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Encyclopedia of Microtonal Music Theory

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[Joe Monzo]

Below is a list of all intervals in the 11-limit within the arbitrarily selected exponent-limits (given in [3, 5 7 11>-monzo form) of [-15...+15, -10...+10 -4...+4 -2...+2>.

(In other words, these intervals also describe the pitches contained in euler genus with the factors 2n * 315 * 510 * 74 * 112.)

Also included is a complete listing for several important EDOs: 12, 17, 19, 22, 31, 41, 46, 53, 55.

(Note that very large ratio terms are given in scientific notation, where " x.yE+z " means " x.y * 10z ".)

ranked in ascending order of cents:


		    cents       tinas    2,3,5,7,11-monzo             ratio              name (if any)


		   0               0.0  [  0   0,   0  0  0 >            1 : 1               prime unity
		   0.022716864     0.2  [ 27 -14,  -3  2 -1 >   6576668672 : 6576582375
		   0.07031446      0.5  [  3 -13,  10 -2  0 >     78125000 : 78121827
		   0.176647523     1.3  [ -3   4,  -2 -2  2 >         9801 : 9800
		   0.196391484     1.4  [-25   3,   9  1 -1 >    369140625 : 369098752
		   0.199364387     1.4  [ 24 -10,  -5  0  1 >    184549376 : 184528125
		   0.219108348     1.6  [  2 -11,   6  3 -2 >     21437500 : 21434787
		   0.246961983     1.8  [  0  -9,   8 -4  2 >     47265625 : 47258883
		   0.325441411     2.3  [ -4   6,  -6  3  0 >       250047 : 250000
		   0.373039007     2.7  [-28   7,   7 -1  1 >   1879453125 : 1879048192
		   0.395755871     2.8  [ -1  -7,   4  1  0 >         4375 : 4374
		   0.463728629     3.3  [ 19   9,  -8 -4 -1 >  10319560704 : 10316796875
		   0.502088934     3.6  [ -7  10,  -8  1  2 >     50014503 : 50000000
		   0.521832895     3.7  [-29   9,   3  4 -1 >   5907360375 : 5905580032
		   0.572403394     4.1  [ -4  -3,   2 -1  2 >         3025 : 3024
		   0.660120113     4.7  [ -6  12,   1 -3 -2 >      2657205 : 2656192
		   0.698480418     5.0  [-32  13,   1  2  1 >   4296700485 : 4294967296
		   0.721197281     5.1  [ -5  -1,  -2  4  0 >         2401 : 2400
		   0.791511742     5.6  [ -2 -14,   8  2  0 >     19140625 : 19131876
		   0.859484499     6.1  [ 18   2,  -4 -3 -1 >      2359296 : 2358125
		   0.882201363     6.3  [ 45 -12,  -7 -1 -2 >  3.51844E+13 : 3.51664E+13
		   0.897844805     6.4  [ -8   3,  -4  2  2 >       160083 : 160000
		   0.920561668     6.6  [ 19 -11,  -7  4  1 >  13846970368 : 13839609375
		   0.968159265     6.9  [ -5 -10,   6  0  2 >      1890625 : 1889568

		   1.055875983     7.5  [ -7   5,   5 -2 -2 >       759375 : 758912
		   1.058848886     7.5  [ 42  -8,  -9 -3  0 >  4.39805E+12 : 4.39536E+12
		   1.094236289     7.8  [-33   6,   5  3  1 >   8595365625 : 8589934592
		   1.18492591      8.4  [ 14   8, -10  0 -1 >    107495424 : 107421875
		   1.232523506     8.8  [-10   9,   3 -4  0 >      2460375 : 2458624
		   1.25524037      8.9  [ 17  -5,   0 -2 -1 >       131072 : 130977
		   1.293600675     9.2  [ -9  -4,   0  3  2 >        41503 : 41472
		   1.381317394     9.8  [-11  11,  -1  1 -2 >      1240029 : 1239040
		   1.431887893    10.2  [ 14  -1,  -2 -4  1 >       180224 : 180075
		   1.451631854    10.3  [ -8  -2,   9 -1 -2 >      1953125 : 1951488
		   1.454604757    10.4  [ 41 -15,  -5 -2  0 >  2.19902E+12 : 2.19718E+12
		   1.489992159    10.6  [-34  -1,   9  4  1 >  51583984375 : 51539607552
		   1.557964917    11.1  [-14  15,  -3 -1  0 >     14348907 : 14336000
		   1.580681781    11.2  [ 13   1,  -6  1 -1 >       172032 : 171875
		   1.603398644    11.4  [ 40 -13,  -9  3 -2 >  3.77132E+14 : 3.76783E+14
		   1.628279377    11.6  [-11   2,   7 -3  0 >       703125 : 702464
		   1.63125228     11.6  [ 38 -11,  -7 -4  2 >  3.32602E+13 : 3.32289E+13
		   1.650996241    11.7  [ 16 -12,   4 -1 -1 >     40960000 : 40920957
		   1.689356546    12.0  [-10 -11,   4  4  2 >    181575625 : 181398528
		   1.757329304    12.5  [ 10   5,  -8 -1  1 >      2737152 : 2734375
		   1.777073265    12.6  [-12   4,   3  2 -2 >       496125 : 495616
		   1.827643764    13.0  [ 13  -8,   2 -3  1 >      2252800 : 2250423
		   1.953720788    13.9  [-15   8,   1  0  0 >        32805 : 32768           skhisma [Ellis], schisma
		   1.976437651    14.1  [ 12  -6,  -2  2 -1 >       200704 : 200475

		   2.130368311    15.2  [-18  12,  -1 -2  2 >     64304361 : 64225280
		   2.150112272    15.3  [-40  11,  10  1 -1 >  1.21097E+13 : 1.20946E+13
		   2.153085175    15.3  [  9  -2,  -4  0  1 >         5632 : 5625
		   2.172829136    15.5  [-13  -3,   7  3 -2 >     26796875 : 26763264
		   2.200682771    15.7  [-15  -1,   9 -4  2 >    236328125 : 236027904
		   2.223399635    15.8  [ 12 -15,   6 -2  1 >    704000000 : 703096443
		   2.279162199    16.2  [-19  14,  -5  3  0 >   1640558367 : 1638400000
		   2.326759795    16.6  [-43  15,   8 -1  1 >  6.16555E+13 : 6.15727E+13
		   2.349476659    16.7  [-16   1,   5  1  0 >        65625 : 65536
		   2.352449561    16.7  [ 33 -12,  -9  0  2 >  1.03938E+12 : 1.03797E+12
		   2.372193522    16.9  [ 11 -13,   2  3 -1 >     17561600 : 17537553
		   2.44016628     17.4  [ 31   3, -10 -2 -2 >  57982058496 : 57900390625
		   2.478526585    17.6  [  5   4, -10  3  1 >      9779616 : 9765625
		   2.51048074     17.9  [ 34 -10,   0 -4 -2 >  17179869184 : 17154974529
		   2.526124182    18.0  [-19   5,   3 -1  2 >      3675375 : 3670016
		   2.548841045    18.1  [  8  -9,   0  1  1 >        19712 : 19683
		   2.674918069    19.0  [-20   7,  -1  4  0 >      5250987 : 5242880
		   2.745232529    19.5  [-17  -6,   9  2  0 >     95703125 : 95551488
		   2.813205287    20.0  [ 3   10,  -3 -3 -1 >       472392 : 471625
		   2.835922151    20.2  [ 30  -4,  -6 -1 -2 >   1073741824 : 1071984375
		   2.851565593    20.3  [-23  11,  -3  2  2 >   1050304563 : 1048576000
		   2.874282456    20.5  [  4  -3,  -6  4  1 >       422576 : 421875
		   2.921880053    20.8  [-20  -2,   7  0  2 >      9453125 : 9437184

		   3.009596771    21.4  [-22  13,   6 -2 -2 >  24911296875 : 24868028416
		   3.012569674    21.4  [ 27   0,  -8 -3  0 >    134217728 : 133984375
		   3.047957077    21.7  [-48  14,   6  3  1 >  2.81971E+14 : 2.81475E+14
		   3.208961158    22.8  [  2   3,   1 -2 -1 >          540 : 539
		   3.231678022    23.0  [ 29 -11,  -2  0 -2 >    536870912 : 535869675
		   3.247321463    23.1  [-24   4,   1  3  2 >     16808715 : 16777216
		   3.385608681    24.1  [ -1   7,  -1 -4  1 >        24057 : 24010
		   3.405352642    24.2  [-23   6,  10 -1 -2 >   7119140625 : 7105150976
		   3.408325545    24.3  [ 26  -7,  -4 -2  0 >     67108864 : 66976875
		   3.443712947    24.5  [-49   7,  10  4  1 >  5.64071E+14 : 5.6295E+14
		   3.534402569    25.2  [ -2   9,  -5  1 -1 >       137781 : 137500
		   3.557119432    25.3  [ 25  -5,  -8  3 -2 >  11509170176 : 11485546875
		   3.582000165    25.5  [-26  10,   8 -3  0 >  23066015625 : 23018340352
		   3.584973068    25.5  [ 23  -3,  -6 -4  2 >   1015021568 : 1012921875
		   3.604717029    25.7  [  1  -4,   5 -1 -1 >         6250 : 6237
		   3.643077334    25.9  [-25  -3,   5  4  2 >    907878125 : 905969664
		   3.711050092    26.4  [ -5  13,  -7 -1  1 >     17537553 : 17500000
		   3.730794053    26.5  [-27  12,   4  2 -2 >  16275380625 : 16240345088
		   3.733766955    26.6  [ 22  -1, -10  1  0 >     29360128 : 29296875
		   3.781364552    26.9  [ -2   0,   3 -3  1 >         1375 : 1372
		   3.804081415    27.1  [ 25 -14,   0 -1  0 >     33554432 : 33480783
		   3.930158439    28.0  [ -3   2,  -1  2 -1 >          441 : 440
		   3.952875303    28.1  [ 24 -12,  -4  4 -2 >  40282095616 : 40190225625
		   3.980728939    28.3  [ 22 -10,  -2 -3  2 >    507510784 : 506345175

