Tuning Methods

Harmonic Series Tunings

Simple Skip-sets

17- through 27-base, skip 2

A red number in the Rounded Tuning Table column flags it as beyond the +/-99 cent limit set by some hardware synthesizer tuning tables.


19-base · 21-base · 23-base · 25-base · 27-base

17-base, Skip 2
Odds 17 - 39
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
117
1:1
10.0041.884252
235
35:34
1.02941176550.18-7.94-850
337
37:34
1.088235294146.39-11.73-1296
419
19:17
1.117647059192.56-65.56-6646
539
39:34
1.147058824237.53-120.59-12145
621
21:17
1.235294118365.83-92.29-92128
723
23:17
1.352941176523.32-34.80-35157
825
25:17
1.470588235667.679.5510144
927
27:17
1.588235294800.9142.7943133
1029
29:17
1.705882353924.6266.5067124
1131
31:17
1.8235294121040.0881.9682115
1233
33:17
1.9411764711148.3290.2090108
 1200.00 
 Play Tuning
17-base · 21-base · 23-base · 25-base · 27-base

19-base, Skip 2
Odds 19 - 41
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
119
1:1
10.0027.432746
239
39:38
1.02631578944.97-27.60-2845
341
41:38
1.078947368131.55-41.02-4187
421
21:19
1.105263158173.27-99.30-9942
523
23:19
1.210526316330.76-41.81-42157
625
25:19
1.315789474475.112.543144
727
27:19
1.421052632608.3535.7836133
829
29:19
1.526315789732.0659.4959124
931
31:19
1.631578947847.5274.9575115
1033
33:19
1.736842105955.7683.1983108
1135
35:19
1.8421052631057.6385.0685102
1237
37:19
1.9473684211153.8381.268196
 1200.00 
 Play Tuning
17-base · 19-base · 23-base · 25-base · 27-base

21-base, Skip 2
Odds 21 - 43
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
121
1:1
10.00-37.13-3742
243
43:42
1.02380952440.74-96.39-9641
323
23:21
1.095238095157.49-79.64-80117
425
25:21
1.19047619301.85-35.28-35144
527
9:7
1.285714286435.08-2.05-2133
629
29:21
1.380952381558.8021.6722124
731
31:21
1.476190476674.2537.1237115
833
11:7
1.571428571782.4945.3645108
935
5:3
1.666666667884.3647.2347102
1037
37:21
1.761904762980.5643.434396
1139
13:7
1.8571428571071.7034.573591
1241
41:21
1.9523809521158.2821.152187
 1200.00 
 Play Tuning
17-base · 19-base · 21-base · 25-base · 27-base

23-base, Skip 2
Odds 23 - 45
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
123
1:1
10.00-89.59-9038
225
25:23
1.086956522144.35-45.24-45144
327
27:23
1.173913043277.59-12.00-12133
429
29:23
1.260869565401.3011.7112124
531
31:23
1.347826087516.7627.1727115
633
33:23
1.434782609625.0035.4135108
735
35:23
1.52173913726.8737.2837102
837
37:23
1.608695652823.0733.483396
939
39:23
1.695652174914.2124.622591
1041
41:23
1.7826086961000.7911.201187
1143
43:23
1.8695652171083.24-6.35-682
1245
45:23
1.9565217391161.95-27.64-2879
 1200.00 
 Play Tuning
17-base · 19-base · 21-base · 23-base · 27-base

25-base, Skip 2
Odds 25 - 47
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
125
1:1
10.00-48.34-48107
227
27:25
1.08133.24-15.10-15133
329
29:25
1.16256.958.619124
431
31:25
1.24372.4124.0724115
533
33:25
1.32480.6532.3132108
635
7:5
1.4582.5134.1734102
737
37:25
1.48678.7230.383096
839
39:25
1.56769.8621.522291
941
41:25
1.64856.438.09887
1043
43:25
1.72938.89-9.45-982
1145
9:5
1.81017.60-30.74-3179
1247
47:25
1.881092.88-55.46-5575
 1200.00 
 Play Tuning
17-base · 19-base · 21-base · 23-base · 25-base

27-base, Skip 2
Odds 27 - 49
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
127
1:1
10.00-12.19-12168
229
29:27
1.074074074123.7111.5212124
331
31:27
1.148148148239.1726.9827115
433
33:27
1.222222222347.4135.2235108
535
35:27
1.296296296449.2737.0837102
637
37:27
1.37037037545.4833.293396
739
39:27
1.444444444636.6224.432491
841
41:27
1.518518519723.2011.011187
943
43:27
1.592592593805.65-6.54-782
1045
45:27
1.666666667884.36-27.83-2879
1147
47:27
1.740740741959.64-52.55-5375
1249
49:27
1.8148148151031.79-80.40-8072
 1200.00 
 Play Tuning


Copyright 2005 by David J. Finnamore
All rights reserved.
tuning@elvenminstrel.com