editing disabled

This table is an updated version of Table 2 of Paul Erlich's A Middle Path. The complexity is now measured a different way (which, however, is proportional to the original complexity for this table), and some temperament names have been updated.

This table comprises all possible seven-limit 2-D cases where complexity/7.65 + damage/10 < 1.

See also Middle Path table of five-limit rank two temperaments, Middle Path table of eleven-limit rank two temperaments.

Vanishing Interval's Ratios
Temperament
name
TOP
period
TOP
generator
Mapp.
of 2
Mapp.
of 3
Mapp.
of 5
Mapp.
of 7
Cmplx
TOP
Dmg
ETs
28/27, 49/48, 64/63, 256/243, 343/324...
Blacksmith
239.18
155.35
5,0
8,0
11,1
14,0
2.01
7.24
15, 25, (30), 35bc, 40b, (45bc), 50bc, (50b)...
36/35, 50/49, 126/125, 360/343, 648/625...
Diminished
298.53
197.08
4,0
7,-1
10,-1
12,-1
2.46
5.87
12, (24d), (36d), (48cdd), 56cddd, (60cddd)...
36/35, 64/63, 81/80, 256/245, 729/700...
Dominant
1195.23
495.88
1,0
2,-1
4,-4
2,2
2.47
4.77
12, (24d), 29cd, (36d), 41cd, 46ccd, (48cdd)...
36/35, 128/125, 225/224, 405/392, 729/686...
August
399.99
107.31
3,0
5,-1
7,0
9,-2
2.58
5.87
12, (24d), 33, (36d), 45cd, (48cdd), 57cd...
50/49, 64/63, 225/224, 2048/2025...
Pajara
598.45
491.88
2,0
4,-1
3,2
4,2
3.23
3.11
22, 32, 34d, (44), 46d, 54, 56d, 58dd, (64bc)...
49/48, 81/80, 245/243, 1323/1280...
Semaphore
1203.67
252.48
1,0
2,-2
4,-8
3,-1
3.48
3.67
19, 33cd, (38d), 43d, 52cd, (57dd), 62dd...
81/80, 126/125, 225/224, 3136/3125...
Meantone
1201.70
504.13
1,0
2,-1
4,-4
7,-10
3.65
1.70
19, 31, (38d), 43, 50, 55d, (57dd), (62), 67d...
50/49, 81/80, 405/392, 4000/3969...
Injera
600.89
507.28
2,0
4,-1
8,-4
9,-4
3.70
3.58
26, 38, 50d, (52c), 62d, 64c, 66bcc, 74dd...
49/48, 225/224, 525/512, 686/675...
Negri
1203.19
1078.35
1,0
-2,4
5,-3
1,2
3.76
3.19
19, 29, (38d), 47d, 48d, (57dd), (58cd)...
64/63, 126/125, 128/125, 4000/3969...
Augene
399.02
90.59*
3,0
5,-1
7,0
8,2
3.76
2.94
27, 39d, 42, 51cd, (54c), 57bc, 63cdd, 66cd...
49/48, 126/125, 875/864, 1029/1000...
Keemun
1203.19
317.84
1,0
0,6
1,5
2,3
3.85
3.19
19, 34, (38d), 53d, (57dd), 61bcdd, (68d)...
81/80, 128/125, 648/625, 2048/2025...
Catler
99.81
75.22
12,0
19,0
28,0
33,1
3.98
3.56
36, 48c, 60cd, 60c, 72cd, (72c), 84cdd, 84c...
50/49, 245/243, 250/243, 2430/2401...
Hedgehog
598.45
436.13
2,0
1,3
1,5
2,5
4.09
3.11
22, 36c, (44), 52bdd, 58c, (66d), (72cc)...
64/63, 245/243, 1728/1715, 2240/2187...
Superpyth
1197.60
708.17
1,0
1,1
-3,9
4,-2
4.48
2.40
22, 27, (44), 49, (54c), (66d), 71d, 76bcd...
126/125, 245/243, 686/675, 4375/4374
Sensi
1198.39
755.23
1,0
6,-7
8,-9
11,-13
4.49
1.61
19, 27, (38d), 46, (54c), (57dd), 65, 73, 76dd...
50/49, 525/512, 1029/1024, 1875/1792...
Lemba
601.70
230.87
2,0
2,3
5,-1
6,-1
4.54
3.74
26, (52c), 62c, (78bcc), 88cc, 104bcc...
64/63, 250/243, 875/864, 6144/6125...
Porcupine
1196.91
1034.59
1,0
-1,3
-2,5
8,-6
4.59
3.09
22, 37, (44), 59, (66d), (74b), 81bd, (88bd)...
81/80, 525/512, 875/864, 4375/4374...
Flattone
1202.54
507.14
1,0
2,-1
4,-4
-1,9
4.77
2.54
26, 45, (52c), 64cd, 71bc, (78bcc), 83bcdd...
225/224, 245/243, 875/864, 3125/3072...
Magic
1201.28
380.80
1,0
0,5
2,1
-1,12
4.82
1.28
22, 41, (44), 60, 63, (66d), 79d, (82), 85...
50/49, 875/864, 1728/1715, 3125/3024...
Doublewide
599.28
326.96
2,0
1,4
3,3
4,3
4.84
3.27
22, (44), 48, (66d), 70c, 74c, (88bd), 92cd...
49/48, 250/243, 4000/3969, 6125/5832...
Nautilus
1202.99
1119.69
1,0
-4,6
-7,10
0,3
4.85
3.48
29, (58cd), (87ccdd), (116ccddd)...
64/63, 686/675, 2401/2400, 6272/6075...
Beatles
1197.10
842.38
1,0
3,-2
-4,9
0,4
5.24
2.90
27, (54c), (81bcd), (108bccd), 118bccd...
81/80, 686/675, 1029/1000, 10976/10935...
Liese
1202.62
569.05
1,0
3,-3
8,-12
8,-11
5.43
2.62
[almost 19], 74d, 93dd, 112bdd, 129dd...
81/80, 1029/1024, 1728/1715, 8748/8575...
Cynder
1201.7
969.18
1,0
4,-3
12,-12
2,1
5.72
1.70
31, 57, (62), 88, (93), 98, (114bc), 119b...
225/224, 1728/1715, 2430/2401, 6144/6125...
Orwell
1199.53
271.49
1,0
0,7
3,-3
1,8
6.20
0.95
31, 53, (62), 75, 84, (93), (106), 115, (124b)...
225/224, 3125/3087, 4000/3969, 5120/5103...
Garibaldi
1200.76
702.64
1,0
1,1
7,-8
11,-14
6.30
0.91
41, 53, (82), 94, (106), 118d, (123c), 135, 147...
126/125, 1728/1715, 2401/2400, 31104/30625...
Myna
1198.83
888.94
1,0
9,-10
9,-9
8,-7
6.31
1.17
58, 89, (116c), 120, 143cd, 147c, 151, 174cd...
225/224, 1029/1024, 2401/2400, 16875/16807...
Miracle
1200.63
116.72
1,0
1,6
3,-7
3,-2
6.55
0.63
41, 72, (82), 103, 113, (123c), 134, (144)...
A BONUS TEMPERAMENT:

2401/2400, 4375/4374, 250047/250000...
Ennealimmal
133.337
84.313
9,0
13,2
19,3
24,2
12.36
0.04

  • Correction from the Xenharmonikon version, which gives the corner case generator 92.46 erroneously.

ET (* =
contorted)
TOP damage
TOP octave
Rank-2 temperaments supported
12


diminished, dominant, august
15


blacksmith
19


semaphore, meantone, negri, keemun, sensi
22


pajara, hedgehog, superpyth, porcupine, magic, doublewide
24d*


diminished, dominant, august
25


blacksmith
26


injera, lemba, flattone
27


augene, superpyth, sensi, beatles
29


negri, nautilus
29cd


dominant
30*


blacksmith
31


meantone, cynder, orwell
32


pajara
33


august
33cd


semaphore
34


keemun
34d


pajara
35bc


blacksmith
36


catler
36c


hedgehog
36d*


diminished, dominant, august
37


porcupine
38


injera
38d*


semaphore, meantone, negri, keemun, sensi
39d


augene
40b


blacksmith
41


magic, garibaldi, miracle
41cd


dominant
42


augene
43


meantone
43d


semaphore
44*


pajara, hedgehog, superpyth, porcupine, magic, doublewide
45


flattone
45bc


blacksmith
45cd


august
46


sensi
46ccd


dominant
46d


pajara
47d


negri
48


doublewide
48c


catler
48cdd*


diminished, dominant, august
48d


negri
49


superpyth
50


meantone
50b*


blacksmith
50bc


blacksmith
50d


injera
51cd


augene
52bdd


hedgehog
52c*


injera, lemba, flattone
52cd


semaphore
53


orwell, garibaldi
53cdd


dominant
53d


keemun
54


pajara
54c*


augene, superpyth, sensi, beatles
55b


blacksmith
55d


meantone
56cddd


diminished
56d


pajara
57


cynder
57bc


augene
57cd


august
57dd*


semaphore, meantone, negri, keemun, sensi
58


myna
58c


hedgehog
58ccdd*


dominant
58cd*


negri, nautilus
58dd


pajara
59


porcupine
60


magic
60b


blacksmith
60bc*


blacksmith
60c


catler
60cd


catler
60cddd*


diminished, dominant, august


mp7r2ms_cd.png
The bubble chart above (source) arranges the temperaments by complexity (x-axis) vs. damage (y-axis). Colors are arbitrary. The size of the bubble is proportional to (complexity*damage). Note that the "bonus temperament" Ennealimmal is not shown (a much larger range would be needed to make it visible).


mp7r2ms_cd_d1.png
The same chart, only "zoomed in".