Map of linear temperaments

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Intended to be a map of all interesting linear temperaments (one period per octave). The only linear temperaments not appearing here should be non-octave ones, such as the Bohlen-Pierce linear temperament.

Please make sure each octave fraction is always the mediant of the ones directly above and below.

For temperaments with more than one period per octave, see Map of rank-2 temperaments.

Generator Cents Comments
0\1 0
1\18 66.667
1\17 70.588
2\33 72.727
1\16 75
3\47 76.596
2\31 77.419 Valentine/Lupercalia
3\46 78.261 Valentine
1\15 80
3\44 81.818
2\29 82.759 Nautilus
5\72 83.333
3\43 83.721
4\57 84.2105
1\14 85.714
4\55 87.364
3\41 87.805 Octacot
5\68 88.235
2\27 88.889 Octacot
3\40 90
1\13 92.308
3\38 94.737
2\25 96 Passion
5\62 96.774
3\37 97.297 Passion
4\49 97.959
1\12 100 Ripple
5\59 101.695
4\47 102.128
7\82 102.439
3\35 102.857
5\58 103.448
2\23 104.348 Ripple
3\34 105.882
1\11 109.091
3\32 112.5
2\21 114.286
5\52 115.385
3\31 116.129 Miracle
10\103 116.505
7\72 116.667
11\113 116.814
4\41 117.073 Miracle
5\51 117.647
1\10 120
4\39 123.077
3\29 124.138 Negri/Negril
8\77 124.675
5\48 125
7\67 125.373
2\19 126.316 Negri
5\47 127.66
3\28 128.571
7\65 129.231
4\37 129.73 Twothirdtonic
9\83 130.1205
5\46 130.435 Twothirdtonic
6\55 130.901
1\9 133.333
7\62 135.484 Doublethink
6\53 135.849
11\97 136.0825
5\44 136.364 Doublethink
9\79 136.709
4\35 137.143
7\61 137.705
3\26 138.462
8\69 139.13.
5\43 139.535 Bleu/Progression
12\103 139.806
7\60 140 Bleu
9\77 140.26
2\17 141.176 Blue/progression
5\42 142.857
3\25 144
7\58 144.828
4\33 145.455
9\74 145.946
5\41 146.341 Indium/bohpier
11\90 146.667
6\49 146.939
19\155 147.097
13\106 147.17
20\163 147.239
7\57 147.368 Indium
8\65 147.692
1\8 150
5\39 153.846
4\31 154.839 Nusecond
11\85 155.294
7\54 155.556
17\131 155.725
10\77 155.844 Greeley
23\177 155.932
13\100 156
16\123 156.098
3\23 156.522 Greeley
5\38 157.895
2\15 160 Porcupine
9\67 161.194
7\52 161.538
12\89 161.798
5\37 162.162
13\96 162.5
8\59 162.712
27\199 162.814
19\140 162.857
30\221 162.896
11\81 162.963
14\103 163.107
3\22 163.636
10\73 164.384
7\51 164.706
11\80 165
4\29 165.517 Porcupine
9\65 166.154
5\36 166.667
11\79 167.089
6\43 167.442 Meantone w/ 4/3 generator split in 3
13\93 167.742
7\50 168
8\57 168.421 Meantone w/ 4/3 generator split in 3
1\7 171.429
8\55 174.5455
7\48 175
13\89 175.281
6\41 175.61 Tetracot/Bunya/Monkey
11\75 176
5\34 176.471
9\61 177.049
4\27 177.778 Tetracot
7\47 178.723
3\20 180
8\53 181.132
5\33 181.818
12\79 182.2785
7\46 182.609 Mitonic/Minortone
9\59 183.051
2\13 184.615
5\32 187.5
3\19 189.474 Deutone
10\63 190.476
7\44 190.909
11\69 191.304
4\25 192 Deutone/Leantone/Tutone
13\81 192.593
9\56 192.857 Leantone
23\143 193.007
14\87 193.103 Luna/Hemithirds
47\292 193.151
33\205 193.171
52\323 193.189
19\118 193.22 Luna/Hemithirds
24\149 193.289
5\31 193.548 Hemiwuerschmidt/Roulette
26\161 193.789
21\130 193.846
37\229 193.8865
16\99 193.939 Hemiwuerschmidt
27\167 194.012
11\68 194.118
17\105 194.286
6\37 194.595 Tutone/Roulette
7\43 195.349
1\6 200
9\53 203.774
8\47 204.255 Baldy
15\88 204.5455
7\41 204.878 Baldy
13\76 205.263
6\35 205.714
11\64 206.25
5\29 206.897
9\52 207.693
4\23 208.696
7\40 210
3\17 211.765 Machine
8\45 213.333
5\28 214.286
7\39 215.385
2\11 218.182 Machine
5\27 222.222
3\16 225 Gorgo/Shoe
10\53 226.415
7\37 227.027 Gorgo/Shoe
11\58 227.586
4\21 228.571
9\47 229.787
5\26 230.769 Cynder/Mothra
11\57 231.579
6\31 232.258 Slendric
13\67 232.836
7\36 233.333 Cynder/Mothra/Rodan
15\77 233.766
8\41 234.146
25\128 234.375
17\87 234.483
26\133 234.5865
9\46 234.783 Slendric/rodan
10\51 235.294
1\5 240 Bug/beep (start)...
