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.

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.

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)
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