dreamy piano keyboard

DAVID'S HOME PAGE

TUNING PAGES MENU

Tuning Methods

A. Rational Tunings

· Prime Limit

· Otonal

· Utonal

· Harmonic Series

· Simple Skip-sets

· Skip 2, 5-15 base

· Skip 2, 17-27 base

· Skip 3, 2-20 base

· Skip 3, 22-29 base

· Skip 3, 31-38 base

· ASPluCTs

· Saturated Ratios

· Tetrachords

· Septimal Chromatic

· Hexanies

B. Equal Temperaments

· Octave Repeating

· 13 EDO

· Non-octave Repeating

· 88c

C. Non-Equal, Non-Rational

· Golden Horagramic

· Lucy Tuning™

· 2pi Roots

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Tuning Methods

Harmonic Series Tunings

Simple Skip-sets

5- through 15-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.

 7-base · 9-base · 11-base · 13-base · 15-base

5-base, Skip 2
Odds 5 - 27
Scale
Degree		Harmonic   Ratio   QuotientCentsTuning
Table		Rounded
Tuning
Table		Gap
in
Cents
15
1:1
10.0034.723589
221
21:20
1.0584.4719.191984
311
11:10
1.1165.00-0.28081
423
23:20
1.15241.96-23.32-2377
525
5:4
1.25386.3121.0321144
613
13:10
1.3454.21-11.07-1168
727
27:20
1.35519.55-45.73-4665
87
7:5
1.4582.51-82.77-8363
915
3:2
1.5701.96-63.32-63119
1017
17:10
1.7918.6453.3653217
119
9:5
1.81017.6052.325299
1219
19:10
1.91111.2045.924694
 1200.00 
 Play Tuning
5-base · 9-base · 11-base · 13-base · 15-base

7-base, Skip 2
Odds 7 - 29
Scale
Degree		Harmonic   Ratio   QuotientCentsTuning
Table		Rounded
Tuning
Table		Gap
in
Cents
17
1:1
10.00-18.38-1863
229
29:28
1.03571428660.75-57.63-5861
315
15:14
1.071428571119.44-98.94-9959
417
17:14
1.214285714336.1317.7518217
59
9:7
1.285714286435.0816.701799
619
19:14
1.357142857528.6910.311094
721
3:2
1.5701.9683.5884173
811
11:7
1.571428571782.4964.116481
923
23:14
1.642857143859.4541.074177
1025
25:14
1.7857142861003.8085.4285144
1113
13:7
1.8571428571071.7053.325368
1227
27:14
1.9285714291137.0418.661965
 1200.00 
 Play Tuning
5-base · 7-base · 11-base · 13-base · 15-base

9-base, Skip 2
Odds 9 - 31
Scale
Degree		Harmonic   Ratio   QuotientCentsTuning
Table		Rounded
Tuning
Table		Gap
in
Cents
19
1:1
10.00-15.98-1699
219
19:18
1.05555555693.60-22.38-2294
321
7:6
1.166666667266.8750.8951173
411
11:9
1.222222222347.4131.433181
523
23:18
1.277777778424.368.38877
625
25:18
1.388888889568.7252.7453144
713
13:9
1.444444444636.6220.642168
827
3:2
1.5701.96-14.02-1465
929
29:18
1.611111111825.679.6910124
1015
5:3
1.666666667884.36-31.62-3259
1131
31:18
1.722222222941.13-74.85-7557
1217
17:9
1.8888888891101.05-14.93-15160
 1200.00 
 Play Tuning
5-base · 7-base · 9-base · 13-base · 15-base

11-base, Skip 2
Odds 11 - 33
Scale
Degree		Harmonic   Ratio   QuotientCentsTuning
Table		Rounded
Tuning
Table		Gap
in
Cents
111
1:1
10.0046.984781
223
23:22
1.04545454576.9623.942477
325
25:22
1.136363636221.3168.2968144
413
13:11
1.181818182289.2136.193668
527
27:22
1.227272727354.551.53265
629
29:22
1.318181818478.2625.2425124
715
15:11
1.363636364536.95-16.07-1659
831
31:22
1.409090909593.72-59.30-5957
933
3:2
1.5701.96-51.06-51108
1017
17:11
1.545454545753.64-99.38-9952
1119
19:11
1.727272727946.20-6.82-7193
1221
21:11
1.9090909091119.4666.4466173
 1200.00 
 Play Tuning
5-base · 7-base · 9-base · 11-base · 15-base

13-base, Skip 2
Odds 13 - 35
Scale
Degree		Harmonic   Ratio   QuotientCentsTuning
Table		Rounded
Tuning
Table		Gap
in
Cents
113
1:1
10.0066.216668
227
27:26
1.03846153865.3431.553265
329
29:26
1.115384615189.0555.2655124
415
15:13
1.153846154247.7413.951459
531
31:26
1.192307692304.51-29.28-2957
633
33:26
1.269230769412.75-21.04-21108
717
17:13
1.307692308464.43-69.36-6952
835
35:26
1.346153846514.61-119.18-11950
919
19:13
1.461538462656.99-76.80-77142
1021
21:13
1.615384615830.25-3.54-4173
1123
23:13
1.769230769987.7553.9654157
1225
25:13
1.9230769231132.1098.3198144
 1200.00 
 Play Tuning
5-base · 7-base · 9-base · 11-base · 13-base

15-base, Skip 2
Odds 15 - 37
Scale
Degree		Harmonic   Ratio   QuotientCentsTuning
Table		Rounded
Tuning
Table		Gap
in
Cents
115
1:1
10.0058.985959
231
31:30
1.03333333356.7715.751657
333
11:10
1.1165.0023.9824108
417
17:15
1.133333333216.69-24.33-2452
535
6:5
1.2315.64-25.38-2599
637
37:30
1.233333333363.08-77.94-7847
719
19:15
1.266666667409.24-131.78-13246
821
7:5
1.4582.51-58.51-59173
923
23:15
1.533333333740.01-1.01-1157
1025
5:3
1.666666667884.3643.3443144
1127
9:5
1.81017.6076.5877133
1229
29:15
1.9333333331141.31100.29100124
 1200.00 
 Play Tuning

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2005 by David J. Finnamore
tuning@elvenminstrel.com