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

128

160

192

224

256



Frequencies of the first eight harmonics, shown in linear space (harmonics equally spaced




Frequencies of the first eight harmonics, shown in log space (pitches equally spaced)