HARMONIC INTERVALS BY RATIO
NOTE: ON THE CD VERSION OF HARMONIC LAW: THE SCIENCE OF VIBRATION, THIS CHART IS INTERACTIVE
AND ALLOWS THE COMPUTATION OF ALL KNOWN INTERVALS/PARTIALS/OVERTONES OF ANY FUNDAMENTAL
FREQUENCY, AS WELL AS, THE STRING LENGTH RATIOS OF ANY MONOCHORD LENGTH.
Descend Zero (0) = Nothing 1:2 2.00 0.5 120 -1200 -180
One Eighth (1/8th) of Total 9:16 1.78 0.5625 106.666 -1050 -157.5
One Fourth (1/4th) of Total 5:8 1.60 0.625 96 -900 -135
One Third (1/3rd) of Total 2:3 1.50 0.666666 90 -8190 -120
One Half (1/2) of Total 3:4 1.33 0.75 80 -600 -90
Two Thirds (2/3) of Total 5:6 1.20 0.833333 72 -400 -60
Seven Eighths (7/8ths) of Total 5:16 1.07 0.9375 64 -150 -22.5
Unison-Tonic (Asc/Des Do) 1:1 1 1 60 0 0
Schisma, Comma-, Diaschisma 10240:10125 0.98877 1.011358 59.3261 13.629 4.08888
Comma/Komma (Major) 81:80 0.98765 1.0125 59.2592 15 4.5
Enharmonic Diesis 128:125 0.97656 1.024 58.5937 28.8 8.64
Minor Semitone/Chrom. Diesis 25:24 0.96 1.041666 57.6 50 15
Pythagorean Semitone/Leimma 256:243 0.94922 1.053497 56.9531 64.197 19.2592
Greater Chromatic Semitone 135:128 0.94815 1.054687 56.8888 65.625 19.6875
Lucy Scale Tonic # 0.94604 1.057041 56.7621 68.4499 20.5349
Major Semitone/Limma 16:15 0.9375 1.066667 56.25 80 24
Apotome Pythagorica 2187:2048 0.93644 1.067871 56.1865 81.4453 24.4335
Minor Second 27:25 0.92593 1.08 55.5555 96 28.8
Equal Temperment (ET-12) Tonic# 0.91667 1.0833 55 29.9988
Lucy Scale 2ndb 23:64 0.90735 1.102116 54.4407 122.54 36.7619
Minor Tone/Smaller Step 10:9 0.9 1.111111 54 133.333 40
Major Second/Sesquioctave 9:8 0.8889 1.125 53.3333 150 45
Just Intonation (12th Harmonic) 8:7 0.875 1.142857 52.5 171.429 51.4285
Lucy Scale 2nd 0.86269 1.159158 51.7617 190.99 57.2969
Just Intonation (10th) &ET-122nd) 7:6 0.85714 1.166666 51.4285 200 60
Augmented Second 75:64 0.85333 1.171875 52.5 206.25 61.875
Minor Third/Sesquiquintan 6:5 0.8333 1.2 50 240 72
Lucy Scale 2nd# 0.82223 1.2162 49.3339 259.44 77.832
Just Intonation (21st Harmonic) 11:9 0.81818 1.222222 49.0909 266.667 80
Major Third/Sesquiquartan 5:4 0.8 1.261266 47.571 313.52 94.0559
Diminshed Fourth 32:25 0.78125 1.28 46.875 336 100.8
Just Intonation (14th Harmonic) 9:7 0.77778 1.285714 46.6666 342.857 102.857
Augmented Third 125:96 0.768 1.302083 46.6666 362.5 108.75
Lucy Scale 3rd# 0.75855 1.318308 45.5128 381.97 114.591
Perfect Fourth/Sesquitertan 4:3 0.75 1.333333 46.08 400 120
Just Intonation (20th Harmonic) 11:8 0.73873 1.353668 44.324 424.402 127.320
Lucy Scale 4thb 0.73349 1.36335 44.0092 436.02 130.806
Lucy Scale 3rd# 0.72709 1.37535 43.6252 1.37535 450.42
Augmented Fourth 25:18 0.72 1.388888 44.324 1.388888 466.667
Just Intonation (9th Harmonic) 7:5 0.71429 1.4 43.2 1.4 480
Tritone 45:32 0.71111 1.40625 43.2 1.40625 487.5
Equal Temperment (ET-12) 4th 0.70588 1.416666 42.6666 1.416666 499.999
Lucy Scale 4th 0.70401 1.420425 42.2408 1.420425 504.51
Diminshed Fifth 64:45 0.70313 1.422222 42.1875 1.422222 506.667
Just Intonation (15th Harmonic) 10:7 0.7 1.428571 42 1.428571 514.286
Diminshed Fifth 36:25 0.69444 1.44 4 42 1.44 528
Lucy Scale 4th# 0.67683 1.477466 40.6100 1.477466 572.96
Perfect Fifth/Fibro. 1st Har. 3:2 0.6667 1.5 40 1.5 600
Lucy Scale 5thb 0.6568 1.522533 39.40801 1.5225333 627.04
Just Intonation (3rd Harmonic) 14:9 0.64286 1.555555 38.5714 1.555555 666.667
Augmented Fifth 25:16 0.64 1.5625 38.5714 1.5625 675
Just Intonation (19th Harmonic) 11:7 0.63662 1.570804 36.661 1.570804 684.965
Lucy Scale 5th 0.63308 1.579575 35 1.579575 695.49
Equal Temperment (ET-12) 5th 0.62999 1.58733 38.197 1.58733 700
Minor Sixth/Fibro. 2nd Har. 8:5 0.625 1.6 37.7993 1.6 720
