-0.21	-0.99	-0.93	+0.74	-0.27	+0.17	-0.22
Error	Relative (%)	+11.0	+21.3	-46.4	-9.4	-9.2	-42.8	-40.0	+32.1	-11.6	+7.5	-9.5
Steps (reduced)		2705 (10)	2782 (10)	2817 (1)	2884 (2)	2974 (4)	3054 (7)	3079 (10)	3150 (4)	3193 (3)	3214 (2)	3273 (6)

519edo, 823edt, 304edf, for comparison:

Approximation of prime harmonics in 519edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.94	-0.19	-0.04	-1.03	+1.09	-0.91	+0.75	+0.63	-0.68	-0.53
Error	Relative (%)	+0.0	+40.4	-8.1	-1.7	-44.5	+47.2	-39.3	+32.6	+27.1	-29.2	-22.8
Steps (reduced)		519 (0)	823 (304)	1205 (167)	1457 (419)	1795 (238)	1921 (364)	2121 (45)	2205 (129)	2348 (272)	2521 (445)	2571 (495)

519edo contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.68	+1.00	-0.54	+0.39	+0.48	-0.21	-0.12	-0.69	+0.65	+1.11	+0.78
Error	Relative (%)	+29.4	+43.1	-23.1	+16.8	+20.9	-9.2	-5.3	-30.0	+28.1	+48.1	+33.8
Steps (reduced)		2704 (109)	2781 (186)	2816 (221)	2883 (288)	2973 (378)	3053 (458)	3078 (483)	3148 (34)	3192 (78)	3213 (99)	3272 (158)

Approximation of prime harmonics in 823edt
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.59	+0.00	+0.76	+0.62	-0.76	-1.09	-1.01	+0.56	+0.27	+1.08	-1.14
Error	Relative (%)	-25.5	+0.0	+32.7	+26.6	-32.8	-47.3	-43.6	+24.2	+11.7	+46.8	-49.2
Steps (reduced)		519 (519)	823 (0)	1206 (383)	1458 (635)	1796 (150)	1921 (275)	2122 (476)	2206 (560)	2349 (703)	2523 (54)	2572 (103)

823edt contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.08	+0.15	+0.89	-0.58	-0.58	+0.94	+1.00	+0.35	-0.67	-0.23	-0.63
Error	Relative (%)	-3.6	+6.3	+38.4	-24.9	-25.2	+40.7	+43.4	+15.2	-28.8	-9.9	-27.1
Steps (reduced)		2705 (236)	2782 (313)	2818 (349)	2884 (415)	2974 (505)	3055 (586)	3080 (611)	3150 (681)	3193 (724)	3214 (745)	3273 (804)

Approximation of prime harmonics in 304edf
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.71	+0.71	+0.72	+0.10	+0.38	-0.20	-0.51	+0.90	+0.33	+0.81	+0.80
Error	Relative (%)	+30.9	+30.9	+31.4	+4.2	+16.3	-8.7	-21.9	+38.8	+14.4	+34.9	+34.7
Steps (reduced)		520 (216)	824 (216)	1207 (295)	1459 (243)	1798 (278)	1923 (99)	2124 (300)	2208 (80)	2351 (223)	2525 (93)	2575 (143)

304edf contd.
Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.71	-0.63	+0.04	+0.76	+0.57	-0.37	-0.35	-1.14	+0.07	+0.46	-0.05
Error	Relative (%)	-30.8	-27.4	+1.7	+32.8	+24.9	-15.9	-15.3	-49.5	+2.9	+20.1	-2.1
Steps (reduced)		2707 (275)	2784 (48)	2820 (84)	2887 (151)	2977 (241)	3057 (17)	3082 (42)	3152 (112)	3196 (156)	3217 (177)	3276 (236)

