Sooty fox scale

This page presents a novelty topic. It features ideas which are less likely to find practical applications in xenharmonic music. It may contain numbers that are impractically large, exceedingly complex, or chosen arbitrarily. Novelty topics are often developed by a single person or a small group. As such, this page may also feature idiosyncratic terms, notations, 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.

Overview

A quick overview of the sooty fox scales:

• 1syfx = An excellent tuning for the equalizer subgroup 2.3.31.37.41.43.47. Alternatively, an okay dual-7 17-limit tuning
• 2syfx = An okay dual-11 tuning for the 5.7.11.13.17.19.23 subgroup
• 3syfx = An okay dual-7 tuning for the 5.7.11.13.17 subgroup
• 4syfx = An excellent tuning for the equalizer subgroup 2.3.17.19.23.29. Alternatively, an okay dual-5 29-limit tuning.
• 5syfx = An excellent 5-limit tuning, also an excellent tuning for several different equalizer subgroups including 2.3.5.47.53.73.79.103.106.131.137
• 6syfx = An excellent full 79-limit tuning
• 7syfx = (poor JI approximation)
• 8syfx = An okay dual-3 13-limit tuning
• 9syfx = An okay full 13-limit tuning
• 10syfx = An excellent no-31s 73-limit tuning
• 11syfx = An excellent tuning for the equalizer subgroup 2.3.71.73.79.83. Alternatively, an okay full 41-limit tuning
• 12syfx = An okay dual-2, dual-11 41-limit tuning

The first sooty fox scale

← 0ed343/338

1ed343/338

2ed343/338 →

Prime factorization	n/a
Step size	25.4224¢
Octave	47\1ed343/338 (1194.85¢) (convergent)
Twelfth	75\1ed343/338 (1906.68¢) (convergent)
Consistency limit	3
Distinct consistency limit	1
Special properties	Highly composite

1ed343/338 or 1syfx for short.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	25.422
2	50.843	31/30
3	76.265
4	101.686	18/17
5	127.108	14/13
6	152.53	12/11, 23/21
7	177.951	10/9, 21/19, 31/28
8	203.373
9	228.794
10	254.216
11	279.637	20/17, 27/23
12	305.059	25/21, 31/26
13	330.481	17/14, 23/19, 29/24
14	355.902
15	381.324
16	406.745	19/15
17	432.167	9/7
18	457.589	13/10, 30/23
19	483.01	29/22
20	508.432
21	533.853	19/14
22	559.275	18/13
23	584.697	7/5
24	610.118	27/19
25	635.54	13/9
26	660.961	19/13
27	686.383
28	711.804
29	737.226	23/15, 26/17
30	762.648	14/9, 31/20
31	788.069	30/19
32	813.491
33	838.912
34	864.334	23/14, 28/17
35	889.756	5/3
36	915.177	17/10
37	940.599	31/18
38	966.02
39	991.442	23/13
40	1016.863	9/5
41	1042.285	31/17
42	1067.707	13/7
43	1093.128
44	1118.55
45	1143.971
46	1169.393
47	1194.815	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
	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
	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, 110ed5, 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
	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
	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
	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
	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 110ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-9.5	-2.2	+0.0	+0.1	+2.8	-7.8	+9.1	-6.2	-7.6	-3.6	+7.5
	Relative (%)	-37.4	-8.7	+0.0	+0.3	+11.1	-30.6	+35.9	-24.3	-30.1	-14.4	+29.8
Steps (reduced)		47 (47)	75 (75)	110 (0)	133 (23)	164 (54)	175 (65)	194 (84)	201 (91)	214 (104)	230 (10)	235 (15)

110ed5 contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+5.2	+4.8	-1.7	-3.7	-9.0	+7.9	+0.9	-9.6	-8.6	-6.1	+9.2
	Relative (%)	+20.5	+18.9	-6.6	-14.5	-35.7	+31.3	+3.5	-37.7	-34.1	-23.9	+36.2
Steps (reduced)		247 (27)	254 (34)	257 (37)	263 (43)	271 (51)	279 (59)	281 (61)	287 (67)	291 (71)	293 (73)	299 (79)

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
	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
	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

← 1ed343/338

2ed343/338

3ed343/338 →

Prime factorization	2 (prime)
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	1
Special properties	Highly composite

2ed343/338 or 2syfx for short.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	12.711
2	25.422
3	38.132	43/42
4	50.843	35/34, 36/35
5	63.554
6	76.265	23/22
7	88.976	39/37, 41/39
8	101.686
9	114.397	31/29
10	127.108	14/13
11	139.819	13/12, 38/35
12	152.53
13	165.24
14	177.951	41/37
15	190.662	19/17
16	203.373
17	216.083	17/15, 43/38
18	228.794
19	241.505
20	254.216	22/19
21	266.927	7/6
22	279.637
23	292.348
24	305.059	37/31, 43/36
25	317.77	6/5
26	330.481	23/19
27	343.191
28	355.902	43/35
29	368.613
30	381.324
31	394.035
32	406.745	19/15, 43/34
33	419.456	37/29
34	432.167
35	444.878	22/17
36	457.589	30/23
37	470.299
38	483.01	41/31
39	495.721
40	508.432
41	521.143	23/17
42	533.853	34/25
43	546.564
44	559.275	29/21
45	571.986
46	584.697	7/5
47	597.407	41/29
48	610.118
49	622.829	43/30
50	635.54
51	648.25
52	660.961	22/15
53	673.672	31/21
54	686.383
55	699.094
56	711.804
57	724.515	35/23, 38/25
58	737.226
59	749.937
60	762.648
61	775.358	36/23
62	788.069
63	800.78
64	813.491
65	826.202	29/18
66	838.912
67	851.623	18/11
68	864.334
69	877.045
70	889.756
71	902.466	37/22
72	915.177	39/23
73	927.888
74	940.599	31/18, 43/25
75	953.31
76	966.02
77	978.731	37/21
78	991.442	39/22
79	1004.153	25/14
80	1016.863
81	1029.574
82	1042.285	31/17, 42/23
83	1054.996	35/19
84	1067.707
85	1080.417
86	1093.128
87	1105.839	36/19
88	1118.55	21/11
89	1131.261	25/13
90	1143.971	29/15
91	1156.682	41/21
92	1169.393
93	1182.104
94	1194.815

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
	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
	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, 219ed5, 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
	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
	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
	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
	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 219ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-4.05	-6.24	+0.00	+2.74	-3.65	-0.24	+6.08	+4.37	+4.40	-2.49	-3.44
	Relative (%)	-31.8	-49.1	+0.0	+21.5	-28.7	-1.9	+47.8	+34.3	+34.6	-19.6	-27.1
Steps (reduced)		94 (94)	149 (149)	219 (0)	265 (46)	326 (107)	349 (130)	386 (167)	401 (182)	427 (208)	458 (20)	467 (29)

219ed5 contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-4.40	-4.00	+2.60	+1.29	-3.14	+2.03	-4.79	-1.81	-0.42	+2.38	+5.58
	Relative (%)	-34.6	-31.4	+20.5	+10.1	-24.7	+16.0	-37.6	-14.2	-3.3	+18.7	+43.9
Steps (reduced)		491 (53)	505 (67)	512 (74)	524 (86)	540 (102)	555 (117)	559 (121)	572 (134)	580 (142)	584 (146)	595 (157)

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
	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
	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

← 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

3ed343/338 or 3syfx for short.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	8.474
2	16.949
3	25.423
4	33.897	50/49
5	42.372	42/41
6	50.846	35/34
7	59.32	30/29
8	67.795	26/25
9	76.269	23/22
10	84.744
11	93.218
12	101.692	52/49
13	110.167	49/46
14	118.641
15	127.115
16	135.59
17	144.064	25/23
18	152.538
19	161.013	34/31
20	169.487	43/39
21	177.961	41/37
22	186.436	49/44
23	194.91	47/42
24	203.384
25	211.859	26/23
26	220.333	25/22, 42/37
27	228.807
28	237.282	47/41
29	245.756
30	254.231	22/19
31	262.705
32	271.179	55/47
33	279.654
34	288.128	13/11
35	296.602	51/43
36	305.077	31/26, 37/31
37	313.551
38	322.025
39	330.5	23/19
40	338.974
41	347.448
42	355.923
43	364.397	21/17, 37/30
44	372.871	31/25, 36/29
45	381.346
46	389.82
47	398.294
48	406.769
49	415.243	47/37
50	423.718
51	432.192
52	440.666	49/38
53	449.141
54	457.615	43/33
55	466.089	55/42
56	474.564	25/19, 46/35
57	483.038	41/31
58	491.512
59	499.987
60	508.461	55/41
61	516.935	31/23
62	525.41	42/31
63	533.884	34/25
64	542.358	26/19, 41/30
65	550.833
66	559.307	29/21, 47/34
67	567.781
68	576.256
69	584.73
70	593.205	31/22
71	601.679	17/12
72	610.153	37/26
73	618.628	10/7
74	627.102
75	635.576
76	644.051
77	652.525	35/24
78	660.999
79	669.474
80	677.948	34/23, 37/25
81	686.422	52/35, 55/37
82	694.897
83	703.371
84	711.845
85	720.32	47/31
86	728.794
87	737.268
88	745.743
89	754.217	17/11
90	762.692
91	771.166
92	779.64
93	788.115	41/26
94	796.589	19/12
95	805.063	35/22
96	813.538
97	822.012	37/23
98	830.486	21/13
99	838.961
100	847.435	31/19
101	855.909	41/25
102	864.384
103	872.858
104	881.332
105	889.807
106	898.281	42/25
107	906.755
108	915.23
109	923.704	29/17
110	932.179	12/7
111	940.653
112	949.127
113	957.602
114	966.076
115	974.55
116	983.025	30/17
117	991.499	55/31
118	999.973	41/23
119	1008.448	34/19
120	1016.922
121	1025.396	47/26
122	1033.871
123	1042.345	42/23
124	1050.819	11/6
125	1059.294
126	1067.768
127	1076.242	41/22
128	1084.717
129	1093.191	47/25
130	1101.666
131	1110.14	19/10
132	1118.614	21/11
133	1127.089	23/12
134	1135.563
135	1144.037
136	1152.512	37/19
137	1160.986
138	1169.46
139	1177.935
140	1186.409
141	1194.883
142	1203.358

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
	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
	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, 329ed5, 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
	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
	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
	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
	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 329ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+2.60	+3.58	+0.00	+1.85	-1.49	-2.75	-1.38	+0.85	+0.38	-2.88	+0.23
	Relative (%)	+30.7	+42.3	+0.0	+21.9	-17.6	-32.5	-16.3	+10.0	+4.5	-34.0	+2.7
Steps (reduced)		142 (142)	225 (225)	329 (0)	398 (69)	490 (161)	524 (195)	579 (250)	602 (273)	641 (312)	688 (30)	702 (44)

329ed5 contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-1.19	-1.06	+1.17	-0.37	+3.35	+4.01	-2.89	+4.07	-3.16	-0.44	-1.69
	Relative (%)	-14.1	-12.5	+13.9	-4.4	+39.6	+47.3	-34.2	+48.0	-37.4	-5.2	-19.9
Steps (reduced)		738 (80)	759 (101)	769 (111)	787 (129)	812 (154)	834 (176)	840 (182)	860 (202)	871 (213)	877 (219)	893 (235)

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
	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
	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
Step size	6.3556¢
Octave	189\4ed343/338 (1201.21¢) (convergent)
Twelfth	299\4ed343/338 (1900.32¢) (semiconvergent)
Consistency limit	3
Distinct consistency limit	2
Special properties	Highly composite

