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.
									Whole 	Ratio 	Harmonic 	 Monochord    String    	Cents	 	Degrees
            NAMEOF					Number Fraction Interval 	  String 	  Length     	From 		of Circle
           INTERVAL					Ratio 	 C/B 	Frequency 	  Length      Ratios    	0-1200 		or Spiral
   
   Descend 	   Zero (0) = Nothing    1:2    2.00     0.5     		120      	0.5      	-1200    	-180
   One Eighth (1/8th) of Total 		 9:16 	1.78     0.5625         106.666     0.5625   	-1050    	-157.5
   One Fourth (1/4th) of Total       5:8    1.60     0.625           96         0.625    	-900     	-135
   One Third (1/3rd) of Total        2:3 	1.50     0.666666 	     90         0.66666   	-8190	 	-120
   One Half (1/2) of Total           3:4 	1.33     0.75 		     80         0.75     	-600     	 -90
   Two Thirds (2/3) of Total         5:6 	1.20     0.833333 	     72         0.833333 	-400    	 -60
   Seven Eighths (7/8ths) of Total  15:16 	1.07     0.9375 	     64         0.9375   	-150    	 -22.5
   Unison-Tonic (Asc/Des Do)         1:1 	1 		 1               60         1.0        	   0		   0   
   Schisma, Comma-, Diaschisma   10240:10125 .98877  1.011358        59.3261    1.011358	 13.629     4.08888
   Comma/Komma (Major)              81:80   0.98765  1.0125          59.2592    1.0125   	 15         4.5
   Enharmonic Diesis               128:125  0.97656  1.024           58.5937    1.024 		 28.8       8.64
   Minor Semitone/Chrom. Diesis     25:24   0.96     1.041666        57.6       1.041666     50        15
   Pythagorean Semitone/Leimma     256:243  0.94922  1.053497        56.9531    1.053497     64.197    19.2592
   Greater Chromatic Semitone      135:128  0.94815  1.054687        56.8888    1.054687     65.625    19.6875
   Lucy Scale Tonic #                     	0.94604  1.057041        56.7621    1.057041     68.4499   20.5349
   Major Semitone/Limma             16:15 	0.9375   1.066667        56.25      1.066667     80        24
   Apotome Pythagorica            2187:2048 0.93644  1.067871        56.1865    1.067871     81.4453   24.4335
   Minor Second                     27:25	0.92593  1.08            55.5555    1.08         96        28.8
   Equal Temperment (ET-12) Tonic#        	0.91667  1.08333         55         1.090909     99.996    29.9988
   Lucy Scale 2ndb                  23:64 	0.90735  1.102116        54.4407    1.102116    122.54     36.7619
   Minor Tone/Smaller Step          10:9 	0.9      1.111111        54         1.111111    133.333    40
   Major Second/Sesquioctave         9:8 	0.8889   1.125           53.3333    1.125       150        45
   Just Intonation (12th Harmonic)   8:7    0.875    1.142857        52.5       1.142857    171.429    51.4285
   Lucy Scale 2nd                           0.86269  1.159158        51.7617    1.159158    190.99     57.2969
   Just Intonation (10th) &ET-122nd) 7:6 	0.85714  1.166666        51.4285    1.166666    200        60
   Augmented Second                 75:64 	0.85333  1.171875        52.5       1.171875    206.25     61.875
   Minor Third/Sesquiquintan         6:5 	0.8333   1.2 3b          50         1.2         240        72
   Lucy Scale 2nd#                       	0.82223  1.2162          49.3339    1.2162      259.44     77.832
   Just Intonation (21st Harmonic)  11:9 	0.81818  1.222222        49.0909    1.222222    266.667	   80
   Major Third/Sesquiquartan         5:4 	0.8      1.25            49.0909    1.25        300        90
   Lucy Scale 3rdb                       	0.79285  1.261266        47.571     1.261266    313.52     94.0559
   Diminshed Fourth                 32:25   0.78125  1.28            46.875     1.28        336       100.8
   Just Intonation (14th Harmonic)   9:7 	0.77778  1.285714        46.6666    1.285714    342.857	  102.857
   Augmented Third                 125:96 	0.768    1.302083        46.6666    1.302083    362.5     108.75
   Lucy Scale 3rd#                        	0.75855  1.318308        45.5128    1.318308    381.97    114.591
   Perfect Fourth/Sesquitertan       4:3 	0.75     1.333333        46.08      1.333333    400	      120
   Just Intonation (20th Harmonic)  11:8 	0.73873  1.353668        44.324     1.353668    424.402	  127.320
   Lucy Scale 4thb                          0.73349  1.36335         44.0092    1.36335     436.02    130.806