@@ Line 1: / Line 1: @@
 {{novelty}}
-A '''sooty fox scale'''{{idiosyncratic}} ('''ed343/338''' or '''syfx'''{{idiosyncratic}}) is an [[equal-step tuning]] in which [[343/338]] is [[Just intonation|justly tuned]] and is divided in a given number of equal steps.
+A '''sooty fox scale'''{{idiosyncratic}} ('''ed343/338''' or '''syfx'''{{idiosyncratic}}) is an [[equal-step tuning]] in which [[343/338]] is [[Just intonation|justly tuned]] and is divided in a given number of equal steps.
 This type of scale is named after the Aleutian sooty fox sparrow, [https://www.inaturalist.org/taxa/343338-Passerella-iliaca-unalaschcensis taxa #343388] on iNaturalist.
@@ Line 26: / Line 26: @@
 === Harmonics ===
-{{Harmonics in equal|1|343|338|intervals=integer|title=Approximation of harmonics in 1syfx}}
+{{Harmonics in equal|1|343|338|intervals=prime|title=Approximation of harmonics in 1syfx}}
-{{Harmonics in equal|1|343|338|intervals=integer|title=1syfx contd.|start=12|collapsed=1}}
+{{Harmonics in equal|1|343|338|intervals=prime|title=1syfx contd.|start=12|collapsed=1}}
 [[47edo]], [[75edt]], [[28edf]] for comparison:
-{{Harmonics in equal|47|intervals=integer|collapsed=1}}
+{{Harmonics in equal|47|intervals=prime|collapsed=1}}
-{{Harmonics in equal|47|intervals=integer|collapsed=1|start=12|title=47edo contd.}}
+{{Harmonics in equal|47|intervals=prime|collapsed=1|start=12|title=47edo contd.}}
-{{Harmonics in equal|75|3|1|intervals=integer|collapsed=1}}
+{{Harmonics in equal|75|3|1|intervals=prime|collapsed=1}}
-{{Harmonics in equal|75|3|1|intervals=integer|collapsed=1|start=12|title=75edt contd.}}
+{{Harmonics in equal|75|3|1|intervals=prime|collapsed=1|start=12|title=75edt contd.}}
-{{Harmonics in equal|28|3|2|intervals=integer|collapsed=1}}
+{{Harmonics in equal|28|3|2|intervals=prime|collapsed=1}}
-{{Harmonics in equal|28|3|2|intervals=integer|collapsed=1|start=12|title=28edf contd.}}
+{{Harmonics in equal|28|3|2|intervals=prime|collapsed=1|start=12|title=28edf contd.}}
 <br>
@@ Line 47: / Line 47: @@
 === Harmonics ===
-{{Harmonics in equal|2|343|338|intervals=integer|title=Approximation of harmonics in 2syfx}}
+{{Harmonics in equal|2|343|338|intervals=prime|title=Approximation of harmonics in 2syfx}}
-{{Harmonics in equal|2|343|338|intervals=integer|title=2syfx contd.|collapsed=1|start=12}}
+{{Harmonics in equal|2|343|338|intervals=prime|title=2syfx contd.|collapsed=1|start=12}}
 [[94edo]], [[150edt]], [[55edf]], for comparison:
-{{Harmonics in equal|94|intervals=integer|collapsed=1}}
+{{Harmonics in equal|94|intervals=prime|collapsed=1}}
-{{Harmonics in equal|94|intervals=integer|collapsed=1|start=12|title=94edo contd.}}
+{{Harmonics in equal|94|intervals=prime|collapsed=1|start=12|title=94edo contd.}}
-{{Harmonics in equal|150|3|1|intervals=integer|collapsed=1}}
+{{Harmonics in equal|150|3|1|intervals=prime|collapsed=1}}
-{{Harmonics in equal|150|3|1|intervals=integer|collapsed=1|start=12|title=150edt contd.}}
+{{Harmonics in equal|150|3|1|intervals=prime|collapsed=1|start=12|title=150edt contd.}}
-{{Harmonics in equal|55|3|2|intervals=integer|collapsed=1}}
+{{Harmonics in equal|55|3|2|intervals=prime|collapsed=1}}
-{{Harmonics in equal|55|3|2|intervals=integer|collapsed=1|start=12|title=55edf contd.}}
+{{Harmonics in equal|55|3|2|intervals=prime|collapsed=1|start=12|title=55edf contd.}}
 <br>
@@ Line 68: / Line 68: @@
 === Harmonics ===
-{{Harmonics in equal|3|343|338|intervals=integer|title=Approximation of harmonics in 3syfx}}
+{{Harmonics in equal|3|343|338|intervals=prime|title=Approximation of harmonics in 3syfx}}
-{{Harmonics in equal|3|343|338|intervals=integer|title=3syfx contd.|collapsed=1|start=12}}
+{{Harmonics in equal|3|343|338|intervals=prime|title=3syfx contd.|collapsed=1|start=12}}
 [[142edo]], [[224edt]], [[83edf]] for comparison:
-{{Harmonics in equal|142|intervals=integer|collapsed=1}}
+{{Harmonics in equal|142|intervals=prime|collapsed=1}}