4ed343/338 or 4syfx for short.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	6.356
2	12.711
3	19.067
4	25.422
5	31.778	49/48, 50/49
6	38.134	51/50, 52/51
7	44.489	35/34, 39/38, 40/39
8	50.845	36/35
9	57.201	34/33
10	63.556
11	69.912	51/49
12	76.267	23/22, 24/23
13	82.623	21/20, 22/21
14	88.979	20/19
15	95.334	18/17, 19/18
16	101.69	17/16, 35/33
17	108.045	49/46, 52/49
18	114.401	15/14
19	120.757
20	127.112	14/13
21	133.468	27/25
22	139.824	13/12, 25/23
23	146.179	38/35
24	152.535	12/11, 49/45
25	158.89	23/21
26	165.246	11/10, 54/49
27	171.602	21/19
28	177.957	51/46
29	184.313	10/9, 49/44
30	190.668	19/17, 39/35
31	197.024
32	203.38
33	209.735	44/39
34	216.091	25/22, 26/23
35	222.447	17/15
36	228.802
37	235.158	8/7, 39/34
38	241.513	15/13, 23/20
39	247.869	38/33
40	254.225	22/19, 51/44
41	260.58
42	266.936	7/6
43	273.291	27/23
44	279.647	20/17, 33/28
45	286.003	46/39
46	292.358	13/11, 19/16
47	298.714	25/21
48	305.07
49	311.425
50	317.781	6/5
51	324.136
52	330.492	23/19
53	336.848	17/14, 39/32, 40/33
54	343.203	28/23
55	349.559	11/9, 27/22, 49/40
56	355.915
57	362.27	16/13, 21/17
58	368.626
59	374.981	26/21
60	381.337	5/4
61	387.693
62	394.048	49/39
63	400.404	44/35
64	406.759	24/19, 33/26
65	413.115	19/15
66	419.471	14/11, 51/40
67	425.826	23/18, 50/39
68	432.182	9/7
69	438.538	49/38
70	444.893	22/17
71	451.249	35/27
72	457.604	13/10, 30/23
73	463.96	17/13
74	470.316	25/19
75	476.671	46/35
76	483.027	33/25
77	489.382
78	495.738
79	502.094	4/3
80	508.449	35/26, 51/38
81	514.805	27/20
82	521.161	23/17
83	527.516	19/14
84	533.872	15/11, 49/36
85	540.227
86	546.583	11/8, 26/19
87	552.939	48/35
88	559.294	18/13
89	565.65	25/18
90	572.005	39/28
91	578.361	46/33
92	584.717	7/5
93	591.072
94	597.428	24/17, 38/27
95	603.784	17/12, 27/19
96	610.139
97	616.495	10/7
98	622.85	23/16, 33/23
99	629.206	49/34
100	635.562	36/25
101	641.917	13/9
102	648.273	35/24
103	654.628	16/11, 19/13, 51/35
104	660.984
105	667.34	22/15
106	673.695	28/19
107	680.051	34/23
108	686.407	40/27, 49/33
109	692.762
110	699.118	3/2
111	705.473
112	711.829
113	718.185	50/33
114	724.54	35/23
115	730.896	38/25
116	737.251	26/17
117	743.607	20/13, 23/15
118	749.963	54/35
119	756.318	17/11
120	762.674
121	769.03	14/9
122	775.385	36/23, 39/25
123	781.741	11/7
124	788.096	30/19
125	794.452	19/12
126	800.808	35/22, 51/32
127	807.163
128	813.519
129	819.874	8/5
130	826.23	21/13
131	832.586
132	838.941	13/8, 34/21
133	845.297
134	851.653	18/11, 44/27, 49/30
135	858.008	23/14
136	864.364	28/17, 33/20
137	870.719	38/23
138	877.075
139	883.431	5/3
140	889.786
141	896.142
142	902.497	42/25
143	908.853	22/13
144	915.209	39/23
145	921.564	17/10
146	927.92	46/27
147	934.276	12/7
148	940.631
149	946.987	19/11
150	953.342	33/19
151	959.698	40/23
152	966.054	7/4
153	972.409
154	978.765	30/17
155	985.12	23/13
156	991.476	39/22
157	997.832	25/14
158	1004.187
159	1010.543	34/19
160	1016.899	9/5
161	1023.254
162	1029.61	38/21
163	1035.965	20/11, 49/27, 51/28
164	1042.321	42/23
165	1048.677	11/6
166	1055.032	35/19
167	1061.388	24/13, 46/25
168	1067.744	50/27
169	1074.099	13/7
170	1080.455
171	1086.81	28/15
172	1093.166	49/26
173	1099.522	32/17
174	1105.877	17/9, 36/19
175	1112.233	19/10
176	1118.588	21/11, 40/21
177	1124.944	23/12, 44/23
178	1131.3	27/14
179	1137.655
180	1144.011	33/17
181	1150.367	35/18
182	1156.722	39/20, 45/23
183	1163.078	51/26
184	1169.433	49/25
185	1175.789
186	1182.145
187	1188.5
188	1194.856
189	1201.211	2/1

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
	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
	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, 438ed5, 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
	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
	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
	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
	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 438ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+2.31	+0.12	+0.00	+2.74	+2.71	-0.24	-0.28	-1.99	-1.96	-2.49	+2.92
	Relative (%)	+36.4	+1.8	+0.0	+43.1	+42.6	-3.7	-4.4	-31.3	-30.8	-39.2	+45.9
Steps (reduced)		189 (189)	299 (299)	438 (0)	530 (92)	653 (215)	698 (260)	771 (333)	801 (363)	853 (415)	916 (40)	935 (59)

438ed5 contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+1.96	+2.36	+2.60	+1.29	-3.14	+2.03	+1.57	-1.81	-0.42	+2.38	-0.78
	Relative (%)	+30.8	+37.1	+40.9	+20.3	-49.4	+32.0	+24.7	-28.5	-6.6	+37.4	-12.2
Steps (reduced)		983 (107)	1011 (135)	1024 (148)	1048 (172)	1080 (204)	1110 (234)	1119 (243)	1144 (268)	1160 (284)	1168 (292)	1189 (313)

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
	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
	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	2

5ed343/338 or 5syfx for short.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	5.085
2	10.169
3	15.254
4	20.338
5	25.423
6	30.507	50/49, 52/51
7	35.592	51/50
8	40.676	39/38, 45/44, 46/45, 49/48
9	45.761	36/35, 40/39
10	50.845	33/32, 35/34
11	55.93	34/33
12	61.014
13	66.099	26/25, 27/26, 28/27, 51/49
14	71.183	24/23, 25/24
15	76.268	22/21
16	81.352	23/22
17	86.437	20/19, 21/20
18	91.521
19	96.606	18/17, 19/18
20	101.69
21	106.775	17/16, 35/33
22	111.859	16/15, 49/46
23	116.944	15/14
24	122.028
25	127.113
26	132.197	14/13, 27/25
27	137.282	13/12
28	142.366	25/23, 38/35
29	147.451
30	152.535	12/11
31	157.62	23/21, 35/32
32	162.704	11/10
33	167.789
34	172.873	21/19
35	177.958	51/46
36	183.042	10/9, 39/35
37	188.127
38	193.211	19/17
39	198.296	28/25
40	203.38	9/8
41	208.465	26/23, 44/39
42	213.549
43	218.634	17/15
44	223.718	25/22
45	228.803	8/7
46	233.887	39/34
47	238.972
48	244.056	23/20
49	249.141	15/13, 22/19, 38/33, 52/45
50	254.225
51	259.31	51/44
52	264.394
53	269.479	7/6
54	274.563	27/23
55	279.648	20/17, 33/28
56	284.732
57	289.817	13/11, 45/38, 46/39
58	294.901	32/27
59	299.986	19/16, 25/21
60	305.07
61	310.155
62	315.239	6/5
63	320.324
64	325.408
65	330.493	23/19
66	335.577	17/14, 40/33
67	340.662	28/23, 39/32
68	345.746	11/9
69	350.831
70	355.915	27/22, 49/40
71	361	16/13
72	366.084	21/17, 26/21
73	371.169
74	376.253
75	381.338
76	386.422	5/4
77	391.507	44/35
78	396.591
79	401.676	24/19, 34/27
80	406.76
81	411.845	19/15, 33/26
82	416.929
83	422.014	14/11, 51/40
84	427.098	23/18, 32/25
85	432.183	9/7, 50/39
86	437.267
87	442.352	22/17, 49/38
88	447.436
89	452.521	13/10, 35/27
90	457.605	30/23
91	462.69
92	467.774	17/13
93	472.859	21/16, 25/19, 46/35
94	477.943	33/25
95	483.028	45/34
96	488.112
97	493.197
98	498.281	4/3
99	503.366
100	508.45	51/38
101	513.535
102	518.619	27/20, 35/26
103	523.704	23/17
104	528.788	19/14
105	533.873	34/25
106	538.957	15/11, 26/19
107	544.042	48/35
108	549.126	11/8
109	554.211
110	559.295
111	564.38	18/13
112	569.464	25/18, 32/23, 39/28
113	574.549
114	579.633	46/33
115	584.718	7/5
116	589.802	45/32
117	594.887	24/17, 38/27
118	599.971
119	605.056	17/12, 27/19
120	610.14
121	615.225	10/7
122	620.309	33/23
123	625.394
124	630.478	23/16, 36/25
125	635.563	13/9, 49/34
126	640.647
127	645.732
128	650.816	16/11, 51/35
129	655.901	35/24
130	660.985	19/13, 22/15
131	666.07	25/17
132	671.154	28/19
133	676.239	34/23
134	681.323	40/27, 52/35
135	686.408
136	691.492
137	696.577
138	701.661	3/2
139	706.746
140	711.83
141	716.915
142	721.999	50/33
143	727.084	32/21, 35/23, 38/25
144	732.168	26/17
145	737.253
146	742.337	23/15, 49/32
147	747.422	20/13, 54/35
148	752.506
149	757.591	17/11
150	762.675
151	767.76	14/9, 39/25
152	772.844	25/16, 36/23
153	777.929	11/7
154	783.013
155	788.098	30/19, 52/33
156	793.182
157	798.267	19/12, 27/17
158	803.351
159	808.436	35/22, 51/32
160	813.52	8/5
161	818.605	45/28
162	823.689
163	828.774
164	833.858	21/13, 34/21
165	838.943	13/8
166	844.027	44/27
167	849.112
168	854.196	18/11, 49/30
169	859.281	23/14
170	864.365	28/17, 33/20
171	869.45	38/23
172	874.534
173	879.619
174	884.703	5/3
175	889.788
176	894.872
177	899.957	32/19, 42/25
178	905.041	27/16
179	910.126	22/13, 39/23
180	915.21
181	920.295	17/10
182	925.379	46/27
183	930.464	12/7
184	935.548
185	940.633
186	945.717
187	950.802	19/11, 26/15, 33/19, 45/26
188	955.886	40/23
189	960.971
190	966.055
191	971.14	7/4
192	976.224	44/25
193	981.309	30/17
194	986.393
195	991.478	23/13, 39/22
196	996.562	16/9
197	1001.647	25/14
198	1006.731	34/19
199	1011.816
200	1016.9	9/5
201	1021.985
202	1027.069	38/21
203	1032.154
204	1037.238	20/11, 51/28
205	1042.323	42/23
206	1047.407	11/6
207	1052.492
208	1057.576	35/19, 46/25
209	1062.661	24/13
210	1067.745	13/7, 50/27
211	1072.83
212	1077.914
213	1082.999	28/15
214	1088.083	15/8
215	1093.168	32/17
216	1098.252
217	1103.337	17/9, 36/19
218	1108.421
219	1113.506	19/10, 40/21
220	1118.59	44/23
221	1123.675	21/11
222	1128.759	23/12, 48/25
223	1133.844	25/13, 27/14, 52/27
224	1138.928
225	1144.013	33/17
226	1149.097
227	1154.182	35/18, 39/20
228	1159.266	45/23
229	1164.351
230	1169.435	49/25, 51/26
231	1174.52
232	1179.604
233	1184.689
234	1189.773
235	1194.858
236	1199.942	2/1

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
	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
	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)

5syfx contd.

