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This table is supposed to be the best guess at what would have appeared in A Middle Path Part 2, had Paul Erlich finished it. It is similar to the Middle Path table of five-limit rank two temperaments and Middle Path table of seven-limit rank two temperaments from Part 1. It is intended to comprise all possible 11-limit 2D cases where complexity/7.65 + damage/10 < 1.

Commas
Name
TOP
period
TOP
generator
Mapping
Cmplx
TOP
Dmg
ETs
36/35, 50/49, 64/63, 81/80, 126/125...
Duodecim
99.59
31.48
[<12 19 28 34 42|, <0 0 0 0 -1|]
2.59
6.14
24d, 36d, 48cdde, (48cdd)...
45/44, 56/55, 81/80, 100/99, 125/121...
Meanenneadecal
1198.56
503.60
[<1 2 4 7 6|, <0 -1 -4 -10 -6|]
3.06
5.32
31e, 50ee, (62eee), 69dee, 81eee...
36/35, 56/55, 64/63, 81/80, 99/98...
Dominant
1195.04
495.58
[<1 2 4 2 1|, <0 -1 -4 2 6|]
3.08
4.96
29cde, 41cdee, 53cddeee...
49/48, 56/55, 77/75, 121/120, 176/175...
Triforce
399.80
155.57
[<3 4 7 8 10|, <0 2 0 1 1|]
3.22
5.29
39, 54cd, 69bcd, (78cd), 93bccdd...
45/44, 50/49, 81/80, 99/98, 100/99...
Injera
601.24
92.99
[<2 3 4 5 6|, <0 1 4 4 6|]
3.38
4.06
26, 38e, 50dee, (52c), 64ce, 66bcc...
33/32, 49/48, 77/75, 99/98, 176/175...
Negric
1205.30
129.26
[<1 2 2 3 3|, <0 -4 3 -2 4|]
3.52
5.30
28de, (56bddeee), (84bbdddeeeee)...
56/55, 64/63, 100/99, 126/125, 176/175...
Augene
398.88
87.10
[<3 5 7 8 10|, <0 -1 0 2 2|]
3.66
3.37
27e, 39dee, 42e, (54cee), 57bce...
45/44, 49/48, 81/80, 100/99, 125/121...
Godzilla
1204.09
254.92
[<1 2 4 3 6|, <0 -2 -8 -1 -12|]
3.71
4.09
33cd, 52cd, (66bccdd), 71bcdd...
50/49, 55/54, 99/98, 100/99, 121/120...
Hedgehog
599.09
163.15
[<2 4 6 7 8|, <0 -3 -5 -5 -4|]
3.75
3.23
22, 36ce, (44), 52bdd, 58ce, (66d)...
49/48, 55/54, 77/75, 126/125, 176/175...
Darjeeling
1202.79
318.16
[<1 0 1 2 0|, <0 6 5 3 13|]
3.81
4.41
34e, 53dee, (68dee), 83ddee...
56/55, 64/63, 77/75, 121/120, 392/375...
Progress
1195.64
559.36
[<1 3 0 0 3|, <0 -3 5 6 1|]
3.81
4.51
47bc, 62bcce, (94bbccce)...
55/54, 64/63, 100/99, 121/120, 176/175...
Porcupine
1198.23
163.15
[<1 2 3 2 4|, <0 -3 -5 6 -4|]
3.90
3.18
22, 37, (44), 52b, 59, (66d), 67b...
49/48, 56/55, 100/99, 126/125, 343/330...
Keemun
1200.82
318.18
[<1 0 1 2 4|, <0 6 5 3 -2|]
4.05
4.50
83dde, 117bddee, 151bdddeee...
49/48, 81/80, 126/125, 225/224, 245/243...
Undevigintone
63.36
30.42
[<19 30 44 53 66|, <0 0 0 0 -1|]
4.07
3.83
38d, 57dd, 57ddee, 76dd, (76dde)...
50/49, 64/63, 99/98, 100/99, 176/175...
Pajara
598.45
106.57
[<2 3 5 6 8|, <0 1 -2 -2 -6|]
4.17
3.11
22, 34d, (44), 46de, 56d, 58ddee...
49/48, 55/54, 100/99, 121/120, 250/243...
Nautilus
1202.66
82.97
[<1 2 3 3 4|, <0 -6 -10 -3 -8|]
4.21
3.48
29, (58cde), 72ccddee, 73cde...
45/44, 81/80, 100/99, 125/121, 385/384...
Flattone
1203.00
508.77
[<1 2 4 -1 6|, <0 -1 -4 9 -6|]
4.30
4.06
26, 45, (52c), 64cde, 71bc, (78bcc)...
50/49, 55/54, 64/63, 225/224, 385/384...
Pajarous
599.29
108.86
[<2 3 5 6 6|, <0 1 -2 -2 5|]
4.44
3.27
22, (44), (66d), (88bd), 98bcd...
56/55, 81/80, 128/125, 176/175, 245/242...
Catcall
99.81
31.73
[<12 19 28 34 42|, <0 0 0 -1 -1|]
4.48
3.56
