User:BudjarnLambeth/Sooty fox scale: Difference between revisions

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[[47edo]], [[109ed5]] for comparison:
[[47edo]], [[75edt]] for comparison:
{{Harmonics in equal|47|intervals=integer|collapsed=1}}
{{Harmonics in equal|47|intervals=integer|collapsed=1}}
{{Harmonics in equal|109|5|1|intervals=integer|collapsed=1}}
{{Harmonics in equal|75|3|1|intervals=integer|collapsed=1}}


== The second sooty fox scale  ==
== The second sooty fox scale  ==
Line 30: Line 30:




[[94edo]], [[218ed5]] for comparison:
[[94edo]], [[150edt]] for comparison:
{{Harmonics in equal|94|intervals=integer|collapsed=1}}
{{Harmonics in equal|94|intervals=integer|collapsed=1}}
{{Harmonics in equal|218|5|1|intervals=integer|collapsed=1}}
{{Harmonics in equal|150|3|1|intervals=integer|collapsed=1}}


== The third sooty fox scale  ==
== The third sooty fox scale  ==
Line 45: Line 45:




[[142edo]], [[327ed5]] for comparison:
[[142edo]], [[224edt]] for comparison:
{{Harmonics in equal|142|intervals=integer|collapsed=1}}
{{Harmonics in equal|142|intervals=integer|collapsed=1}}
{{Harmonics in equal|327|5|1|intervals=integer|collapsed=1}}
{{Harmonics in equal|224|5|1|intervals=integer|collapsed=1}}


== The fourth sooty fox scale  ==
== The fourth sooty fox scale  ==
Line 57: Line 57:




[[189edo]], [[436ed5]] for comparison:
[[189edo]], [[299edt]] for comparison:
{{Harmonics in equal|189|intervals=integer|collapsed=1}}
{{Harmonics in equal|189|intervals=integer|collapsed=1}}
{{Harmonics in equal|436|5|1|intervals=integer|collapsed=1}}
{{Harmonics in equal|299|3|1|intervals=integer|collapsed=1}}


== The fifth sooty fox scale  ==
== The fifth sooty fox scale  ==
Line 69: Line 69:




[[236edo]], [[545ed5]] for comparison:
[[236edo]], [[374edt]] for comparison:
{{Harmonics in equal|236|intervals=integer|collapsed=1}}
{{Harmonics in equal|236|intervals=integer|collapsed=1}}
{{Harmonics in equal|545|5|1|intervals=integer|collapsed=1}}
{{Harmonics in equal|374|3|1|intervals=integer|collapsed=1}}


[[Category:Equal-step tunings]]
[[Category:Equal-step tunings]]

Revision as of 18:58, 26 October 2024

This page presents a novelty topic.

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

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

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

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

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 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -5.1 +4.7 -10.3 +10.1 -0.4 +12.4 +10.0 +9.4 +5.0 -7.5 -5.6
Relative (%) -20.2 +18.6 -40.5 +39.9 -1.7 +48.6 +39.3 +37.2 +19.7 -29.4 -21.9
Step 47 75 94 110 122 133 142 150 157 163 169


47edo, 75edt for comparison:

Approximation of harmonics in 47edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.0 -12.6 +0.0 -3.3 -12.6 +1.4 +0.0 +0.3 -3.3 +10.4 -12.6
Relative (%) +0.0 -49.3 +0.0 -13.1 -49.3 +5.4 +0.0 +1.4 -13.1 +40.7 -49.3
Steps
(reduced) 		47
(0) 		74
(27) 		94
(0) 		109
(15) 		121
(27) 		132
(38) 		141
(0) 		149
(8) 		156
(15) 		163
(22) 		168
(27)
Approximation of harmonics in 75edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -8.1 +0.0 +9.1 +3.2 -8.1 +4.0 +1.0 +0.0 -4.9 +7.6 +9.1
Relative (%) -32.0 +0.0 +36.1 +12.7 -32.0 +15.7 +4.1 +0.0 -19.3 +30.1 +36.1
Steps
(reduced) 		47
(47) 		75
(0) 		95
(20) 		110
(35) 		122
(47) 		133
(58) 		142
(67) 		150
(0) 		157
(7) 		164
(14) 		170
(20)

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 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -5.15 +4.72 +2.42 -2.56 -0.42 -0.36 -2.73 -3.26 +5.00 +5.24 -5.57
Relative (%) -40.5 +37.2 +19.0 -20.2 -3.3 -2.8 -21.5 -25.7 +39.4 +41.3 -43.8
Steps
(reduced) 		94
(0) 		150
(0) 		189
(1) 		219
(1) 		244
(0) 		265
(1) 		283
(1) 		299
(1) 		314
(0) 		327
(1) 		338
(0)


94edo, 150edt for comparison:

Approximation of harmonics in 94edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.00 +0.17 +0.00 -3.33 +0.17 +1.39 +0.00 +0.35 -3.33 -2.38 +0.17
Relative (%) +0.0 +1.4 +0.0 -26.1 +1.4 +10.9 +0.0 +2.7 -26.1 -18.7 +1.4
Steps
(reduced) 		94
(0) 		149
(55) 		188
(0) 		218
(30) 		243
(55) 		264
(76) 		282
(0) 		298
(16) 		312
(30) 		325
(43) 		337
(55)
Approximation of harmonics in 150edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +4.57 +0.00 -3.54 +3.22 +4.57 +3.97 +1.03 +0.00 -4.89 -5.06 -3.54
Relative (%) +36.1 +0.0 -27.9 +25.4 +36.1 +31.3 +8.2 +0.0 -38.5 -39.9 -27.9
Steps
(reduced) 		95
(95) 		150
(0) 		189
(39) 		220
(70) 		245
(95) 		266
(116) 		284
(134) 		300
(0) 		314
(14) 		327
(27) 		339
(39)

