Tuning Methods

Harmonic Series Tunings

Simple Skip-sets

2- through 20-base, skip 3

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


4-base · 16-base · 17-base · 19-base · 20-base



2-base, Skip 3
2[14]-47
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
121:110.0045.2545170
21717:161.0625104.9650.2150105
33535:321.09375155.140.39050
43819:161.1875297.5142.7643142
555:41.25386.3131.563289
64141:321.28125429.06-25.69-2643
71111:81.375551.32-3.43-3122
82323:161.4375628.27-26.48-2677
94747:321.46875665.51-89.24-8937
102613:81.625840.53-14.22-14175
11147:41.75968.8314.0814128
122929:161.81251029.58-25.17-2561
 1200.00 

2-base · 16-base · 17-base · 19-base · 20-base



4-base, Skip 3
4[13]-46
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
141:110.0011.811255
23417:161.0625104.9616.7717105
33737:321.15625251.3463.1563146
41919:161.1875297.519.32946
5105:41.25386.31-1.88-289
64343:321.34375511.5223.3323125
72211:81.375551.32-36.87-3740
84623:161.4375628.27-59.92-6077
92525:161.5625772.63-15.56-16144
101313:81.625840.53-47.66-4868
1177:41.75968.83-19.36-19128
123131:161.93751145.0456.8557176
 1200.00 

2-base · 4-base · 17-base · 19-base · 20-base



16-base, Skip 3
16-49
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
1161:110.0028.002855
23417:161.0625104.9632.9633105
33737:321.15625251.3479.3479146
41919:161.1875297.5125.512646
5405:41.25386.3114.311489
64343:321.34375511.5239.5240125
72211:81.375551.32-20.68-2140
84623:161.4375628.27-43.73-4477
94949:321.53125737.65-34.35-34109
102525:161.5625772.63-99.37-9935
11287:41.75968.83-3.17-3196
123131:161.93751145.0473.0473176
 1200.00 

2-base · 4-base · 16-base · 19-base · 20-base



17-base, Skip 3
17-50
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
1171:110.0066.5567105
23535:341.02941176550.1816.741750
33819:171.117647059192.5659.1159142
42020:171.176470588281.3647.914889
54141:341.205882353324.11-9.34-943
64422:171.294117647446.3612.9213122
72323:171.352941176523.32-10.13-1077
84747:341.382352941560.55-72.89-7337
95025:171.470588235667.67-65.77-66107
102626:171.529411765735.57-97.87-9868
112929:171.705882353924.62-8.82-9189
123232:171.8823529411095.0461.6062170
 1200.00 

2-base · 4-base · 16-base · 17-base · 20-base



19-base, Skip 3
19-52
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
1191:110.0051.585246
24020:191.05263157988.8040.384089
34343:381.131578947214.0065.5866125
42222:191.157894737253.805.38540
54623:191.210526316330.76-17.66-1877
64949:381.289473684440.14-8.28-8109
72525:191.315789474475.11-73.31-7335
85226:191.368421053543.01-105.41-10568
92828:191.473684211671.31-77.11-77128
103131:191.631578947847.52-0.90-1176
113434:191.7894736841007.4459.0259160
123737:191.9473684211153.83105.41105146
 1200.00 

2-base · 4-base · 16-base · 17-base · 19-base



20-base, Skip 3
20-53
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
1201:110.00100.8010189
24141:401.02542.7543.554443
34411:101.1165.0065.8066122
42323:201.15241.9642.764377
54747:401.175279.19-20.01-2037
6505:41.25386.31-12.89-13107
72613:101.3454.21-44.99-4568
85353:401.325487.19-112.01-11233
92929:201.45643.26-55.94-56156
10328:51.6813.6914.4914170
11357:41.75968.8369.6370155
123819:101.91111.20112.00112142
 1200.00 


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