|
Todo: improve synopsis, clarify, link
|
Below are tabulated bases (temperamental Minkowski bases) of minimal temperamental complexity for the pitch classes of various regular temperaments.
Rank-3
7-limit temperaments
| Comma
|
Name
|
Gen 1
|
Length
|
Gen 2
|
Length
|
Angle
|
| 686/675
|
Sengic
|
15/14
|
0.6977
|
3/2
|
1.4208
|
103.732
|
| 64/63
|
Archytas
|
3/2
|
1.0508
|
5/4
|
2.3219
|
90.000
|
| 875/864
|
Keemic
|
6/5
|
0.8879
|
3/2
|
1.3391
|
77.834
|
| 81/80
|
Didymus
|
3/2
|
0.5451
|
8/7
|
2.8074
|
90.000
|
| 3125/3087
|
Gariboh
|
25/21
|
0.5928
|
21/20
|
1.2018
|
80.810
|
| 2430/2401
|
Nuwell
|
7/6
|
0.6247
|
9/7
|
1.1894
|
94.044
|
| 50421/50000
|
Trimyna
|
7/5
|
0.3158
|
5/4
|
1.7938
|
94.101
|
| 245/243
|
Sensamagic
|
3/2
|
0.9644
|
9/7
|
1.0807
|
96.914
|
| 126/125
|
Starling
|
6/5
|
1.068
|
5/4
|
1.206
|
100.364
|
| 4000/3969
|
Octagar
|
63/50
|
0.8966
|
21/20
|
1.0605
|
97.743
|
| 1728/1715
|
Orwellismic
|
7/6
|
0.7526
|
3/2
|
1.3931
|
97.508
|
| 1029/1024
|
Gamelismic
|
8/7
|
0.5192
|
5/4
|
2.3219
|
90.000
|
| 225/224
|
Marvel
|
16/15
|
1.256
|
3/2
|
1.369
|
106.958
|
| 3136/3125
|
Hemimean
|
28/25
|
0.5055
|
3/2
|
1.5849
|
90.000
|
| 5120/5103
|
Aberschismic
|
3/2
|
0.5670
|
10/9
|
1.8063
|
82.112
|
| 6144/6125
|
Porwell
|
35/32
|
0.9584
|
35/24
|
1.1877
|
92.681
|
| 65625/65536
|
Horwell
|
5/4
|
0.6213
|
16/15
|
1.3863
|
64.638
|
| 703125/702464
|
Metric
|
75/56
|
0.7305
|
375/224
|
0.7675
|
97.289
|
| 420175/419904
|
Wizmic
|
245/216
|
0.5541
|
324/245
|
0.9731
|
79.663
|
| 2401/2400
|
Breedsmic
|
49/40
|
0.7858
|
8/7
|
1.1241
|
107.367
|
| 4375/4374
|
Ragismic
|
10/9
|
0.7890
|
6/5
|
0.9208
|
105.299
|
11-limit temperaments
| Commas
|
Name
|
Gen 1
|
Length
|
Gen 2
|
Length
|
Angle
|
| 225/224, 385/384
|
Marvel
|
16/15
|
1.0364
|
5/4
|
1.0759
|
104.028
|
| 225/224, 441/440
|
Prodigy
|
16/15
|
0.9111
|
3/2
|
0.9477
|
65.933
|
| 99/98, 176/175
|
Minerva
|
16/15
|
0.8997
|
5/4
|
1.0457
|
98.604
|
| 126/125, 176/175
|
Thrush
|
5/4
|
0.8576
|
6/5
|
0.9314
|
74.624
|
| 56/55, 100/99
|
Thrasher
|
6/5
|
0.9089
|
5/4
|
1.2007
|
98.845
|