   Lucy Scale 3rd#                       	0.72709  1.37535         43.6252    1.37535     450.42    135.126
   Augmented Fourth                 25:18 	0.72     1.388888        44.324     1.388888    466.667   140
   Just Intonation (9th Harmonic)    7:5 	0.71429  1.4             43.2       1.4         480       144
   Tritone                          45:32 	0.71111  1.40625         43.2       1.40625     487.5     146.25
   Equal Temperment (ET-12) 4th           	0.70588  1.416666        42.6666    1.416666    499.999   149.999
   Lucy Scale 4th                         	0.70401  1.420425        42.2408    1.420425    504.51    151.353
   Diminshed Fifth                  64:45 	0.70313  1.422222        42.1875    1.422222    506.667   152
   Just Intonation (15th Harmonic)  10:7 	0.7      1.428571        42         1.428571    514.286   154.285
   Diminshed Fifth                  36:25 	0.69444  1.44 4          42         1.44        528       158.4
   Lucy Scale 4th#                          0.67683  1.477466        40.6100    1.477466    572.96    171.888
   Perfect Fifth/Fibro. 1st Har.     3:2    0.6667   1.5             40         1.5         600       180
   Lucy Scale 5thb                          0.6568   1.522533        39.40801   1.5225333   627.04    188.112
   Just Intonation (3rd Harmonic)   14:9    0.64286  1.555555        38.5714    1.555555    666.667	  200
   Augmented Fifth                  25:16   0.64     1.5625          38.5714    1.5625      675       202.5
   Just Intonation (19th Harmonic)  11:7    0.63662  1.570804        36.661     1.570804    684.965	  205.489
   Lucy Scale 5th                           0.63308  1.579575        35         1.579575    695.49    208.647
   Equal Temperment (ET-12) 5th          	0.62999  1.58733         38.197     1.58733     700       211.438
   Minor Sixth/Fibro. 2nd Har.       8:5 	0.625    1.6             37.7993    1.6         720       216
   Fibonacci 3rd Harmonic           21:13 	0.61905  1.615384        37.1429    1.615384    738.462   221.538
   Fibonacci 8th Harmonic         1597:987 	0.61803  1.618034        37.0820    1.618034    741.641   222.492
   Fibonacci 7th Harmonic          610:377 	0.61803  1.618037        37.0819    1.618031    741.645   222.493
   Fibonacci 6th Harmonic          233:144 	0.61803  1.618055        37.0815    1.618055    741.667   222.5
   Fibonacci 5th Harmonic           89:55 	0.61798  1.618181        37.0786    1.618181    741.818   222.545
   Fibonacci 4th Harmonic           34:21 	0.61765  1.619047        37.0588    1.619047    742.857   222.857
   Fibonacci Perfect Har. 6th       13:8 	0.61538  1.625           36.9230    1.625       750       225
   Lucy Scale 5th#                       	0.61102  1.636616        38.4       1.636616    763.94    229.182
   Major Sixth                       5:3  	0.6      1.666667        36         1.666667    800       240
   Lucy Scale 6thb                       	0.59464  1.681691        41.6666    1.681691    818.03    245.409
   Just Intonation (22st Harmonic)  12:7 	0.58333  1.714285        35         1.714285    857.143   257.142
   Augmented Sixth                 125:72 	0.576    1.736111        37.9849    1.736111    883.333   265
   Lucy Scale 6th#                       	0.57513  1.738733        34.5078    1.738733    886.48    265.944
   Harmonic Seventh                  7:4	0.57143  1.75            34.2857    1.75      	900       270
   Dominant or Minor Seventh        16:9 	0.5625   1.777778        33.75      1.777778    933.333   280
   Lucy Scale 6th#                      	0.55686  1.795775        48         1.795775    954.93    286.479
   Equal Temperment (ET-12) 7thb    11:6 	0.54545  1.833333        32.7272    1.833333   1000       300
   Minor Seventh/Tonic Seventh       9:5 	0.55556  1.8             33.3333    1.8         960       288
   Lucy Scale 7thb                      	0.54323  1.840841        31.4285    1.840841   1009.01    302.703
   Just Intonation (23nd Harmonic)  13:7 	0.53846  1.857142        32.3076    1.857143   1028.57	  308.571
   Major Seventh                    15:8	0.5333   1.875           32.3077    1.875      1050       315
   Lucy Scale 7th#                      	0.5269   1.897891        31.614     1.897891   1077.47    323.241