		   4.000472899    28.5  [  0 -11,   9  0 -1 >      1953125 : 1948617
		   4.106805963    29.2  [ -6   6,  -3  0  1 >         8019 : 8000
		   4.126549923    29.4  [-28   5,   8  3 -2 >  32558203125 : 32480690176
		   4.129522826    29.4  [ 21  -8,  -6  2  0 >    102760448 : 102515625
		   4.154403559    29.6  [-30   7,  10 -4  2 >  2.58425E+12 : 2.57805E+12
		   4.177120423    29.7  [ -3  -7,   7 -2  1 >       859375 : 857304
		   4.303197447    30.6  [-31   9,   6  1  0 >   2152828125 : 2147483648
		   4.306170349    30.6  [ 18  -4,  -8  0  2 >     31719424 : 31640625
		   4.32591431     30.8  [ -4  -5,   3  3 -1 >        42875 : 42768
		   4.393887068    31.3  [ 16  11,  -9 -2 -2 >  11609505792 : 11580078125
		   4.432247373    31.5  [-10  12,  -9  3  1 >   2005126893 : 2000000000
		   4.464201528    31.8  [ 19  -2,   1 -4 -2 >      2621440 : 2614689
		   4.47984497     31.9  [-34  13,   4 -1  2 >  1.20571E+11 : 1.20259E+11
		   4.502561833    32.0  [ -7  -1,   1  1  1 >          385 : 384
		   4.525278697    32.2  [ 20 -15,  -2  3  0 >    359661568 : 358722675
		   4.628638857    32.9  [-35  15,   0  4  0 >  34451725707 : 34359738368
		   4.663565915    33.2  [ 43 -12,  -4 -4 -1 >  8.79609E+12 : 8.77243E+12
		   4.698953317    33.4  [-32   2,  10  2  0 >   4306640625 : 4294967296
		   4.70192622     33.5  [ 17 -11,  -4  1  2 >    111017984 : 110716875
		   4.721670181    33.6  [ -5 -12,   7  4 -1 >    187578125 : 187067232
		   4.789642939    34.1  [ 15   4,  -5 -1 -2 >      2654208 : 2646875
		   4.828003244    34.4  [-11   5,  -5  4  1 >      6417873 : 6400000
		   4.859957399    34.6  [ 18  -9,   5 -3 -2 >    819200000 : 816903549
		   4.875600841    34.7  [-35   6,   8  0  2 >  34456640625 : 34359738368
		   4.898317704    34.9  [ -8  -8,   5  2  1 >      1684375 : 1679616
		   4.966290462    35.3  [ 12   8,  -7 -3  0 >     26873856 : 26796875
		   4.989007325    35.5  [ 39  -6, -10 -1 -1 >  5.49756E+11 : 5.48174E+11

		   5.027367631    35.8  [ 13  -5, -10  4  2 >   2379948032 : 2373046875
		   5.162681946    36.7  [-13  11,   2 -2 -1 >      4428675 : 4415488
		   5.185398809    36.9  [ 14  -3,  -1  0 -2 >        16384 : 16335
		   5.201042251    37.0  [-39  12,   2  3  2 >   5.5141E+11 : 5.49756E+11
		   5.294073575    37.7  [ -9 -15,   9  3  1 >   7369140625 : 7346640384
		   5.339329469    38.0  [-16  15,   0 -4  1 >    157837977 : 157351936
		   5.362046333    38.2  [ 11   1,  -3 -2  0 >         6144 : 6125
		   5.384763196    38.3  [ 38 -13,  -6  0 -1 >  2.74878E+11 : 2.74024E+11
		   5.432360793    38.7  [ 14 -12,   7 -4  0 >   1280000000 : 1275989841
		   5.51084022     39.2  [ 10   3,  -7  3 -2 >      9483264 : 9453125
		   5.538693856    39.4  [  8   5,  -5 -4  2 >      7527168 : 7503125
		   5.558437817    39.6  [-14   4,   6 -1 -1 >      1265625 : 1261568
		   5.561410719    39.6  [ 35  -9,  -8 -2  1 >  3.77957E+11 : 3.76745E+11
		   5.58115468     39.7  [ 13 -10,   3  1 -2 >      7168000 : 7144929
		   5.596798122    39.8  [-40   5,   6  4  2 >  1.10307E+12 : 1.09951E+12
		   5.687487743    40.5  [  7   7,  -9  1  0 >      1959552 : 1953125
		   5.73508534     40.8  [-17   8,   4 -3  1 >     45106875 : 44957696
		   5.757802203    41.0  [ 10  -6,   1 -1  0 >         5120 : 5103
		   5.883879227    41.9  [-18  10,   0  2 -1 >      2893401 : 2883584
		   5.906596091    42.0  [  9  -4,  -3  4 -2 >      1229312 : 1225125
		   5.934449727    42.2  [  7  -2,  -1 -3  2 >        15488 : 15435
		   5.954193687    42.4  [-15  -3,  10  0 -1 >      9765625 : 9732096

		   6.060526751    43.1  [-21  14,  -2  0  1 >     52612659 : 52428800
		   6.080270711    43.3  [-43  13,   9  3 -2 >  1.06807E+15 : 1.06433E+15
		   6.083243614    43.3  [  6   0,  -5  2  0 >         3136 : 3125
		   6.105960478    43.4  [ 33 -14,  -8  4 -1 >  2.06244E+13 : 2.05518E+13
		   6.130841211    43.6  [-18   1,   8 -2  1 >     12890625 : 12845056
		   6.153558074    43.8  [  9 -13,   5  0  0 >      1600000 : 1594323         amity
		   6.244247696    44.4  [ 56 -11, -10 -3 -2 >  7.20576E+16 : 7.17982E+16
		   6.259891137    44.5  [  3   4,  -7  0  2 >        78408 : 78125
		   6.279635098    44.7  [-19   3,   4  3 -1 >      5788125 : 5767168
		   6.282608001    44.7  [ 30 -10, -10  2  1 >  5.78747E+11 : 5.7665E+11
		   6.330205597    45.0  [  6  -9,   3 -2  2 >       968000 : 964467
		   6.417922316    45.7  [  4   6,   2 -4 -2 >       291600 : 290521
		   6.456282621    45.9  [-22   7,   2  1  1 >      4209975 : 4194304
		   6.478999485    46.1  [  5  -7,  -1  3  0 >        10976 : 10935
		   6.617286703    47.1  [ 28  -4,  -3 -4 -1 >    268435456 : 267411375
		   6.655647008    47.4  [  2  -3,  -3  1  2 >         3388 : 3375
		   6.675390969    47.5  [-20  -4,   8  4 -1 >    937890625 : 934281216
		   6.743363727    48.0  [  0  12,  -4 -1 -2 >       531441 : 529375
		   6.781724032    48.3  [-26  13,  -4  4  1 >  42107664753 : 41943040000
		   6.813678187    48.5  [  3  -1,   6 -3 -2 >       125000 : 124509
		   6.816651089    48.5  [ 52 -14,  -8 -4  0 >   4.5036E+15 : 4.4859E+15
		   6.829321628    48.6  [-50  14,   9  0  2 >  1.13035E+15 : 1.1259E+15
		   6.852038492    48.8  [-23   0,   6  2  1 >      8421875 : 8388608
		   6.874755356    48.9  [  4 -14,   3  4  0 >      4802000 : 4782969
		   6.942728113    49.4  [ 24   2,  -9 -1 -1 >    150994944 : 150390625
		   6.981088419    49.7  [ -2   3,  -9  4  2 >      7844067 : 7812500

		   7.013042573    49.9  [ 27 -11,   1 -3 -1 >    671088640 : 668375631
		   7.051402879    50.2  [  1 -10,   1  2  2 >        59290 : 59049
		   7.139119597    50.8  [ -1   5,   0  0 -2 >          243 : 242
		   7.209434057    51.3  [  2  -8,  10 -2 -2 >     39062500 : 38900169
		   7.247794363    51.6  [-24  -7,  10  3  1 >  36845703125 : 36691771392
		   7.315767121    52.1  [ -4   9,  -2 -2  0 >        19683 : 19600
		   7.338483984    52.2  [ 23  -5,  -5  0 -1 >      8388608 : 8353125
		   7.386081581    52.6  [ -1  -4,   8 -4  0 >       390625 : 388962
		   7.464561008    53.1  [ -5  11,  -6  3 -2 >     60761421 : 60500000
		   7.492414644    53.3  [ -7  13,  -4 -4  2 >    192913083 : 192080000
		   7.512158605    53.5  [-29  12,   7 -1 -1 >  41518828125 : 41339060224
		   7.515131507    53.5  [ 20  -1,  -7 -2  1 >     11534336 : 11484375
		   7.534875468    53.6  [ -2  -2,   4  1 -2 >         4375 : 4356
		   7.537848371    53.6  [ 47 -15, -10  0  0 >  1.40737E+14 : 1.40126E+14
		   7.55051891     53.7  [-55  13,   7  4  2 >  3.61863E+16 : 3.60288E+16
		   7.585445967    54.0  [ 23 -14,   3 -4  1 >  11534336000 : 11483908569
		   7.641208531    54.4  [ -8  15,  -8  1  0 >    100442349 : 100000000
		   7.711522991    54.9  [ -5   2,   2 -1  0 >          225 : 224             septimal-kleisma
		   7.734239855    55.0  [ 22 -12,  -1  1 -1 >     29360128 : 29229255
		   7.860316879    55.9  [ -6   4,  -2  4 -2 >       194481 : 193600
		   7.888170514    56.1  [ -8   6,   0 -3  2 >        88209 : 87808
		   7.910887378    56.3  [ 19  -8,  -3 -1  1 >      5767168 : 5740875
		   7.930631339    56.4  [ -3  -9,   8  2 -2 >     19140625 : 19053144