8\39 246.154
7\34 247.059
13\63 247.619
6\29 248.276 Semaphore, bridgetown
17\82 248.7805
11\53 249.057 bridgetown
16\77 249.351
5\24 250 Semaphore/Godzilla
14\67 250.746
9\43 251.163
13\62 251.613
4\19 252.632 Godzilla
7\33 254.5455
3\14 257.143
11\51 258.8235
8\37 259.46 Superpelog
13\60 260
5\23 260.87
12\55 261.818
7\32 262.5 Septimin/superpelog
16\73 263.014
9\41 263.415
29\132 263.636
20\91 263.736 Septimin
31\141 263.83
11\50 264
13\59 264.407
2\9 266.667
9\40 270
7\31 270.968 Orson/Orwell/Winston
26\115 271.304
19\84 271.429
31\137 271.533
12\53 271.698
17\75 272
5\22 272.727 Orson/orwell/blair
13\57 273.684
8\35 274.286
11\48 275
3\13 276.923 Lovecraft
7\30 280
4\17 282.353 Huxley
9\38 284.2105
5\21 285.714
11\46 286.4565
6\25 288
13\54 288.889
7\29 289.655
8\33 290.909
1\4 300 ...Bug/beep (end)
11\43 306.977
10\39 307.692
19\74 308.108
9\35 308.571
26\101 308.911
17\66 309.091
25\97 309.278
8\31 309.677 Myna
31\120 310
23\89 310.112
38\147 310.204
15\58 310.345
37\143 310.4895
22\85 310.588
29\112 310.714
7\27 311.111 Myna
20\77 311.688
13\50 312
19\73 312.329
6\23 313.043
23\88 313.636
17\65 313.846
28\107 314.019
11\42 314.286
38\145 314.483
27\103 314.563
43\164 314.634
16\61 314.754
53\202 314.8515
37\141 314.894
58\221 314.932
21\80 315
68\259 315.058
47\179 315.084
73\278 315.108
26\99 315.152 Parakleismic
57\217 315.207
31\118 315.254
36\137 315.3285
5\19 315.789 Keemun (start)...
29\110 316.364
24\91 316.4835
43\163 316.564
19\72 316.667 Hanson/Catakleismic
52\197 316.751
33\125 316.8
47\178 316.854
14\53 316.981 catakleismic
37\140 317.143
23\87 317.241
32\121 317.355
9\34 317.647
22\83 318.072
13\49 318.367
17\64 318.75
4\15 320 ...Keemun (end)/Orgone
19\71 321.127
15\56 321.429
26\97 321.6495
11\41 321.951 Superkleismic
29\108 322.222
18\67 322.388
25\93 322.581
7\26 323.077 Superkleismic
38\141 323.404
31\115 323.478
55\204 323.529
24\89 323.596
65\241 323.6515
41\152 323.684
58\215 323.721
17\63 323.81
44\163 323.926
27\100 324
37\137 324.088
10\37 324.324
23\85 324.706
13\48 325
16\59 325.424
3\11 327.273 Dicot (start).../Orgone
11\40 330
8\29 331.0345
13\47 331.915
5\18 333.333
17\61 334.426
12\43 334.884
19\68 335.294
7\25 336
23\82 336.585
16\57 336.842
25\89 337.079
9\32 337.5 Sixix
29\103 337.864
20\71 338.028
31\110 338.182
11\39 338.462
35\124 338.71
24\85 338.8235
37\131 338.931
13\46 339.13 Amity/Hitchcock
54\191 339.267
41\145 339.31
69/244 339.344
28\99 339.394
99\350 339.429
71\251 339.442
114\403 339.454
43\152 339.474
101\357 339.496
58\205 339.512
73\258 339.535
15\53 339.623 Amity
32\113 339.823
17\60 340
19\67 340.2985
2\7 342.857
13\45 346.667
11\38 347.368
20\69 347.826
9\31 348.387 Mohajira (meantone-style neutral thirds)
25\86 348.837
16\55 349.091
23\79 349.367
7\24 350 Neutral thirds
26\89 350.562