-{{Harmonics in equal|142|intervals=integer|collapsed=1|start=12|title=142edo contd.}}
+{{Harmonics in equal|142|intervals=prime|collapsed=1|start=12|title=142edo contd.}}
-{{Harmonics in equal|224|3|1|intervals=integer|collapsed=1}}
+{{Harmonics in equal|224|3|1|intervals=prime|collapsed=1}}
-{{Harmonics in equal|224|3|1|intervals=integer|collapsed=1|start=12|title=224edt contd.}}
+{{Harmonics in equal|224|3|1|intervals=prime|collapsed=1|start=12|title=224edt contd.}}
-{{Harmonics in equal|83|3|2|intervals=integer|collapsed=1}}
+{{Harmonics in equal|83|3|2|intervals=prime|collapsed=1}}
-{{Harmonics in equal|83|3|2|intervals=integer|collapsed=1|start=12|title=83edf contd.}}
+{{Harmonics in equal|83|3|2|intervals=prime|collapsed=1|start=12|title=83edf contd.}}
 <br>
@@ Line 86: / Line 86: @@
 === Harmonics ===
-{{Harmonics in equal|4|343|338|intervals=integer|title=Approximation of harmonics in 4syfx}}
+{{Harmonics in equal|4|343|338|intervals=prime|title=Approximation of harmonics in 4syfx}}
-{{Harmonics in equal|4|343|338|intervals=integer|title=4syfx contd.|collapsed=1|start=12}}
+{{Harmonics in equal|4|343|338|intervals=prime|title=4syfx contd.|collapsed=1|start=12}}
 [[189edo]], [[299edt]], [[110edf]] for comparison:
-{{Harmonics in equal|189|intervals=integer|collapsed=1}}
+{{Harmonics in equal|189|intervals=prime|collapsed=1}}
-{{Harmonics in equal|189|intervals=integer|collapsed=1|start=12|title=189edo contd.}}
+{{Harmonics in equal|189|intervals=prime|collapsed=1|start=12|title=189edo contd.}}
-{{Harmonics in equal|299|3|1|intervals=integer|collapsed=1}}
+{{Harmonics in equal|299|3|1|intervals=prime|collapsed=1}}
-{{Harmonics in equal|299|3|1|intervals=integer|collapsed=1|start=12|title=299edt contd.}}
+{{Harmonics in equal|299|3|1|intervals=prime|collapsed=1|start=12|title=299edt contd.}}
-{{Harmonics in equal|110|3|2|intervals=integer|collapsed=1}}
+{{Harmonics in equal|110|3|2|intervals=prime|collapsed=1}}
-{{Harmonics in equal|110|3|2|intervals=integer|collapsed=1|start=12|title=110edf contd.}}
+{{Harmonics in equal|110|3|2|intervals=prime|collapsed=1|start=12|title=110edf contd.}}
 <br>
@@ Line 104: / Line 104: @@
 === Harmonics ===
-{{Harmonics in equal|5|343|338|intervals=integer|title=Approximation of harmonics in 5syfx}}
+{{Harmonics in equal|5|343|338|intervals=prime|title=Approximation of harmonics in 5syfx}}
-{{Harmonics in equal|5|343|338|intervals=integer|title=5syfx contd.|collapsed=1|start=12}}
+{{Harmonics in equal|5|343|338|intervals=prime|title=5syfx contd.|collapsed=1|start=12}}
 [[236edo]], [[374edt]], [[138edf]] for comparison:
-{{Harmonics in equal|236|intervals=integer|collapsed=1}}
+{{Harmonics in equal|236|intervals=prime|collapsed=1}}
-{{Harmonics in equal|236|intervals=integer|collapsed=1||start=12|title=236edo contd.}}
+{{Harmonics in equal|236|intervals=prime|collapsed=1||start=12|title=236edo contd.}}
-{{Harmonics in equal|374|3|1|intervals=integer|collapsed=1}}
+{{Harmonics in equal|374|3|1|intervals=prime|collapsed=1}}
-{{Harmonics in equal|374|3|1|intervals=integer|collapsed=1|start=12|title=374edt contd.}}
+{{Harmonics in equal|374|3|1|intervals=prime|collapsed=1|start=12|title=374edt contd.}}
-{{Harmonics in equal|138|3|2|intervals=integer|collapsed=1}}
+{{Harmonics in equal|138|3|2|intervals=prime|collapsed=1}}
-{{Harmonics in equal|138|3|2|intervals=integer|collapsed=1|start=12|title=138edf contd.}}
+{{Harmonics in equal|138|3|2|intervals=prime|collapsed=1|start=12|title=138edf contd.}}
 <br>
@@ Line 122: / Line 122: @@
 === Harmonics ===
-{{Harmonics in equal|6|343|338|intervals=integer|title=Approximation of harmonics in 6syfx}}
+{{Harmonics in equal|6|343|338|intervals=prime|title=Approximation of harmonics in 6syfx}}
-{{Harmonics in equal|6|343|338|intervals=integer|title=6syfx contd.|collapsed=1|start=12}}
+{{Harmonics in equal|6|343|338|intervals=prime|title=6syfx contd.|collapsed=1|start=12}}