Harmonic		83	89	97	101	103	107	109	113	127	131	137
Error	Absolute (¢)	+2.09	-1.80	+1.72	-2.14	-0.49	-0.35	-1.91	+1.80	-2.12	+0.13	-1.14
	Relative (%)	+41.2	-35.3	+33.9	-42.0	-9.7	-7.0	-37.5	+35.3	-41.6	+2.5	-22.3
Steps (reduced)		1505 (0)	1528 (3)	1558 (3)	1571 (1)	1578 (3)	1591 (1)	1597 (2)	1610 (0)	1649 (4)	1660 (0)	1675 (0)

5syfx contd.

Harmonic		139	149	151	157	163	167	173	179	181	191	193
Error	Absolute (¢)	-0.80	+0.95	-1.80	+1.93	-1.99	+1.80	+1.71	-1.39	-0.29	-1.87	+0.44
	Relative (%)	-15.8	+18.7	-35.3	+37.9	-39.1	+35.4	+33.6	-27.3	-5.6	-36.7	+8.6
Steps (reduced)		1680 (0)	1704 (4)	1708 (3)	1722 (2)	1734 (4)	1743 (3)	1755 (0)	1766 (1)	1770 (0)	1788 (3)	1792 (2)

5syfx contd.

Harmonic		197	199	211	223	227	229
Error	Absolute (¢)	+0.52	-1.72	-1.40	-0.55	-0.83	-0.76
	Relative (%)	+10.1	-33.8	-27.5	-10.9	-16.2	-14.9
Steps (reduced)		1799 (4)	1802 (2)	1822 (2)	1841 (1)	1847 (2)	1850 (0)

236edo, 374edt, 548ed5, 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
	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
	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
	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
	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 548ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.05	-0.35	+0.00	+2.21	-2.35	-1.75	+1.60	+2.25	+1.99	+2.36	-1.24
	Relative (%)	-1.1	-6.8	+0.0	+43.4	-46.3	-34.4	+31.5	+44.3	+39.1	+46.4	-24.4
Steps (reduced)		236 (236)	374 (374)	548 (0)	663 (115)	816 (268)	873 (325)	965 (417)	1003 (455)	1068 (520)	1147 (51)	1169 (73)

548ed5 contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-2.48	-2.24	+1.74	+0.29	+0.76	-1.87	+1.43	+1.72	-2.07	+0.69	+1.22
	Relative (%)	-48.7	-44.0	+34.3	+5.7	+14.9	-36.7	+28.2	+33.8	-40.6	+13.5	+24.0
Steps (reduced)		1229 (133)	1264 (168)	1281 (185)	1311 (215)	1352 (256)	1388 (292)	1400 (304)	1432 (336)	1451 (355)	1461 (365)	1488 (392)

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
	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
	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)

Recommended equalizer subgroups

This article or section contains multiple idiosyncratic terms. Such terms are used by only a few people and are not regularly used within the community.

Give a few of these a try, see which ones vibe with you. They’re all new and unexplored. So go out and explore, curious sooty fox!

All-stops

• 2.3.5.47.53.73.79.103.106
• 2.3.5.47.53.73.79.103.106.131.137
• 2.3.5.47.53.73.79.103.106.131.137.181.193.197
• 2.3.5.47.53.73.79.103.106.131.137.181.193.197.223.229

Hollow middles

• 2.3.5.73.79.103.106.131.137.181.193.197.223.229
• 2.3.5.103.106.131.137.181.193.197.223.229
• 2.3.5.131.137.181.193.197.223.229
• 2.3.5.181.193.197.223.229

Triplets & quadruplets

• 2.3.5.47.53.73.79
• 2.3.5.73.79.103.106
• 2.3.5.103.106.131.137
• 2.3.5.181.193.197
• 2.3.5.193.197.223.229

The sixth sooty fox scale

← 5ed343/338

6ed343/338

7ed343/338 →

Prime factorization	2 × 3
Step size	4.23707¢
Octave	283\6ed343/338 (1199.09¢)
Twelfth	449\6ed343/338 (1902.44¢) (semiconvergent)
Consistency limit	3
Distinct consistency limit	2
Special properties	Highly composite

6ed343/338 or 6syfx for short.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	4.237
2	8.474
3	12.711
4	16.948
5	21.185
6	25.422
7	29.659	52/51
8	33.897	46/45, 51/50
9	38.134	49/48, 50/49
10	42.371	40/39, 45/44
11	46.608	36/35, 39/38
12	50.845	34/33, 35/34
13	55.082
14	59.319	28/27
15	63.556
16	67.793	27/26
17	72.03	24/23, 51/49
18	76.267	23/22
19	80.504	22/21
20	84.741	21/20
21	88.978	20/19
22	93.216	19/18
23	97.453	18/17
24	101.69	35/33, 52/49
25	105.927
26	110.164	49/46
27	114.401
28	118.638
29	122.875	15/14
30	127.112	14/13
31	131.349	27/25
32	135.586
33	139.823	13/12, 38/35
34	144.06	49/45
35	148.297	12/11, 25/23
36	152.535
37	156.772	23/21
38	161.009
39	165.246	11/10
40	169.483	54/49
41	173.72	21/19
42	177.957
43	182.194	10/9, 51/46
44	186.431	39/35, 49/44
45	190.668	19/17
46	194.905
47	199.142
48	203.379
49	207.616	9/8, 44/39
50	211.854	26/23
51	216.091	17/15
52	220.328
53	224.565	25/22
54	228.802	8/7
55	233.039
56	237.276	39/34
57	241.513	23/20, 38/33
58	245.75
59	249.987	15/13
60	254.224	22/19
61	258.461	51/44
62	262.698
63	266.935	7/6
64	271.172
65	275.41
66	279.647	20/17, 27/23
67	283.884	46/39
68	288.121	13/11, 33/28
69	292.358
70	296.595	45/38
71	300.832	19/16
72	305.069	25/21
73	309.306
74	313.543	6/5
75	317.78
76	322.017
77	326.254
78	330.491	23/19, 40/33
79	334.729
80	338.966	17/14, 28/23
81	343.203
82	347.44	11/9
83	351.677	49/40
84	355.914	16/13, 27/22
85	360.151
86	364.388	21/17
87	368.625	26/21
88	372.862
89	377.099
90	381.336
91	385.573
92	389.81	5/4
93	394.048	44/35, 49/39
94	398.285	34/27
95	402.522	24/19
96	406.759	19/15
97	410.996
98	415.233	14/11, 33/26
99	419.47
100	423.707	23/18, 51/40
101	427.944
102	432.181	50/39
103	436.418	9/7
104	440.655	49/38
105	444.892	22/17
106	449.129	35/27
107	453.367	13/10
108	457.604
109	461.841	30/23
110	466.078	17/13
111	470.315	46/35
112	474.552	21/16
113	478.789	25/19, 33/25
114	483.026
115	487.263	45/34
116	491.5
117	495.737	4/3
118	499.974
119	504.211
120	508.448
121	512.685	51/38
122	516.923	35/26
123	521.16	23/17, 27/20
124	525.397
125	529.634	19/14, 34/25
126	533.871	49/36
127	538.108	15/11
128	542.345	26/19
129	546.582
130	550.819
131	555.056	11/8
132	559.293
133	563.53	18/13
134	567.767	32/23
135	572.004	25/18, 46/33
136	576.242	39/28
137	580.479	7/5
138	584.716
139	588.953	38/27
140	593.19	24/17
141	597.427
142	601.664
143	605.901	17/12
144	610.138	27/19
145	614.375
146	618.612	10/7
147	622.849
148	627.086	33/23, 36/25
149	631.323	23/16, 49/34
150	635.561	13/9
151	639.798
152	644.035
153	648.272
154	652.509	51/35
155	656.746	19/13, 35/24
156	660.983	22/15
157	665.22
158	669.457	25/17, 28/19
159	673.694
160	677.931	34/23, 40/27
161	682.168	49/33, 52/35
162	686.405
163	690.642
164	694.88
165	699.117
166	703.354	3/2
167	707.591
168	711.828
169	716.065
170	720.302	50/33
171	724.539
172	728.776	35/23
173	733.013	26/17
174	737.25	23/15
175	741.487	49/32
176	745.724	20/13
177	749.961	54/35
178	754.198	17/11
179	758.436
180	762.673	14/9
181	766.91	39/25
182	771.147
183	775.384	36/23
184	779.621
185	783.858	11/7, 52/33
186	788.095
187	792.332	30/19
188	796.569	19/12
189	800.806	27/17
190	805.043	35/22
191	809.28
192	813.517
193	817.755
194	821.992
195	826.229
196	830.466	21/13
197	834.703	34/21
198	838.94
199	843.177	13/8, 44/27
200	847.414	49/30
201	851.651	18/11
202	855.888
203	860.125	23/14, 28/17
204	864.362
205	868.599	33/20, 38/23
206	872.836
207	877.074
208	881.311
209	885.548	5/3
210	889.785
211	894.022	42/25
212	898.259	32/19
213	902.496
214	906.733
215	910.97	22/13
216	915.207	39/23
217	919.444	17/10, 46/27
218	923.681
219	927.918
220	932.155	12/7
221	936.393
222	940.63
223	944.867	19/11
224	949.104	26/15
225	953.341	45/26
226	957.578	33/19, 40/23
227	961.815
228	966.052
229	970.289	7/4
230	974.526	44/25
231	978.763
232	983	30/17
233	987.237	23/13
234	991.474	39/22
235	995.711
236	999.949
237	1004.186
238	1008.423	34/19
239	1012.66
240	1016.897	9/5
241	1021.134
242	1025.371	38/21
243	1029.608	49/27
244	1033.845	20/11
245	1038.082
246	1042.319	42/23, 51/28
247	1046.556
248	1050.793	11/6
249	1055.03
250	1059.268	24/13, 35/19
251	1063.505
252	1067.742	50/27
253	1071.979	13/7
254	1076.216
255	1080.453
256	1084.69
257	1088.927
258	1093.164
259	1097.401	49/26
260	1101.638	17/9
261	1105.875	36/19
262	1110.112	19/10
263	1114.349	40/21
264	1118.587	21/11
265	1122.824	44/23
266	1127.061	23/12
267	1131.298	52/27
268	1135.535	25/13
269	1139.772	27/14
270	1144.009
271	1148.246	33/17
272	1152.483	35/18
273	1156.72	39/20
274	1160.957	49/25
275	1165.194	45/23
276	1169.431	51/26
277	1173.668
278	1177.906
279	1182.143
280	1186.38
281	1190.617
282	1194.854
283	1199.091	2/1

