Middle Path table of seven-limit rank two temperaments

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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".