Temperaments arranged by standard deviation of major thirds.

A viewpoint of hundreds of temperaments. The bands representing major thirds swell and distort as equal temperament gives way to others, as if watching the evolution of temperament in reverse. Alternate tunings color the graphs towards unplayability at the end. Interesting to see how even theoretical baroque temperaments (e.g., abell8) appear at the top of the list, as the third size is perfectly balanced.

To get started, click on a graph below, or click here to browse.

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:0.2764
:0.4082
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:0.4082
:0.4082
:0.4082
:0.4082
:0.4082
:0.4082
:0.4714
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:0.4714
:0.493
:0.493
:0.5528
:0.5774
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:0.9428
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:0.9538
:1.0375
:1.2247
:1.4142
:1.4142
:1.4142
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:1.4142
:1.5723
:1.633
:1.8856
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:1.9773
:2.1213
:2.1602
:2.273
:2.3094
:2.3452
:2.3805
:2.5495
:2.708
:2.8284
:2.8284
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:2.8284
:2.8284
:2.8577
:2.9439
:3
:3.0231
:3.0231
:3.0551
:3.0551
:3.0822
:3.0912
:3.1623
:3.1623
:3.2005
:3.303
:3.5551
:3.559
:3.559
:3.5824
:3.6286
:3.6391
:3.6742
:3.6818
:3.7887
:3.8261
:3.8261
:3.8297
:3.8297
:3.8613
:3.9158
:3.9158
:3.9255
:3.9546
:3.9546
:4
:4
:4.0095
:4.062
:4.0918
:4.1028
:4.1231
:4.1324
:4.1633
:4.2426
:4.2426
:4.259
:4.259
:4.259
:4.2907
:4.3012
:4.31
:4.3205
:4.4721
:4.4721
:4.4721
:4.5461
:4.5826
:4.5826
:4.6188
:4.6547
:4.714
:4.7434
:4.761
:4.8448
:4.8498
:4.9833
:5.0056
:5.0332
:5.0332
:5.0498
:5.0799
:5.0881
:5.1126
:5.1316
:5.2414
:5.2493
:5.2493
:5.2915
:5.3515
:5.3671
:5.416
:5.5277
:5.6193
:5.6569
:5.6569
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:5.6569
:5.6569
:5.73
:5.8023
:5.8232
:5.831
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:5.8878
:5.8878
:6.0415
:6.1101
:6.1101
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:6.1215
:6.1283
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:6.1283
:6.1486
:6.1644
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:6.1644
:6.1644
:6.2561
:6.2628
:6.2716
:6.3509
:6.3569
:6.414
:6.4593
:6.5192
:6.532
:6.6708
:6.6849
:6.6958
:6.751
:6.7823
:6.7823
:6.8191
:6.8191
:6.8191
:6.892
:6.9442
:6.9622
:6.9642
:7
:7.0099
:7.0475
:7.0489
:7.0529
:7.0711
:7.0882
:7.1117
:7.1995
:7.2226
:7.2572
:7.2915
:7.303
:7.303
:7.3258
:7.3485
:7.3485
:7.4498
:7.4722
:7.4833
:7.4833
:7.5056
:7.5277
:7.5609
:7.6594
:7.7244
:7.8085
:7.8789
:7.8828
:7.9582
:7.9582
:8
:8.0876
:8.0915
:8.0932
:8.0932
:8.2462
:8.271
:8.4853
:8.4853
:8.4853
:8.4853
:8.4853
:8.4984
:8.641
:8.641
:8.7066
:8.7655
:8.7939
:8.7939
:8.7939
:8.8266
:8.8318
:8.86
:8.9815
:9.0277
:9.0646
:9.0872
:9.0921
:9.1238
:9.1287
:9.1511
:9.1693
:9.1924
:9.2376
:9.2631
:9.2811
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:9.3986
:9.4281
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:9.4516
:9.5219
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:9.5394
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:9.7468
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:11.129
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:12.3895
:12.4329
:12.53
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:12.7279
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:12.8258
:12.8482
:12.9387
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:13.1709
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:13.1993
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:13.5277
:13.686
:13.6931
:13.9072
:13.9311
:14.133
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:40.2012
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:63.5826
:64.3584
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:69.0036
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:72.5
:72.896
:72.9149
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:78.7695
:79.1426
:79.3305
:79.7108
:80.1197
:80.6102
:80.9181
:82.3756
:82.8467
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:85.0818
:85.4078
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:85.7088
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:89.574
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:97.8935
:100.3328
:100.8563
:102.1543
:102.528
:102.9466
:105.7607
:105.9527
:106.205
:107.5291
:107.7838
:109.1855
:110.8639
:112.1762
:112.6609
:118.6304
:119.2653
:119.8207
:121.5946
:121.6847
:124.5392
:125.2294
:126.9652
:129.0713
:130.1076
:130.2325
:130.2358
:130.5846
:136.6565
:138.0878
:140.8556
:141.4214
:149.6575
:149.6663
:153.864
:155.2779
:163.1533
:164.6509
:166.1545
:170.9152
:180.2036
:180.2036
:188.604
:195.282
:195.282
:196.0102
:207.0499
:207.0499
:211.5699
:211.5699
:211.8285
:280.3714
:291.6267
:302.7826
:330.926
:334.0657
:340.2521
:368.702
:376.0326
:442.1674
:442.3485
:463.8249
:573.6828
:593.834
:599.3042
:608.0781
:758.1998
:767.3635
:788.0391
:803.7447
:895.7146
:896.6114
:1507.5517