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
	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	83
Error	Absolute (¢)	-1.67	-1.43	+0.85	-0.60	-0.98	-0.22	+1.39	-0.03	+1.27	-0.21	-1.37	+2.09
	Relative (%)	-39.5	-33.8	+20.1	-14.2	-23.2	-5.2	+32.7	-0.7	+30.0	-5.0	-32.4	+49.4
Steps (reduced)		1475 (5)	1517 (5)	1537 (1)	1573 (1)	1622 (2)	1666 (4)	1680 (0)	1718 (2)	1742 (2)	1753 (1)	1785 (3)	1806 (0)

283edo, 449edt, 658ed5, 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
	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	83
Error	Absolute (¢)	-1.17	-0.79	+1.56	+0.22	-0.01	+0.90	-1.69	+1.26	-1.60	+1.19	+0.13	-0.58
	Relative (%)	-27.5	-18.7	+36.7	+5.1	-0.1	+21.2	-39.9	+29.7	-37.8	+28.0	+3.0	-13.6
Steps (reduced)		1474 (59)	1516 (101)	1536 (121)	1572 (157)	1621 (206)	1665 (250)	1678 (263)	1717 (19)	1740 (42)	1752 (54)	1784 (86)	1804 (106)

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
	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	83
Error	Absolute (¢)	+0.96	+1.16	-0.82	+1.93	+1.49	-2.03	-0.44	-1.89	-0.62	-2.12	+0.92	+0.13
	Relative (%)	+22.7	+27.3	-19.3	+45.5	+35.2	-47.9	-10.4	-44.7	-14.6	-50.0	+21.8	+3.1
Steps (reduced)		1476 (129)	1518 (171)	1537 (190)	1574 (227)	1623 (276)	1666 (319)	1680 (333)	1718 (371)	1742 (395)	1753 (406)	1786 (439)	1806 (10)

Approximation of prime harmonics in 658ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.63	-0.66	+0.00	+1.85	-1.49	+1.48	-1.38	+0.85	+0.38	+1.36	+0.23
	Relative (%)	-38.5	-15.5	+0.0	+43.7	-35.2	+35.0	-32.6	+20.0	+9.0	+32.0	+5.4
Steps (reduced)		283 (283)	449 (449)	658 (0)	796 (138)	980 (322)	1049 (391)	1158 (500)	1204 (546)	1282 (624)	1377 (61)	1404 (88)

658ed5 contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-1.19	-1.06	+1.17	-0.37	-0.88	-0.23	+1.34	-0.17	+1.07	-0.44	-1.69
	Relative (%)	-28.2	-25.1	+27.7	-8.8	-20.8	-5.4	+31.7	-4.0	+25.3	-10.5	-39.8
Steps (reduced)		1476 (160)	1518 (202)	1538 (222)	1574 (258)	1623 (307)	1667 (351)	1681 (365)	1719 (403)	1743 (427)	1754 (438)	1786 (470)

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
	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	83
Error	Absolute (¢)	-1.41	-1.52	+0.59	-1.16	-1.96	-1.56	-0.08	-1.81	-0.71	+1.94	+0.51	-0.43
	Relative (%)	-33.3	-36.0	+14.1	-27.5	-46.3	-37.0	-1.8	-42.8	-16.8	+45.9	+12.0	-10.2
Steps (reduced)		1478 (150)	1520 (26)	1540 (46)	1576 (82)	1625 (131)	1669 (9)	1683 (23)	1721 (61)	1745 (85)	1757 (97)	1789 (129)	1809 (149)

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.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	3.632
2	7.264
3	10.895
4	14.527
5	18.159
6	21.791
7	25.422
8	29.054
9	32.686
10	36.318	46/45
11	39.949
12	43.581
13	47.213	36/35, 39/38
14	50.845	34/33, 35/34
15	54.477
16	58.108
17	61.74
18	65.372
19	69.004	26/25, 51/49
20	72.635	25/24
21	76.267
22	79.899	23/22
23	83.531
24	87.163
25	90.794
26	94.426	19/18
27	98.058	18/17
28	101.69	35/33
29	105.321
30	108.953
31	112.585	49/46
32	116.217
33	119.848	15/14
34	123.48
35	127.112	14/13
36	130.744
37	134.376
38	138.007
39	141.639	13/12, 25/23, 38/35
40	145.271
41	148.903	12/11, 49/45
42	152.534
43	156.166	23/21
44	159.798
45	163.43
46	167.061	11/10, 54/49
47	170.693
48	174.325	21/19
49	177.957
50	181.589	51/46
51	185.22
52	188.852	39/35
53	192.484	19/17
54	196.116	28/25
55	199.747
56	203.379
57	207.011
58	210.643	26/23
59	214.275
60	217.906	17/15
61	221.538	25/22
62	225.17
63	228.802
64	232.433
65	236.065
66	239.697	39/34
67	243.329	38/33
68	246.96	15/13, 52/45
69	250.592	22/19
70	254.224
71	257.856
72	261.488
73	265.119
74	268.751	7/6
75	272.383
76	276.015
77	279.646	27/23
78	283.278	46/39
79	286.91	33/28
80	290.542	13/11
81	294.173	45/38
82	297.805
83	301.437
84	305.069
85	308.701
86	312.332
87	315.964	6/5
88	319.596
89	323.228
90	326.859
91	330.491	23/19
92	334.123
93	337.755	17/14, 28/23
94	341.386
95	345.018	11/9
96	348.65
97	352.282
98	355.914
99	359.545
100	363.177
101	366.809	21/17, 26/21
102	370.441
103	374.072
104	377.704
105	381.336
106	384.968
107	388.6	5/4
108	392.231
109	395.863	34/27, 49/39
110	399.495
111	403.127
112	406.758
113	410.39	19/15
114	414.022	33/26
115	417.654	14/11
116	421.285
117	424.917	23/18
118	428.549
119	432.181
120	435.813	9/7
121	439.444
122	443.076	22/17, 49/38
123	446.708	35/27
124	450.34
125	453.971
126	457.603	13/10, 30/23
127	461.235
128	464.867	17/13
129	468.498
130	472.13	25/19, 46/35
131	475.762
132	479.394
133	483.026	33/25
134	486.657	45/34
135	490.289
136	493.921
137	497.553
138	501.184
139	504.816
140	508.448
141	512.08	51/38
142	515.712	35/26
143	519.343
144	522.975	23/17
145	526.607
146	530.239	19/14
147	533.87	34/25
148	537.502	15/11
149	541.134	26/19
150	544.766
151	548.397
152	552.029
153	555.661
154	559.293
155	562.925	18/13
156	566.556	25/18
157	570.188
158	573.82	46/33
159	577.452
160	581.083
161	584.715	7/5
162	588.347	38/27
163	591.979
164	595.61
165	599.242
166	602.874
167	606.506	17/12
168	610.138	27/19
169	613.769
170	617.401
171	621.033
172	624.665	33/23
173	628.296
174	631.928	36/25
175	635.56	13/9, 49/34
176	639.192
177	642.824
178	646.455
179	650.087
180	653.719	51/35
181	657.351	19/13
182	660.982	22/15
183	664.614	25/17
184	668.246	28/19
185	671.878
186	675.509	34/23
187	679.141
188	682.773	52/35
189	686.405	49/33
190	690.037
191	693.668
192	697.3
193	700.932
194	704.564	3/2
195	708.195
196	711.827
197	715.459
198	719.091
199	722.722
200	726.354	35/23, 38/25
201	729.986
202	733.618	26/17
203	737.25
204	740.881	23/15
205	744.513
206	748.145
207	751.777	54/35
208	755.408	17/11
209	759.04
210	762.672	14/9
211	766.304
212	769.936
213	773.567	36/23
214	777.199
215	780.831	11/7
216	784.463	52/33
217	788.094	30/19
218	791.726
219	795.358
220	798.99	19/12
221	802.621	27/17
222	806.253	35/22
223	809.885
224	813.517
225	817.149
226	820.78
227	824.412	45/28
228	828.044
229	831.676	21/13, 34/21
230	835.307
231	838.939
232	842.571
233	846.203
234	849.834
235	853.466	18/11
236	857.098
237	860.73	23/14, 28/17
238	864.362
239	867.993	38/23
240	871.625
241	875.257
242	878.889
243	882.52	5/3
244	886.152
245	889.784
246	893.416
247	897.047
248	900.679	42/25
249	904.311
250	907.943	22/13
251	911.575
252	915.206	39/23
253	918.838	46/27
254	922.47
255	926.102
256	929.733	12/7
257	933.365
258	936.997
259	940.629
260	944.261
261	947.892	19/11
262	951.524	26/15, 45/26
263	955.156	33/19
264	958.788
265	962.419
266	966.051
267	969.683
268	973.315
269	976.946	44/25
270	980.578	30/17
271	984.21
272	987.842	23/13
273	991.474
274	995.105
275	998.737
276	1002.369	25/14
277	1006.001	34/19
278	1009.632
279	1013.264
280	1016.896
281	1020.528	9/5
282	1024.159	38/21
283	1027.791
284	1031.423	20/11, 49/27
285	1035.055
286	1038.687
287	1042.318	42/23
288	1045.95
289	1049.582	11/6
290	1053.214
291	1056.845	35/19, 46/25
292	1060.477
293	1064.109
294	1067.741
295	1071.373	13/7
296	1075.004
297	1078.636	28/15
298	1082.268
299	1085.9
300	1089.531
301	1093.163
302	1096.795
303	1100.427	17/9, 49/26
304	1104.058	36/19
305	1107.69
306	1111.322
307	1114.954
308	1118.586
309	1122.217	21/11
310	1125.849	48/25
311	1129.481	23/12, 25/13
312	1133.113
313	1136.744
314	1140.376	27/14
315	1144.008
316	1147.64	33/17
317	1151.271	35/18
318	1154.903
319	1158.535
320	1162.167	45/23
321	1165.799
322	1169.43	51/26
323	1173.062
324	1176.694
325	1180.326
326	1183.957
327	1187.589
328	1191.221
329	1194.853
330	1198.485	2/1

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
	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
	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)

330edo, 524edt, 767ed5, 187edf for comparison:

Approximation of prime harmonics in 330edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.14	-0.86	-1.55	+1.41	-0.53	+0.50	+0.67	+0.82	-0.49	+0.42
	Relative (%)	+0.0	-3.8	-23.6	-42.7	+38.8	-14.5	+13.7	+18.4	+22.5	-13.4	+11.5
Steps (reduced)		330 (0)	523 (193)	766 (106)	926 (266)	1142 (152)	1221 (231)	1349 (29)	1402 (82)	1493 (173)	1603 (283)	1635 (315)

320edo contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.43	+0.03	+1.21	-0.05	-0.78	-0.99	-0.52	+0.69	-1.51	+1.30	-0.90
	Relative (%)	-12.0	+0.8	+33.3	-1.4	-21.4	-27.2	-14.3	+19.1	-41.7	+35.8	-24.8
Steps (reduced)		1719 (69)	1768 (118)	1791 (141)	1833 (183)	1890 (240)	1941 (291)	1957 (307)	2002 (22)	2029 (49)	2043 (63)	2080 (100)

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
	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
	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 767ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-1.19	+1.60	+0.00	-1.27	+0.91	-1.32	-0.75	-0.77	-0.96	+0.97	+1.76
	Relative (%)	-32.9	+44.1	+0.0	-35.1	+25.0	-36.2	-20.7	-21.3	-26.3	+26.8	+48.6
Steps (reduced)		330 (330)	524 (524)	767 (0)	927 (160)	1143 (376)	1222 (455)	1350 (583)	1403 (636)	1494 (727)	1605 (71)	1637 (103)