36, 48ce, (72ce), 84cee, (96cceee)...
55/54, 99/98, 176/175, 225/224, 245/243...
Telepathy
1199.00
381.39
[<1 0 2 -1 -1|, <0 5 1 12 14|]
4.52
3.15
22, 41e, (44), 63e, (66d), (82eee)...
55/54, 100/99, 121/120, 225/224, 250/243...
Porky
1198.78
163.50
[<1 2 3 5 4|, <0 -3 -5 -16 -4|]
4.61
3.22
22, 29, (44), 51, (58cde), (66d)...
56/55, 100/99, 126/125, 245/243, 540/539...
Sensis
1196.58
442.49
[<1 -1 -1 -2 2|, <0 7 9 13 4|]
4.68
3.42
27e, (54cee), 73ee, (81bcdeee)...
55/54, 64/63, 99/98, 245/243, 352/343...
Suprapyth
1198.59
490.29
[<1 2 6 2 1|, <0 -1 -9 2 6|]
4.68
3.18
22, (44), (66d), (88bd), 93bde...
50/49, 64/63, 225/224, 245/243, 250/243...
Vigintiduo
54.48
10.51
[<22 35 51 62 76|, <0 0 0 0 1|]
4.74
3.28
66de, 88bde, 110bdd, 110bddee...
81/80, 99/98, 126/125, 176/175, 225/224...
Meantone
1201.61
504.02
[<1 2 4 7 11|, <0 -1 -4 -10 -18|]
4.96
1.74
31, 43, 50e, 55de, (62), 74, 81ee...
50/49, 55/54, 176/175, 352/343, 540/539...
Fleetwood
599.28
272.31
[<2 5 6 7 11|, <0 -4 -3 -3 -9|]
4.96
3.27
22, (44), (66d), (88bd), (110bdde)...
50/49, 121/120, 176/175, 352/343, 385/384...
Astrology
599.32
217.89
[<2 5 5 6 8|, <0 -5 -1 -1 -3|]
5.07
3.28
22, (44), (66d), (88bd), (110bdde)...
49/48, 55/54, 225/224, 441/440, 525/512...
Negroni
1203.19
124.84
[<1 2 2 3 5|, <0 -4 3 -2 -15|]
5.11
3.19
77cddee, 106ccdddeee...
64/63, 99/98, 121/120, 352/343, 540/539...
Quasisupra
1197.34
490.80
[<1 2 -3 2 1|, <0 -1 13 2 6|]
5.29
2.66
39d, 61d, (78cdd), 83d, 100bcdd...
99/98, 121/120, 176/175, 225/224, 385/384...
Orwell
1201.25
271.43
[<1 0 3 1 3|, <0 7 -3 8 2|]
5.30
1.36
31, 53, (62), 75, 84e, (93e), 97de...
81/80, 99/98, 121/120, 441/440, 540/539...
Squares
1201.70
426.46
[<1 3 8 6 7|, <0 -4 -16 -9 -10|]
5.37
1.70
31, 45e, (62), 76e, 79c, 90bcdee...
64/63, 100/99, 176/175, 245/243, 540/539...
Superpyth
1197.60
489.43
[<1 2 6 2 10|, <0 -1 -9 2 -16|]
5.42
2.40
49, 71d, 76bcdee, 93bd, (98bde)...
121/120, 126/125, 176/175, 385/384, 441/440...
Valentine
1200.87
77.63
[<1 1 2 3 3|, <0 9 5 -3 7|]
5.82
1.54
31, 46, (62), 77, (92), (93e), 107c...
81/80, 121/120, 176/175, 243/242, 385/384...
Mohajira
1201.70
348.78
[<1 1 0 6 2|, <0 2 8 -11 5|]
6.01
1.70
31, (62), (93e), (124be), 148be...
100/99, 225/224, 245/243, 385/384, 540/539...
Magic
1200.75
380.92
[<1 0 2 -1 6|, <0 5 1 12 -8|]
6.07
1.68
41, 63, (82), 104, (123c), (126c)...
81/80, 126/125, 225/224, 385/384, 540/539...
Meanpop
1201.70
504.13
[<1 2 4 7 -2|, <0 -1 -4 -10 13|]
6.08
1.70
31, 50, (62), 81, (93e), (100d), 112b...
81/80, 121/120, 126/125, 225/224, 243/242...
Migration
1201.70
348.78
[<1 1 0 -3 2|, <0 2 8 20 5|]
6.10
1.70
31, (62), (93e), 100de, (124be)...
99/98, 121/120, 126/125, 540/539, 891/875...
Nusecond
1200.46
154.74
[<1 3 4 5 5|, <0 -11 -13 -17 -12|]
6.13
1.70
31, (62), (93e), 101, (124be), 132ce...
100/99, 225/224, 245/242, 441/440, 625/616...
Cassandra
1201.36
497.94
[<1 2 -1 -3 -4|, <0 -1 8 14 18|]
6.19
1.79
152cd, 193ccd, 234ccd, 263cccdd...
225/224, 243/242, 385/384, 441/440, 540/539...
Miracle
1200.63
116.72
[<1 1 3 3 2|, <0 6 -7 -2 15|]
7.14
0.63
72, (144), (216c), (288cd), (360bcd)...
A BONUS TEMPERAMENT:

2401/2400, 3025/3024, 4375/4374, 9801/9800...
Hemiennealimmal
66.67
17.64
[<18 28 41 50 62|, <0 2 3 2 1|]
23.81
0.05


Comparisons of closely related temperaments

36/35, 50/49, 64/63, 81/80, 126/125...
Duodecim
99.59
31.48
[<12 19 28 34 42|, <0 0 0 0 -1|]
2.59
6.14
24d, 36d, 48cdde, (48cdd)...
56/55, 81/80, 128/125, 176/175, 245/242...
Catcall
99.81
31.73
[<12 19 28 34 42|, <0 0 0 -1 -1|]
4.48
3.56
36, 48ce, (72ce), 84cee, (96cceee)...
Since the TOP tunings of duodecim and catcall are so similar, there is little practical use for duodecim temperament. If notes so altered from 12edo are available, there is no reason not to use them for ratios of 7 as well as ratios of 11.

45/44, 56/55, 81/80, 100/99, 125/121...
Meanenneadecal
1198.56
503.60
[<1 2 4 7 6|, <0 -1 -4 -10 -6|]
3.06
5.32
31e, 50ee, (62eee), 69dee, 81eee...
36/35, 56/55, 64/63, 81/80, 99/98...
Dominant
1195.04
495.58
[<1 2 4 2 1|, <0 -1 -4 2 6|]
3.08
4.96
29cde, 41cdee, 53cddeee...
45/44, 81/80, 100/99, 125/121, 385/384...
Flattone
1203.00
508.77
[<1 2 4 -1 6|, <0 -1 -4 9 -6|]
4.30
4.06
26, 45, (52c), 64cde, 71bc, (78bcc)...
81/80, 99/98, 126/125, 176/175, 225/224...
Meantone
1201.61
504.02
[<1 2 4 7 11|, <0 -1 -4 -10 -18|]
4.96
1.74
31, 43, 50e, 55de, (62), 74, 81ee...
81/80, 126/125, 225/224, 385/384, 540/539...
Meanpop
1201.70
504.13
[<1 2 4 7 -2|, <0 -1 -4 -10 13|]
6.08
1.70
31, 50, (62), 81, (93e), (100d), 112b...
These temperaments all temper out 81/80, making them extensions of 5-limit meantone. The differences are in the mappings of 7 and 11.