19\65 350.769
31\106 350.943
12\41 351.22 No-5's neutral thirds / hemififths
41\140 351.429
29\99 351.515
46\157 351.592 hemififths
17\58 351.724
39\133 351.88
22\75 352
27\92 352.174
5\17 352.941 No-5's neutral thirds/Beatles
18\61 354.098
13\44 354.5455
21\71 354.930
8\27 355.556
27\91 356.044
19\64 356.25 Beatles
30\101 356.436
11\37 356.757 Huntington/Silver
36\121 357.025
25\84 357.143
39\131 357.252
14\47 357.447 Silver
31\104 357.692
17\57 357.895
20\67 358.209
3\10 360 ...Dicot (end)
13\43 362.791
10\33 363.636
17\56 364.286
7\23 365.217
25\82 365.854
18\59 366.102
29\95 366.316
11\36 366.667
48\157 366.879
37\121 366.942 2/phi as a frequency ratio is around here
63\206 366.99
26\85 367.059
67\219 367.123
41\134 367.164
56\183 367.213
15\49 367.347
34\111 367.568
19\62 367.742
23\75 368
4\13 369.231
13\42 371.429
9\29 372.414
14\45 373.333
5\16 375 Magic
21\67 376.119
16\51 376.471
27\86 376.744
11\35 377.143 Muggles
28\89 377.528
17\54 377.778
23\73 378.082
6\19 378.947 Muggles
25\79 379.747
19\60 380
32\101 380.198
13\41 380.488
33\104 380.769
20\63 380.952
27\85 381.1765
7\22 381.818 Magic
22\69 382.609
15\47 382.979
23\72 383.333
8\25 384
25\78 384.615
17\53 384.906
26\81 385.185
9\28 385.714
28\87 386.207
19\59 386.441
29\90 386.667
10\31 387.097 Würschmidt
51\158 387.342
41\127 387.402
72\223 387.444
31\96 387.5
83\257 387.549
52\161 387.578
73\226 387.611
21\65 387.692
74\229 387.773
53\164 387.805
85\263 387.833
32\99 387.879
75\232 387.931
43\133 387.97
54\167 388.024
11\34 388.235 Würschmidt
34\105 388.571
23\71 388.732
35\108 388.889
12\37 389.189
25\77 389.61
13\40 390
14\43 390.698
1\3 400 Father (start)...
13\38 410.526
12\35 411.429
23\67 411.94
11\32 412.5
32\93 412.903
21\61 413.115
31\90 413.333
10\29 413.793 Roman
29\84 414.286
19\55 414.5455
28\81 414.815
9\26 415.385
35\101 415.842
26\75 416
43\124 416.129
17\49 416.327 Sqrtphi
59\170 416.471
42\121 416.529
67\193 416.58
25\72 416.667 Sqrtphi
58\167 416.7665
33\95 416.842
41\118 416.949
8\23 417.391
23\66 418.181
15\43 418.605
22\63 419.048
7\20 420
27\77 420.779
20\57 421.053
33\94 421.277
13\37 421.622 Bossier
32\91 421.978
19\54 422.222
25\71 422.535
6\17 423.529
29\82 424.39
23\65 424.615
40\113 424.779
17\48 425 Squares
45\127 425.297
28\79 425.3165
39\110 425.4545
11\31 425.806 Squares
27\76 426.316
16\45 426.667
21\59 427.119
5\14 428.571
19\53 430.189
14\39 430.769
23\64 431.25
9\25 432
22\61 432.787
13\36 433.333
17\47 434.043
4\11 436.364
19\52 438.4615
15\41 439.024
26\71 439.437
11\30 440
40\109 440.367
29\79 440.506
47\128 440.625
18\49 440.816 Clyde
61\166 440.964
43\117 441.026
441.081
25\68 441.176
68\185 441.29
32\87 441.379
39\106 441.509
7\19 57\155 442.105 Sensi/Clyde
31\84 442.857
24\65 443.077
41\111 443.243
17\46 443.478
44\119 443.6975
27\73 443.836