767ed5 contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.61	+0.89	-1.64	+0.58	-0.36	-0.75	-0.34	+0.71	-1.60	+1.17	-1.17
	Relative (%)	+16.7	+24.6	-45.2	+15.9	-9.8	-20.7	-9.4	+19.5	-43.9	+32.2	-32.1
Steps (reduced)		1721 (187)	1770 (236)	1792 (258)	1835 (301)	1892 (358)	1943 (409)	1959 (425)	2004 (470)	2031 (497)	2045 (511)	2082 (548)

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
	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
	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.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	3.178
2	6.356
3	9.533
4	12.711
5	15.889
6	19.067
7	22.245
8	25.422
9	28.6
10	31.778	52/51
11	34.956	46/45, 51/50
12	38.134	50/49
13	41.312	45/44
14	44.489	39/38
15	47.667	35/34
16	50.845
17	54.023	34/33
18	57.201
19	60.378	28/27
20	63.556
21	66.734	26/25
22	69.912
23	73.09
24	76.267	23/22
25	79.445	22/21
26	82.623	21/20
27	85.801
28	88.979
29	92.156
30	95.334
31	98.512
32	101.69	18/17, 35/33
33	104.868	52/49
34	108.045	49/46
35	111.223
36	114.401	16/15
37	117.579
38	120.757	15/14
39	123.935
40	127.112
41	130.29	14/13
42	133.468
43	136.646
44	139.824
45	143.001	38/35
46	146.179	25/23
47	149.357
48	152.535
49	155.713	23/21
50	158.89
51	162.068	11/10
52	165.246
53	168.424
54	171.602
55	174.779	21/19
56	177.957
57	181.135	10/9, 51/46
58	184.313	49/44
59	187.491	39/35
60	190.668	19/17
61	193.846
62	197.024	28/25
63	200.202
64	203.38	9/8
65	206.558
66	209.735	44/39
67	212.913	26/23
68	216.091	17/15
69	219.269
70	222.447	25/22
71	225.624
72	228.802
73	231.98
74	235.158	39/34
75	238.336
76	241.513
77	244.691	38/33
78	247.869	52/45
79	251.047
80	254.225	22/19
81	257.402	51/44
82	260.58
83	263.758	7/6
84	266.936
85	270.114
86	273.291
87	276.469
88	279.647
89	282.825	20/17, 33/28
90	286.003	46/39
91	289.181	13/11
92	292.358
93	295.536	32/27, 45/38
94	298.714
95	301.892	25/21
96	305.07
97	308.247
98	311.425
99	314.603
100	317.781	6/5
101	320.959
102	324.136
103	327.314
104	330.492	23/19
105	333.67
106	336.848	17/14
107	340.025
108	343.203	28/23
109	346.381
110	349.559
111	352.737
112	355.915
113	359.092
114	362.27
115	365.448	21/17
116	368.626	26/21
117	371.804
118	374.981
119	378.159
120	381.337
121	384.515	5/4
122	387.693
123	390.87
124	394.048	49/39
125	397.226	34/27, 44/35
126	400.404
127	403.582
128	406.759	19/15
129	409.937
130	413.115	33/26
131	416.293
132	419.471	14/11, 51/40
133	422.648
134	425.826
135	429.004
136	432.182	50/39
137	435.36
138	438.538	49/38
139	441.715
140	444.893	22/17
141	448.071
142	451.249	13/10
143	454.427
144	457.604
145	460.782
146	463.96
147	467.138	17/13
148	470.316
149	473.493	46/35
150	476.671	25/19
151	479.849	33/25
152	483.027
153	486.205	45/34
154	489.382
155	492.56
156	495.738
157	498.916	4/3
158	502.094
159	505.271
160	508.449
161	511.627	51/38
162	514.805	35/26
163	517.983
164	521.161	23/17, 27/20
165	524.338
166	527.516	19/14
167	530.694
168	533.872	34/25
169	537.05
170	540.227
171	543.405	26/19
172	546.583
173	549.761
174	552.939
175	556.116
176	559.294
177	562.472
178	565.65	25/18
179	568.828
180	572.005	39/28
181	575.183	46/33
182	578.361
183	581.539	7/5
184	584.717
185	587.894	45/32
186	591.072
187	594.25
188	597.428
189	600.606	17/12
190	603.784
191	606.961
192	610.139
193	613.317
194	616.495
195	619.673	10/7
196	622.85
197	626.028	33/23
198	629.206
199	632.384
200	635.562
201	638.739
202	641.917
203	645.095
204	648.273
205	651.451
206	654.628	51/35
207	657.806	19/13
208	660.984	22/15
209	664.162
210	667.34	25/17
211	670.517
212	673.695	28/19
213	676.873
214	680.051	40/27
215	683.229	49/33
216	686.407	52/35
217	689.584
218	692.762
219	695.94
220	699.118
221	702.296	3/2
222	705.473
223	708.651
224	711.829
225	715.007
226	718.185
227	721.362	50/33
228	724.54	38/25
229	727.718	35/23
230	730.896
231	734.074	26/17
232	737.251	23/15
233	740.429
234	743.607
235	746.785
236	749.963
237	753.141
238	756.318	17/11
239	759.496
240	762.674	14/9
241	765.852
242	769.03	39/25
243	772.207
244	775.385
245	778.563
246	781.741	11/7
247	784.919
248	788.096	52/33
249	791.274
250	794.452
251	797.63
252	800.808
253	803.985	27/17, 35/22, 51/32
254	807.163
255	810.341
256	813.519
257	816.697	8/5
258	819.874
259	823.052	45/28
260	826.23
261	829.408
262	832.586	21/13
263	835.764	34/21
264	838.941
265	842.119
266	845.297
267	848.475
268	851.653
269	854.83
270	858.008	23/14
271	861.186
272	864.364	28/17, 33/20
273	867.542
274	870.719	38/23
275	873.897
276	877.075
277	880.253
278	883.431	5/3
279	886.608
280	889.786
281	892.964
282	896.142
283	899.32	42/25
284	902.497
285	905.675	27/16
286	908.853
287	912.031	22/13
288	915.209	39/23
289	918.387	17/10
290	921.564
291	924.742
292	927.92
293	931.098
294	934.276
295	937.453
296	940.631
297	943.809
298	946.987	19/11
299	950.165	26/15
300	953.342
301	956.52	33/19
302	959.698
303	962.876
304	966.054	7/4
305	969.231
306	972.409
307	975.587
308	978.765	44/25
309	981.943
310	985.12	30/17
311	988.298	23/13
312	991.476	39/22
313	994.654
314	997.832	16/9
315	1001.01
316	1004.187	25/14
317	1007.365
318	1010.543	34/19
319	1013.721
320	1016.899
321	1020.076	9/5
322	1023.254
323	1026.432	38/21
324	1029.61
325	1032.788
326	1035.965
327	1039.143	51/28
328	1042.321
329	1045.499	42/23
330	1048.677
331	1051.854
332	1055.032	46/25
333	1058.21	35/19
334	1061.388
335	1064.566	50/27
336	1067.744
337	1070.921	13/7
338	1074.099
339	1077.277
340	1080.455	28/15
341	1083.633
342	1086.81	15/8
343	1089.988
344	1093.166
345	1096.344	49/26
346	1099.522	17/9
347	1102.699
348	1105.877
349	1109.055	19/10
350	1112.233
351	1115.411
352	1118.588	40/21
353	1121.766	21/11
354	1124.944	44/23
355	1128.122
356	1131.3
357	1134.477	25/13
358	1137.655
359	1140.833
360	1144.011
361	1147.189	33/17
362	1150.367
363	1153.544	39/20
364	1156.722
365	1159.9
366	1163.078	49/25
367	1166.256
368	1169.433	51/26
369	1172.611
370	1175.789
371	1178.967
372	1182.145
373	1185.322
374	1188.5
375	1191.678
376	1194.856
377	1198.034
378	1201.211	2/1

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
	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
	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, 877ed5, 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
	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
	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
	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
	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 877ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.94	+1.13	+0.00	-1.10	+1.15	+1.05	+0.48	-1.45	+1.38	+0.40	-0.69
	Relative (%)	+29.7	+35.4	+0.0	-34.7	+36.1	+33.2	+15.2	-45.6	+43.6	+12.4	-21.7
Steps (reduced)		378 (378)	599 (599)	877 (0)	1060 (183)	1307 (430)	1398 (521)	1544 (667)	1604 (727)	1709 (832)	1835 (81)	1871 (117)

877ed5 contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+1.18	+1.38	+1.53	+0.04	-1.44	+0.34	-0.19	-0.58	+0.70	+0.26	+0.13
	Relative (%)	+37.2	+43.5	+48.2	+1.3	-45.5	+10.6	-5.9	-18.2	+22.0	+8.3	+4.1
Steps (reduced)		1968 (214)	2024 (270)	2050 (296)	2098 (344)	2163 (409)	2222 (468)	2240 (486)	2291 (537)	2323 (569)	2338 (584)	2381 (627)

