| Ratio: |
Cents
| Name (if any) |
| 1/1 |
0.000 |
tonic |
| 32805/32768 |
1.954 |
schisma (3 to the 8th/2to the 12th
x 5/8) |
| 126/125 |
13.795 |
|
| 121/120 |
14.367 |
| 100/99 |
17.399 |
| 99/98 |
17.576 |
| 81/80 |
21.506 |
syntonic comma |
| 531441/524288 |
23.460 |
Pythagorean comma (3 to the 12th/2
to the 19th) |
| 65/64 |
26.841 |
65th harmonic |
| 64/63 |
27.264 |
|
| 63/62 |
27.700 |
| 58/57 |
30.109 |
| 57/56 |
30.642 |
| 56/55 |
31.194 |
Ptolemy's enharmonic |
| 55/54 |
31.768 |
|
| 52/51 |
33.618 |
| 51/50 |
34.284 |
| 50/49 |
34.977 |
| 49/48 |
35.698 |
| 46/45 |
38.052 |
inferior quarter-tone (Ptolemy) |
| 45/44 |
38.907 |
|
| 128/125 |
41.059 |
diminished second (16/15 x 24/25) |
| 525/512 |
43.408 |
enharmonic diesis (Avicenna) |
| 40/39 |
43.831 |
|
| 39/38 |
44.970 |
superior quarter-tone (Eratosthenes) |
| 77/75 |
45.561 |
|
| 36/35 |
48.770 |
superior quarter-tone (Archytas) |
| 250/243 |
49.166 |
|
| 35/34 |
50.184 |
E.T. 1/4-tone approximation |
| 34/33 |
51.682 |
|
| 33/32 |
53.273 |
33rd harmonic |
| 32/31 |
54.964 |
inferior quarter-tone (Didymus) |
| 125/121 |
56.305 |
|
| 31/30 |
56.767 |
superior quarter-tone (Didymus) |
| 30/29 |
58.692 |
|
| 29/28 |
60.751 |
| 57/55 |
61.836 |
| 28/27 |
62.961 |
inferior quarter-tone (Archytas) |
| 80/77 |
66.170 |
|
| 27/26 |
65.337 |
| 26/25 |
67.900 |
1/3-tone (Avicenna) |
| 51/49 |
69.261 |
|
| 126/121 |
70.100 |
| 25/24 |
70.672 |
minor 5-limit half-step |
| 24/23 |
73.681 |
|
| 117/112 |
75.612 |
| 23/22 |
76.956 |
| 67/64 |
79.307 |
67th harmonic |
| 22/21 |
80.537 |
hard 1/2-step (Ptolemy, Avicenna,
Safiud) |
| 21/20 |
84.467 |
|
| 81/77 |
87.676 |
| 20/19 |
88.801 |
| 256/243 |
90.225 |
Pythagorean half-step |
| 58/55 |
91.946 |
|
| 135/128 |
92.179 |
limma ascendant |
| 96/91 |
92.601 |
|
| 19/18 |
93.603 |
| 55/52 |
97.107 |
| 128/121 |
97.364 |
| 18/17 |
98.955 |
E.T. half-step approximation |
| 2 to the 1/12th |
100.000 |
equal-tempered half-step |
| 35/33 |
101.867 |
|
| 52/49 |
102.880 |
| 86/81 |
103.698 |
| 17/16 |
104.955 |
overtone half-step |
| 33/31 |
108.237 |
|
| 49/46 |
109.381 |
| 16/15 |
111.731 |
major 5-limit half-step |
| 31/29 |
115.458 |
|
| 77/72 |
116.234 |
| 15/14 |
119.443 |
Cowell just half-step |
| 29/27 |
123.712 |
|
| 14/13 |
128.298 |
| 69/64 |
130.229 |
69th harmonic |
| 55/51 |
130.726 |
|
| 27/25 |
133.238 |
alternate Renaissance half-step |
| 121/112 |
133.810 |
|
| 13/12 |
138.573 |
3/4-tone (Avicenna) |
| 64/59 |
140.828 |
|
| 38/35 |
142.373 |
| 63/58 |
143.159 |
| 88/81 |
143.498 |
| 25/23 |
144.353 |
