List of rank one temperaments by step size

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Cents Rank 1 temperament
10877.6643 e2π (exp(2*pi)), the "natural" unit of the Riemann zeta function
1901.9550 1EDT (3/1, "tritave")
1200.0000 1EDO (2/1, "octave")
950.9775 2EDT
833.0903 1ED1.618 (phi, "Golden Ratio")
701.9550 1ED1.5 (3/2, "perfect fifth")
633.9850 3EDT
600.0000 2EDO
475.4888 4EDT
416.5451 2ED1.618
400.0000 3EDO
380.3910 5EDT
350.9775 2ED1.5
316.9925 6EDT
300.0000 4EDO
277.6968 3ED1.618
271.7079 7EDT
240.0000 5EDO
237.7444 8EDT
233.9850 3ED1.5
211.3283 9EDT
208.2726 4ED1.618
200.0000 6EDO
190.1955 10EDT
175.4888 4ED1.5 (suggested as a theoretical basis for Georgian music)
172.9050 11EDT
171.4286 7EDO
166.6181 5ED1.618
158.4963 12EDT
150.0000 8EDO
146.4760 TOP 3.5 BP == TOP 3.5.7 BP
146.3042 13EDT (Bohlen-Pierce equal temperament)
140.3910 5ED1.5
138.8484 6ED1.618
135.8539 14EDT
133.3333 9EDO
126.7970 15EDT
120.0000 10EDO
119.0129 7ED1.618
118.8722 16EDT
116.9925 6ED1.5
111.8797 17EDT
109.0909 11EDO
105.6642 18EDT
104.1363 8ED1.618
100.2793 7ED1.5
100.1029 19EDT
100.0000 12EDO (standard equal temperament)
95.0978 20EDT
92.5656 9ED1.618
92.3077 13EDO
90.5693 21EDT
88.0000 88cET
87.7444 8ED1.5
86.4525 22EDT
85.7143 14EDO
83.3090 10ED1.618
82.6937 23EDT
80.0000 15EDO
79.2481 24EDT
77.9950 Carlos alpha (that is, 9ED1.5)
77.6279 TOP 11-limit valentine, no octaves
76.0782 25EDT
75.7355 11ED1.618
75.0000 16EDO
73.1521 26EDT
70.5882 17EDO
70.4428 27EDT
70.1955 10ED1.5
69.4242 12ED1.618
67.9270 28EDT
66.6667 18EDO
65.5847 29EDT
64.0839 13ED1.618
63.8141 Carlos beta (that is, 11ED1.5)
63.3985 30EDT
63.1579 19EDO
61.3534 31EDT
60.0000 20EDO
59.5064 14ED1.618
59.4361 32EDT
58.4963 12ED1.5
57.6350 33EDT
57.1429 21EDO
55.9399 34EDT
55.5394 15ED1.618
54.5455 22EDO
54.3416 35EDT
53.9965 13ED1.5
52.8321 36EDT
52.1739 23EDO
52.0681 16ED1.618
51.4042 37EDT
50.1396 14ED1.5
50.0514 38EDT
50.0000 24EDO
49.0053 17ED1.618
48.7681 39EDT
48.0000 25EDO
47.5489 40EDT
46.7970 15ED1.5
46.3891 41EDT
46.2828 18ED1.618
46.1538 26EDO
45.2846 42EDT
44.4444 27EDO
44.2315 43EDT
43.8722 16ED1.5
43.8469 19ED1.618
43.2263 44EDT
42.8571 28EDO
42.2657 45EDT
41.6545 20ED1.618
41.3793 29EDO
41.3468 46EDT
41.2915 17ED1.5
40.4671 47EDT
40.0000 30EDO
39.6710 21ED1.618
39.6241 48EDT
38.9975 18ED1.5
38.8154 49EDT
38.7097 31EDO
38.0391 50EDT
37.8677 22ED1.618
37.5000 32EDO
37.2932 51EDT
36.9450 19ED1.5
36.5761 52EDT
36.3636 33EDO
36.2213 23ED1.618
35.8859 53EDT
35.2941 34EDO
35.2214 54EDT
35.0978 Carlos gamma (that is, 20ED1.5)
34.7121 24ED1.618
34.5810 55EDT
34.2857 35EDO
33.9635 56EDT
33.4264 21ED1.5
33.3676 57EDT
33.3333 36EDO
33.3236 25ED1.618
32.7923 58EDT
32.4324 37EDO
32.2365 59EDT
32.0419 26ED1.618
31.9070 22ED1.5
31.6993 60EDT
31.5789 38EDO
31.1796 61EDT
30.8552 27ED1.618
30.7692 39EDO
30.6767 62EDT
30.5198 23ED1.5
30.1898 63EDT
30.0000 40EDO
29.7532 28ED1.618
29.7180 64EDT
29.2683 41EDO
29.2608 65EDT
29.2481 24ED1.5
28.8175 66EDT
28.7273 29ED1.618
28.5714 42EDO
28.3874 67EDT
28.0782 25ED1.5
27.9699 68EDT
27.9070 43EDO
27.7697 30ED1.618
27.5646 69EDT
27.2727 44EDO
27.1708 70EDT
26.9983 26ED1.5
26.8739 31ED1.618
26.7881 71EDT
26.6667 45EDO
26.4160 72EDT
26.0870 46EDO
26.0542 73EDT