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
	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
	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.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	2.825
2	5.649
3	8.474
4	11.299
5	14.123
6	16.948
7	19.773
8	22.597
9	25.422
10	28.247
11	31.072
12	33.896	51/50
13	36.721	49/48
14	39.546
15	42.37	39/38
16	45.195	40/39
17	48.02	36/35
18	50.844	33/32, 34/33, 35/34
19	53.669
20	56.494
21	59.318
22	62.143
23	64.968
24	67.792
25	70.617	26/25
26	73.442	24/23
27	76.266	23/22
28	79.091
29	81.916	22/21
30	84.741	21/20
31	87.565	20/19
32	90.39
33	93.215
34	96.039	19/18
35	98.864	18/17
36	101.689	35/33, 52/49
37	104.513
38	107.338
39	110.163	49/46
40	112.987
41	115.812
42	118.637
43	121.461
44	124.286
45	127.111
46	129.935	14/13
47	132.76	27/25
48	135.585
49	138.409	13/12
50	141.234
51	144.059	38/35
52	146.884
53	149.708	12/11
54	152.533	35/32
55	155.358
56	158.182	23/21
57	161.007
58	163.832
59	166.656	11/10
60	169.481
61	172.306	21/19
62	175.13
63	177.955
64	180.78
65	183.604	10/9
66	186.429	39/35, 49/44
67	189.254
68	192.078
69	194.903	19/17
70	197.728
71	200.553
72	203.377
73	206.202
74	209.027
75	211.851	26/23
76	214.676
77	217.501	17/15
78	220.325
79	223.15
80	225.975
81	228.799
82	231.624	8/7
83	234.449
84	237.273	39/34
85	240.098
86	242.923	23/20
87	245.747	15/13, 38/33
88	248.572
89	251.397
90	254.222	22/19
91	257.046
92	259.871
93	262.696
94	265.52
95	268.345	7/6
96	271.17
97	273.994
98	276.819
99	279.644
100	282.468	20/17, 33/28
101	285.293
102	288.118	13/11, 46/39
103	290.942
104	293.767
105	296.592	19/16
106	299.416	25/21
107	302.241
108	305.066
109	307.89
110	310.715
111	313.54
112	316.365	6/5
113	319.189
114	322.014
115	324.839
116	327.663
117	330.488	23/19
118	333.313	17/14, 40/33
119	336.137
120	338.962
121	341.787	28/23
122	344.611
123	347.436
124	350.261
125	353.085	49/40
126	355.91
127	358.735
128	361.559	16/13
129	364.384
130	367.209	21/17
131	370.034	26/21
132	372.858
133	375.683
134	378.508
135	381.332
136	384.157	5/4
137	386.982
138	389.806
139	392.631
140	395.456
141	398.28	44/35
142	401.105	34/27
143	403.93	24/19
144	406.754
145	409.579
146	412.404	33/26
147	415.228
148	418.053	14/11, 51/40
149	420.878
150	423.703
151	426.527	23/18
152	429.352	50/39
153	432.177
154	435.001
155	437.826
156	440.651	49/38
157	443.475
158	446.3
159	449.125	22/17
160	451.949	35/27
161	454.774	13/10
162	457.599	30/23
163	460.423
164	463.248	17/13
165	466.073
166	468.897	21/16
167	471.722
168	474.547	46/35
169	477.371
170	480.196
171	483.021	33/25, 45/34
172	485.846
173	488.67
174	491.495
175	494.32
176	497.144
177	499.969	4/3
178	502.794
179	505.618
180	508.443
181	511.268
182	514.092	35/26
183	516.917	27/20
184	519.742
185	522.566
186	525.391	23/17
187	528.216	19/14
188	531.04
189	533.865	34/25
190	536.69
191	539.515
192	542.339	26/19
193	545.164
194	547.989	48/35
195	550.813	11/8
196	553.638
197	556.463
198	559.287
199	562.112	18/13
200	564.937
201	567.761	25/18
202	570.586
203	573.411	32/23
204	576.235	46/33
205	579.06
206	581.885
207	584.709	7/5
208	587.534
209	590.359
210	593.184
211	596.008
212	598.833	24/17
213	601.658	17/12
214	604.482
215	607.307
216	610.132
217	612.956
218	615.781	10/7
219	618.606
220	621.43
221	624.255	33/23
222	627.08	23/16
223	629.904
224	632.729	36/25
225	635.554
226	638.378	13/9
227	641.203
228	644.028
229	646.852
230	649.677	16/11, 51/35
231	652.502	35/24
232	655.327
233	658.151	19/13
234	660.976
235	663.801
236	666.625	25/17
237	669.45
238	672.275	28/19
239	675.099	34/23
240	677.924
241	680.749
242	683.573
243	686.398	49/33, 52/35
244	689.223
245	692.047
246	694.872
247	697.697
248	700.521	3/2
249	703.346
250	706.171
251	708.996
252	711.82
253	714.645
254	717.47	50/33
255	720.294
256	723.119
257	725.944	35/23
258	728.768
259	731.593	32/21
260	734.418
261	737.242	26/17, 49/32
262	740.067
263	742.892
264	745.716	20/13
265	748.541	54/35
266	751.366	17/11
267	754.19
268	757.015
269	759.84
270	762.665
271	765.489
272	768.314
273	771.139	39/25
274	773.963	36/23
275	776.788
276	779.613
277	782.437	11/7
278	785.262
279	788.087	30/19, 52/33
280	790.911
281	793.736
282	796.561	19/12
283	799.385	27/17
284	802.21	35/22
285	805.035
286	807.859
287	810.684
288	813.509
289	816.334	8/5
290	819.158
291	821.983
292	824.808
293	827.632
294	830.457	21/13
295	833.282	34/21
296	836.106
297	838.931	13/8
298	841.756
299	844.58
300	847.405
301	850.23	18/11
302	853.054
303	855.879
304	858.704	23/14
305	861.528
306	864.353
307	867.178	33/20
308	870.002	38/23
309	872.827
310	875.652
311	878.477
312	881.301
313	884.126	5/3
314	886.951
315	889.775
316	892.6
317	895.425
318	898.249
319	901.074
320	903.899	32/19
321	906.723
322	909.548
323	912.373	22/13, 39/23
324	915.197
325	918.022	17/10
326	920.847
327	923.671
328	926.496
329	929.321
330	932.146	12/7
331	934.97
332	937.795
333	940.62
334	943.444
335	946.269	19/11
336	949.094
337	951.918
338	954.743	26/15, 33/19
339	957.568	40/23
340	960.392
341	963.217
342	966.042
343	968.866	7/4
344	971.691
345	974.516
346	977.34
347	980.165
348	982.99	30/17
349	985.815
350	988.639	23/13, 39/22
351	991.464
352	994.289
353	997.113
354	999.938
355	1002.763
356	1005.587	34/19
357	1008.412
358	1011.237
359	1014.061
360	1016.886	9/5
361	1019.711
362	1022.535
363	1025.36
364	1028.185	38/21
365	1031.009
366	1033.834	20/11
367	1036.659
368	1039.483
369	1042.308	42/23
370	1045.133
371	1047.958
372	1050.782	11/6
373	1053.607
374	1056.432	35/19
375	1059.256
376	1062.081	24/13
377	1064.906
378	1067.73	50/27
379	1070.555	13/7
380	1073.38
381	1076.204
382	1079.029
383	1081.854
384	1084.678
385	1087.503
386	1090.328
387	1093.152
388	1095.977
389	1098.802	49/26
390	1101.627	17/9
391	1104.451	36/19
392	1107.276
393	1110.101
394	1112.925	19/10
395	1115.75	40/21
396	1118.575	21/11
397	1121.399
398	1124.224	44/23
399	1127.049	23/12
400	1129.873	25/13
401	1132.698
402	1135.523
403	1138.347
404	1141.172
405	1143.997
406	1146.821
407	1149.646	33/17
408	1152.471	35/18
409	1155.296	39/20
410	1158.12
411	1160.945
412	1163.77	51/26
413	1166.594
414	1169.419
415	1172.244
416	1175.068
417	1177.893
418	1180.718
419	1183.542
420	1186.367
421	1189.192
422	1192.016
423	1194.841
424	1197.666
425	1200.49	2/1

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
	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
	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, 986ed5, 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
	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
	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
	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
	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 986ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+1.00	-0.14	+0.00	-0.38	-0.11	-1.08	+0.77	+0.37	+0.23	+0.20	+0.61
	Relative (%)	+35.3	-5.0	+0.0	-13.5	-3.8	-38.1	+27.1	+13.0	+8.3	+7.3	+21.5
Steps (reduced)		425 (425)	673 (673)	986 (0)	1192 (206)	1469 (483)	1571 (585)	1736 (750)	1804 (818)	1921 (935)	2063 (91)	2104 (132)

986ed5 contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.51	-0.19	-0.70	+0.73	-0.97	-0.13	-1.33	+0.15	-1.33	-1.39	+0.33
	Relative (%)	-17.9	-6.9	-24.8	+26.0	-34.5	-4.7	-47.0	+5.3	-47.2	-49.1	+11.8
Steps (reduced)		2212 (240)	2275 (303)	2304 (332)	2359 (387)	2432 (460)	2498 (526)	2518 (546)	2576 (604)	2611 (639)	2628 (656)	2677 (705)

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
	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
	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	2

10ed343/338 or 10syfx for short.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	2.542
2	5.085
3	7.627
4	10.169
5	12.711
6	15.254
7	17.796
8	20.338
9	22.88
10	25.423
11	27.965
12	30.507
13	33.049	51/50
14	35.592	49/48, 50/49, 52/51
15	38.134	45/44, 46/45
16	40.676
17	43.218	40/39
18	45.761	39/38
19	48.303	36/35
20	50.845	34/33, 35/34
21	53.387	33/32
22	55.93
23	58.472
24	61.014
25	63.556	27/26, 28/27
26	66.099
27	68.641	26/25, 51/49
28	71.183	25/24
29	73.725	24/23
30	76.268	23/22
31	78.81
32	81.352	22/21
33	83.894	21/20
34	86.437
35	88.979	20/19
36	91.521
37	94.063	19/18
38	96.606
39	99.148	18/17
40	101.69	35/33
41	104.232	17/16, 52/49
42	106.775
43	109.317	49/46
44	111.859	16/15
45	114.401
46	116.944
47	119.486	15/14
48	122.028
49	124.57
50	127.113	14/13
51	129.655
52	132.197	27/25
53	134.739
54	137.282
55	139.824	13/12
56	142.366	38/35
57	144.908	25/23
58	147.451	49/45
59	149.993	12/11
60	152.535
61	155.077	35/32
62	157.62	23/21
63	160.162
64	162.704
65	165.246	11/10
66	167.789	54/49
67	170.331
68	172.873	21/19
69	175.415
70	177.958	51/46
71	180.5
72	183.042	10/9
73	185.584	49/44
74	188.127	39/35
75	190.669
76	193.211	19/17
77	195.753	28/25
78	198.296
79	200.838
80	203.38	9/8
81	205.922
82	208.465	44/39
83	211.007
84	213.549	26/23
85	216.091	17/15
86	218.634
87	221.176	25/22
88	223.718
89	226.26
90	228.803
91	231.345	8/7
92	233.887
93	236.429
94	238.972	39/34
95	241.514	23/20
96	244.056	38/33
97	246.598	15/13
98	249.141
99	251.683	52/45
100	254.225	22/19, 51/44
101	256.767
102	259.31
103	261.852
104	264.394
105	266.936	7/6
106	269.479
107	272.021
108	274.563
109	277.105	27/23
110	279.648
111	282.19	20/17
112	284.732	33/28, 46/39
113	287.274
114	289.817	13/11
115	292.359	45/38
116	294.901	32/27
117	297.443	19/16
118	299.986
119	302.528	25/21
120	305.07
121	307.612
122	310.155
123	312.697
124	315.239	6/5
125	317.781
126	320.324
127	322.866
128	325.408
129	327.95
130	330.493	23/19
131	333.035	40/33
132	335.577	17/14
133	338.119
134	340.662	28/23
135	343.204	39/32
136	345.746
137	348.288	11/9
138	350.831	49/40
139	353.373	27/22
140	355.915
141	358.457	16/13
142	361
143	363.542
144	366.084	21/17
145	368.626
146	371.169	26/21
147	373.711
148	376.253
149	378.795
150	381.338
151	383.88
152	386.422	5/4
153	388.964
154	391.507
155	394.049	49/39
156	396.591	44/35
157	399.133	34/27
158	401.676
159	404.218	24/19
160	406.76
161	409.302	19/15
162	411.845	33/26
163	414.387
164	416.929	14/11
165	419.471	51/40
166	422.014
167	424.556	23/18
168	427.098	32/25
169	429.64	50/39
170	432.183
171	434.725	9/7
172	437.267
173	439.809	49/38
174	442.352
175	444.894
176	447.436	22/17
177	449.978	35/27
178	452.521
179	455.063	13/10
180	457.605
181	460.147	30/23
182	462.69	17/13
183	465.232
184	467.774
185	470.316	21/16
186	472.859	46/35
187	475.401	25/19
188	477.943
189	480.485	33/25
190	483.028
191	485.57	45/34
192	488.112
193	490.654
194	493.197
195	495.739
196	498.281	4/3
197	500.823
198	503.366
199	505.908
200	508.45	51/38
201	510.992
202	513.535	35/26
203	516.077
204	518.619	27/20
205	521.161
206	523.704	23/17
207	526.246
208	528.788	19/14
209	531.33	34/25
210	533.873	49/36
211	536.415	15/11
212	538.957
213	541.499
214	544.042	26/19
215	546.584	48/35
216	549.126
217	551.668	11/8
218	554.211
219	556.753
220	559.295
221	561.837	18/13
222	564.38
223	566.922
224	569.464	25/18
225	572.006	32/23
226	574.549	39/28, 46/33
227	577.091
228	579.633
229	582.175	7/5
230	584.718
231	587.26
232	589.802	45/32
233	592.344	38/27
234	594.887
235	597.429	24/17
236	599.971
237	602.513	17/12
238	605.056
239	607.598	27/19
240	610.14
241	612.682
242	615.225
243	617.767	10/7
244	620.309
245	622.851
246	625.394	33/23
247	627.936	23/16
248	630.478	36/25
249	633.02	49/34
250	635.563
251	638.105	13/9
252	640.647
253	643.189
254	645.732
255	648.274	16/11
256	650.816	51/35
257	653.358	35/24
258	655.901	19/13
259	658.443
260	660.985
261	663.527	22/15
262	666.07
263	668.612	25/17
264	671.154	28/19
265	673.696
266	676.239	34/23
267	678.781
268	681.323	40/27
269	683.865	49/33
270	686.408	52/35
271	688.95
272	691.492
273	694.034
274	696.577
275	699.119
276	701.661	3/2
277	704.203
278	706.746
279	709.288
280	711.83
281	714.372
282	716.915
283	719.457	50/33
284	721.999
285	724.541	38/25
286	727.084	35/23
287	729.626	32/21
288	732.168
289	734.71
290	737.253	26/17, 49/32
291	739.795	23/15
292	742.337
293	744.879	20/13
294	747.422
295	749.964	54/35
296	752.506	17/11
297	755.048
298	757.591
299	760.133
300	762.675
301	765.217	14/9
302	767.76
303	770.302	39/25
304	772.844	25/16
305	775.386	36/23
306	777.929
307	780.471
308	783.013	11/7
309	785.555
310	788.098	52/33
311	790.64	30/19
312	793.182
313	795.724	19/12
314	798.267
315	800.809	27/17
316	803.351	35/22
317	805.893	51/32
318	808.436
319	810.978
320	813.52	8/5
321	816.062
322	818.605
323	821.147	45/28
324	823.689
325	826.231
326	828.774	21/13
327	831.316
328	833.858	34/21
329	836.4
330	838.943
331	841.485	13/8
332	844.027
333	846.569	44/27
334	849.112	49/30
335	851.654	18/11
336	854.196
337	856.738
338	859.281	23/14
339	861.823
340	864.365	28/17
341	866.907	33/20
342	869.45	38/23
343	871.992
344	874.534
345	877.076
346	879.619
347	882.161
348	884.703	5/3
349	887.245
350	889.788
351	892.33
352	894.872
353	897.414	42/25
354	899.957
355	902.499	32/19
356	905.041	27/16
357	907.583
358	910.126	22/13
359	912.668
360	915.21	39/23
361	917.752	17/10
362	920.295
363	922.837	46/27
364	925.379
365	927.921
366	930.464
367	933.006	12/7
368	935.548
369	938.09
370	940.633
371	943.175
372	945.717	19/11
373	948.259	45/26
374	950.802
375	953.344	26/15
376	955.886	33/19
377	958.428	40/23
378	960.971
379	963.513
380	966.055
381	968.597	7/4
382	971.14
383	973.682
384	976.224
385	978.766	44/25
386	981.309
387	983.851	30/17
388	986.393	23/13
389	988.935
390	991.478	39/22
391	994.02
392	996.562	16/9
393	999.104
394	1001.647
395	1004.189	25/14
396	1006.731	34/19
397	1009.273
398	1011.816
399	1014.358
400	1016.9	9/5
401	1019.442
402	1021.985
403	1024.527
404	1027.069	38/21
405	1029.611
406	1032.154	49/27
407	1034.696	20/11
408	1037.238	51/28
409	1039.781
410	1042.323	42/23
411	1044.865
412	1047.407
413	1049.95	11/6
414	1052.492
415	1055.034	46/25
416	1057.576	35/19
417	1060.119	24/13
418	1062.661
419	1065.203
420	1067.745	50/27
421	1070.288
422	1072.83	13/7
423	1075.372
424	1077.914
425	1080.457	28/15
426	1082.999
427	1085.541
428	1088.083	15/8
429	1090.626
430	1093.168
431	1095.71	32/17, 49/26
432	1098.252
433	1100.795	17/9
434	1103.337
435	1105.879	36/19
436	1108.421
437	1110.964	19/10
438	1113.506
439	1116.048	40/21
440	1118.59	21/11
441	1121.133
442	1123.675	44/23
443	1126.217	23/12
444	1128.759	48/25
445	1131.302	25/13
446	1133.844
447	1136.386	27/14, 52/27
448	1138.928
449	1141.471
450	1144.013
451	1146.555
452	1149.097	33/17
453	1151.64	35/18
454	1154.182
455	1156.724	39/20
456	1159.266
457	1161.809	45/23
458	1164.351	49/25, 51/26
459	1166.893
460	1169.435
461	1171.978
462	1174.52
463	1177.062
464	1179.604
465	1182.147
466	1184.689
467	1187.231
468	1189.773
469	1192.316
470	1194.858
471	1197.4
472	1199.942	2/1