| 62/57 |
145.568 |
| 135/124 |
147.145 |
| 49/45 |
147.433 |
| 12/11 |
150.637 |
undecimal "median" 1/2-step |
| 59/54 |
153.307 |
|
| 35/32 |
155.140 |
35th harmonic |
| 23/21 |
157.493 |
|
| 57/52 |
158.940 |
| 34/31 |
159.920 |
| 800/729 |
160.897 |
| 56/51 |
161.916 |
| 11/10 |
165.004 |
| 54/49 |
168.219 |
| 32/29 |
170.423 |
| 21/19 |
173.268 |
| 31/28 |
176.210 |
| 567/512 |
176.646 |
| 51/46 |
178.642 |
| 71/64 |
179.697 |
71st harmonic |
| 10/9 |
182.404 |
minor whole-tone |
| 49/40 |
186.340 |
|
| 39/35 |
187.343 |
| 29/26 |
189.050 |
| 125/112 |
190.115 |
| 48/43 |
190.437 |
| 19/17 |
192.558 |
| 160/143 |
194.468 |
| 28/25 |
196.198 |
| 121/108 |
196.771 |
| 55/49 |
199.987 |
| 2 to the 1/6th |
200.000 |
equal-tempered whole-tone |
| 64/57 |
200.532 |
|
| 9/8 |
203.910 |
major whole-tone |
| 62/55 |
207.404 |
|
| 44/39 |
208.843 |
| 35/31 |
210.104 |
| 26/23 |
212.253 |
| 112/99 |
213.598 |
| 17/15 |
216.687 |
| 25/22 |
221.309 |
| 58/51 |
222.667 |
| 256/225 |
222.463 |
| 33/29 |
223.696 |
| 729/640 |
225.416 |
| 57/50 |
226.840 |
| 73/64 |
227.789 |
73rd harmonic |
| 8/7 |
231.174 |
septimal whole-tone |
| 63/55 |
235.104 |
|
| 55/48 |
235.685 |
| 39/34 |
237.527 |
| 225/196 |
238.886 |
| 31/27 |
239.171 |
| 147/128 |
239.607 |
| 169/147 |
241.449 |
| 23/20 |
241.961 |
| 2187/1900 |
243.547 |
| 38/33 |
244.240 |
| 144/125 |
244.969 |
diminished third (6/5 x 24/25) |
| 121/105 |
245.541 |
|
| 15/13 |
247.741 |
| 52/45 |
250.313 |
| 37/32 |
251.344 |
37th harmonic |
| 81/70 |
252.680 |
|
| 125/108 |
253.076 |
| 22/19 |
253.805 |
| 51/44 |
255.602 |
| 196/169 |
256.596 |
consonant interval (Avicenna) |
| 29/25 |
256.950 |
|
| 36/31 |
258.874 |
| 93/80 |
260.679 |
| 57/49 |
261.816 |
| 64/55 |
262.368 |
| 7/6 |
266.871 |
septimal minor third |
| 90/77 |
270.080 |
|
| 75/64 |
274.582 |
augmented second (9/8 x 25/24) |
| 34/29 |
275.378 |
|
| 88/75 |
276.736 |
| 27/23 |
277.591 |
| 20/17 |
281.358 |
| 33/28 |
284.447 |
| 46/39 |
285.802 |
| 13/11 |
289.210 |
| 58/49 |
291.925 |
| 45/38 |
292.721 |
| 32/27 |
294.135 |
Pythagorean minor third |
| 19/16 |
297.513 |
overtone minor third |
| 2 to the 1/4th |
300.000 |
equal-tempered minor third |
| 25/21 |
301.847 |
|
| 31/26 |
304.508 |
| 105/88 |
305.777 |
| 55/46 |
309.368 |
| 6/5 |
315.641 |
5-limit minor third |
| 77/64 |
320.144 |
77th harmonic |
| 35/29 |
325.562 |
|
| 29/24 |
327.622 |
| 75/62 |
329.550 |
| 98/81 |
329.832 |
| 121/100 |
330.008 |
| 23/19 |
330.761 |
| 63/52 |
332.208 |
| 40/33 |
333.041 |
| 17/14 |
336.130 |
| 243/200 |
337.148 |
