Reversed meantone
Reversed meantone is a temperament which tempers out the 41-limit comma 82/81.
Properties
As meantone is based on the syntonic comma, 81/80, tempering the fifth flat, tempering 82/81 instead results in a sharper fifth, and a major third equivalent to the 41st harmonic instead of the 5th, so it might as well be called reverse meantone. As a very high limit interval, however, that 41/32 is far less recognizable as an interval than meantone’s 5/4, and would more likely be heard as a flat 9/7. Additionally, the 41st is very delicate, and mistuning by several cents destroys it, so if its use is intended as more than a joke exact quarter comma tempering is best, although 39edo does a fair job.
Related to this idea, 162/161 is a 23-limit comma (specifically 161 = 7 × 23), and 163/162 being prime would indeed be ridiculous.
The more well known 64/63 comma equates 9/8 with 8/7 instead of 10/9, which also results in a sharper fifth, and the major third is equivalent to 9/7.
Temperament data
Subgroup: 2.3.41
Comma list: 82/81
Gencom: [2 4/3; 82/81]
Sval mapping: [⟨1 2 7], ⟨0 -1 -4]]
POTE generator: ~4/3 = 494.5086
TOP generators: ~2 = 1199.6961, ~4/3 = 494.3834
Subgroup: 2.3.7.41
Comma list: 64/63, 82/81
Gencom: [2 4/3; 64/63 82/81]
Sval mapping: [⟨1 2 2 7], ⟨0 -1 2 -4]]
POTE generator: ~4/3 = 490.0323
TOP generators: ~2 = 1197.2342, ~4/3 = 488.9029
Subgroup: 2.3.7.11.41
Comma list: 64/63, 82/81, 99/98
Gencom: [2 4/3; 64/63 82/81 99/98]
Sval mapping: [⟨1 2 2 1 7], ⟨0 -1 2 6 -4]]
POTE generator: ~4/3 = 492.1787
TOP generators: ~2 = 1197.9683, ~4/3 = 491.3454
Non-octave
As meantone is based within the octave and on the syntonic comma, 81/80, tempering the fifth flat, and the thirds to be simple rational intervals, basing it within the third or fifth harmonic or the perfect fifth or the major tenth, sixth or third instead still may temper 81/80, even if it might as well be called reverse meantone. Of these, the major third of 5/4 is the least recognizable as an interval, though still very recognizable. Additionally, the major third of 5/4 is a very narrow interval to base a temperament within, so if its use is intended as more than a joke it might as well be the augmented temperament 4ned5/2.
Temperament data
Subgroup: 3.2.5
Comma list: 81/80
Gencom: [3 3/2; 81/80]
Sval mapping: [⟨1 1 0], ⟨0 -1 4]]
POTE generator: ~3/2 = 698.3375
TOP generators: ~3 = 1898.4460, ~3/2 = 697.0491
Subgroup: 3.2.5.7
Comma list: 64/63, 81/80
Gencom: [3 3/2; 64/63 81/80]
Sval mapping: [⟨1 1 0 3], ⟨0 -1 4 -13]]
POTE generator: ~3/2 = 698.5001
TOP generators: ~3 = 1898.4580, ~3/2 = 697.2159
Subgroup: 3.2.5.7.11
Comma list: 64/63, 81/80, 99/98