 [[283edo]], [[449edt]], [[166edf]] for comparison:
-{{Harmonics in equal|283|intervals=integer|collapsed=1}}
+{{Harmonics in equal|283|intervals=prime|collapsed=1}}
-{{Harmonics in equal|283|intervals=integer|collapsed=1||start=12|title=283edo contd.}}
+{{Harmonics in equal|283|intervals=prime|collapsed=1||start=12|title=283edo contd.}}
-{{Harmonics in equal|449|3|1|intervals=integer|collapsed=1}}
+{{Harmonics in equal|449|3|1|intervals=prime|collapsed=1}}
-{{Harmonics in equal|449|3|1|intervals=integer|collapsed=1|start=12|title=449edt contd.}}
+{{Harmonics in equal|449|3|1|intervals=prime|collapsed=1|start=12|title=449edt contd.}}
-{{Harmonics in equal|166|3|2|intervals=integer|collapsed=1}}
+{{Harmonics in equal|166|3|2|intervals=prime|collapsed=1}}
-{{Harmonics in equal|166|3|2|intervals=integer|collapsed=1|start=12|title=166edf contd.}}
+{{Harmonics in equal|166|3|2|intervals=prime|collapsed=1|start=12|title=166edf contd.}}
 <br>
@@ Line 140: / Line 140: @@
 === Harmonics ===
-{{Harmonics in equal|7|343|338|intervals=integer|title=Approximation of harmonics in 7syfx}}
+{{Harmonics in equal|7|343|338|intervals=prime|title=Approximation of harmonics in 7syfx}}
-{{Harmonics in equal|7|343|338|intervals=integer|title=7syfx contd.|collapsed=1|start=12}}
+{{Harmonics in equal|7|343|338|intervals=prime|title=7syfx contd.|collapsed=1|start=12}}
 [[320edo]], [[524edt]], [[187edf]] for comparison:
-{{Harmonics in equal|320|intervals=integer|collapsed=1}}
+{{Harmonics in equal|320|intervals=prime|collapsed=1}}
-{{Harmonics in equal|320|intervals=integer|collapsed=1||start=12|title=320edo contd.}}
+{{Harmonics in equal|320|intervals=prime|collapsed=1||start=12|title=320edo contd.}}
-{{Harmonics in equal|524|3|1|intervals=integer|collapsed=1}}
+{{Harmonics in equal|524|3|1|intervals=prime|collapsed=1}}
-{{Harmonics in equal|524|3|1|intervals=integer|collapsed=1|start=12|title=524edt contd.}}
+{{Harmonics in equal|524|3|1|intervals=prime|collapsed=1|start=12|title=524edt contd.}}
-{{Harmonics in equal|187|3|2|intervals=integer|collapsed=1}}
+{{Harmonics in equal|187|3|2|intervals=prime|collapsed=1}}
-{{Harmonics in equal|187|3|2|intervals=integer|collapsed=1|start=12|title=187edf contd.}}
+{{Harmonics in equal|187|3|2|intervals=prime|collapsed=1|start=12|title=187edf contd.}}
 <br>
@@ Line 158: / Line 158: @@
 === Harmonics ===
-{{Harmonics in equal|8|343|338|intervals=integer|title=Approximation of harmonics in 8syfx}}
+{{Harmonics in equal|8|343|338|intervals=prime|title=Approximation of harmonics in 8syfx}}
-{{Harmonics in equal|8|343|338|intervals=integer|title=8syfx contd.|collapsed=1|start=12}}
+{{Harmonics in equal|8|343|338|intervals=prime|title=8syfx contd.|collapsed=1|start=12}}
 [[378edo]], [[599edt]], [[221edf]] for comparison:
-{{Harmonics in equal|378|intervals=integer|collapsed=1}}
+{{Harmonics in equal|378|intervals=prime|collapsed=1}}
-{{Harmonics in equal|378|intervals=integer|collapsed=1||start=12|title=378edo contd.}}
+{{Harmonics in equal|378|intervals=prime|collapsed=1||start=12|title=378edo contd.}}
-{{Harmonics in equal|599|3|1|intervals=integer|collapsed=1}}
+{{Harmonics in equal|599|3|1|intervals=prime|collapsed=1}}
-{{Harmonics in equal|599|3|1|intervals=integer|collapsed=1|start=12|title=599edt contd.}}
+{{Harmonics in equal|599|3|1|intervals=prime|collapsed=1|start=12|title=599edt contd.}}
-{{Harmonics in equal|221|3|2|intervals=integer|collapsed=1}}
+{{Harmonics in equal|221|3|2|intervals=prime|collapsed=1}}
-{{Harmonics in equal|221|3|2|intervals=integer|collapsed=1|start=12|title=221edf contd.}}
+{{Harmonics in equal|221|3|2|intervals=prime|collapsed=1|start=12|title=221edf contd.}}
 <br>
@@ Line 176: / Line 176: @@
 === Harmonics ===
-{{Harmonics in equal|9|343|338|intervals=integer|title=Approximation of harmonics in 9syfx}}
+{{Harmonics in equal|9|343|338|intervals=prime|title=Approximation of harmonics in 9syfx}}