		   8.036964402    57.2  [ -9   8,  -4  2  0 >       321489 : 320000
		   8.059681266    57.4  [ 18  -6,  -7  4 -1 >    629407744 : 626484375
		   8.084561999    57.5  [-33   9,   9 -2  1 >  4.22877E+11 : 4.20907E+11
		   8.107278862    57.7  [ -6  -5,   6  0  0 >        15625 : 15552           kleisma [Tanaka]
		   8.197968483    58.3  [ 41  -3,  -9 -3 -2 >  2.19902E+12 : 2.18863E+12
		   8.213611925    58.4  [-12  12,  -6  0  2 >     64304361 : 64000000
		   8.233355886    58.6  [-34  11,   5  3 -1 >  1.89879E+11 : 1.88979E+11
		   8.236328789    58.6  [ 15  -2,  -9  2  1 >     17661952 : 17578125
		   8.283926385    58.9  [ -9  -1,   4 -2  2 >        75625 : 75264
		   8.306643249    59.1  [ 18 -15,   1  0  1 >     14417920 : 14348907
		   8.371643104    59.6  [-11  14,   3 -4 -2 >    597871125 : 594987008
		   8.410003409    59.8  [-37  15,   3  1  1 >  1.38108E+11 : 1.37439E+11
		   8.432720273    60.0  [-10   1,   0  3  0 >         1029 : 1024
		   8.503034733    60.5  [ -7 -12,  10  1  0 >     68359375 : 68024448
		   8.571007491    61.0  [ 13   4,  -2 -4 -1 >       663552 : 660275
		   8.593724354    61.2  [ 40 -10,  -5 -2 -2 >  1.09951E+12 : 1.09407E+12
		   8.609367796    61.3  [-13   5,  -2  1  2 >       205821 : 204800
		   8.629111757    61.4  [-35   4,   9  4 -1 >  3.79846E+11 : 3.77957E+11
		   8.632084659    61.4  [ 14  -9,  -5  3  1 >     61816832 : 61509375
		   8.679682256    61.8  [-10  -8,   8 -1  2 >     47265625 : 47029248
		   8.767398975    62.4  [-12   7,   7 -3 -2 >    170859375 : 169996288
		   8.770371877    62.4  [ 37  -6,  -7 -4  0 >  1.37439E+11 : 1.36744E+11
		   8.80575928     62.7  [-38   8,   7  2  1 >   2.7628E+11 : 2.74878E+11
		   8.828476144    62.8  [-11  -6,   4  4  0 >      1500625 : 1492992
		   8.896448901    63.3  [  9  10,  -8 -1 -1 >     30233088 : 30078125
		   8.934809207    63.6  [-17  11,  -8  4  2 >  51464923587 : 51200000000
		   8.966763361    63.8  [ 12  -3,   2 -3 -1 >       102400 : 101871

		   9.005123667    64.1  [-14  -2,   2  2  2 >       148225 : 147456
		   9.073096424    64.6  [  6  14, -10 -3  1 >   3367210176 : 3349609375
		   9.092840385    64.7  [-16  13,   1  0 -2 >      7971615 : 7929856
		   9.166127748    65.2  [ 36 -13,  -3 -3  0 >  68719476736 : 68356598625
		   9.292204772    66.1  [  8   3,  -4  0 -1 >         6912 : 6875
		   9.314921636    66.3  [ 35 -11,  -7  2 -2 >  1.68363E+12 : 1.67459E+12
		   9.339802369    66.5  [-16   4,   9 -4  0 >    158203125 : 157351936
		   9.362519232    66.6  [ 11 -10,   6 -2 -1 >     32000000 : 31827411
		   9.400879537    66.9  [-15  -9,   6  3  2 >    648484375 : 644972544
		   9.468852295    67.4  [  5   7,  -6 -2  1 >       769824 : 765625
		   9.488596256    67.5  [-17   6,   5  1 -2 >     15946875 : 15859712
		   9.491569159    67.5  [ 32  -7,  -9  0  0 >   4294967296 : 4271484375      escapade
		   9.539166755    67.9  [  8  -6,   4 -4  1 >      1760000 : 1750329
		   9.617646183    68.4  [  4   9, -10  3 -1 >    108020304 : 107421875
		   9.665243779    68.8  [-20  10,   3 -1  0 >      7381125 : 7340032
		   9.687960643    68.9  [  7  -4,   0  1 -1 >          896 : 891
		   9.814037667    69.8  [-21  12,  -1  4 -2 >   1275989841 : 1268776960
		   9.841891302    70.0  [-23  14,   1 -3  2 >   2893696245 : 2877292544
		   9.864608166    70.2  [  4   0,  -2 -1  1 >          176 : 175             x 46-edo
		   9.884352127    70.3  [-18  -1,   9  2 -2 >     95703125 : 95158272
		   9.88732503     70.4  [ 31 -14,  -5  1  0 >  15032385536 : 14946778125
		   9.934922626    70.7  [  7 -13,   8 -3  1 >    550000000 : 546852789

		  10.01340205     71.3  [  3   2,  -6  4 -1 >       172872 : 171875
		  10.06099965     71.6  [-21   3,   7  0  0 >      2109375 : 2097152         semicomma
		  10.06397255     71.6  [ 28 -10,  -7 -1  2 >  32480690176 : 32292421875
		  10.08371651     71.8  [  6 -11,   4  2 -1 >      1960000 : 1948617
		  10.15168927     72.2  [ 26   5,  -8 -3 -2 >  16307453952 : 16212109375
		  10.19004958     72.5  [  0   6,  -8  2  1 >       392931 : 390625
		  10.23764717     72.8  [-24   7,   5 -2  2 >    826959375 : 822083584
		  10.26036404     73.0  [  3  -7,   2  0  1 >         2200 : 2187
		  10.38644106     73.9  [-25   9,   1  3  0 >     33756345 : 33554432
		  10.52472828     74.9  [ -2  12,  -1 -4 -1 >       531441 : 528220
		  10.54744514     75.1  [ 25  -2,  -4 -2 -2 >     33554432 : 33350625
		  10.56308858     75.2  [-28  13,  -1  1  2 >   1350391581 : 1342177280
		  10.58283254     75.3  [-50  12,  10  4 -1 >  1.24608E+16 : 1.23849E+16
		  10.58580545     75.3  [ -1  -1,  -4  3  1 >         3773 : 3750
		  10.6177596      75.6  [ 28 -15,   6 -4 -2 >   4.1943E+12 : 4.16866E+12
		  10.63340304     75.7  [-25   0,   9 -1  2 >    236328125 : 234881024
		  10.65611991     75.8  [  2 -14,   6  1  1 >      4812500 : 4782969
		  10.72111976     76.3  [-27  15,   8 -3 -2 >  5.60504E+12 : 5.57044E+12
		  10.72409267     76.3  [ 22   2,  -6 -4  0 >     37748736 : 37515625
		  10.74680953     76.5  [ 49 -12,  -9 -2 -1 >   5.6295E+14 : 5.59466E+14
		  10.78219693     76.7  [-26   2,   5  4  0 >     67528125 : 67108864
		  10.78516983     76.7  [ 23 -11,  -9  3  2 >  3.48152E+11 : 3.4599E+11
		  10.87288655     77.4  [ 21   4, -10  1 -2 >   1189085184 : 1181640625
		  10.92048415     77.7  [ -3   5,   3 -3 -1 >        30375 : 30184
		  10.94320101     77.9  [ 24  -9,   0 -1 -2 >     16777216 : 16671501
		  10.95884445     78.0  [-29   6,   3  2  2 >    540280125 : 536870912
		  10.98156132     78.1  [ -2  -8,   0  4  1 >        26411 : 26244

		  11.11984854     79.1  [ 21  -5,  -2 -3  0 >      2097152 : 2083725
		  11.24592556     80.0  [ -7  11,  -3  0 -1 >       177147 : 176000
		  11.26864242     80.2  [ 20  -3,  -6  2 -2 >     51380224 : 51046875
		  11.29352316     80.4  [-31  12,  10 -4  0 >  5.18985E+12 : 5.15611E+12
		  11.31624002     80.5  [ -4  -2,   7 -2 -1 >        78125 : 77616
		  11.31921292     80.5  [ 45 -15,  -7 -3  1 >  3.87028E+14 : 3.84506E+14
		  11.35460033     80.8  [-30  -1,   7  3  2 >   3242421875 : 3221225472
		  11.42257308     81.3  [-10  15,  -5 -2  1 >    157837977 : 156800000
		  11.44231704     81.4  [-32  14,   6  1 -2 >  5.23137E+11 : 5.19691E+11
		  11.44528995     81.4  [ 17   1,  -8  0  0 >       393216 : 390625          würschmidt-comma
		  11.49288754     81.8  [ -7   2,   5 -4  1 >       309375 : 307328
		  11.51560441     81.9  [ 20 -12,   2 -2  0 >     26214400 : 26040609
		  11.62193747     82.7  [ 14   5, -10 -2  2 >    481738752 : 478515625
		  11.64168143     82.8  [ -8   4,   1  1 -1 >         2835 : 2816
		  11.66439829     83.0  [ 19 -10,  -2  3 -2 >    179830784 : 178623225
		  11.69225193     83.2  [ 17  -8,   0 -4  2 >     15859712 : 15752961
		  11.81832895     84.1  [-11   8,  -1 -1  1 >        72171 : 71680
		  11.83807291     84.2  [-33   7,  10  2 -2 >  1.04651E+12 : 1.03938E+12
		  11.84104582     84.3  [ 16  -6,  -4  1  0 >       458752 : 455625
		  11.88864341     84.6  [ -8  -5,   9 -3  1 >     21484375 : 21337344
		  11.96712284     85.2  [-12  10,  -5  4 -1 >    141776649 : 140800000