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
	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
	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, 1096ed5, 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
	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
	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
	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
	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 1096ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.05	-0.35	+0.00	-0.34	+0.19	+0.80	-0.94	-0.29	-0.56	-0.18	-1.24
	Relative (%)	-2.2	-13.6	+0.0	-13.2	+7.4	+31.3	-37.0	-11.3	-21.9	-7.2	-48.7
Steps (reduced)		472 (472)	748 (748)	1096 (0)	1325 (229)	1633 (537)	1747 (651)	1929 (833)	2005 (909)	2135 (1039)	2293 (101)	2338 (146)

1096ed5 contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.07	+0.31	-0.80	+0.29	+0.76	+0.68	-1.11	-0.83	+0.48	+0.69	+1.22
	Relative (%)	+2.6	+12.0	-31.4	+11.5	+29.8	+26.6	-43.6	-32.5	+18.7	+27.0	+48.0
Steps (reduced)		2459 (267)	2529 (337)	2561 (369)	2622 (430)	2704 (512)	2777 (585)	2799 (607)	2863 (671)	2903 (711)	2922 (730)	2976 (784)

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
	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
	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	2

11ed343/338 or 11syfx for short.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	2.311
2	4.622
3	6.933
4	9.244
5	11.556
6	13.867
7	16.178
8	18.489
9	20.8
10	23.111
11	25.422
12	27.733
13	30.044
14	32.355	51/50, 52/51
15	34.667	50/49
16	36.978	46/45
17	39.289
18	41.6
19	43.911	39/38, 40/39
20	46.222
21	48.533
22	50.844	34/33
23	53.155
24	55.467	33/32
25	57.778
26	60.089
27	62.4	28/27
28	64.711
29	67.022	27/26, 51/49
30	69.333
31	71.644	24/23
32	73.955
33	76.266
34	78.578	22/21, 23/22
35	80.889
36	83.2
37	85.511	21/20
38	87.822	20/19
39	90.133
40	92.444
41	94.755	19/18
42	97.066
43	99.377	18/17
44	101.689
45	104	35/33
46	106.311	17/16
47	108.622
48	110.933	49/46
49	113.244
50	115.555
51	117.866
52	120.177	15/14
53	122.489
54	124.8
55	127.111
56	129.422	14/13
57	131.733	27/25
58	134.044
59	136.355
60	138.666	13/12
61	140.977	38/35
62	143.288
63	145.6	25/23
64	147.911	49/45
65	150.222	12/11
66	152.533
67	154.844
68	157.155	23/21
69	159.466
70	161.777
71	164.088	11/10
72	166.4	54/49
73	168.711
74	171.022
75	173.333	21/19
76	175.644
77	177.955	51/46
78	180.266
79	182.577	10/9
80	184.888
81	187.199
82	189.511
83	191.822
84	194.133	19/17, 28/25
85	196.444
86	198.755
87	201.066
88	203.377
89	205.688	9/8
90	207.999	44/39
91	210.311	26/23
92	212.622
93	214.933	17/15
94	217.244
95	219.555
96	221.866
97	224.177
98	226.488
99	228.799
100	231.11
101	233.422
102	235.733
103	238.044	39/34
104	240.355
105	242.666	23/20
106	244.977	38/33
107	247.288
108	249.599	15/13
109	251.91	22/19
110	254.221
111	256.533	51/44
112	258.844
113	261.155
114	263.466
115	265.777
116	268.088	7/6
117	270.399
118	272.71
119	275.021
120	277.333	27/23
121	279.644
122	281.955	20/17
123	284.266	33/28
124	286.577	46/39
125	288.888	13/11
126	291.199
127	293.51	45/38
128	295.821
129	298.132
130	300.444
131	302.755	25/21
132	305.066
133	307.377
134	309.688
135	311.999
136	314.31	6/5
137	316.621
138	318.932
139	321.244
140	323.555
141	325.866
142	328.177
143	330.488	23/19
144	332.799	40/33
145	335.11	17/14
146	337.421
147	339.732	28/23
148	342.043
149	344.355	39/32
150	346.666	11/9
151	348.977
152	351.288
153	353.599	49/40
154	355.91	27/22
155	358.221	16/13
156	360.532
157	362.843
158	365.155
159	367.466	21/17, 26/21
160	369.777
161	372.088
162	374.399
163	376.71
164	379.021
165	381.332
166	383.643
167	385.954
168	388.266	5/4
169	390.577
170	392.888
171	395.199
172	397.51	34/27
173	399.821
174	402.132	24/19
175	404.443
176	406.754
177	409.065	19/15
178	411.377
179	413.688	33/26
180	415.999
181	418.31	14/11
182	420.621	51/40
183	422.932
184	425.243	23/18
185	427.554
186	429.865
187	432.177	50/39
188	434.488	9/7
189	436.799
190	439.11
191	441.421	49/38
192	443.732
193	446.043	22/17
194	448.354
195	450.665	35/27
196	452.976	13/10
197	455.288
198	457.599
199	459.91	30/23
200	462.221
201	464.532	17/13
202	466.843
203	469.154
204	471.465	46/35
205	473.776
206	476.088	25/19
207	478.399	33/25
208	480.71
209	483.021
210	485.332
211	487.643
212	489.954
213	492.265
214	494.576
215	496.887	4/3
216	499.199
217	501.51
218	503.821
219	506.132
220	508.443	51/38
221	510.754
222	513.065
223	515.376
224	517.687
225	519.999	27/20
226	522.31
227	524.621	23/17
228	526.932
229	529.243	19/14
230	531.554
231	533.865
232	536.176
233	538.487	15/11
234	540.798	26/19
235	543.11
236	545.421
237	547.732
238	550.043
239	552.354	11/8
240	554.665
241	556.976
242	559.287
243	561.598
244	563.909	18/13
245	566.221
246	568.532
247	570.843	25/18
248	573.154	39/28
249	575.465	46/33
250	577.776
251	580.087
252	582.398	7/5
253	584.709
254	587.021
255	589.332
256	591.643	38/27
257	593.954
258	596.265	24/17
259	598.576
260	600.887
261	603.198	17/12
262	605.509
263	607.82	27/19
264	610.132
265	612.443
266	614.754
267	617.065	10/7
268	619.376
269	621.687
270	623.998	33/23
271	626.309
272	628.62
273	630.932
274	633.243
275	635.554	13/9
276	637.865
277	640.176
278	642.487
279	644.798
280	647.109	16/11
281	649.42
282	651.731
283	654.043
284	656.354
285	658.665	19/13
286	660.976	22/15
287	663.287
288	665.598
289	667.909
290	670.22	28/19
291	672.531
292	674.843	34/23
293	677.154
294	679.465	40/27
295	681.776
296	684.087
297	686.398	49/33
298	688.709
299	691.02
300	693.331
301	695.642
302	697.954
303	700.265
304	702.576	3/2
305	704.887
306	707.198
307	709.509
308	711.82
309	714.131
310	716.442
311	718.753
312	721.065	50/33
313	723.376	38/25
314	725.687
315	727.998	35/23
316	730.309
317	732.62
318	734.931	26/17
319	737.242
320	739.553	23/15
321	741.865
322	744.176
323	746.487	20/13
324	748.798	54/35
325	751.109
326	753.42	17/11
327	755.731
328	758.042
329	760.353
330	762.664
331	764.976	14/9
332	767.287
333	769.598
334	771.909
335	774.22	36/23
336	776.531
337	778.842
338	781.153	11/7
339	783.464
340	785.776	52/33
341	788.087
342	790.398	30/19
343	792.709
344	795.02
345	797.331	19/12
346	799.642
347	801.953	27/17
348	804.264
349	806.575
350	808.887	51/32
351	811.198
352	813.509
353	815.82
354	818.131
355	820.442
356	822.753	45/28
357	825.064
358	827.375
359	829.687
360	831.998	21/13, 34/21
361	834.309
362	836.62
363	838.931
364	841.242	13/8
365	843.553	44/27
366	845.864
367	848.175
368	850.486	49/30
369	852.798	18/11
370	855.109
371	857.42
372	859.731	23/14
373	862.042
374	864.353	28/17
375	866.664	33/20
376	868.975	38/23
377	871.286
378	873.598
379	875.909
380	878.22
381	880.531
382	882.842
383	885.153	5/3
384	887.464
385	889.775
386	892.086
387	894.397
388	896.709	42/25
389	899.02
390	901.331
391	903.642
392	905.953
393	908.264
394	910.575	22/13
395	912.886	39/23
396	915.197
397	917.508	17/10
398	919.82
399	922.131	46/27
400	924.442
401	926.753
402	929.064
403	931.375	12/7
404	933.686
405	935.997
406	938.308
407	940.62
408	942.931
409	945.242
410	947.553	19/11
411	949.864
412	952.175
413	954.486	33/19
414	956.797	40/23
415	959.108
416	961.419
417	963.731
418	966.042
419	968.353
420	970.664	7/4
421	972.975
422	975.286
423	977.597
424	979.908
425	982.219
426	984.531	30/17
427	986.842
428	989.153	23/13
429	991.464	39/22
430	993.775
431	996.086
432	998.397
433	1000.708
434	1003.019
435	1005.33	25/14, 34/19
436	1007.642
437	1009.953
438	1012.264
439	1014.575
440	1016.886	9/5
441	1019.197
442	1021.508
443	1023.819
444	1026.13	38/21
445	1028.442
446	1030.753
447	1033.064	49/27
448	1035.375	20/11
449	1037.686	51/28
450	1039.997
451	1042.308	42/23
452	1044.619
453	1046.93
454	1049.241	11/6
455	1051.553
456	1053.864	46/25
457	1056.175
458	1058.486	35/19
459	1060.797	24/13
460	1063.108
461	1065.419
462	1067.73	50/27
463	1070.041	13/7
464	1072.352
465	1074.664
466	1076.975
467	1079.286	28/15
468	1081.597
469	1083.908
470	1086.219
471	1088.53
472	1090.841
473	1093.152	32/17
474	1095.464
475	1097.775
476	1100.086	17/9
477	1102.397
478	1104.708	36/19
479	1107.019
480	1109.33
481	1111.641	19/10
482	1113.952	40/21
483	1116.263
484	1118.575
485	1120.886	21/11, 44/23
486	1123.197
487	1125.508
488	1127.819	23/12
489	1130.13
490	1132.441	52/27
491	1134.752
492	1137.063	27/14
493	1139.375
494	1141.686
495	1143.997
496	1146.308
497	1148.619	33/17
498	1150.93
499	1153.241	35/18
500	1155.552	39/20
501	1157.863
502	1160.174
503	1162.486	45/23
504	1164.797	49/25
505	1167.108	51/26
506	1169.419
507	1171.73
508	1174.041
509	1176.352
510	1178.663
511	1180.974
512	1183.286
513	1185.597
514	1187.908
515	1190.219
516	1192.53
517	1194.841
518	1197.152
519	1199.463	2/1