-{{Harmonics in equal|9|343|338|intervals=integer|title=9syfx contd.|collapsed=1|start=12}}
+{{Harmonics in equal|9|343|338|intervals=prime|title=9syfx contd.|collapsed=1|start=12}}
 [[425edo]], [[673edt]], [[249edf]] for comparison:
-{{Harmonics in equal|425|intervals=integer|collapsed=1}}
+{{Harmonics in equal|425|intervals=prime|collapsed=1}}
-{{Harmonics in equal|425|intervals=integer|collapsed=1||start=12|title=425edo contd.}}
+{{Harmonics in equal|425|intervals=prime|collapsed=1||start=12|title=425edo contd.}}
-{{Harmonics in equal|673|3|1|intervals=integer|collapsed=1}}
+{{Harmonics in equal|673|3|1|intervals=prime|collapsed=1}}
-{{Harmonics in equal|673|3|1|intervals=integer|collapsed=1|start=12|title=673edt contd.}}
+{{Harmonics in equal|673|3|1|intervals=prime|collapsed=1|start=12|title=673edt contd.}}
-{{Harmonics in equal|249|3|2|intervals=integer|collapsed=1}}
+{{Harmonics in equal|249|3|2|intervals=prime|collapsed=1}}
-{{Harmonics in equal|249|3|2|intervals=integer|collapsed=1|start=12|title=249edf contd.}}
+{{Harmonics in equal|249|3|2|intervals=prime|collapsed=1|start=12|title=249edf contd.}}
 <br>
@@ Line 194: / Line 194: @@
 === Harmonics ===
-{{Harmonics in equal|10|343|338|intervals=integer|title=Approximation of harmonics in 10syfx}}
+{{Harmonics in equal|10|343|338|intervals=prime|title=Approximation of harmonics in 10syfx}}
-{{Harmonics in equal|10|343|338|intervals=integer|title=10syfx contd.|collapsed=1|start=12}}
+{{Harmonics in equal|10|343|338|intervals=prime|title=10syfx contd.|collapsed=1|start=12}}
 [[472edo]], [[748edt]], [[276edf]] for comparison:
-{{Harmonics in equal|472|intervals=integer|collapsed=1}}
+{{Harmonics in equal|472|intervals=prime|collapsed=1}}
-{{Harmonics in equal|472|intervals=integer|collapsed=1||start=12|title=472edo contd.}}
+{{Harmonics in equal|472|intervals=prime|collapsed=1||start=12|title=472edo contd.}}
-{{Harmonics in equal|748|3|1|intervals=integer|collapsed=1}}
+{{Harmonics in equal|748|3|1|intervals=prime|collapsed=1}}
-{{Harmonics in equal|748|3|1|intervals=integer|collapsed=1|start=12|title=748edt contd.}}
+{{Harmonics in equal|748|3|1|intervals=prime|collapsed=1|start=12|title=748edt contd.}}
-{{Harmonics in equal|276|3|2|intervals=integer|collapsed=1}}
+{{Harmonics in equal|276|3|2|intervals=prime|collapsed=1}}
-{{Harmonics in equal|276|3|2|intervals=integer|collapsed=1|start=12|title=276edf contd.}}
+{{Harmonics in equal|276|3|2|intervals=prime|collapsed=1|start=12|title=276edf contd.}}
 <br>
@@ Line 212: / Line 212: @@
 === Harmonics ===
-{{Harmonics in equal|11|343|338|intervals=integer|title=Approximation of harmonics in 11syfx}}
+{{Harmonics in equal|11|343|338|intervals=prime|title=Approximation of harmonics in 11syfx}}
-{{Harmonics in equal|11|343|338|intervals=integer|title=11syfx contd.|collapsed=1|start=12}}
+{{Harmonics in equal|11|343|338|intervals=prime|title=11syfx contd.|collapsed=1|start=12}}
 [[519edo]], [[823edt]], [[304edf]], for comparison:
-{{Harmonics in equal|519|intervals=integer|collapsed=1}}
+{{Harmonics in equal|519|intervals=prime|collapsed=1}}
-{{Harmonics in equal|519|intervals=integer|collapsed=1||start=12|title=519edo contd.}}
+{{Harmonics in equal|519|intervals=prime|collapsed=1||start=12|title=519edo contd.}}
-{{Harmonics in equal|823|3|1|intervals=integer|collapsed=1}}
+{{Harmonics in equal|823|3|1|intervals=prime|collapsed=1}}
-{{Harmonics in equal|823|3|1|intervals=integer|collapsed=1|start=12|title=823edt contd.}}
+{{Harmonics in equal|823|3|1|intervals=prime|collapsed=1|start=12|title=823edt contd.}}
-{{Harmonics in equal|304|3|2|intervals=integer|collapsed=1}}
+{{Harmonics in equal|304|3|2|intervals=prime|collapsed=1}}
-{{Harmonics in equal|304|3|2|intervals=integer|collapsed=1|start=12|title=304edf contd.}}
+{{Harmonics in equal|304|3|2|intervals=prime|collapsed=1|start=12|title=304edf contd.}}
 [[Category:Equal-step tunings]]