		  12.01472044     85.5  [-36  11,   8  0  0 >  69198046875 : 68719476736
		  12.01769334     85.5  [ 13  -2,  -6 -1  2 >       991232 : 984375
		  12.0374373      85.7  [ -9  -3,   5  2 -1 >       153125 : 152064
		  12.0880078      86.0  [ 16 -15,   4 -3  2 >   4956160000 : 4921675101
		  12.10541006     86.1  [ 11  13,  -7 -3 -2 >   3265173504 : 3242421875
		  12.14377036     86.4  [-15  14,  -7  2  1 >   2578020291 : 2560000000
		  12.16648723     86.6  [ 12   0, -10  4  0 >      9834496 : 9765625
		  12.19136796     86.8  [-39  15,   6 -2  2 >  2.71284E+13 : 2.6938E+13
		  12.21408482     86.9  [-12   1,   3  0  1 >         4125 : 4096
		  12.23680169     87.1  [ 15 -13,   0  2  0 >      1605632 : 1594323
		  12.41344921     88.3  [ 12  -9,  -2  0  2 >       495616 : 492075
		  12.43319317     88.5  [-10 -10,   9  3 -1 >    669921875 : 665127936
		  12.50116593     89.0  [ 10   6,  -3 -2 -2 >       746496 : 741125
		  12.53952624     89.2  [-16   7,  -3  3  1 >      8251551 : 8192000
		  12.57148039     89.5  [ 13  -7,   7 -4 -2 >    640000000 : 635369427
		  12.58712383     89.6  [-40   8,  10 -1  2 >  7.75274E+12 : 7.69658E+12
		  12.6098407      89.7  [-13  -6,   7  1  1 >      6015625 : 5971968
		  12.67781345     90.2  [  7  10,  -5 -4  0 >      7558272 : 7503125
		  12.70053032     90.4  [ 34  -4,  -8 -2 -1 >  17179869184 : 17054296875
		  12.73591772     90.6  [-41  10,   6  4  0 >  2.21526E+12 : 2.19902E+12
		  12.73889062     90.6  [  8  -3,  -8  3  2 >     10624768 : 10546875
		  12.82660734     91.3  [  6  12,  -9  1 -2 >    238085568 : 236328125
		  12.87420494     91.6  [-18  13,   4 -3 -1 >    996451875 : 989069312
		  12.87717784     91.6  [ 31   0, -10 -4  1 >  23622320128 : 23447265625
		  12.8969218      91.8  [  9  -1,   1 -1 -2 >         2560 : 2541
		  12.91256524     91.9  [-44  14,   4  2  2 >  1.77239E+13 : 1.75922E+13
		  12.93528211     92.0  [-17   0,   1  4  1 >       132055 : 131072

		  13.07356932     93.0  [  6   3,  -1 -3  0 >         1728 : 1715
		  13.09628619     93.2  [ 33 -11,  -4 -1 -1 >   8589934592 : 8525199375
		  13.13464649     93.5  [  7 -10,  -4  4  2 >     37186688 : 36905625
		  13.22236321     94.1  [  5   5,  -5  2 -2 >       381024 : 378125
		  13.26996081     94.4  [-19   6,   8 -2 -1 >    284765625 : 282591232
		  13.27293371     94.4  [ 30  -7,  -6 -3  1 >  11811160064 : 11720953125
		  13.29267767     94.6  [  8  -8,   5  0 -2 >       800000 : 793881
		  13.30832111     94.7  [-45   7,   8  3  2 >  3.54559E+13 : 3.51844E+13
		  13.39901073     95.3  [  2   9,  -7  0  0 >        78732 : 78125           semisixths
		  13.4217276      95.5  [ 29  -5, -10  2 -1 >  26306674688 : 26103515625
		  13.44660833     95.7  [-22  10,   6 -4  1 >  10149046875 : 10070523904
		  13.46932519     95.8  [  5  -4,   3 -2  0 >         4000 : 3969
		  13.57565826     96.6  [ -1  13,  -9 -2  2 >    192913083 : 191406250
		  13.59540222     96.7  [-23  12,   2  1 -1 >     93002175 : 92274688
		  13.61811908     96.9  [  4  -2,  -1  3 -2 >         5488 : 5445
		  13.64597272     97.1  [  2   0,   1 -4  2 >         2420 : 2401
		  13.66868958     97.3  [ 29 -14,  -2 -2  1 >   5905580032 : 5859137025
		  13.68843354     97.4  [  7 -15,   9  1 -2 >   1750000000 : 1736217747
		  13.79476661     98.2  [  1   2,  -3  1  0 >          126 : 125             small septimal-comma
		  13.81748347     98.3  [ 28 -12,  -6  3 -1 >  92073361408 : 91341421875
		  13.8423642      98.5  [-23   3,  10 -3  1 >   2900390625 : 2877292544
		  13.86508107     98.7  [  4 -11,   7 -1  0 >      1250000 : 1240029
		  13.95577069     99.3  [ 51  -9,  -8 -4 -2 >   2.2518E+15 : 2.23372E+15
		  13.97141413     99.4  [ -2   6,  -5 -1  2 >        88209 : 87500
		  13.99115809     99.6  [-24   5,   6  2 -1 >    186046875 : 184549376
		  13.99413099     99.6  [ 25  -8,  -8  1  1 >   2583691264 : 2562890625

		  14.01387495     99.7  [  3  -9,   3  4 -2 >      2401000 : 2381643
		  14.04172859     99.9  [  1  -7,   5 -3  2 >       756250 : 750141
		  14.12020802    100.5  [ -3   8,  -9  4  0 >     15752961 : 15625000
		  14.16780561    100.8  [-27   9,   4  0  1 >    135320625 : 134217728
		  14.19052248    101.0  [  0  -5,   1  2  0 >          245 : 243             minor Bohlen-Pierce diesis
		  14.36717       102.2  [ -3  -1,  -1  0  2 >          121 : 120             x 46-edo
		  14.38691396    102.4  [-25  -2,  10  3 -1 >   3349609375 : 3321888768
		  14.38988686    102.4  [ 24 -15,  -4  2  1 >   9042919424 : 8968066875
		  14.43748446    102.7  [  0 -14,   9 -2  2 >    236328125 : 234365481
		  14.45488672    102.9  [ -5  14,  -2 -2 -2 >      4782969 : 4743200
		  14.49324702    103.1  [-31  15,  -2  3  1 >  54138426111 : 53687091200
		  14.52520118    103.4  [ -2   1,   8 -4 -2 >      1171875 : 1162084
		  14.56356148    103.6  [-28   2,   8  1  1 >    270703125 : 268435456
		  14.58627835    103.8  [ -1 -12,   5  3  0 >      1071875 : 1062882
		  14.6542511     104.3  [ 19   4,  -7 -2 -1 >     42467328 : 42109375
		  14.67696797    104.4  [ 46 -10, -10  0 -2 >  7.03687E+13 : 6.97747E+13
		  14.69261141    104.6  [ -7   5,  -7  3  2 >     10085229 : 10000000
		  14.72456556    104.8  [ 22  -9,   3 -4 -1 >    524288000 : 519847713
		  14.76292587    105.1  [ -4  -8,   3  1  2 >       105875 : 104976
		  14.83089863    105.5  [ 16   8,  -9 -4  1 >   4729798656 : 4689453125
		  14.85064259    105.7  [ -6   7,   2 -1 -2 >        54675 : 54208
		  14.88900289    105.9  [-32   8,   2  4  1 >   4332064275 : 4294967296

		  15.02729011    106.9  [ -9  11,   0 -3  0 >       177147 : 175616
		  15.05000698    107.1  [ 18  -3,  -3 -1 -1 >       262144 : 259875
		  15.08836728    107.4  [ -8  -2,  -3  4  2 >       290521 : 288000
		  15.15868174    107.9  [ -5 -15,   7  2  2 >    463203125 : 459165024
		  15.176084      108.0  [-10  13,  -4  2 -2 >     78121827 : 77440000
		  15.2236816     108.3  [-34  14,   9 -2 -1 >  9.34174E+12 : 9.25995E+12
		  15.2266545     108.4  [ 15   1,  -5 -3  1 >      1081344 : 1071875
		  15.24639846    108.5  [ -7   0,   6  0 -2 >        15625 : 15488
		  15.24937136    108.5  [ 42 -13,  -8 -1  0 >  4.39805E+12 : 4.35948E+12
		  15.2620419     108.6  [-60  15,   9  3  2 >  1.16313E+18 : 1.15292E+18
		  15.37544839    109.4  [ 14   3,  -9  2 -1 >     21676032 : 21484375
		  15.42304598    109.7  [-10   4,   4 -2  0 >        50625 : 50176
		  15.42601889    109.8  [ 39  -9, -10 -3  2 >  6.65205E+13 : 6.59304E+13
		  15.44576285    109.9  [ 17 -10,   1  0 -1 >       655360 : 649539
		  15.57183987    110.8  [-11   6,   0  3 -2 >       250047 : 247808
		  15.59969351    111.0  [-13   8,   2 -4  2 >     19847025 : 19668992
		  15.62241037    111.2  [ 14  -6,  -1 -2  1 >       180224 : 178605
		  15.64215433    111.3  [ -8  -7,  10  1 -2 >     68359375 : 67744512
		  15.74848739    112.1  [-14  10,  -2  1  0 >       413343 : 409600
		  15.77120426    112.2  [ 13  -4,  -5  3 -1 >      2809856 : 2784375
		  15.81880185    112.6  [-11  -3,   8 -1  0 >       390625 : 387072
		  15.90949147    113.2  [ 36  -1,  -7 -4 -2 >  68719476736 : 68090859375
		  15.92513492    113.3  [-17  14,  -4 -1  2 >    578739249 : 573440000
		  15.94487888    113.5  [-39  13,   7  2 -1 >  6.10327E+12 : 6.04731E+12
		  15.94785178    113.5  [ 10   0,  -7  1  1 >        78848 : 78125
		  15.96759574    113.6  [-12  -1,   4  4 -2 >      1500625 : 1486848
		  15.97056864    113.6  [ 37 -14, -10  3  0 >  4.71416E+13 : 4.67087E+13
		  15.99544938    113.8  [-14   1,   6 -3  2 >      5671875 : 5619712

		  16.01816624    114.0  [ 13 -13,   3 -1  1 >     11264000 : 11160261
		  16.14424326    114.9  [-15   3,   2  2  0 >        33075 : 32768
		  16.16696013    115.0  [ 12 -11,  -1  4 -1 >      9834496 : 9743085
		  16.30524735    116.0  [ 35  -8,  -3 -3 -2 >  34359738368 : 34037647875
		  16.32089079    116.1  [-18   7,   0  0  2 >       264627 : 262144
		  16.34360765    116.3  [  9  -7,  -3  2  1 >       275968 : 273375
		  16.39120525    116.6  [-15  -6,  10 -2  2 >   1181640625 : 1170505728
		  16.47892197    117.3  [-17   9,   9 -4 -2 >  38443359375 : 38079168512
		  16.51728227    117.5  [-43  10,   9  1  1 >  8.88042E+12 : 8.79609E+12
		  16.53999913    117.7  [-16  -4,   6  3  0 >      5359375 : 5308416
		  16.60797189    118.2  [  4  12,  -6 -2 -1 >      8503056 : 8421875
		  16.63068876    118.3  [ 31  -2,  -9  0 -2 >   2147483648 : 2126953125
		  16.6463322     118.5  [-22  13,  -6  3  2 >  66169187469 : 65536000000
		  16.67828635    118.7  [  7  -1,   4 -4 -1 >        80000 : 79233
		  16.70100322    118.8  [ 34 -15,   1 -2 -2 >  85899345920 : 85074669603
		  16.71664666    119.0  [-19   0,   4  1  2 >       529375 : 524288
		  16.73936352    119.1  [  8 -14,   1  3  1 >      4829440 : 4782969
		  16.80436338    119.6  [-21  15,   3 -1 -2 >   1793613375 : 1776287744
		  16.87765074    120.1  [ 31 -11,  -1 -4  0 >   2147483648 : 2126649735
		  16.93575501    120.5  [-17 -11,  10  4  0 >  23447265625 : 23219011584

