The 66 Harmonically Resonant Divisions of An Octave

Ratio
Decimal
Cents From Tonic


Cents Off Tempered
1/1
1.000000
00.000

Tonic D
0.000
81/80
1.012500
21.506
 
21.506
46/45
1.022222
38.051


38.051
31/30
1.033333
56.767
 
-43.230
25/24
1.041667
70.672


-29.330
256/243
1.053498
90.225
 
-9.775


100.00

Tempered
D#/Eb
16/15
1.066667
111.73


11.731
27/25
1.080000
133.24
 
33.238
135/124
1.088710
147.14


47.143
11/10
1.100000
165.00
 
-35.000
10/9
1.111111
182.40


-17.600


200.00

Tempered
E/Fb
9/8
1.125000
203.91
 
3.910
256/225
1.137778
223.46


23.463
15/13
1.153846
247.74
 
47.741
93/80
1.162500
260.68


-39.320
75/64
1.171875
274.58
 
-25.420
32/27
1.185185
294.13


-5.865


300.00

Tempered
F/E#
6/5
1.200000
315.64


15.641
75/62
1.209677
329.55
 
29.547
128/105
1.219048
342.91


42.905
100/81
1.234568
364.81
 
-35.190
5/4
1.250000
386.31


-13.690


400.00

Tempered
F#/Gb
81/64
1.265250
407.82
 
7.820
32/25
1.280000
427.37


27.373
31/24
1.291667
443.80
 
43.081
125/96
1.302083
456.99


-43.010
320/243
1.316872
476.54
 
-23.460
4/3
1.333333
498.04


-1.955


500.00
 
Tempered
G
27/20
1.350000
519.55
 
19.551
512/375
1.365333
539.10


39.104
62/45
1.377778
554.81
 
-45.190
25/18
1.388889
568.72


-31.280
45/32
1.406250
590.22
 
-9.776


600.00

Tempered
G#/Ab
64/45
1.422222
609.78


9.776
36/25
1.440000
631.28
 
31.283
90/62
1.451613
645.19


45.188
375/256
1.464844
660.90
 
-39.100
40/27
1.481481
680.45


-19.550


700.00

Tempered
A
3/2
1.500000
701.96
 
1.955
243/160
1.518750
723.46


23.461
192/125
1.536000
743.01
 
43.014
31/20
1.550000
758.72
 
-41.280
25/16
1.562500
772.63
 
-27.370
128/81
1.580247
792.78


-7.820


800.00

Tempered
A#/Bb
8/5
1.600000
813.69
 
13.686
50/31
1.612903
827.59


27.592
81/50
1.620000
835.19
 
35.193
400/243
1.646091
862.85
 
-37.150
5/3
1.666667
884.36
 
-15.640


900.00

Tempered
B/Cb
27/16
1.687500
905.87


5.865
128/75
1.706670
925.42
 
25.418
31/18
1.722222
941.13


41.126
125/72
1.736111
955.03
 
-44.970
225/128
1.757813
976.54


-23.460
16/9
1.777778
996.09
 
-3.910


1000.0
 
Tempered
C
9/5
1.800000
1017.6


17.596
29/16
1.812500
1029.6
 
29.577
11/6
1.833333
1049.4


49.363
50/27
1.851852
1066.8
 
-33.240
15/8
1.875000
1088.3
 
-11.730


1100.0

Tempered
C#/Db
243/128
1.898438
1109.8
 
9.775
48/25
1.920000
1129.3


29.328
31/16
1.937500
1145.0
 
45.036
125/64
1.953125
1158.9


-41.060
160/81
13975309
1178.5
 
-21.510
2/1
2.000000
1200.0
 
Octave D
0.000

HTML version of Harmonic Grid created by Sherwood Jessie