37\100 444
10\27 444.444 Sensi
33\89 444.944
23\62 445.161
36\97 445.361
13\35 445.714
29\78 446.154
16\43 446.512
19\51 447.059
3\8 450
23\61 452.459
20\53 452.83
37\98 453.061
17\45 453.333 Semidim
48\127 453.543
31\82 453.6585
45\119 453.7815
14\37 454.05 Tridec/Semidim/Ammonite
53\140 454.286
39\103 454.369
64\169 454.438 Ammonite
25\66 454.545
61\161 454.658
36\95 454.737
47\124 454.839
11\29 455.172 Tridec
30\79 455.696
19\50 456
27\71 456.338
8\21 457.143
29\76 457.895
21\55 458.182
34\89 458.427
13\34 458.824
31\81 459.259
18\47 459.5745
23\60 460
5\13 461.538 A-team
22\57 463.158
17\44 463.636
29\75 464
12\31 464.516 Semisept
31\80 465
19\49 465.306
26\67 465.672
7\18 466.667 A-team
23\59 467.797
16\41 468.293
25\64 468.75
9\23 469.565
29\74 470.27
20\51 470.588
31\79 470.886
11\28 471.429
35\89 471.91
24\61 472.131
37\94 472.34
13\33 472.727
41\104 473.077
28\71 473.239
43\109 473.3945
15\38 473.684
47\119 473.95
32\81 474.074
49\124 474,1935
17\43 474.419
53\134 474.627
36\91 474.725
55\139 474.82
19\48 475 Vulture
59\149 475.168
40\101 475.2475
61\154 475.325
21\53 475.472 Vulture/Buzzard
65\164 475.61
44\111 475.676
67\169 475.74
23\58 475.862
48\121 476.033
25\63 476.1905
27\68 476;471
2\5 480 ...Father (end)
17\42 485.714
15\37 486.486 Ultrapyth
28\69 486.9565
13\32 487.5 Ultrapyth
24\59 488.136
11\27 488.889 Superpyth
31\76 489.474
20\49 489.796
29\71 490.141
9\22 490.909 Superpyth
25\61 491.803
16\39 492.308 Supra
23\56 492.857
7\17 494.118
26\63 495.238
19\46 495.652 Leapday
50\121 495.868
31\75 496
43\104 496.154
12\29 496.552 Garibaldi/Cassandra/Leapday
29\70 497.143
17\41 497.561
56\135 497.778
39\94 497.872 Helmholtz/cassandra
61\147 497.959
22\53 498.113 Pythagorean/helmholtz/garibaldi
27\65 498.4615
5\12 500 Meantone/dominant
23\55 501.818
18\43 502.326 grosstone
49\117 502.564
31\74 502.703 grosstone
44\105 502.857
13\31 503.226 huygens/meanpop
47\112 503.571
34\81 503.704
55\131 503;817
21\50 504 meanpop
29\69 504.348
8\19 505.263 flattone/meanenneadecal
27\64 506.25
19\45 506.667
30\71 507.042
11\26 507.692 Meantone/flattone
14\33 509.091
3\7 514.286
31\72 516.666 Marvo/Gravity
28\65 516.923 Gravity
25\58 517.241
22\51 517.647
19\44 518.182
16\37 518.919
13\30 520
10\23 521.739 Mavila
7\16 525
11\25 528 Mavila/Mabila
4\9 533.333 Pelogic
13\29 537.931 Avila
9\20 540 Score/Avila
14\31 541.935 Casablanca
33\73 542.466 Casablanca
19\42 542.857
5\11 545.4545
26\57 547.368 Heinz
47\103 547.573
21\46 547.826 Heinz
16\35 548.571
11\24 550
6\13 553.846 Thuja
19\41 556.098
13\28 557.143
7\15 560 Thuja/Progress
8\17 564.706 Progress
25\53 566.038
17\36 566.667 Liese
9\19 568.421 Liese/Triton
19\40 570
10\21 571.429 Triton
11\23 573.913
12\25 576
13\27 577.778
14\29 579.31 Tritonic
29\60 580
15\31 580.645 Tritonic
16\33 581.812
1\2 600