User:BudjarnLambeth/Sooty fox scale

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

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

A quick overview of the sooty fox scales:

• 1syfx = An okay dual-7 17-limit tuning
• 2syfx = (poor JI approximation)
• 3syfx = (poor JI approximation)
• 4syfx = A pretty good dual-5 29-limit tuning
• 5syfx = An excellent 5-limit tuning, can be extended to an okay dual-7, dual-11 17-limit tuning
• 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 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 ¢)
Twelfth	75\1ed343/338 (1906.68 ¢)
Consistency limit	3
Distinct consistency limit	3

1ed343/338 or 1syfx for short.

Intervals

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

Harmonics

Approximation of harmonics in 1syfx

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-5.1	+4.7	+10.1	+12.4	-7.5	+8.4	+1.6	+12.4	+12.1	-7.8	+3.8
	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, 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 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) (highly composite)
Step size	12.7112 ¢
Octave	94\2ed343/338 (1194.85 ¢) (→ 47\1ed343/338)
Twelfth	150\2ed343/338 (1906.68 ¢) (→ 75\1ed343/338)
Consistency limit	2
Distinct consistency limit	2

2ed343/338 or 2syfx for short.

Intervals

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

Harmonics

Approximation of harmonics in 2syfx

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-5.15	+4.72	-2.56	-0.36	+5.24	-4.32	+1.57	-0.32	-0.59	+4.86	+3.81
	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, 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 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	8.5
2	16.9
3	25.4
4	33.9	50/49
5	42.4	42/41
6	50.8	35/34
7	59.3	30/29
8	67.8	26/25
9	76.3	23/22
10	84.7
11	93.2
12	101.7	52/49
13	110.2	49/46
14	118.6
15	127.1
16	135.6
17	144.1	25/23
18	152.5
19	161	34/31
20	169.5	43/39
21	178	41/37
22	186.4	49/44
23	194.9	47/42
24	203.4
25	211.9	26/23
26	220.3	25/22, 42/37
27	228.8
28	237.3	47/41
29	245.8
30	254.2	22/19
31	262.7
32	271.2	55/47
33	279.7
34	288.1	13/11
35	296.6	51/43
36	305.1	31/26, 37/31
37	313.6
38	322
39	330.5	23/19
40	339
41	347.4
42	355.9
43	364.4	21/17, 37/30
44	372.9	31/25, 36/29
45	381.3
46	389.8
47	398.3
48	406.8
49	415.2	47/37
50	423.7
51	432.2
52	440.7	49/38
53	449.1
54	457.6	43/33
55	466.1	55/42
56	474.6	25/19, 46/35
57	483	41/31
58	491.5
59	500
60	508.5	55/41
61	516.9	31/23
62	525.4	42/31
63	533.9	34/25
64	542.4	26/19, 41/30
65	550.8
66	559.3	29/21, 47/34
67	567.8
68	576.3
69	584.7
70	593.2	31/22
71	601.7	17/12
72	610.2	37/26
73	618.6	10/7
74	627.1
75	635.6
76	644.1
77	652.5	35/24
78	661
79	669.5
80	677.9	34/23, 37/25
81	686.4	52/35, 55/37
82	694.9
83	703.4
84	711.8
85	720.3	47/31
86	728.8
87	737.3
88	745.7
89	754.2	17/11
90	762.7
91	771.2
92	779.6
93	788.1	41/26
94	796.6	19/12
95	805.1	35/22
96	813.5
97	822	37/23
98	830.5	21/13
99	839
100	847.4	31/19
101	855.9	41/25
102	864.4
103	872.9
104	881.3
105	889.8
106	898.3	42/25
107	906.8
108	915.2
109	923.7	29/17
110	932.2	12/7
111	940.7
112	949.1
113	957.6
114	966.1
115	974.6
116	983	30/17
117	991.5	55/31
118	1000	41/23
119	1008.4	34/19
120	1016.9
121	1025.4	47/26
122	1033.9
123	1042.3	42/23
124	1050.8	11/6
125	1059.3
126	1067.8
127	1076.2	41/22
128	1084.7
129	1093.2	47/25
130	1101.7
131	1110.1	19/10
132	1118.6	21/11
133	1127.1	23/12
134	1135.6
135	1144
136	1152.5	37/19
137	1161
138	1169.5
139	1177.9
140	1186.4
141	1194.9
142	1203.4

Harmonics

Approximation of harmonics in 3syfx

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3.33	-3.75	+1.68	+3.88	+1.01	-0.08	+1.57	+3.91	+3.64	+0.63	+3.81
	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, 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 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 (highly composite)
Step size	6.3556 ¢
Octave	189\4ed343/338 (1201.21 ¢) (convergent)
Twelfth	299\4ed343/338 (1900.32 ¢) (semiconvergent)
Consistency limit	3
Distinct consistency limit	3

4ed343/338 or 4syfx for short.

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, 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 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	6

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)

236edo, 374edt, 138edf for comparison:

Approximation of prime harmonics in 236edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.26	+0.13	+2.36	-2.17	-1.54	+1.82	+2.49	+2.23	-2.46	-0.97
	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 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)

The sixth sooty fox scale

← 5ed343/338

6ed343/338

7ed343/338 →

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

6ed343/338 or 6syfx for short.

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, 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 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.

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)

320edo, 524edt, 187edf for comparison:

Approximation of prime harmonics in 320edo

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

320edo contd.

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

Approximation of prime harmonics in 524edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+1.43	+0.00	+1.28	-0.48	+1.04	-1.42	-1.25	-1.44	+1.73	-0.30	+0.39
	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 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.

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, 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 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.

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, 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 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	12

10ed343/338 or 10syfx for short.

Harmonics

Approximation of harmonics in 10syfx

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.06	-0.36	-0.02	-0.36	+0.16	+0.76	-0.98	-0.32	-0.59	-0.22	+1.26
	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, 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 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	4

11ed343/338 or 11syfx for short.

Harmonics

Approximation of harmonics in 11syfx

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.53	+0.10	+0.91	+0.80	-0.53	-0.85	-0.74	+0.83	+0.56	-0.92	-0.82
	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)

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

Approximation of prime harmonics in 519edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.94	-0.19	-0.04	-1.03	+1.09	-0.91	+0.75	+0.63	-0.68	-0.53
	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 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 (highly composite)
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

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, 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 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)