| 62/51 |
338.125 |
| 28/23 |
340.552 |
| 39/32 |
342.483 |
39th harmonic |
| 128/105 |
342.905 |
|
| 8000/6561 |
343.304 |
| 11/9 |
347.408 |
undecimal "median" third |
| 60/49 |
350.617 |
|
| 49/40 |
351.351 |
| 38/31 |
352.477 |
| 27/22 |
354.547 |
| 16/13 |
359.472 |
| 79/64 |
364.537 |
79th harmonic |
| 100/81 |
364.807 |
|
| 121/98 |
364.984 |
| 21/17 |
365.826 |
| 99/80 |
368.914 |
| 26/21 |
369.747 |
| 57/46 |
371.194 |
| 31/25 |
372.408 |
| 36/29 |
374.333 |
| 56/45 |
378.602 |
| 96/77 |
381.811 |
| 8192/6561 |
384.360 |
Pythagorean "schismatic" third |
| 5/4 |
386.314 |
5-limit major third |
| 64/51 |
393.090 |
|
| 49/39 |
395.183 |
| 44/35 |
396.192 |
| 39/31 |
397.447 |
| 34/27 |
399.090 |
| 2 to the 1/3rd |
400.000 |
equal-tempered major third |
| 63/50 |
400.108 |
|
| 121/96 |
400.681 |
| 29/23 |
401.303 |
| 125/99 |
403.713 |
| 24/19 |
404.442 |
| 512/405 |
405.866 |
| 62/49 |
407.384 |
| 81/64 |
407.820 |
Pythagorean major third |
| 19/15 |
409.244 |
|
| 33/26 |
412.745 |
| 80/63 |
413.578 |
| 14/11 |
417.508 |
| 51/40 |
420.612 |
| 125/98 |
421.289 |
| 23/18 |
424.364 |
| 32/25 |
427.373 |
diminished fourth |
| 41/32 |
429.062 |
41st harmonic |
| 50/39 |
430.160 |
|
| 77/60 |
431.875 |
| 9/7 |
435.084 |
septimal major third |
| 58/45 |
439.353 |
|
| 49/38 |
440.154 |
| 40/31 |
441.278 |
| 31/24 |
443.081 |
| 1323/1024 |
443.517 |
| 128/99 |
444.772 |
| 22/17 |
446.363 |
| 57/44 |
448.150 |
| 162/125 |
448.879 |
| 35/27 |
449.275 |
| 83/64 |
450.047 |
83rd harmonic
|
| 100/77 |
452.484 |
|
| 13/10 |
454.214 |
| 125/96 |
456.986 |
augmented third (5/4 x 25/24) |
| 30/23 |
459.994 |
|
| 64/49 |
462.348 |
| 98/75 |
463.069 |
| 17/13 |
464.428 |
| 72/55 |
466.278 |
| 55/42 |
466.867 |
| 38/29 |
467.936 |
| 21/16 |
470.781 |
septimal fourth |
| 46/35 |
473.152 |
|
| 25/19 |
475.114 |
| 320/243 |
476.539 |
| 29/22 |
478.259 |
| 675/512 |
478.492 |
| 33/25 |
480.646 |
| 45/34 |
485.286 |
| 85/64 |
491.269 |
85th harmonic |
| 4/3 |
498.045 |
perfect fourth |
| 2 to the 5/12ths |
500.000 |
equal-tempered perfect fourth |
| 75/56 |
505.757 |
|
| 51/38 |
509.415 |
| 43/32 |
511.518 |
43rd harmonic |
| 121/90 |
512.412 |
|
| 39/29 |
512.905 |
| 35/26 |
514.612 |
| 66/49 |
515.621 |
| 31/23 |
516.761 |
| 27/20 |
519.551 |
| 23/17 |
523.319 |
| 42/31 |
525.745 |
| 19/14 |
528.687 |
| 110/81 |
529.812 |
| 87/64 |
531.532 |
87th harmonic |
| 34/25 |
532.328 |
|
| 49/36 |
533.761 |
| 15/11 |
536.951 |
| 512/375 |
539.104 |
| 26/19 |
543.015 |
| 63/46 |
544.462 |
| 48/35 |
546.835 |
| 1000/729 |
547.211 |
