Harmonic Series Tunings: Simple Skip-sets

dreamy piano keyboard

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TUNING PAGES MENU

A. Rational Tunings

· Prime Limit

· 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

· Saturated Ratios

· Tetrachords

· Septimal Chromatic

· Hexanies

B. Equal Temperaments

· Octave Repeating

· Non-octave Repeating

· 88c

C. Non-Equal, Non-Rational

· Golden Horagramic

· Lucy Tuning™

· 2pi Roots

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

Quotient

Cents

Tuning
Table

Rounded
Tuning
Table

Gap
in
Cents

1

17

1

:

1

1

0.00

41.88

42

52

2

35

35

:

34

1.029411765

50.18

-7.94

-8

50

3

37

37

:

34

1.088235294

146.39

-11.73

-12

96

4

19

19

:

17

1.117647059

192.56

-65.56

-66

46

5

39

39

:

34

1.147058824

237.53

-120.59

-121

45

6

21

21

:

17

1.235294118

365.83

-92.29

-92

128

7

23

23

:

17

1.352941176

523.32

-34.80

-35

157

8

25

25

:

17

1.470588235

667.67

9.55

10

144

9

27

27

:

17

1.588235294

800.91

42.79

43

133

10

29

29

:

17

1.705882353

924.62

66.50

67

124

11

31

31

:

17

1.823529412

1040.08

81.96

82

115

12

33

33

:

17

1.941176471

1148.32

90.20

90

108

1200.00

17-base · 21-base · 23-base · 25-base · 27-base

19-base, Skip 2

Odds 19 - 41

Scale
Degree

Harmonic

Ratio

Quotient

Cents

Tuning
Table

Rounded
Tuning
Table

Gap
in
Cents

1

19

1

:

1

1

0.00

27.43

27

46

2

39

39

:

38

1.026315789

44.97

-27.60

-28

45

3

41

41

:

38

1.078947368

131.55

-41.02

-41

87

4

21

21

:

19

1.105263158

173.27

-99.30

-99

42

5

23

23

:

19

1.210526316

330.76

-41.81

-42

157

6

25

25

:

19

1.315789474

475.11

2.54

3

144

7

27

27

:

19

1.421052632

608.35

35.78

36

133

8

29

29

:

19

1.526315789

732.06

59.49

59

124

9

31

31

:

19

1.631578947

847.52

74.95

75

115

10

33

33

:

19

1.736842105

955.76

83.19

83

108

11

35

35

:

19

1.842105263

1057.63

85.06

85

102

12

37

37

:

19

1.947368421

1153.83

81.26

81

96

1200.00

17-base · 19-base · 23-base · 25-base · 27-base

21-base, Skip 2

Odds 21 - 43

Scale
Degree

Harmonic

Ratio

Quotient

Cents

Tuning
Table

Rounded
Tuning
Table

Gap
in
Cents

1

21

1

:

1

1

0.00

-37.13

-37

42

2

43

43

:

42

1.023809524

40.74

-96.39

-96

41

3

23

23

:

21

1.095238095

157.49

-79.64

-80

117

4

25

25

:

21

1.19047619

301.85

-35.28

-35

144

5

27

9

:

7

1.285714286

435.08

-2.05

-2

133

6

29

29

:

21

1.380952381

558.80

21.67

22

124

7

31

31

:

21

1.476190476

674.25

37.12

37

115

8

33

11

:

7

1.571428571

782.49

45.36

45

108

9

35

5

:

3

1.666666667

884.36

47.23

47

102

10

37

37

:

21

1.761904762

980.56

43.43

43

96

11

39

13

:

7

1.857142857

1071.70

34.57

35

91

12

41

41

:

21

1.952380952

1158.28

21.15

21

87

1200.00

17-base · 19-base · 21-base · 25-base · 27-base

23-base, Skip 2

Odds 23 - 45

Scale
Degree

Harmonic

Ratio

Quotient

Cents

Tuning
Table

Rounded
Tuning
Table

Gap
in
Cents

1

23

1

:

1

1

0.00

-89.59

-90

38

2

25

25

:

23

1.086956522

144.35

-45.24

-45

144

3

27

27

:

23

1.173913043

277.59

-12.00

-12

133

4

29

29

:

23

1.260869565

401.30

11.71

12

124

5

31

31

:

23

1.347826087

516.76

27.17

27

115

6

33

33

:

23

1.434782609

625.00

35.41

35

108

7

35

35

:

23

1.52173913

726.87

37.28

37

102

8

37

37

:

23

1.608695652

823.07

33.48

33

96

9

39

39

:

23

1.695652174

914.21

24.62

25

91

10

41

41

:

23

1.782608696

1000.79

11.20

11

87

11

43

43

:

23

1.869565217

1083.24

-6.35

-6

82

12

45

45

:

23

1.956521739

1161.95

-27.64

-28

79

1200.00

17-base · 19-base · 21-base · 23-base · 27-base

25-base, Skip 2

Odds 25 - 47

Scale
Degree

Harmonic

Ratio

Quotient

Cents

Tuning
Table

Rounded
Tuning
Table

Gap
in
Cents

1

25

1

:

1

1

0.00

-48.34

-48

107

2

27

27

:

25

1.08

133.24

-15.10

-15

133

3

29

29

:

25

1.16

256.95

8.61

9

124

4

31

31

:

25

1.24

372.41

24.07

24

115

5

33

33

:

25

1.32

480.65

32.31

32

108

6

35

7

:

5

1.4

582.51

34.17

34

102

7

37

37

:

25

1.48

678.72

30.38

30

96

8

39

39

:

25

1.56

769.86

21.52

22

91

9

41

41

:

25

1.64

856.43

8.09

8

87

10

43

43

:

25

1.72

938.89

-9.45

-9

82

11

45

9

:

5

1.8

1017.60

-30.74

-31

79

12

47

47

:

25

1.88

1092.88

-55.46

-55

75

1200.00

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

27-base, Skip 2

Odds 27 - 49

Scale
Degree

Harmonic

Ratio

Quotient

Cents

Tuning
Table

Rounded
Tuning
Table

Gap
in
Cents

1

27

1

:

1

1

0.00

-12.19

-12

168

2

29

29

:

27

1.074074074

123.71

11.52

12

124

3

31

31

:

27

1.148148148

239.17

26.98

27

115

4

33

33

:

27

1.222222222

347.41

35.22

35

108

5

35

35

:

27

1.296296296

449.27

37.08

37

102

6

37

37

:

27

1.37037037

545.48

33.29

33

96

7

39

39

:

27

1.444444444

636.62

24.43

24

91

8

41

41

:

27

1.518518519

723.20

11.01

11

87

9

43

43

:

27

1.592592593

805.65

-6.54

-7

82

10

45

45

:

27

1.666666667

884.36

-27.83

-28

79

11

47

47

:

27

1.740740741

959.64

-52.55

-53

75

12

49

49

:

27

1.814814815

1031.79

-80.40

-80

72

1200.00

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