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 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3.33 -3.75 -1.82 +1.68 -0.42 +3.88 +1.51 +0.98 -3.47 +1.01 +2.90
Relative (%) +39.3 -44.2 -21.5 +19.8 -5.0 +45.8 +17.8 +11.5 -41.0 +11.9 +34.3
Steps
(reduced) 		142
(1) 		224
(2) 		283
(1) 		329
(2) 		366
(0) 		398
(2) 		425
(2) 		449
(2) 		470
(2) 		490
(1) 		508
(1)


142edo, 224edt for comparison:

Approximation of harmonics in 142edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.00 -0.55 +0.00 +2.42 -0.55 +3.01 +0.00 -1.09 +2.42 -2.02 -0.55
Relative (%) +0.0 -6.5 +0.0 +28.6 -6.5 +35.6 +0.0 -12.9 +28.6 -23.9 -6.5
Steps
(reduced) 		142
(0) 		225
(83) 		284
(0) 		330
(46) 		367
(83) 		399
(115) 		426
(0) 		450
(24) 		472
(46) 		491
(65) 		509
(83)
Approximation of harmonics in 224ed5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -5.87 +1.20 +0.71 +0.00 -4.67 +2.12 -5.16 +2.39 -5.87 +3.27 +1.90
Relative (%) -47.2 +9.6 +5.7 +0.0 -37.5 +17.0 -41.5 +19.2 -47.2 +26.3 +15.3
Steps
(reduced) 		96
(96) 		153
(153) 		193
(193) 		224
(0) 		249
(25) 		271
(47) 		289
(65) 		306
(82) 		320
(96) 		334
(110) 		346
(122)

The fourth sooty fox scale

← 3ed343/338 4ed343/338 5ed343/338 →
Prime factorization 22 (highly composite)
Step size 6.3556 ¢ 
Octave 189\4ed343/338 (1201.21 ¢)
(convergent)
Twelfth 299\4ed343/338 (1900.32 ¢)
(semiconvergent)
Consistency limit 3
Distinct consistency limit 3

4ed343/338 or 4syfx for short.

Harmonics

Approximation of harmonics in 4syfx
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +1.21 -1.63 +2.42 -2.56 -0.42 -0.36 -2.73 +3.09 -1.35 -1.11 +0.79
Relative (%) +19.0 -25.7 +38.0 -40.3 -6.7 -5.6 -43.0 +48.7 -21.3 -17.5 +12.4
Steps
(reduced) 		189
(1) 		299
(3) 		378
(2) 		438
(2) 		488
(0) 		530
(2) 		566
(2) 		599
(3) 		627
(3) 		653
(1) 		677
(1)


189edo, 299edt for comparison:

Approximation of harmonics in 189edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.00 +2.81 +0.00 +0.99 +2.81 +2.60 +0.00 -0.74 +0.99 +1.06 +2.81
Relative (%) +0.0 +44.2 +0.0 +15.6 +44.2 +41.0 +0.0 -11.6 +15.6 +16.7 +44.2
Steps
(reduced) 		189
(0) 		300
(111) 		378
(0) 		439
(61) 		489
(111) 		531
(153) 		567
(0) 		599
(32) 		628
(61) 		654
(87) 		678
(111)
Approximation of harmonics in 299edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +2.24 +0.00 -1.88 -0.17 +2.24 +2.53 +0.36 +0.00 +2.07 +2.45 -1.88
Relative (%) +35.2 +0.0 -29.6 -2.7 +35.2 +39.8 +5.6 +0.0 +32.5 +38.5 -29.6
Steps
(reduced) 		189
(189) 		299
(0) 		377
(78) 		438
(139) 		488
(189) 		530
(231) 		566
(267) 		598
(0) 		627
(29) 		653
(55) 		676
(78)

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 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -0.06 -0.36 -0.13 -0.02 -0.42 +2.18 -0.19 -0.72 -0.08 -2.38 -0.49
Relative (%) -1.2 -7.1 -2.5 -0.4 -8.3 +43.0 -3.7 -14.2 -1.6 -46.9 -9.6
Steps
(reduced) 		236
(1) 		374
(4) 		472
(2) 		548
(3) 		610
(0) 		663
(3) 		708
(3) 		748
(3) 		784
(4) 		816
(1) 		846
(1)


236edo, 374edt for comparison:

Approximation of harmonics in 236edo
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.00 -0.26 +0.00 +0.13 -0.26 +2.36 +0.00 -0.52 +0.13 -2.17 -0.26
Relative (%) +0.0 -5.1 +0.0 +2.5 -5.1 +46.4 +0.0 -10.2 +2.5 -42.6 -5.1
Steps
(reduced) 		236
(0) 		374
(138) 		472
(0) 		548
(76) 		610
(138) 		663
(191) 		708
(0) 		748
(40) 		784
(76) 		816
(108) 		846
(138)
Approximation of harmonics in 374edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +0.16 +0.00 +0.33 +0.51 +0.16 -2.26 +0.49 +0.00 +0.67 -1.60 +0.33
Relative (%) +3.2 +0.0 +6.5 +10.0 +3.2 -44.5 +9.7 +0.0 +13.2 -31.4 +6.5
Steps
(reduced) 		236
(236) 		374
(0) 		472
(98) 		548
(174) 		610
(236) 		662
(288) 		708
(334) 		748
(0) 		784
(36) 		816
(68) 		846
(98)
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