| 11/8 |
551.318 |
undecimal tritone (11th harmonic) |
| 62/45 |
554.812 |
|
| 40/29 |
556.737 |
| 29/21 |
558.796 |
| 112/81 |
561.006 |
| 18/13 |
563.382 |
| 25/18 |
568.717 |
augmented fourth (4/3 x 25/24) |
| 89/64 |
570.880 |
89th harmonic |
| 32/23 |
571.726 |
|
| 39/28 |
573.657 |
| 46/33 |
575.022 |
| 88/63 |
578.582 |
| 7/5 |
582.512 |
septimal tritone |
| 108/77 |
585.721 |
|
| 1024/729 |
588.270 |
low Pythagorean tritone |
| 45/32 |
590.224 |
high 5-limit tritone |
| 38/27 |
591.648 |
|
| 31/22 |
593.718 |
| 55/39 |
595.170 |
| 24/17 |
597.000 |
| Square root of 2 |
600.000 |
equal-tempered tritone |
| 99/70 |
600.088 |
|
| 17/12 |
603.000 |
| 44/31 |
606.304 |
| 125/88 |
607.623 |
| 27/19 |
608.352 |
| 91/64 |
609.354 |
91st harmonic |
| 64/45 |
609.776 |
low 5-limit tritone |
| 729/512 |
611.730 |
high Pythagorean tritone |
| 57/40 |
613.154 |
|
| 77/54 |
614.279 |
| 10/7 |
617.488 |
septimal tritone |
| 63/44 |
621.418 |
|
| 33/23 |
624.999 |
| 56/39 |
626.343 |
| 23/16 |
628.274 |
23rd harmonic |
| 36/25 |
631.283 |
diminished fifth (3/2 x 24/25) |
| 121/84 |
631.855 |
|
| 49/34 |
632.719 |
| 13/9 |
636.618 |
| 81/56 |
638.994 |
| 55/38 |
640.141 |
| 42/29 |
641.204 |
| 29/20 |
643.263 |
| 45/31 |
645.211 |
| 93/64 |
646.991 |
93rd harmonic |
| 16/11 |
648.682 |
|
| 51/35 |
651.794 |
| 729/500 |
652.789 |
| 35/24 |
653.185 |
| 19/13 |
656.985 |
| 375/256 |
660.896 |
| 22/15 |
663.049 |
| 47/32 |
665.507 |
47th harmonic |
| 72/49 |
666.258 |
|
| 25/17 |
667.672 |
| 81/55 |
670.188 |
| 28/19 |
671.313 |
| 31/21 |
674.255 |
| 189/128 |
674.691 |
| 34/23 |
676.681 |
| 40/27 |
680.449 |
dissonant "wolf" 5-limit fifth |
| 46/31 |
683.263 |
|
| 95/64 |
683.827 |
95th harmonic |
| 49/33 |
684.403 |
|
| 52/35 |
685.412 |
| 58/39 |
687.095 |
| 125/84 |
688.160 |
| 112/75 |
694.243 |
| 121/81 |
694.816 |
| 2 to the 7/12ths |
700.000 |
equal-tempered perfect fifth |
| 3/2 |
701.955 |
perfect fifth |
| 121/80 |
716.322 |
|
| 50/33 |
719.380 |
| 97/64 |
719.895 |
97th harmonic |
| 1024/675 |
721.508 |
|
| 44/29 |
721.766 |
| 243/160 |
723.461 |
| 38/25 |
724.886 |
| 35/23 |
726.865 |
| 32/21 |
729.219 |
| 29/19 |
732.064 |
| 84/55 |
733.149 |
| 55/36 |
733.748 |
| 26/17 |
735.572 |
| 75/49 |
736.931 |
| 49/32 |
737.652 |
49th harmonic |
| 23/15 |
740.006 |
|
| 192/125 |
743.014 |
diminished sixth (8/5 x 24/25) |
| 20/13 |
745.786 |
|
| 77/50 |
747.516 |
| 54/35 |
750.752 |
| 125/81 |
751.121 |
| 17/11 |
753.637 |
| 99/64 |
755.228 |
99th harmonic |
| 48/31 |
756.946 |
|
| 31/20 |
758.722 |
| 45/29 |
760.674 |