26.0341 32ED1.618
25.9983 27ED1.5
25.7021 74EDT
25.5319 47EDO
25.3594 75EDT
25.2452 33ED1.618
25.0698 28ED1.5
25.0257 76EDT
25.0000 48EDO
24.7007 77EDT
24.5027 34ED1.618
24.4898 49EDO
24.3840 78EDT
24.2053 29ED1.5
24.0754 79EDT
24.0000 50EDO
23.8026 35ED1.618
23.7744 80EDT
23.5294 51EDO
23.4809 81EDT
23.3985 30ED1.5
23.1946 82EDT
23.1414 36ED1.618
23.0769 52EDO
22.9151 83EDT
22.6437 31ED1.5
22.6423 84EDT
22.6415 53EDO
22.5160 37ED1.618
22.3759 85EDT
22.2222 54EDO
22.1158 86EDT
21.9361 32ED1.5
21.9234 38ED1.618
21.8616 87EDT
21.8182 55EDO
21.6131 88EDT
21.4286 56EDO
21.3703 89EDT
21.3613 39ED1.618
21.2714 33ED1.5
21.1328 90EDT
21.0526 57EDO
20.9006 91EDT
20.8273 40ED1.618
20.6897 58EDO
20.6734 92EDT
20.6457 34ED1.5
20.4511 93EDT
20.3390 59EDO
20.3193 41ED1.618
20.2336 94EDT
20.0559 35ED1.5
20.0206 95EDT
20.0000 60EDO
19.8355 42ED1.618
19.8120 96EDT
19.6721 61EDO
19.6078 97EDT
19.4988 36ED1.5
19.4077 98EDT
19.3742 43ED1.618
19.3548 62EDO
19.2117 99EDT
19.0476 63EDO
19.0196 100EDT
18.9718 37ED1.5
18.9339 44ED1.618
18.8312 101EDT
18.7500 64EDO
18.6466 102EDT
18.5131 45ED1.618
18.4725 38ED1.5
18.4656 103EDT
18.4615 65EDO
18.2880 104EDT
18.1818 66EDO
18.1139 105EDT
18.1107 46ED1.618
17.9988 39ED1.5
17.9430 106EDT
17.9104 67EDO
17.7753 107EDT
17.7253 47ED1.618
17.6471 68EDO
17.6107 108EDT
17.5489 40ED1.5
17.4491 109EDT
17.3913 69EDO
17.3560 48ED1.618
17.2905 110EDT
17.1429 70EDO
17.1347 111EDT
17.1209 41ED1.5
17.0018 49ED1.618
16.9817 112EDT
16.9014 71EDO
16.8315 113EDT
16.7132 42ED1.5
16.6838 114EDT
16.6667 72EDO
16.6618 50ED1.618
16.5387 115EDT
16.4384 73EDO
16.3962 116EDT
16.3351 51ED1.618
16.3245 43ED1.5
16.2560 117EDT
16.2162 74EDO
16.1183 118EDT
16.0210 52ED1.618
16.0000 75EDO
15.9828 119EDT
15.9535 44ED1.5
15.8496 120EDT
15.7895 76EDO
15.7187 53ED1.618
15.7186 121EDT
15.5990 45ED1.5
15.5898 122EDT
15.5844 77EDO
15.4630 123EDT
15.4276 54ED1.618
15.3846 78EDO
15.3383 124EDT
15.2599 46ED1.5
15.2156 125EDT
15.1899 79EDO
15.1471 55ED1.618
15.0949 126EDT
15.0000 80EDO
14.9760 127EDT
14.9352 47ED1.5
14.8766 56ED1.618
14.8590 128EDT
14.8148 81EDO
14.7438 129EDT
14.6341 82EDO
14.6304 130EDT
14.6241 48ED1.5
14.6156 57ED1.618
14.5187 131EDT
14.4578 83EDO
14.4088 132EDT
14.3636 58ED1.618
14.3256 49ED1.5
14.3004 133EDT
14.2857 84EDO
14.1937 134EDT
14.1202 59ED1.618
14.1176 85EDO
14.0886 135EDT
14.0391 50ED1.5
13.9850 136EDT
13.9535 86EDO
13.8848 60ED1.618
13.8829 137EDT
13.7931 87EDO
13.7823 138EDT
13.7638 51ED1.5
13.6831 139EDT
13.6572 61ED1.618
13.6364 88EDO
13.5854 140EDT
13.4991 52ED1.5
13.4890 141EDT
13.4831 89EDO
13.4369 62ED1.618
13.3940 142EDT
13.3333 90EDO
13.3004 143EDT
13.2444 53ED1.5
13.2237 63ED1.618
13.2080 144EDT
13.1868 91EDO
13.1169 145EDT
13.0435 92EDO
13.0271 146EDT
13.0170 64ED1.618
12.9992 54ED1.5
12.9385 147EDT
12.9032 93EDO
12.8510 148EDT
12.8168 65ED1.618
12.7660 94EDO
12.7648 149EDT
12.7628 55ED1.5
12.6797 150EDT
12.6316 95EDO
12.6226 66ED1.618
12.5957 151EDT
12.5349 56ED1.5
12.5129 152EDT
12.5000 96EDO
12.4342 67ED1.618
12.4311 153EDT
12.3711 97EDO
12.3504 154EDT
12.3150 57ED1.5
12.2707 155EDT
12.2513 68ED1.618
12.2449 98EDO
12.1920 156EDT
12.1212 99EDO
12.1144 157EDT
12.1027 58ED1.5
12.0738 69ED1.618
12.0377 158EDT
12.0000 100EDO
1.0000 1200EDO