   Equal Temperment (ET-12) 7th         	0.52174  1.91666         32         1.91666    1099.99    329.997
   Diminshed Octave                 48:25 	0.52083  1.92            31.25      1.92       1104       331.2
   Lucy Scale Octave b                   	0.51468  1.942958        30.8807    1.942958   1131.55    339.465
   Lucy Scale 7th#                       	0.51153  1.954933        30.6915    1.954933   1145.92    343.776
   Augmented Seventh               125:64 	0.512    1.953125        30.72      1.953125   1143.75    343.125
   First Octave (1st Overtone)       2:1  	0.5      2               30         2          1200       360
   Pythagoras's Leimma                   	0.4933   2.027229        29.5971    2.027229   1216.34    364.901
   Minor Ninth                      32:15 	0.46875  2.133333        28.125     2.133333   1280       384
   Major Ninth                       9:4 	0.44444  2.25 Re         26.666     2.25       1350       405
   Harmonic Minor Tenth              7:3 	0.42857  2.333333        25.7142    2.333333   1400       420
   Minor Tenth                      12:5 	0.41667  2.4             25         2.4        1440       432
   Major Tenth                       5:2 	0.4      2.5             24         2.5        1500       450
   Perfect Eleventh                  8:3 	0.375    2.666666        22.5       2.666666   1600       480
   Harmonic Eleventh                11:4 	0.36364  2.75            21.8181    2.75       1650       495
   Augmented Eleventh               45:16 	0.35556  2.8125          21.3333    2.8125     1687.5     506.25
   Perfect Twelfth                   3:1 	0.33333  3               20         3          1800       540
   Augmented Twelfth                25:8 	0.32     3.125           19.2       3.125      1875       562.5
   Minor Thirteenth                 16:5 	0.3125   3.2             18.75      3.2        1920       576
   Harmonic Thirteenth              13:4 	0.30769  3.25            18.4615    3.25       1950       585
   Major Thirteenth                 10:3 	0.3      3.333333        18         3.333333   2000       600
   Harmonic Fourteenth               7:2 	0.28571  3.5             17.1428    3.5        2100       630
   Dominant Fourteenth              32:9	0.28125  3.555555        16.875     3.555555   2133.33    640
   Tonic Fourteenth                 18:5	0.27778  3.6             16.6666    3.6        2160       648
   Major Fourteenth                 15:4	0.26667  3.75            16         3.75       2250       675
   Second Octave (3rd OT)            4:1 	0.25     4               15         4          2400       720
   Fourth Natural Overtone           5:1 	0.2      5               12         5          3000       900
   Fifth Natural Overtone            6:1 	0.16667  6               10         6          3600      1080
   Sixth Natural Overtone            7:1 	0.14286  7                8.57142   7          4200      1260
   Third Octave (7th OT)             8:1 	0.125    8                7.5       8          4800      1440
   Eighth Natural Overtone           9:1 	0.11111  9                6.66666   9          5400      1620
   Ninth Natural Overtone           10:1 	0.1     10                         10         6000       1800
   Tenth Natural Overtone           11:1 	0.09091 11                5.45454  11          6600      1980
   Eleventh Natural Overtone        12:1 	0.08333 12                         12          7200      2160
   Twelfth Natural Overtone         13:1	0.07692 13                4.61538  13         7800       2340
   Thirteenth Natural Overtone      14:1 	0.07143 14                4.28571  14         8400       2520
   Fourteenth Natural Overtone      15:1	0.06667 15                         15         9000       2700
   Fourth Octave (15th OT)          16:1 	0.0625  16                3.75     16         9600       2880
   Fifth Octave                     32:1 	0.0313  32                1.875    32        19200       5760
   Sixth Octave                     64:1	0.0156  64                0.9375   64        38400      11520
   Seventh Octave                  128:1 	0.0078 128                0.46875 128        76800      23040
   Eighth Octave                   256:1 	0.0039 256                0.23438 256       153600      46080
   Final Octave Ascend               ?:1 	   ?    ?                 0        ?           ?          ?