		  17.00372776    121.0  [  3   5,  -2 -1 -1 >         1944 : 1925
		  17.02644463    121.2  [ 30  -9,  -5  1 -2 >   7516192768 : 7442634375
		  17.04208807    121.3  [-23   6,  -2  4  2 >    211789809 : 209715200
		  17.07404222    121.5  [  6  -8,   8 -3 -1 >     25000000 : 24754653
		  17.11240253    121.8  [-20  -7,   8  2  2 >   2316015625 : 2293235712
		  17.18037529    122.3  [  0   9,  -4 -3  1 >       216513 : 214375
		  17.20011925    122.4  [-22   8,   7  0 -2 >    512578125 : 507510784
		  17.20309215    122.4  [ 27  -5,  -7 -1  0 >    134217728 : 132890625
		  17.32916917    123.3  [ -1  11,  -8  2 -1 >      8680203 : 8593750
		  17.37676677    123.7  [-25  12,   5 -2  0 >   1660753125 : 1644167168
		  17.37973967    123.7  [ 24  -1,  -9 -3  2 >   2030043136 : 2009765625
		  17.39948363    123.8  [  2  -2,   2  0 -1 >          100 : 99
		  17.5058167     124.6  [ -4  15, -10  0  1 >    157837977 : 156250000
		  17.52556066    124.7  [-26  14,   1  3 -2 >   8202791835 : 8120172544
		  17.57613116    125.1  [ -1   2,   0 -2  1 >           99 : 98
		  17.59884802    125.2  [ 26 -12,  -3  0  0 >     67108864 : 66430125        misty
		  17.64644562    125.6  [  2 -11,  10 -4  1 >    429687500 : 425329947
		  17.72492504    126.1  [ -2   4,  -4  3 -1 >        27783 : 27500
		  17.77252264    126.5  [-26   5,   9 -1  0 >    474609375 : 469762048
		  17.77549554    126.5  [ 23  -8,  -5 -2  2 >   1015021568 : 1004653125
		  17.7952395     126.6  [  1  -9,   6  1 -1 >       218750 : 216513
		  17.86321226    127.1  [ 21   7,  -6 -4 -2 >   4586471424 : 4539390625
		  17.90157257    127.4  [ -5   8,  -6  1  1 >       505197 : 500000
		  17.92131653    127.5  [-27   7,   5  4 -2 >  16409334375 : 16240345088
		  17.92428943    127.5  [ 22  -6,  -9  3  0 >   1438646272 : 1423828125
		  17.94917016    127.7  [-29   9,   7 -3  2 >  1.86066E+11 : 1.84147E+11
		  17.97188703    127.9  [ -2  -5,   4 -1  1 >         6875 : 6804

		  18.09796405    128.8  [-30  11,   3  2  0 >   1085025375 : 1073741824
		  18.12068092    128.9  [ -3  -3,   0  4 -1 >         2401 : 2376
		  18.17125141    129.3  [ 22 -15,  -1 -1  2 >    507510784 : 502211745
		  18.25896813    129.9  [ 20   0,  -2 -3 -2 >      1048576 : 1037575
		  18.27461158    130.0  [-33  15,   1  0  2 >   8681088735 : 8589934592
		  18.29732844    130.2  [ -6   1,  -2  2  1 >         1617 : 1600
		  18.3200453     130.4  [ 21 -13,  -5  4  0 >   5035261952 : 4982259375
		  18.3676429     130.7  [ -3 -12,   8  0  1 >      4296875 : 4251528
		  18.45833252    131.3  [ 44 -10,  -7 -3 -1 >  1.75922E+13 : 1.74056E+13
		  18.49371992    131.6  [-31   4,   7  3  0 >   2170546875 : 2147483648
		  18.49669283    131.6  [ 18  -9,  -7  2  2 >   1554251776 : 1537734375
		  18.58440954    132.2  [ 16   6,  -8  0 -2 >     47775744 : 47265625
		  18.63200714    132.6  [ -8   7,   5 -4 -1 >      6834375 : 6761216
		  18.654724      132.7  [ 19  -7,   2 -2 -2 >     13107200 : 12966723
		  18.67036745    132.9  [-34   8,   5  1  2 >  17366146875 : 17179869184
		  18.69308431    133.0  [ -7  -6,   2  3  1 >        94325 : 93312
		  18.76105707    133.5  [ 13  10, -10 -2  0 >    483729408 : 478515625
		  18.83137153    134.0  [ 16  -3,   0 -4  0 >        65536 : 64827
		  18.95744855    134.9  [-12  13,  -1 -1 -1 >      1594323 : 1576960
		  18.98016541    135.1  [ 15  -1,  -4  1 -2 >       229376 : 226875
		  18.99580886    135.2  [-38  14,  -1  4  2 >  1.38955E+12 : 1.37439E+12

		  19.02776301    135.4  [ -9   0,   9 -3 -1 >      1953125 : 1931776
		  19.03073591    135.4  [ 40 -13,  -5 -4  1 >  1.20946E+13 : 1.19624E+13
		  19.05047987    135.6  [ 18 -14,   6 -1 -2 >   4096000000 : 4051174743
		  19.06612332    135.7  [-35   1,   9  2  2 >  34740234375 : 34359738368
		  19.08884018    135.8  [ -8 -13,   6  4  1 >    412671875 : 408146688
		  19.15681294    136.3  [ 12   3,  -6 -1  0 >       110592 : 109375
		  19.1795298     136.5  [ 39 -11,  -9  1 -1 >  3.84829E+12 : 3.80589E+12
		  19.2271274     136.8  [ 15 -10,   4 -3  0 >     20480000 : 20253807
		  19.30560683    137.4  [ 11   5, -10  4 -2 >   1194891264 : 1181640625
		  19.33346046    137.6  [  9   7,  -8 -3  2 >    135489024 : 133984375
		  19.35320442    137.7  [-13   6,   3  0 -1 >        91125 : 90112
		  19.37592129    137.9  [ 14  -8,   0  2 -2 >       802816 : 793881
		  19.52985195    139.0  [-16  10,   1 -2  1 >      3247695 : 3211264
		  19.55256881    139.1  [ 11  -4,  -2  0  0 >         2048 : 2025            diaschisma [Ellis], diminished comma [Rameau]
		  19.67864583    140.0  [-17  12,  -3  3 -1 >    182284263 : 180224000
		  19.72624343    140.4  [-41  13,  10 -1  0 >  1.55696E+13 : 1.53932E+13
		  19.72921633    140.4  [  8   0,  -4 -2  2 >        30976 : 30625
		  19.74896029    140.5  [-14  -1,   7  1 -1 >       546875 : 540672
		  19.7519332     140.6  [ 35 -14,  -7  0  1 >  3.77957E+11 : 3.73669E+11
		  19.77167716    140.7  [ 13 -15,   4  3 -2 >   1756160000 : 1736217747
		  19.79953079    140.9  [ 11 -13,   6 -4  2 >   3872000000 : 3827969523
		  19.81693305    141.0  [  6  15,  -5 -4 -2 >    918330048 : 907878125
		  19.87503732    141.4  [-42  15,   6  4 -2 >  5.38308E+14 : 5.32164E+14
		  19.87801022    141.4  [  7   2,  -8  3  0 >       395136 : 390625
		  19.92560782    141.8  [-17   3,   5 -1  1 >       928125 : 917504
		  19.94832468    141.9  [ 10 -11,   2  1  0 >       179200 : 177147

		  20.01629744    142.4  [ 30   5, -10 -4 -1 >  2.60919E+11 : 2.5792E+11
		  20.05465774    142.7  [  4   6, -10  1  2 >      9879408 : 9765625
		  20.0744017     142.8  [-18   5,   1  4 -1 >      2917215 : 2883584
		  20.1249722     143.2  [  7  -7,   0 -1  2 >        15488 : 15309
		  20.21268892    143.8  [  5   8,  -1 -3 -2 >       209952 : 207515
		  20.25104923    144.1  [-21   9,  -1  2  1 >     10609137 : 10485760
		  20.27376609    144.3  [  6  -5,  -4  4  0 >       153664 : 151875
		  20.32136369    144.6  [-18  -4,   9  0  1 >     21484375 : 21233664
		  20.41205331    145.2  [ 29  -2,  -6 -3 -1 >    536870912 : 530578125
		  20.44744071    145.5  [-46  12,   8  3  0 >  7.12048E+13 : 7.03687E+13
		  20.45041361    145.5  [  3  -1,  -6  2  2 >        47432 : 46875
		  20.47313048    145.7  [ 30 -15,  -9  4  1 >  2.83586E+13 : 2.80252E+13
		  20.52072807    146.0  [  6 -14,   4  0  2 >      4840000 : 4782969
		  20.53813033    146.1  [  1  14,  -7  0 -2 >      9565938 : 9453125
		  20.58572793    146.5  [-23  15,   6 -4 -1 >  2.24202E+11 : 2.21552E+11
		  20.60844479    146.6  [  4   1,   3 -2 -2 >         6000 : 5929
		  20.6468051     146.9  [-22   2,   3  3  1 >      4244625 : 4194304
		  20.78509232    147.9  [  1   5,   1 -4  0 >         2430 : 2401
		  20.80780918    148.1  [ 28  -9,  -2 -2 -1 >    268435456 : 265228425
		  20.84616948    148.3  [  2  -8,  -2  3  2 >       166012 : 164025
		  20.9338862     149.0  [  0   7,  -3  1 -2 >        15309 : 15125
		  20.9814838     149.3  [-24   8,  10 -3 -1 >  64072265625 : 63300435968
		  20.9844567     149.3  [ 25  -5,  -4 -4  1 >    369098752 : 364651875

