Harmonics

Relative frequencies of the first eight harmonics for five octaves of chromatic pitches

c

1

2

3

4

5

6

7

8

1.059463

2.118926

3.178389

4.237852

5.297315

6.356779

7.416242

8.475705

d

1.122462

2.244924

3.367386

4.489848

5.61231

6.734772

7.857234

8.979696

1.189207

2.378414

3.567621

4.756828

5.946036

7.135243

8.32445

9.513657

e

1.259921

2.519842

3.779763

5.039684

6.299605

7.559526

8.819447

10.07937

f

1.33484

2.66968

4.00452

5.339359

6.674199

8.009039

9.343879

10.67872

1.414214

2.828427

4.242641

5.656854

7.071068

8.485281

9.899495

11.31371

g

1.498307

2.996614

4.494921

5.993228

7.491535

8.989842

10.48815

11.98646

1.587401

3.174802

4.762203

6.349604

7.937005

9.524406

11.11181

12.69921

a

1.681793

3.363586

5.045378

6.727171

8.408964

10.09076

11.77255

13.45434

1.781797

3.563595

5.345392

7.12719

8.908987

10.69078

12.47258

14.25438

b

1.887749

3.775497

5.663246

7.550995

9.438743

11.32649

13.21424

15.10199

c

2

4

6

8

10

12

14

16

2.118926

4.237852

6.356779

8.475705

10.59463

12.71356

14.83248

16.95141

d

2.244924

4.489848

6.734772

8.979696

11.22462

13.46954

15.71447

17.95939

2.378414

4.756828

7.135243

9.513657

11.89207

14.27049

16.6489

19.02731

e

2.519842

5.039684

7.559526

10.07937

12.59921

15.11905

17.63889

20.15874

f

2.66968

5.339359

8.009039

10.67872

13.3484

16.01808

18.68776

21.35744

2.828427

5.656854

8.485281

11.31371

14.14214

16.97056

19.79899

22.62742

g

2.996614

5.993228

8.989842

11.98646

14.98307

17.97968

20.9763

23.97291

3.174802

6.349604

9.524406

12.69921

15.87401

19.04881

22.22361

25.39842

a

3.363586

6.727171

10.09076

13.45434

16.81793

20.18151

23.5451

26.90869

3.563595

7.12719

10.69078

14.25438

17.81797

21.38157

24.94516

28.50876

b

3.775497

7.550995

11.32649

15.10199

18.87749

22.65298

26.42848

30.20398

c

4

8

12

16

20

24

28

32

4.237852

8.475705

12.71356

16.95141

21.18926

25.42711

29.66497

33.90282

d

4.489848

8.979696

13.46954

17.95939

22.44924

26.93909

31.42894

35.91879

4.756828

9.513657

14.27049

19.02731

23.78414

28.54097

33.2978

38.05463

e

5.039684

10.07937

15.11905

20.15874

25.19842

30.23811

35.27779

40.31747

f

5.339359

10.67872

16.01808

21.35744

26.6968

32.03616

37.37552

42.71488

5.656854

11.31371

16.97056

22.62742

28.28427

33.94113

39.59798

45.25483

g

5.993228

11.98646

17.97968

23.97291

29.96614

35.95937

41.9526

47.94583

6.349604

12.69921

19.04881

25.39842

31.74802

38.09763

44.44723

50.79683

a

6.727171

13.45434

20.18151

26.90869

33.63586

40.36303

47.0902

53.81737

7.12719

14.25438

21.38157

28.50876

35.63595

42.76314

49.89033

57.01752

b

7.550995

15.10199

22.65298

30.20398

37.75497

45.30597

52.85696

60.40796

c

8

16

24

32

40

48

56

64

8.475705

16.95141

25.42711

33.90282

42.37852

50.85423

59.32993

67.80564

d

8.979696

17.95939

26.93909

35.91879

44.89848

53.87818

62.85787

71.83757

9.513657

19.02731

28.54097

38.05463

47.56828

57.08194

66.5956

76.10926

e

10.07937

20.15874

30.23811

40.31747

50.39684

60.47621

70.55558

80.63495

f

10.67872

21.35744

32.03616

42.71488

53.39359

64.07231

74.75103

85.42975

11.31371

22.62742

33.94113

45.25483

56.56854

67.88225

79.19596

90.50967

g

11.98646

23.97291

35.95937

47.94583

59.93228

71.91874

83.9052

95.89165

12.69921

25.39842

38.09763

50.79683

63.49604

76.19525

88.89446

101.5937

a

13.45434

26.90869

40.36303

53.81737

67.27171

80.72606

94.1804

107.6347

14.25438

28.50876

42.76314

57.01752

71.2719

85.52628

99.78066

114.035

b

15.10199

30.20398

45.30597

60.40796

75.50995

90.61193

105.7139

120.8159

c

16

32

48

64

80

96

112

128

16.95141

33.90282

50.85423

67.80564

84.75705

101.7085

118.6599

135.6113

d

17.95939

35.91879

53.87818

71.83757

89.79696

107.7564

125.7157

143.6751

19.02731

38.05463

57.08194

76.10926

95.13657

114.1639

133.1912

152.2185

e

20.15874

40.31747

60.47621

80.63495

100.7937

120.9524

141.1112

161.2699

f

21.35744

42.71488

64.07231

85.42975

106.7872

128.1446

149.5021

170.8595

22.62742

45.25483

67.88225

90.50967

113.1371

135.7645

158.3919

181.0193

g

23.97291

47.94583

71.91874

95.89165

119.8646

143.8375

167.8104

191.7833

25.39842

50.79683

76.19525

101.5937

126.9921

152.3905

177.7889

203.1873

a

26.90869

53.81737

80.72606

107.6347

134.5434

161.4521

188.3608

215.2695

28.50876

57.01752

85.52628

114.035

142.5438

171.0526

199.5613

228.0701

b

30.20398

60.40796

90.61193

120.8159

151.0199

181.2239

211.4278

241.6318

c

32

64

96