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
	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
	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)

11syfx contd.

Harmonic		83	89	97	101	103	107	109	113	127	131	137
Error	Absolute (¢)	-0.22	-0.87	+0.34	-0.29	+0.43	-0.82	-0.52	-0.51	+0.66	+0.13	-1.14
	Relative (%)	-9.4	-37.7	+14.6	-12.5	+18.7	-35.3	-22.6	-22.3	+28.5	+5.5	-49.1
Steps (reduced)		3310 (10)	3362 (7)	3427 (6)	3457 (3)	3472 (7)	3500 (2)	3514 (5)	3541 (10)	3629 (10)	3652 (0)	3685 (0)

519edo, 823edt, 1206ed5, 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
	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
	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
	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
	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 1206ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.91	-0.52	+0.00	-0.30	+0.43	+0.02	-0.03	-0.82	+1.11	-0.50	-0.44
	Relative (%)	-39.6	-22.3	+0.0	-12.9	+18.5	+0.7	-1.2	-35.6	+48.0	-21.6	-18.9
Steps (reduced)		519 (519)	823 (823)	1206 (0)	1458 (252)	1797 (591)	1922 (716)	2123 (917)	2206 (1000)	2350 (1144)	2523 (111)	2573 (161)

1206ed5 contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.53	+0.71	-0.88	-0.07	-0.14	-0.97	-0.93	+0.69	-0.35	+0.07	-0.37
	Relative (%)	+23.1	+30.9	-38.0	-3.1	-5.9	-42.1	-40.1	+29.8	-15.4	+3.0	-15.8
Steps (reduced)		2706 (294)	2783 (371)	2818 (406)	2885 (473)	2975 (563)	3055 (643)	3080 (668)	3151 (739)	3194 (782)	3215 (803)	3274 (862)

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
	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
	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)

The twelfth sooty fox scale

← 11ed343/338

12ed343/338

13ed343/338 →

Prime factorization	22 × 3
Step size	2.11853¢
Octave	566\12ed343/338 (1199.09¢) (→283\6ed343/338)
Twelfth	898\12ed343/338 (1902.44¢) (→449\6ed343/338)
Consistency limit	2
Distinct consistency limit	2
Special properties	Highly composite

12ed343/338 or 12syfx for short.

Harmonics

Approximation of harmonics in 12syfx

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.910	+0.488	-0.443	-0.358	+1.007	-0.083	-0.552	-0.323	-0.593	+0.626	-0.432
	Relative (%)	-43.0	+23.0	-20.9	-16.9	+47.5	-3.9	-26.0	-15.2	-28.0	+29.5	-20.4
Steps (reduced)		566 (2)	898 (10)	1315 (7)	1590 (6)	1960 (4)	2096 (8)	2315 (11)	2406 (6)	2562 (6)	2752 (4)	2806 (10)

12syfx contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.447	+0.685	+0.853	-0.602	-0.984	-0.220	-0.732	-0.028	-0.846	-0.213	+0.744
	Relative (%)	+21.1	+32.3	+40.2	-28.4	-46.4	-10.4	-34.6	-1.3	-39.9	-10.0	+35.1
Steps (reduced)		2951 (11)	3035 (11)	3074 (2)	3146 (2)	3244 (4)	3332 (8)	3359 (11)	3436 (4)	3483 (3)	3506 (2)	3571 (7)

566edo, 898edt, 1315ed5, 331edf, for comparison:

Approximation of prime harmonics in 566edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.188	-0.448	+0.079	-0.081	-0.952	+1.052	-0.693	-0.713	+0.811	-0.159
	Relative (%)	+0.0	-8.9	-21.1	+3.7	-3.8	-44.9	+49.6	-32.7	-33.6	+38.3	-7.5
Steps (reduced)		566 (0)	897 (331)	1314 (182)	1589 (457)	1958 (260)	2094 (396)	2314 (50)	2404 (140)	2560 (296)	2750 (486)	2804 (540)

566edo contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.953	-0.794	-0.564	+0.218	-0.006	+0.899	+0.430	-0.862	+0.515	-0.934	+0.127
	Relative (%)	+44.9	-37.4	-26.6	+10.3	-0.3	+42.4	+20.3	-40.6	+24.3	-44.1	+6.0
Steps (reduced)		2949 (119)	3032 (202)	3071 (241)	3144 (314)	3242 (412)	3330 (500)	3357 (527)	3433 (37)	3481 (85)	3503 (107)	3568 (172)

Approximation of prime harmonics in 898edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.900	+0.000	+0.961	+0.896	-0.058	+0.897	+0.309	+0.489	+0.134	-0.869	+0.162
	Relative (%)	+42.5	+0.0	+45.4	+42.3	-2.7	+42.4	+14.6	+23.1	+6.3	-41.0	+7.7
Steps (reduced)		567 (567)	898 (0)	1316 (418)	1591 (693)	1960 (164)	2097 (301)	2316 (520)	2407 (611)	2563 (767)	2752 (58)	2807 (113)

898edt contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.962	-0.963	-0.817	-0.192	-0.627	+0.089	-0.438	+0.225	-0.619	+0.001	+0.923
	Relative (%)	+45.4	-45.5	-38.6	-9.1	-29.6	+4.2	-20.7	+10.6	-29.2	+0.1	+43.6
Steps (reduced)		2952 (258)	3035 (341)	3074 (380)	3147 (453)	3245 (551)	3333 (639)	3360 (666)	3437 (743)	3484 (790)	3507 (813)	3572 (878)

Approximation of prime harmonics in 1315ed5

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.720	+0.790	+0.000	+0.177	-0.452	+0.623	+0.228	+0.488	+0.270	-0.567	+0.513
	Relative (%)	-34.0	+37.3	+0.0	+8.4	-21.3	+29.4	+10.8	+23.0	+12.7	-26.7	+24.2
Steps (reduced)		566 (566)	898 (898)	1315 (0)	1590 (275)	1959 (644)	2096 (781)	2315 (1000)	2406 (1091)	2562 (1247)	2751 (121)	2806 (176)

1315ed5 contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-0.678	-0.412	-0.231	+0.458	+0.109	+0.902	+0.399	-0.989	+0.327	+0.968	-0.172
	Relative (%)	-32.0	-19.4	-10.9	+21.6	+5.1	+42.6	+18.8	-46.7	+15.4	+45.7	-8.1
Steps (reduced)		2950 (320)	3034 (404)	3073 (443)	3146 (516)	3244 (614)	3332 (702)	3359 (729)	3435 (805)	3483 (853)	3506 (876)	3570 (940)

Approximation of prime harmonics in 331edf

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.322	+0.322	+0.299	+0.982	+1.032	+0.239	+0.247	+0.674	+0.743	+0.255	-0.686
	Relative (%)	+15.2	+15.2	+14.1	+46.3	+48.7	+11.3	+11.6	+31.8	+35.0	+12.0	-32.3
Steps (reduced)		566 (235)	897 (235)	1314 (321)	1589 (265)	1958 (303)	2094 (108)	2313 (327)	2404 (87)	2560 (243)	2749 (101)	2803 (155)

331edf contd.

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+0.509	+0.930	-0.938	-0.115	-0.284	+0.672	+0.218	-1.030	+0.374	+1.058	+0.036
	Relative (%)	+24.0	+43.9	-44.2	-5.4	-13.4	+31.7	+10.3	-48.6	+17.6	+49.9	+1.7
Steps (reduced)		2948 (300)	3032 (53)	3070 (91)	3143 (164)	3241 (262)	3329 (19)	3356 (46)	3432 (122)	3480 (170)	3503 (193)	3567 (257)