36/35, 56/55, 64/63, 81/80, 99/98...
Dominant
1195.04
495.58
[<1 2 4 2 1|, <0 -1 -4 2 6|]
3.08
4.96
29cde, 41cdee, 53cddeee...
55/54, 64/63, 99/98, 245/243, 352/343...
Suprapyth
1198.59
490.29
[<1 2 6 2 1|, <0 -1 -9 2 6|]
4.68
3.18
22, (44), (66d), (88bd), 93bde...
64/63, 99/98, 121/120, 352/343, 540/539...
Quasisupra
1197.34
490.80
[<1 2 -3 2 1|, <0 -1 13 2 6|]
5.29
2.66
39d, 61d, (78cdd), 83d, 100bcdd...
64/63, 100/99, 176/175, 245/243, 540/539...
Superpyth
1197.60
489.43
[<1 2 6 2 10|, <0 -1 -9 2 -16|]
5.42
2.40
49, 71d, 76bcdee, 93bd, (98bde)...
In contrast, these temperaments all temper out 64/63, making them extensions of archy temperament. The differences are in the mappings of 5 and 11. Temperaments in both this and the above list comprise the dominant family, which has only one representative here. Note that cassandra is in neither of the two families, because it preserves both 64/63 and 81/80 as non-vanishing intervals (and makes them both equal to the Pythagorean comma).

33/32, 49/48, 77/75, 99/98, 176/175...
Negric
1205.30
129.26
[<1 2 2 3 3|, <0 -4 3 -2 4|]
3.52
5.30
28de, (56bddeee), (84bbdddeeeee)...
49/48, 55/54, 225/224, 441/440, 525/512...
Negroni
1203.19
124.84
[<1 2 2 3 5|, <0 -4 3 -2 -15|]
5.11
3.19
77cddee, 106ccdddeee...
The difference is only in the mapping of 11. The two temperaments intersect in 19edo (using the 19e val tempering out 33/32), which is a fine tuning for negric (despite that it doesn't show up in the list), but sub-optimal for negroni (which does not temper out 33/32).

50/49, 64/63, 99/98, 100/99, 176/175...
Pajara
598.45
106.57
[<2 3 5 6 8|, <0 1 -2 -2 -6|]
4.17
3.11
22, 34d, (44), 46de, 56d, 58ddee...
50/49, 55/54, 64/63, 225/224, 385/384...
Pajarous
599.29
108.86
[<2 3 5 6 6|, <0 1 -2 -2 5|]
4.44
3.27
22, (44), (66d), (88bd), 98bcd...
The difference is only in the mapping of 11. The two temperaments intersect in 22edo, a fine tuning for both.

49/48, 55/54, 77/75, 126/125, 176/175...
Darjeeling
1202.79
318.16
[<1 0 1 2 0|, <0 6 5 3 13|]
3.81
4.41
34e, 53dee, (68dee), 83ddee...
49/48, 56/55, 100/99, 126/125, 343/330...
Keemun
1200.82
318.18
[<1 0 1 2 4|, <0 6 5 3 -2|]
4.05
4.50
83dde, 117bddee, 151bdddeee...
The difference is only in the mapping of 11. The two intersect in 15edo, which is, however, not a great tuning for either. In 19edo, darjeeling uses the 19e val, which tempers out 33/32, whereas keemun uses the patent val.

55/54, 64/63, 100/99, 121/120, 176/175...
Porcupine
1198.23
163.15
[<1 2 3 2 4|, <0 -3 -5 6 -4|]
3.90
3.18
22, 37, (44), 52b, 59, (66d), 67b...
55/54, 100/99, 121/120, 225/224, 250/243...
Porky
1198.78
163.50
[<1 2 3 5 4|, <0 -3 -5 -16 -4|]
4.61
3.22
22, 29, (44), 51, (58cde), (66d)...
The difference is only in the mapping of 7. The two intersect in 22edo, which is probably the only reasonable incarnation of porky temperament.