| 14/9 |
764.916 |
septimal minor sixth |
| 120/77 |
768.125 |
|
| 39/25 |
769.855 |
| 25/16 |
772.627 |
augmented fifth |
| 36/23 |
775.636 |
|
| 11/7 |
782.492 |
undecimal minor sixth |
| 63/40 |
786.422 |
|
| 52/33 |
787.283 |
| 101/64 |
789.854 |
101st harmonic |
| 30/19 |
790.756 |
|
| 128/81 |
792.180 |
Pythagorean minor sixth |
| 49/31 |
792.644 |
|
| 405/256 |
794.134 |
| 19/12 |
795.558 |
| 46/29 |
798.726 |
| 100/63 |
799.892 |
| 2 to the 2/3rds |
800.000 |
equal-tempered minor sixth |
| 27/17 |
800.910 |
|
| 62/39 |
802.553 |
| 35/22 |
803.822 |
| 51/32 |
806.910 |
51st harmonic |
| 8/5 |
813.686 |
5-limit minor sixth |
| 6561/4096 |
815.640 |
Pythagorean "schismatic" sixth |
| 77/48 |
818.189 |
|
| 45/28 |
821.427 |
| 103/64 |
823.801 |
103rd harmonic |
| 29/18 |
825.667 |
|
| 50/31 |
827.600 |
| 121/75 |
828.053 |
| 21/13 |
830.253 |
| 55/34 |
832.706 |
| 34/21 |
834.175 |
| 81/50 |
835.193 |
| 125/77 |
838.797 |
| 13/8 |
840.528 |
overtone sixth |
| 57/35 |
844.328 |
|
| 44/27 |
845.483 |
| 31/19 |
847.523 |
| 80/49 |
848.662 |
| 49/30 |
849.413 |
| 18/11 |
852.592 |
undecimal "median" sixth |
| 105/64 |
857.095 |
105th harmonic |
| 64/39 |
857.517 |
|
| 23/14 |
859.448 |
| 51/31 |
861.905 |
| 400/243 |
862.852 |
| 28/17 |
863.870 |
| 33/20 |
866.959 |
| 38/23 |
869.239 |
| 81/49 |
870.168 |
| 48/29 |
872.409 |
| 53/32 |
873.505 |
53rd harmonic |
| 58/35 |
874.438 |
|
| 63/38 |
875.223 |
| 128/77 |
879.856 |
| 107/64 |
889.760 |
107th harmonic |
| 5/3 |
884.359 |
5-limit major sixth |
| 57/34 |
894.513 |
|
| 52/31 |
895.524 |
| 42/25 |
898.153 |
| 121/72 |
898.726 |
| 2 to the 3/4ths |
900.000 |
equal-tempered major sixth |
| 32/19 |
902.487 |
|
| 27/16 |
905.865 |
Pythagorean major sixth |
| 49/29 |
908.107 |
|
| 22/13 |
910.790 |
| 39/23 |
914.208 |
| 56/33 |
915.553 |
| 17/10 |
918.641 |
| 109/64 |
921.821 |
109th harmonic |
| 46/27 |
922.442 |
|
| 75/44 |
923.264 |
| 29/17 |
924.622 |
| 128/75 |
925.418 |
diminished seventh (16/9 x 24/25) |
| 77/45 |
929.920 |
|
| 12/7 |
933.129 |
septimal major sixth |
| 55/32 |
937.632 |
55th harmonic |
| 31/18 |
941.126 |
|
| 441/256 |
941.562 |
| 50/29 |
943.084 |
| 19/11 |
946.195 |
| 216/125 |
946.924 |
| 121/70 |
947.496 |
| 45/26 |
949.730 |
| 26/15 |
952.259 |
| 111/64 |
953.299 |
111th harmonic |
| 125/72 |
955.031 |
augmented sixth (5/3 x 25/24) |
| 33/19 |
955.760 |
|
| 40/23 |
958.039 |
| 54/31 |
960.864 |
| 96/55 |
964.323 |
| 110/63 |
964.896 |
| 7/4 |
968.826 |
septimal minor seventh |
| 58/33 |
976.304 |
|
| 225/128 |
976.537 |
| 51/29 |