		  21.00420066    149.5  [  3  -6,   7 -1 -2 >       625000 : 617463
		  21.0198441     149.6  [-50   9,  10  2  2 >  1.13965E+15 : 1.1259E+15
		  21.04256097    149.7  [-23  -5,   7  4  1 >   2063359375 : 2038431744
		  21.11053373    150.2  [ -3  11,  -5 -1  0 >       177147 : 175000
		  21.13325059    150.4  [ 24  -3,  -8  1 -1 >    117440512 : 116015625
		  21.18084819    150.7  [  0  -2,   5 -3  0 >         3125 : 3087
		  21.18382109    150.7  [ 49 -15,  -9 -4  2 >  6.81169E+16 : 6.72885E+16
		  21.24192535    151.2  [  1 -15,   2  4  2 >     14526050 : 14348907
		  21.25932761    151.3  [ -4  13,  -9  4 -2 >   3827969523 : 3781250000
		  21.28718125    151.5  [ -6  15,  -7 -3  2 >   1736217747 : 1715000000
		  21.30692521    151.6  [-28  14,   4  0 -1 >   2989355625 : 2952790016
		  21.30989811    151.6  [ 21   1, -10 -1  1 >     69206016 : 68359375
		  21.32964207    151.8  [ -1   0,   1  2 -2 >          245 : 242
		  21.38021257    152.1  [ 24 -12,   0 -3  1 >    184549376 : 182284263
		  21.5062896     153.0  [ -4   4,  -1  0  0 >           81 : 80              5-limit JI syntonic-comma = comma of Didymus
		  21.52900646    153.2  [ 23 -10,  -4  2 -1 >    411041792 : 405961875
		  21.57660406    153.5  [ -1  -9,   9 -2  0 >      1953125 : 1928934
		  21.68293712    154.3  [ -7   8,  -3 -2  2 >       793881 : 784000
		  21.70268108    154.4  [-29   7,   8  1 -1 >   5980078125 : 5905580032
		  21.70565398    154.5  [ 20  -6,  -6  0  1 >     11534336 : 11390625
		  21.72539794    154.6  [ -2  -7,   5  3 -2 >      1071875 : 1058508
		  21.75325158    154.8  [ -4  -5,   7 -4  2 >      9453125 : 9335088
		  21.8181818     155.3  [1/55  0,   0  0  0 >                                1/55-edo (diminished-2nd)
		  21.83173101    155.4  [ -8  10,  -7  3  0 >     20253807 : 20000000
		  21.8793286     155.7  [-32  11,   6 -1  1 >  30447140625 : 30064771072
		  21.90204547    155.9  [ -5  -3,   3  1  0 >          875 : 864
		  21.97001823    156.3  [ 15  13,  -9 -4 -1 >  52242776064 : 51583984375

		  22.00837853    156.6  [-11  14,  -9  1  2 >   4051174743 : 4000000000
		  22.02812249    156.7  [-33  13,   2  4 -1 >  95699238075 : 94489280512
		  22.06304955    157.0  [ 45 -14,  -2 -4 -2 >  3.51844E+13 : 3.47388E+13
		  22.07869299    157.1  [ -8   1,   1 -1  2 >         1815 : 1792
		  22.10140985    157.3  [ 19 -13,  -2  1  1 >     40370176 : 39858075
		  22.12115382    157.4  [ -3 -14,   9  4 -2 >   4689453125 : 4629913992
		  22.22748688    158.2  [ -9   3,  -3  4  0 >        64827 : 64000
		  22.27508447    158.5  [-33   4,  10  0  1 >   8701171875 : 8589934592
		  22.29780134    158.7  [ -6 -10,   7  2  0 >      3828125 : 3779136
		  22.3657741     159.2  [ 14   6,  -5 -3 -1 >     11943936 : 11790625
		  22.38849096    159.3  [ 41  -8,  -8 -1 -2 >  2.19902E+12 : 2.17077E+12
		  22.4041344     159.4  [-12   7,  -5  2  2 >     12966723 : 12800000
		  22.42685126    159.6  [ 15  -7,  -8  4  1 >    865435648 : 854296875
		  22.47444886    159.9  [ -9  -6,   5  0  2 >       378125 : 373248
		  22.56216558    160.5  [-11   9,   4 -2 -2 >     12301875 : 12142592
		  22.56513848    160.6  [ 38  -4, -10 -3  0 >  2.74878E+11 : 2.71318E+11
		  22.60052589    160.8  [-37  10,   4  3  1 >  1.39245E+11 : 1.37439E+11
		  22.64150943    161.1  [1/53  0,   0  0  0 >                               1/53-edo (pythagorean-comma = ~531441:524288 [3^12]; syntonic-comma = ~81:80, diaschisma = ~2048:2025)
		  22.7388131     161.8  [-14  13,   2 -4  0 >     39858075 : 39337984
		  22.76152997    162.0  [ 13  -1,  -1 -2 -1 >         8192 : 8085
		  22.78424683    162.1  [ 40 -15,  -4  0 -2 >  1.09951E+12 : 1.08514E+12
		  22.79989027    162.2  [-13   0,  -1  3  2 >        41503 : 40960
		  22.83184443    162.5  [ 16 -14,   9 -4 -1 >     1.28E+11 : 1.26323E+11
		  22.87020473    162.7  [-10 -13,   9  1  2 >   1654296875 : 1632586752
		  22.88760699    162.9  [-15  15,  -2  1 -2 >    100442349 : 99123200
		  22.93817749    163.2  [ 10   3,  -3 -4  1 >       304128 : 300125
		  22.95792145    163.4  [-12   2,   8 -1 -2 >      3515625 : 3469312
		  22.96089435    163.4  [ 37 -11,  -6 -2  0 >  1.37439E+11 : 1.35628E+11
		  22.99628176    163.6  [-38   3,   8  4  1 >  2.78554E+11 : 2.74878E+11

		  23.08697138    164.3  [  9   5,  -7  1 -1 >       870912 : 859375
		  23.10968824    164.4  [ 36  -9, -10  3 -2 >  2.35708E+13 : 2.32582E+13
		  23.13456897    164.6  [-15   6,   6 -3  0 >     11390625 : 11239424
		  23.13754188    164.6  [ 34  -7,  -8 -4  2 >  2.07876E+12 : 2.05117E+12
		  23.15728584    164.8  [ 12  -8,   3 -1 -1 >       512000 : 505197
		  23.19564614    165.1  [-14  -7,   3  4  2 >     36315125 : 35831808
		  23.2636189     165.5  [  6   9,  -9 -1  1 >     13856832 : 13671875
		  23.28336286    165.7  [-16   8,   2  2 -2 >      8037225 : 7929856
		  23.33393336    166.0  [  9  -4,   1 -3  1 >        28160 : 27783
		  23.46001038    166.9  [-19  12,   0  0  0 >       531441 : 524288          3-limit pythagorean augmented-7th [3^12] = pythagorean-comma
		  23.48272725    167.1  [  8  -2,  -3  2 -1 >        12544 : 12375
		  23.53032484    167.4  [-16  -1,  10 -2  0 >      9765625 : 9633792
		  23.53329775    167.5  [ 33 -14,  -4 -3  2 >  1.03938E+12 : 1.02535E+12
		  23.55304171    167.6  [ 11 -15,   7  0 -1 >    160000000 : 157837977
		  23.65640187    168.3  [-44  15,   9  1 -1 >  1.96176E+14 : 1.93514E+14
		  23.65937477    168.4  [  5   2,  -5  0  1 >         3168 : 3125
		  23.67911873    168.5  [-17   1,   6  3 -2 >     16078125 : 15859712
		  23.68209163    168.5  [ 32 -12,  -8  2  0 >  2.10453E+11 : 2.07594E+11
		  23.70697237    168.7  [-19   3,   8 -4  2 >   1276171875 : 1258815488
		  23.72968923    168.9  [  8 -11,   5 -2  1 >      8800000 : 8680203
		  23.85576626    169.8  [-20   5,   4  1  0 >      1063125 : 1048576
		  23.85873916    169.8  [ 29  -8, -10  0  2 >  64961380352 : 64072265625
		  23.87848312    169.9  [  7  -9,   1  3 -1 >       219520 : 216513

		  24.01677034    170.9  [ 30  -6,  -1 -4 -2 >   1073741824 : 1058949045
		  24.03241378    171.0  [-23   9,   2 -1  2 >     59541075 : 58720256
		  24.05513064    171.2  [  4  -5,  -1  1  1 >         1232 : 1215
		  24.0748746     171.3  [-18  -6,  10  4 -2 >  23447265625 : 23123460096
		  24.18120767    172.1  [-24  11,  -2  4  0 >    425329947 : 419430400
		  24.25152213    172.6  [-21  -2,   8  2  0 >     19140625 : 18874368
		  24.25449503    172.6  [ 28 -15,  -6  1  2 >  2.27365E+11 : 2.24202E+11
		  24.31949488    173.1  [ -1  14,  -4 -3 -1 >      4782969 : 4716250
		  24.34221175    173.2  [ 26   0,  -7 -1 -2 >     67108864 : 66171875
		  24.35785519    173.3  [-27  15,  -4  2  2 >  85074669603 : 83886080000
		  24.38057205    173.5  [  0   1,  -7  4  1 >        79233 : 78125
		  24.41252621    173.7  [ 29 -13,   3 -3 -2 >  67108864000 : 66169187469
		  24.42816965    173.8  [-24   2,   6  0  2 >     17015625 : 16777216
		  24.45088651    174.0  [  3 -12,   3  2  1 >       539000 : 531441
		  24.51885927    174.5  [ 23   4,  -9 -3  0 >    679477248 : 669921875
		  24.71525075    175.9  [ -2   7,   0 -2 -1 >         2187 : 2156
		  24.73796762    176.0  [ 25  -7,  -3  0 -2 >     33554432 : 33078375
		  24.75361106    176.1  [-28   8,   0  3  2 >    272301183 : 268435456
		  24.78556521    176.4  [  1  -6,  10 -4 -1 >     19531250 : 19253619
		  24.82392552    176.6  [-25  -5,  10  1  2 >   8271484375 : 8153726976
		  24.89189828    177.1  [ -5  11,  -2 -4  1 >      1948617 : 1920800
		  24.91164224    177.3  [-27  10,   9 -1 -2 >   1.1533E+11 : 1.13682E+11
		  24.91461514    177.3  [ 22  -3,  -5 -2  0 >      4194304 : 4134375
		  24.95000254    177.5  [-53  11,   9  4  1 >  9.13795E+15 : 9.0072E+15

