Tuning Methods

Harmonic Series Tunings

Simple Skip-sets

5- through 25-base, skip 4

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

 

17-base · 19-base · 21-base · 23-base · 25-base



15-base, Skip 4
15-59
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
1151:110.00-55.67-5629
23131:301.03333333356.77-98.91-9957
3357:61.166666667266.8711.2011210
41919:151.266666667409.2453.5754142
53913:101.3454.21-1.46-145
64343:301.433333333623.2567.5768169
72323:151.533333333740.0184.3384117
84747:301.566666667777.2421.562237
95117:101.7918.6462.9763141
10279:51.81017.6061.926299
115511:61.8333333331049.36-6.31-632
125959:301.9666666671170.9015.2315122
 1200.00 

15-base · 19-base · 21-base · 23-base · 25-base



17-base, Skip 4
17-61
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
1171:110.00-64.16-6452
23737:341.088235294146.39-17.77-18146
34141:341.205882353324.1159.9560178
42121:171.235294118365.831.67242
54545:341.323529412485.2721.1121119
64949:341.441176471632.7068.5469147
72525:171.470588235667.673.51435
85353:341.558823529768.554.394101
95757:341.676470588894.5130.3630126
102929:171.705882353924.62-39.54-4030
116161:341.7941176471011.93-52.23-5287
123333:171.9411764711148.32-15.84-16136
 1200.00 

15-base · 17-base · 21-base · 23-base · 25-base



19-base, Skip 4
19-63
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
1191:110.0028.5329142
23939:381.02631578944.97-26.50-2645
34343:381.131578947214.0042.5443169
42323:191.210526316330.7659.2959117
54747:381.236842105367.99-3.48-337
65151:381.342105263509.4037.9338141
72727:191.421052632608.3536.883799
85555:381.447368421640.12-31.35-3132
95959:381.552631579761.66-9.81-10122
103131:191.631578947847.52-23.95-2486
116363:381.657894737875.22-96.25-9628
123535:191.8421052631057.63-13.84-14182
 1200.00 

15-base · 17-base · 19-base · 23-base · 25-base



21-base, Skip 4
21-65
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
1211:110.0018.181842
24515:141.071428571119.4437.6238119
3497:61.166666667266.8785.0585147
42525:211.19047619301.8520.022035
55353:421.261904762402.7220.9021101
65719:141.357142857528.6946.8647126
72929:211.380952381558.80-23.03-2330
86161:421.452380952646.10-35.72-3687
96565:421.547619048756.06-25.76-26110
103311:71.571428571782.49-99.33-9926
113737:211.761904762980.56-1.26-1198
124141:211.9523809521158.2876.4676178
 1200.00 

15-base · 17-base · 19-base · 21-base · 25-base



23-base, Skip 4
23-67
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
1231:110.0077.4877117
24747:461.0217391337.2314.711537
35151:461.108695652178.6456.1156141
42727:231.173913043277.5955.075599
55555:461.195652174309.36-13.17-1332
65959:461.282608696430.908.378122
73131:231.347826087516.76-5.76-686
86363:461.369565217544.46-78.06-7828
96767:461.456521739651.03-71.49-71107
103535:231.52173913726.87-95.66-9676
113939:231.695652174914.21-8.32-8187
124343:231.8695652171083.2460.7261169
 1200.00 

15-base · 17-base · 19-base · 21-base · 23-base



25-base, Skip 4
25-69
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
1251:110.0038.403835
25353:501.06100.8839.2839101
35757:501.14226.8465.2465126
42929:251.16256.95-4.65-530
56161:501.22344.26-17.34-1787
66513:101.3454.21-7.38-7110
73333:251.32480.65-80.95-8126
86969:501.38557.60-103.99-10477
93737:251.48678.72-82.88-83121
104141:251.64856.43-5.16-5178
11459:51.81017.6056.0056161
124949:251.961165.02103.43103147
 1200.00 


Copyright 2005 by David J. Finnamore
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tuning@elvenminstrel.com