977.368 |
| 44/25 |
978.725 |
| 30/17 |
983.313 |
| 113/64 |
984.215 |
113th harmonic |
| 99/56 |
986.402 |
|
| 23/13 |
987.747 |
| 62/35 |
989.896 |
| 39/22 |
991.165 |
| 55/31 |
992.631 |
| 16/9 |
996.090 |
Pythagorean small min. seventh |
| 57/32 |
999.468 |
57th harmonic |
| 2 to the 5/6ths |
1000.000 |
equal-tempered minor seventh |
| 98/55 |
1000.020 |
|
| 25/14 |
1003.802 |
| 34/19 |
1007.442 |
| 52/29 |
1010.986 |
| 88/49 |
1013.666 |
| 115/64 |
1014.588 |
115th harmonic |
| 9/5 |
1017.596 |
5-limit large minor seventh |
| 56/31 |
1023.790 |
|
| 38/21 |
1026.732 |
| 29/16 |
1029.577 |
29th harmonic |
| 49/27 |
1031.823 |
|
| 20/11 |
1034.996 |
| 51/28 |
1038.121 |
| 729/400 |
1039.103 |
| 31/17 |
1040.080 |
| 42/23 |
1042.507 |
| 117/64 |
1044.438 |
117th harmonic |
| 64/35 |
1044.860 |
|
| 4000/2187 |
1045.266 |
| 11/6 |
1049.363 |
undecimal "median" seventh |
| 90/49 |
1052.572 |
|
| 57/31 |
1054.432 |
| 46/25 |
1055.684 |
| 81/44 |
1056.502 |
| 35/19 |
1057.627 |
| 59/32 |
1059.172 |
59th harmonic |
| 24/13 |
1061.427 |
|
| 50/27 |
1066.772 |
| 63/34 |
1067.780 |
| 13/7 |
1071.702 |
| 119/64 |
1073.781 |
119th harmonic |
| 54/29 |
1076.326 |
|
| 28/15 |
1080.557 |
| 58/31 |
1084.542 |
| 15/8 |
1088.269 |
5-limit major seventh |
| 62/33 |
1091.763 |
|
| 32/17 |
1095.045 |
| 49/26 |
1097.163 |
| 66/35 |
1098.133 |
| 2 to the 11/12ths |
1100.000 |
equal-tempered major seventh |
| 17/9 |
1101.045 |
|
| 121/64 |
1102.636 |
121st harmonic |
| 125/66 |
1105.668 |
|
| 36/19 |
1106.397 |
| 256/135 |
1107.821 |
| 55/29 |
1108.094 |
| 243/128 |
1109.775 |
Pythagorean major seventh |
| 19/10 |
1111.199 |
|
| 40/21 |
1115.533 |
| 61/32 |
1116.885 |
61st harmonic |
| 21/11 |
1119.463 |
|
| 44/23 |
1123.084 |
| 23/12 |
1126.319 |
| 48/25 |
1129.338 |
| 121/63 |
1129.900 |
| 123/64 |
1131.017 |
123rd harmonic |
| 25/13 |
1132.100 |
|
| 77/40 |
1133.830 |
| 52/27 |
1134.703 |
| 27/14 |
1137.039 |
septimal major seventh |
| 56/29 |
1139.249 |
|
| 29/15 |
1141.308 |
| 60/31 |
1143.233 |
| 31/16 |
1145.036 |
31st harmonic |
| 64/33 |
1146.727 |
|
| 33/17 |
1148.318 |
| 243/125 |
1150.834 |
| 35/19 |
1151.230 |
| 39/20 |
1156.169 |
| 125/64 |
1158.941 |
augmented seventh (15/8 x 25/24) |
| 88/45 |
1161.094 |
|
| 45/23 |
1161.991 |
| 96/49 |
1164.303 |
| 49/25 |
1165.066 |
| 51/26 |
1166.424 |
| 108/55 |
1168.233 |
| 55/28 |
1168.847 |
| 57/29 |
1169.891 |
| 63/32 |
1172.736 |
63rd harmonic |
| 160/81 |
1178.494 |
|
| 99/50 |
1182.601 |
| 125/63 |
1186.205 |
| 127/64 |
1186.422 |
127th harmonic |
| 2/1 |
1200.000 |
octave |