Gencom: [2 3/2; 64/63 81/80 99/98]
Sval mapping: [⟨1 1 0 4 7], ⟨0 -1 4 -6 -13]]
POTE generator: ~3/2 = 702.7738
TOP generators: ~3 = 1893.9031, ~3/2 = 699.7986
Subgroup: 5.2.3 (3/2.5)
Comma list: 81/80
Gencom: [3/2 10/9; 81/80]
Sval mapping: [⟨4 2 3], ⟨0 -1 —1]]
POTE generator: ~3/2 = 696.5784, ~10/9 = 192.5712
TOP generators: ~3/2 = 697.0491, ~10/9 = [[1]]
Subgroup: 5.2.3.7
Comma list: 64/63, 81/80
Gencom: [3/2 10/9; 64/63 81/80]
Sval mapping: [⟨4 2 3 6], ⟨0 -1 —1 -4]]
POTE generator: ~3/2 = 696.5784, ~10/9 = 201.7001
TOP generators: ~3/2 = 697.2159, ~10/9 = 202.3697
Subgroup: 5.2.3.7.11
Comma list: 64/63, 81/80, 99/98
Gencom: [3/2 10/9; 64/63 81/80 99/98]
Sval mapping: [⟨4 2 3 6 8], ⟨0 -1 —1 -4 -7]]
POTE generator: ~3/2 = 696.5784, ~10/9 = 204.5471
TOP generators: ~3/2 = 699.7986, ~10/9 = 205.4927
Subgroup: 3/2.2.3.5
Comma list: 81/80
Gencom: [3/2 9/8; 81/80]
Sval mapping: [⟨1 2 3 4], ⟨0 -1 -1 0]]
POTE generator: ~9/8 = 198.7378
TOP generators: ~3/2 = 699.3710, ~9/8 = 198.0062
Subgroup: 3/2.2.3.5.7
Comma list: 64/63, 81/80
Gencom: [3/2 9/8; 64/63 81/80]
Sval mapping: [⟨1 2 3 4 6], ⟨0 -1 -1 0 -4]]
POTE generator: ~9/8 = 205.3121
TOP generators: ~3/2 = 700.2305, ~9/8 = 204.8077
Subgroup: 3/2.2.3.5.7.11
Comma list: 64/63, 81/80, 99/98
Gencom: [3/2 9/8; 64/63 81/80 99/98]
Sval mapping: [⟨1 2 3 4 4 4], ⟨0 -1 -1 0 3 7]]
POTE generator: ~9/8 = 195.0236
TOP generators: ~3/2 = 698.2079, ~9/8 = 193.9826
Subgroup: 5/2.2.3.5
Comma list: 81/80
Gencom: [5/2 3/2; 81/80]
Sval mapping: [⟨1 -1 -1 0], ⟨0 4 5 4]]
POTE generator: ~3/2 = 696.9241
TOP generators: ~5/2 = 1586.4184, ~3/2 = 696.9702
Subgroup: 5/2.2.3.5.7
Comma list: 64/63, 81/80
Gencom: [5/2 3/2; 64/63 81/80]
Sval mapping: [⟨1 -1 -1 0 3], ⟨0 4 5 4 -2]]
POTE generator: ~3/2 = 696.7420
TOP generators: ~5/2 = 1587.1426, ~3/2 = 697.1060
Subgroup: 5/2.2.3.5.7.11
Comma list: 81/80, 126:125, 176:175
Gencom: [5/2 3/2; 81/80 126:125 176:175]
Sval mapping: [⟨1 -1 -1 0 3 7], ⟨0 4 5 4 -2 -10]]
POTE generator: ~3/2 = 696.3353
TOP generators: ~5/2 = 1587.1426, ~3/2 = 697.2531
Subgroup: 5/3.2.3.5
Comma list: 81/80
Gencom: [5/3 10/9; 81/80]
Val mapping: [⟨1 2 3 4], ⟨0 -3 -4 -4]]
POTE generator: ~10/9 = 189.0028
TOP generators: ~5/3 = 884.9987, ~10/9 = 189.1396
Subgroup: 5/3.2.3.5.7
Comma list: 126/125, 81/80
Gencom: [5/3 10/9; 126/125 81/80]
Sval mapping: [⟨1 2 3 4 6], ⟨0 -3 -4 -4 -10]]
POTE generator: ~10/9 = 192.2011
TOP generators: ~5/3 = 887.4720, ~10/9 = 192.8777
Subgroup: 5/3.2.3.5.7.11
Comma list: 81/80, 126/125, 100/99
Gencom: [5/3 ; 81/80 126/125 100/99]
Sval mapping: [⟨1 2 3 4 4 6], ⟨0 -3 -4 -4 -1 -6]]
POTE generator: ~10/9 = 190.2709
TOP generators: ~5/3 = 886.3893, ~10/9 = 190.7078