Fibonacci 3rd Harmonic 21:13 0.61905 1.615384 37.1429 1.615384 738.462
Fibonacci 8th Harmonic 1597:987 0.61803 1.618034 37.0820 1.618034 741.641
Fibonacci 7th Harmonic 610:377 0.61803 1.618037 37.0819 1.618031 741.645
Fibonacci 6th Harmonic 233:144 0.61803 1.618055 37.0815 1.618055 741.667
Fibonacci 5th Harmonic 89:55 0.61798 1.618181 37.0786 1.618181 741.818
Fibonacci 4th Harmonic 34:21 0.61765 1.619047 37.0588 1.619047 742.857
Fibonacci Perfect Har. 6th 13:8 0.61538 1.625 36.9230 1.625 750
Lucy Scale 5th# 0.61102 1.636616 38.4 1.636616 763.94
Major Sixth 5:3 0.6 1.666667 36 1.666667 800
Lucy Scale 6thb 0.59464 1.681691 41.6666 1.681691 818.03
Just Intonation (22st Harmonic) 12:7 0.58333 1.714285 35 1.714285 857.143
Augmented Sixth 125:72 0.576 1.736111 37.9849 1.736111 883.333
Lucy Scale 6th# 0.57513 1.738733 34.5078 1.738733 886.48
Harmonic Seventh 7:4 0.57143 1.75 34.2857 1.75 900
Dominant or Minor Seventh 16:9 0.5625 1.777778 33.75 1.777778 933.333
Lucy Scale 6th# 0.55686 1.795775 48 1.795775 954.93
Equal Temperment (ET-12) 7thb 11:6 0.54545 1.833333 32.7272 1.833333 1000
Minor Seventh/Tonic Seventh 9:5 0.55556 1.8 33.3333 1.8 960
Lucy Scale 7thb 0.54323 1.840841 31.4285 1.840841 1009.01
Just Intonation (23nd Harmonic) 13:7 0.53846 1.857142 32.3076 1.857143 1028.57
Major Seventh 15:8 0.5333 1.875 32.3077 1.875 1050
Lucy Scale 7th# 0.5269 1.897891 31.614 1.897891 1077.47
Equal Temperment (ET-12) 7th 0.52174 1.91666 32 1.91666 1099.99
Diminshed Octave 48:25 0.52083 1.92 31.25 1.92 1104
Lucy Scale Octave b 0.51468 1.942958 30.8807 1.942958 1131.55
Lucy Scale 7th# 0.51153 1.954933 30.6915 1.954933 1145.92
Augmented Seventh 125:64 0.512 1.953125 30.72 1.953125 1143.75
First Octave (1st Overtone) 2:1 0.5 2 30 2 1200
Pythagoras's Leimma 0.4933 2.027229 29.5971 2.027229 1216.34
Minor Ninth 32:15 0.46875 2.133333 28.125 2.133333 1280
Major Ninth 9:4 0.44444 2.25 Re 26.666 2.25 1350
Harmonic Minor Tenth 7:3 0.42857 2.333333 25.7142 2.333333 1400
Minor Tenth 12:5 0.41667 2.4 25 2.4 1440
Major Tenth 5:2 0.4 2.5 24 2.5 1500
Perfect Eleventh 8:3 0.375 2.666666 22.5 2.666666 1600
Harmonic Eleventh 11:4 0.36364 2.75 21.8181 2.75 1650
Augmented Eleventh 45:16 0.35556 2.8125 21.3333 2.8125 1687.5
Perfect Twelfth 3:1 0.33333 3 20 3 1800
Augmented Twelfth 25:8 0.32 3.125 19.2 3.125 1875
Minor Thirteenth 16:5 0.3125 3.2 18.75 3.2 1920
Harmonic Thirteenth 13:4 0.30769 3.25 18.4615 3.25 1950
Major Thirteenth 10:3 0.3 3.333333 18 3.333333 2000
Harmonic Fourteenth 7:2 0.28571 3.5 17.1428 3.5 2100
Dominant Fourteenth 32:9 0.28125 3.555555 16.875 3.555555 2133.33
Tonic Fourteenth 18:5 0.27778 3.6 16.6666 3.6 2160
Major Fourteenth 15:4 0.26667 3.75 16 3.75 2250
Second Octave (3rd OT) 4:1 0.25 4 15 4 2400
Fourth Natural Overtone 5:1 0.2 5 12 5 3000
Fifth Natural Overtone 6:1 0.16667 6 10 6 3600
Sixth Natural Overtone 7:1 0.14286 7 8.57142 7 4200
Third Octave (7th OT) 8:1 0.125 8 7.5 8 4800
Eighth Natural Overtone 9:1 0.11111 9 6.66666 9 5400
Ninth Natural Overtone 10:1 0.1 10 10 6000
Tenth Natural Overtone 11:1 0.09091 11 5.45454 11 6600
Eleventh Natural Overtone 12:1 0.08333 12 12 7200
Twelfth Natural Overtone 13:1 0.07692 13 4.61538 13 7800
Thirteenth Natural Overtone 14:1 0.07143 14 4.28571 14 8400
Fourteenth Natural Overtone 15:1 0.06667 15 15 9000
Fourth Octave (15th OT) 16:1 0.0625 16 3.75 16 9600
Fifth Octave 32:1 0.0313 32 1.875 32 19200
Sixth Octave 64:1 0.0156 64 0.9375 64 38400
Seventh Octave 128:1 0.0078 128 0.46875 128 76800
Eighth Octave 256:1 0.0039 256 0.23438 256 153600
Final Octave Ascend ?:1 ? ? 0 ? ?
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