		  25.04069217    178.2  [ -6  13,  -6  1 -1 >     11160261 : 11000000
		  25.06340903    178.3  [ 21  -1,  -9  3 -2 >    719323136 : 708984375
		  25.08828976    178.5  [-30  14,   7 -3  0 >  3.73669E+11 : 3.68293E+11
		  25.09126266    178.5  [ 19   1,  -7 -4  2 >    190316544 : 187578125
		  25.11100663    178.7  [ -3   0,   4 -1 -1 >          625 : 616
		  25.11397953    178.7  [ 46 -13, -10 -2  1 >  7.74056E+14 : 7.62908E+14
		  25.13372349    178.8  [ 24 -14,   1  1 -2 >    587202560 : 578739249
		  25.14936693    179.0  [-29   1,   4  4  2 >    544726875 : 536870912
		  25.28765415    179.9  [ -6   4,   2 -3  1 >        22275 : 21952
		  25.31037101    180.1  [ 21 -10,  -1 -1  0 >      2097152 : 2066715
		  25.43644804    181.0  [ -7   6,  -2  2 -1 >        35721 : 35200
		  25.4591649     181.2  [ 20  -8,  -5  4 -2 >   2517630976 : 2480878125
		  25.48701854    181.4  [ 18  -6,  -3 -3  2 >     31719424 : 31255875
		  25.5067625     181.5  [ -4  -7,   8  0 -1 >       390625 : 384912
		  25.61309556    182.3  [-10  10,  -4  0  1 >       649539 : 640000
		  25.63283952    182.4  [-32   9,   7  3 -2 >  5.27443E+11 : 5.19691E+11
		  25.63581242    182.4  [ 17  -4,  -7  2  0 >      6422528 : 6328125
		  25.66069316    182.6  [-34  11,   9 -4  2 >  4.18648E+13 : 4.12489E+13
		  25.68341002    182.8  [ -7  -3,   6 -2  1 >       171875 : 169344
		  25.80948704    183.7  [-35  13,   5  1  0 >  34875815625 : 34359738368
		  25.81245995    183.7  [ 14   0,  -9  0  2 >      1982464 : 1953125
		  25.83220391    183.8  [ -8  -1,   2  3 -1 >         8575 : 8448
		  25.88277441    184.2  [ 17 -13,   1 -2  2 >     79298560 : 78121827
		  25.90017666    184.3  [ 12  15, -10 -2 -2 >  58773123072 : 57900390625
		  25.97049112    184.8  [ 15   2,   0 -4 -2 >       294912 : 290521

		  26.00885143    185.1  [-11   3,   0  1  1 >         2079 : 2048
		  26.03156829    185.2  [ 16 -11,  -3  3  0 >     22478848 : 22143375
		  26.07916589    185.6  [ -8 -10,  10 -1  1 >    107421875 : 105815808
		  26.0869565     185.6  [1/46  0,   0  0  0 >                              1/46-edo
		  26.16985551    186.2  [ 39  -8,  -5 -4 -1 >  5.49756E+11 : 5.41508E+11
		  26.20524291    186.5  [-36   6,   9  2  0 >  69767578125 : 68719476736
		  26.20821582    186.5  [ 13  -7,  -5  1  2 >      6938624 : 6834375
		  26.22795978    186.6  [ -9  -8,   6  4 -1 >     37515625 : 36951552
		  26.29593254    187.1  [ 11   8,  -6 -1 -2 >     13436928 : 13234375
		  26.33429284    187.4  [-15   9,  -6  4  1 >    519847713 : 512000000
		  26.366247      187.6  [ 14  -5,   4 -3 -2 >     10240000 : 10085229
		  26.38189044    187.7  [-39  10,   7  0  2 >  5.58198E+11 : 5.49756E+11
		  26.4046073     187.9  [-12  -4,   4  2  1 >       336875 : 331776
		  26.47258006    188.4  [  8  12,  -8 -3  0 >    136048896 : 133984375
		  26.56561138    189.0  [ 38 -15,  -1 -3 -1 >  2.74878E+11 : 2.70692E+11
		  26.60397169    189.3  [ 12 -14,  -1  2  2 >     24285184 : 23914845
		  26.66897154    189.8  [-17  15,   1 -2 -1 >     71744535 : 70647808
		  26.69168841    189.9  [ 10   1,  -2  0 -2 >         3072 : 3025
		  26.76200287    190.4  [ 13 -12,   8 -2 -2 >   3200000000 : 3150913689
		  26.80036317    190.7  [-13 -11,   8  3  1 >   1473828125 : 1451188224
		  26.86833593    191.2  [  7   5,  -4 -2  0 >        31104 : 30625
		  26.89105279    191.4  [ 34  -9,  -7  0 -1 >  17179869184 : 16915078125
		  26.93865039    191.7  [ 10  -8,   6 -4  0 >     16000000 : 15752961

		  27.01712982    192.2  [  6   7,  -8  3 -2 >     48009024 : 47265625
		  27.04498345    192.4  [  4   9,  -6 -4  2 >     38106288 : 37515625
		  27.06472741    192.6  [-18   8,   5 -1 -1 >     20503125 : 20185088
		  27.06770032    192.6  [ 31  -5,  -9 -2  1 >  23622320128 : 23255859375
		  27.08744428    192.7  [  9  -6,   2  1 -2 >        89600 : 88209
		  27.10308772    192.9  [-44   9,   5  4  2 >  1.78698E+13 : 1.75922E+13
		  27.19377734    193.5  [  3  11, -10  1  0 >      9920232 : 9765625
		  27.24137494    193.8  [-21  12,   3 -3  1 >    730731375 : 719323136
		  27.2640918     194.0  [  6  -2,   0 -1  0 >           64 : 63              septimal-comma, archytas-comma
		  27.33440626    194.5  [  9 -15,  10 -3  0 >   5000000000 : 4921675101
		  27.39016882    194.9  [-22  14,  -1  2 -1 >    234365481 : 230686720
		  27.41288569    195.1  [  5   0,  -4  4 -2 >        76832 : 75625
		  27.44073932    195.3  [  3   2,  -2 -3  2 >         8712 : 8575
		  27.46048328    195.4  [-19   1,   9  0 -1 >      5859375 : 5767168
		  27.46345619    195.4  [ 30 -12,  -5 -1  1 >  11811160064 : 11625271875
		  27.48320015    195.6  [  8 -13,   6  2 -2 >    196000000 : 192913083
		  27.58953321    196.3  [  2   4,  -6  2  0 >        15876 : 15625
		  27.61225007    196.5  [ 29 -10,  -9  4 -1 >  1.28903E+12 : 1.26863E+12
		  27.63713081    196.7  [-22   5,   7 -2  1 >    208828125 : 205520896
		  27.65984767    196.8  [  5  -9,   4  0  0 >        20000 : 19683           minimal-diesis
		  27.76618073    197.6  [ -1   8,  -8  0  2 >       793881 : 781250
		  27.78592469    197.7  [-23   7,   3  3 -1 >     93767625 : 92274688
		  27.83649519    198.1  [  2  -5,   2 -2  2 >        12100 : 11907
		  27.92421191    198.7  [  0  10,   1 -4 -2 >       295245 : 290521
		  27.96257222    199.0  [-26  11,   1  1  1 >     68201595 : 67108864
		  27.98528908    199.1  [  1  -3,  -2  3  0 >          686 : 675

		  28.1235763     200.1  [ 24   0,  -4 -4 -1 >     16777216 : 16506875
		  28.14629316    200.3  [ 51 -14,  -7 -2 -2 >   2.2518E+15 : 2.21549E+15
		  28.1589637     200.4  [-51  14,  10  2  0 >  2.28873E+15 : 2.2518E+15
		  28.1619366     200.4  [ -2   1,  -4  1  2 >         2541 : 2500
		  28.18168057    200.5  [-24   0,   7  4 -1 >    187578125 : 184549376
		  28.18465347    200.6  [ 25 -13,  -7  3  1 >  1.26601E+11 : 1.24556E+11
		  28.23225106    200.9  [  1 -12,   6 -1  2 >      3781250 : 3720087
		  28.31996778    201.5  [ -1   3,   5 -3 -2 >        84375 : 83006
		  28.32294069    201.5  [ 48 -10,  -9 -4  0 >  2.81475E+14 : 2.76908E+14
		  28.35832809    201.8  [-27   4,   5  2  1 >    136434375 : 134217728
		  28.38104495    202.0  [  0 -10,   2  4  0 >        60025 : 59049
		  28.44901771    202.4  [ 20   6, -10 -1 -1 >    764411904 : 751953125
		  28.48737802    202.7  [ -6   7, -10  4  2 >    635369427 : 625000000
		  28.51933217    202.9  [ 23  -7,   0 -3 -1 >      8388608 : 8251551
		  28.55769248    203.2  [ -3  -6,   0  2  2 >         5929 : 5832
		  28.64540919    203.8  [ -5   9,  -1  0 -2 >        19683 : 19360
		  28.71572365    204.3  [ -2  -4,   9 -2 -2 >      1953125 : 1920996
		  28.75408396    204.6  [-28  -3,   9  3  1 >   7369140625 : 7247757312
		  28.82205672    205.1  [ -8  13,  -3 -2  0 >      1594323 : 1568000
		  28.84477358    205.3  [ 19  -1,  -6  0 -1 >       524288 : 515625
		  28.86749044    205.4  [ 46 -15,  -9  2 -2 >  3.44807E+15 : 3.39105E+15
		  28.89237118    205.6  [ -5   0,   7 -4  0 >        78125 : 76832
		  28.91508804    205.8  [ 22 -14,   4 -2 -1 >   2621440000 : 2578020291
		  28.95344835    206.0  [ -4 -13,   4  3  2 >     25939375 : 25509168
		  28.9708506     206.2  [ -9  15,  -7  3 -2 >   4921675101 : 4840000000

