Tuning Methods

Harmonic Series Tunings

Simple Skip-sets

3- through 13-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.

 

5-base · 7-base · 9-base · 11-base · 13-base



3-base, Skip 4
3-47
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
131:110.00-111.52-11236
2279:81.125203.91-7.61-8204
377:61.166666667266.87-44.65-4563
4155:41.25386.31-25.21-25119
53131:241.291666667443.08-68.44-6857
63535:241.458333333653.1841.6642210
71919:121.583333333795.5684.0484142
83913:81.625840.5329.012945
94343:241.7916666671009.5698.0498169
101111:61.8333333331049.3637.843840
112323:121.9166666671126.3214.801577
124747:241.9583333331163.55-47.97-4837
 1200.00 

3-base · 7-base · 9-base · 11-base · 13-base



5-base, Skip 4
5-49
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
151:110.0047.1347135
24141:401.02542.75-10.12-1043
32121:201.0584.47-68.41-6842
4459:81.125203.91-48.96-49119
54949:401.225351.34-1.54-2147
6255:41.25386.31-66.56-6735
71313:101.3454.21-98.66-9968
82929:201.45643.26-9.61-10189
93333:201.65866.96114.09114224
101717:101.7918.6465.776652
1199:51.81017.6064.726599
123737:201.851065.0312.161247
 1200.00 

3-base · 5-base · 9-base · 11-base · 13-base



7-base, Skip 4
7-51
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
171:110.00-53.40-5363
21515:141.071428571119.44-33.95-34119
33131:281.107142857176.21-77.19-7757
4355:41.25386.3132.9233210
51919:141.357142857528.6975.2975142
63939:281.392857143573.6620.262045
74343:281.535714286742.6989.3089169
81111:71.571428571782.4929.102940
92323:141.642857143859.456.05677
104747:281.678571429896.68-56.71-5737
115151:281.8214285711038.08-15.31-15141
122727:141.9285714291137.04-16.36-1699
 1200.00 

3-base · 5-base · 7-base · 11-base · 13-base



9-base, Skip 4
9-53
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
191:110.0031.123199
23737:361.02777777847.43-21.44-2147
34141:361.138888889225.1556.2856178
4217:61.166666667266.87-2.01-242
5455:41.25386.3117.4417119
64949:361.361111111533.7464.8765147
72525:181.388888889568.72-0.16035
81313:91.444444444636.62-32.26-3268
95353:361.472222222669.59-99.28-9933
102929:181.611111111825.67-43.21-43156
113311:61.8333333331049.3680.4980224
121717:91.8888888891101.0532.173252
 1200.00 

3-base · 5-base · 7-base · 9-base · 13-base



11-base, Skip 4
11-55
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
1111:110.0031.703240
22323:221.04545454576.968.65977
34747:441.068181818114.19-54.12-5437
45151:441.159090909255.59-12.71-13141
52727:221.227272727354.55-13.76-1499
6555:41.25386.31-81.99-8232
71515:111.363636364536.95-31.35-31151
83131:221.409090909593.72-74.59-7557
93535:221.590909091803.8235.5236210
101919:111.727272727946.2077.8978142
113939:221.772727273991.1622.862345
124343:221.9545454551160.2091.9092169
 1200.00 

3-base · 5-base · 7-base · 9-base · 11-base



13-base, Skip 4
13-57
Scale
Degree
Harmonic   Ratio   QuotientCentsTuning
Table
Rounded
Tuning
Table
Gap
in
Cents
1131:110.00-5.56-668
25353:521.01923076932.98-72.58-7333
35757:521.096153846158.94-46.61-47126
42929:261.115384615189.05-116.51-11730
53333:261.269230769412.757.197224
61717:131.307692308464.43-41.13-4152
73737:261.423076923610.825.265146
84141:261.576923077788.5382.9883178
92121:131.615384615830.2524.702542
104545:261.730769231949.7044.1444119
114949:261.8846153851097.1291.5792147
122525:131.9230769231132.1026.542735
 1200.00 


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