55/54, 99/98, 176/175, 225/224, 245/243...
Telepathy
1199.00
381.39
[<1 0 2 -1 -1|, <0 5 1 12 14|]
4.52
3.15
22, 41e, (44), 63e, (66d), (82eee)...
100/99, 225/224, 245/243, 385/384, 540/539...
Magic
1200.75
380.92
[<1 0 2 -1 6|, <0 5 1 12 -8|]
6.07
1.68
41, 63, (82), 104, (123c), (126c)...
The difference is only in the mapping of 11. The two intersect in 22edo, which is a fine telepathy tuning but slightly sub-optimal for magic. Since telepathy is significantly higher in error, it can be regarded as an alternate version of magic that exists in 22edo.

81/80, 121/120, 176/175, 243/242, 385/384...
Mohajira
1201.70
348.78
[<1 1 0 6 2|, <0 2 8 -11 5|]
6.01
1.70
31, (62), (93e), (124be), 148be...
81/80, 121/120, 126/125, 225/224, 243/242...
Migration
1201.70
348.78
[<1 1 0 -3 2|, <0 2 8 20 5|]
6.10
1.70
31, (62), (93e), 100de, (124be)...
The TOP tunings of mohajira and migration are not merely close, but exactly equal, because the prime 7 does not affect the TOP tuning. The two temperaments intersect in 31edo, which is also near-optimal for both.

ET
TOP damage
TOP octave
Rank-2 temperaments supported
22


hedgehog, porcupine, pajara, pajarous, telepathy, porky, suprapyth, fleetwood, astrology
24d


duodecim
26


injera, flattone
27e


augene, sensis
28de


negric
29


nautilus, porky
29cde


dominant
31


meantone, orwell, squares, valentine, mohajira, meanpop, migration, nusecond
31e


meanenneadecal
33cd


godzilla
34d


pajara
34e


darjeeling
36


catcall
36ce


hedgehog
36d


duodecim
37


porcupine
38d


undevigintone
38e


injera
39


triforce
39d


quasisupra
39dee


augene
41


magic
41cdee


dominant
41e


telepathy
42e


augene
43


meantone
44*


hedgehog, porcupine, pajara, pajarous, telepathy, porky, suprapyth, fleetwood, astrology
45


flattone
45e


squares
46


valentine
46de


pajara
47bc


progress
48cdd*


duodecim
48cdde


duodecim
48ce


catcall
49


superpyth
50


meanpop
50dee


injera
50e


meantone
50ee


meanenneadecal
51


porky
52b


porcupine
52bdd


hedgehog
52c*


injera, flattone
52cd


godzilla
53


orwell
53cddeee


dominant
53dee


darjeeling
54cd


triforce
54cee*


augene, sensis
55de


meantone
56bddeee*


negric
56d


pajara
57bce


augene
57dd


undevigintone
57ddee


undevigintone
58cde*


nautilus, porky
58ce


hedgehog
58ccddee*


dominant
58ddee


pajara
59


porcupine
60cddd


duodecim
60cdddee


duodecim
61d


quasisupra
62*


meantone, orwell, squares, valentine, mohajira, meanpop, migration, nusecond
62bcce


progress
62eee*


meanenneadecal
63


magic
63e


telepathy
64cd


injera
64cde


flattone
65ccdddeeee


dominant
66bcc


injera
66bccdd*


godzilla
66d*


hedgehog, porcupine, pajara, pajarous, telepathy, porky, suprapyth, fleetwood, astrology
66de


vigintiduo
67b


porcupine
68dde*


pajara
68dee*


darjeeling
69bcd


triforce
69bcee


augene
69dee


meanenneadecal
70ccddeee


dominant
70ddeee


pajara
71bc


flattone
71bcdd


godzilla
71d


superpyth
72


miracle
72bce


augene
72ccddee


nautilus
72ccee*


hedgehog
72cddd*


duodecim
72cddde*


duodecim
72cdddeee


duodecim
72ce*


catcall