User:BudjarnLambeth/Sooty fox scale: Difference between revisions

Revision as of 20:41, 26 October 2024

Contents

The first sooty fox scale

Intervals

Harmonics

The second sooty fox scale

Intervals

Harmonics

The third sooty fox scale

Intervals

Harmonics

The fourth sooty fox scale

Harmonics

The fifth sooty fox scale

Harmonics

The sixth sooty fox scale

Harmonics

The seventh sooty fox scale

Harmonics

The eighth sooty fox scale

Harmonics

The ninth sooty fox scale

Harmonics

The tenth sooty fox scale

Harmonics

The eleventh sooty fox scale

Harmonics

Navigation menu

User:BudjarnLambeth/Sooty fox scale: Difference between revisions

Revision as of 20:41, 26 October 2024

The first sooty fox scale

Intervals

Harmonics

The second sooty fox scale

Intervals

Harmonics

The third sooty fox scale

Intervals

Harmonics

The fourth sooty fox scale

Harmonics

The fifth sooty fox scale

Harmonics

The sixth sooty fox scale

Harmonics

The seventh sooty fox scale

Harmonics

The eighth sooty fox scale

Harmonics

The ninth sooty fox scale

Harmonics

The tenth sooty fox scale

Harmonics

The eleventh sooty fox scale

Harmonics

Navigation menu

Search