		  29.0214211     206.5  [ 16   3,  -8 -2  1 >     19464192 : 19140625
		  29.04116506    206.7  [ -6   2,   3  1 -2 >         7875 : 7744
		  29.09173556    207.0  [ 19 -10,   2 -4  1 >    144179200 : 141776649
		  29.21781259    207.9  [ -9   6,   1 -1  0 >         3645 : 3584
		  29.24052945    208.1  [ 18  -8,  -2  1 -1 >      1835008 : 1804275
		  29.2682927     208.3  [1/41  0,   0  0  0 >                                1/41-edo (~pythagorean augmented-7th)
		  29.36660648    209.0  [-10   8,  -3  4 -2 >     15752961 : 15488000
		  29.39446011    209.2  [-12  10,  -1 -3  2 >      7144929 : 7024640
		  29.41420407    209.3  [-34   9,  10  0 -1 >  1.92217E+11 : 1.88979E+11
		  29.41717697    209.3  [ 15  -4,  -4 -1  1 >       360448 : 354375
		  29.43692094    209.5  [ -7  -5,   7  2 -2 >      3828125 : 3763584
		  29.543254      210.2  [-13  12,  -5  2  0 >     26040609 : 25600000
		  29.56597086    210.4  [ 14  -2,  -8  4 -1 >     39337984 : 38671875
		  29.5908516     210.6  [-37  13,   8 -2  1 >  6.85061E+12 : 6.73451E+12
		  29.61356846    210.7  [-10  -1,   5  0  0 >         3125 : 3072            magic-comma, small diesis [Ellis]
		  29.61654136    210.7  [ 39 -14,  -9 -1  2 >  6.65205E+13 : 6.53922E+13
		  29.63628532    210.9  [ 17 -15,   2  2 -1 >    160563200 : 157837977
		  29.70425808    211.4  [ 37   1, -10 -3 -2 >  4.12317E+11 : 4.05303E+11
		  29.73964548    211.6  [-38  15,   4  3 -1 >  3.07605E+12 : 3.02366E+12
		  29.74261839    211.6  [ 11   2, -10  2  1 >      9934848 : 9765625
		  29.79021598    212.0  [-13   3,   3 -2  2 >       408375 : 401408
		  29.81293285    212.1  [ 14 -11,   0  0  1 >       180224 : 177147
		  29.93900987    213.0  [-14   5,  -1  3  0 >        83349 : 81920

		  30.00932433    213.5  [-11  -8,   9  1  0 >     13671875 : 13436928
		  30.07729709    214.0  [  9   8,  -3 -4 -1 >      3359232 : 3301375
		  30.10001395    214.2  [ 36  -6,  -6 -2 -2 >  68719476736 : 67535015625
		  30.11565739    214.3  [-17   9,  -3  1  2 >     16671501 : 16384000
		  30.13540135    214.4  [-39   8,   8  4 -1 >   6.1535E+12 : 6.04731E+12
		  30.13837426    214.5  [ 10  -5,  -6  3  1 >      3863552 : 3796875
		  30.18597185    214.8  [-14  -4,   7 -1  2 >      9453125 : 9289728
		  30.27368857    215.4  [-16  11,   6 -3 -2 >   2767921875 : 2719940608
		  30.27666147    215.4  [ 33  -2,  -8 -4  0 >   8589934592 : 8441015625
		  30.31204888    215.7  [-42  12,   6  2  1 >  4.47573E+12 : 4.39805E+12
		  30.33476574    215.9  [-15  -2,   3  4  0 >       300125 : 294912
		  30.4027385     216.3  [  5  14,  -9 -1 -1 >    153055008 : 150390625
		  30.4410988     216.6  [-21  15,  -9  4  2 >  4.16866E+12 : 4.096E+12
		  30.47305296    216.8  [  8   1,   1 -3 -1 >         3840 : 3773
		  30.49576982    217.0  [ 35 -13,  -2 -1 -2 >  34359738368 : 33759789525
		  30.51141326    217.1  [-18   2,   1  2  2 >       266805 : 262144
		  30.53413013    217.3  [  9 -12,  -2  4  1 >     13522432 : 13286025
		  30.66944444    218.2  [-17   4,  10 -2 -2 >    791015625 : 777125888
		  30.67241734    218.3  [ 32  -9,  -4 -3  0 >   4294967296 : 4219543125
		  30.70780475    218.5  [-43   5,  10  3  1 >  8.95351E+12 : 8.79609E+12
		  30.79849437    219.2  [  4   7,  -5  0 -1 >        34992 : 34375
		  30.82121123    219.3  [ 31  -7,  -8  2 -2 >  1.05227E+11 : 1.0337E+11
		  30.84609197    219.5  [-20   8,   8 -4  0 >   2562890625 : 2517630976
		  30.86880883    219.7  [  7  -6,   5 -2 -1 >       400000 : 392931
		  30.90716913    219.9  [-19  -5,   5  3  2 >    129696875 : 127401984
		  30.97514189    220.4  [  1  11,  -7 -2  1 >      3897234 : 3828125
		  30.99488585    220.6  [-21  10,   4  1 -2 >    258339375 : 253755392
		  30.99785876    220.6  [ 28  -3, -10  0  0 >    268435456 : 263671875

		  31.04545635    220.9  [  4  -2,   3 -4  1 >        22000 : 21609
		  31.17153338    221.8  [-24  14,   2 -1  0 >    119574225 : 117440512
		  31.19425024    222.0  [  3   0,  -1  1 -1 >           56 : 55
		  31.2169671     222.1  [ 30 -14,  -4  3 -2 >  3.68293E+11 : 3.61712E+11
		  31.24482074    222.3  [ 28 -12,  -2 -4  2 >  32480690176 : 31899746025
		  31.2645647     222.5  [  6 -13,   9 -1 -1 >    125000000 : 122762871
		  31.302925      222.7  [-20 -12,   9  4  2 >  5.67424E+11 : 5.57256E+11
		  31.37089776    223.2  [  0   4,  -3 -1  1 >          891 : 875
		  31.39064172    223.4  [-22   3,   8  2 -2 >    516796875 : 507510784
		  31.39361463    223.4  [ 27 -10,  -6  1  0 >    939524096 : 922640625
		  31.44121222    223.7  [  3  -9,   7 -3  1 >      6875000 : 6751269
		  31.51969165    224.3  [ -1   6,  -7  4 -1 >      1750329 : 1718750
		  31.56728925    224.6  [-25   7,   6  0  0 >     34171875 : 33554432        ampersand-comma
		  31.57026215    224.6  [ 24  -6,  -8 -1  2 >   2030043136 : 1993359375
		  31.59000611    224.8  [  2  -7,   3  2 -1 >        24500 : 24057
		  31.65797887    225.3  [ 22   9,  -9 -3 -2 >  82556485632 : 81060546875
		  31.69633917    225.5  [ -4  10,  -9  2  1 >     31827411 : 31250000
		  31.74393677    225.9  [-28  11,   4 -2  2 >  13396741875 : 13153337344
		  31.76665363    226.0  [ -1  -3,   1  0  1 >           55 : 54
		  31.89273066    226.9  [-29  13,   0  3  0 >    546852789 : 536870912
		  31.96304512    227.4  [-26   0,  10  1  0 >     68359375 : 67108864
		  31.96601802    227.5  [ 23 -13,  -4  0  2 >   1015021568 : 996451875
		  31.98576198    227.6  [  1 -14,   7  3 -1 >     53593750 : 52612659

		  32.05373474    228.1  [ 21   2,  -5 -2 -2 >     18874368 : 18528125
		  32.09209504    228.4  [ -5   3,  -5  3  1 >       101871 : 100000
		  32.1240492     228.6  [ 24 -11,   5 -4 -2 >  52428800000 : 51464923587
		  32.13969264    228.7  [-29   4,   8 -1  2 >   3828515625 : 3758096384
		  32.1624095     228.9  [ -2 -10,   5  1  1 >       240625 : 236196
		  32.23038226    229.3  [ 18   6,  -7 -4  0 >    191102976 : 187578125
		  32.25309913    229.5  [ 45  -8, -10 -2 -1 >  3.51844E+13 : 3.4535E+13
		  32.28848653    229.8  [-30   6,   4  4  0 >   1093955625 : 1073741824
		  32.29145943    229.8  [ 19  -7, -10  3  2 >  21759524864 : 21357421875
		  32.42677375    230.7  [ -7   9,   2 -3 -1 >       492075 : 482944
		  32.44949061    230.9  [ 20  -5,  -1 -1 -2 >      1048576 : 1029105
		  32.46513405    231.0  [-33  10,   2  2  2 >   8752538025 : 8589934592
		  32.48785091    231.2  [ -6  -4,  -1  4  1 >        26411 : 25920
		  32.62613813    232.2  [ 17  -1,  -3 -3  0 >       131072 : 128625
		  32.648855      232.3  [ 44 -15,  -6 -1 -1 >  1.75922E+13 : 1.72635E+13
		  32.6872153     232.6  [ 18 -14,  -6  4  2 >  76158337024 : 74733890625
		  32.75221516    233.1  [-11  15,  -4  0 -1 >     14348907 : 14080000
		  32.77493202    233.2  [ 16   1,  -7  2 -2 >      9633792 : 9453125
		  32.82252962    233.6  [ -8   2,   6 -2 -1 >       140625 : 137984
		  32.82550252    233.6  [ 41 -11,  -8 -3  1 >  2.41893E+13 : 2.37349E+13
		  32.84524648    233.7  [ 19 -12,   3  0 -2 >     65536000 : 64304361
		  32.86088992    233.8  [-34   3,   6  3  2 >  17509078125 : 17179869184
		  32.95157954    234.5  [ 13   5,  -9  0  0 >      1990656 : 1953125
		  32.99917714    234.8  [-11   6,   4 -4  1 >      5011875 : 4917248

		  33.021894      235.0  [ 16  -8,   1 -2  0 >       327680 : 321489
		  33.14797103    235.9  [-12   8,   0  1 -1 >        45927 : 45056
		  33.17068789    236.0  [ 15  -6,  -3  3 -2 >     11239424 : 11026125
		  33.19854153    236.2  [ 13  -4,  -1 -4  2 >       991232 : 972405
		  33.21828549    236.4  [ -9  -5,  10 -1 -1 >      9765625 : 9580032
		  33.25664579    236.6  [-35  -4,  10  4  2 >  2.83712E+12 : 2.78314E+12
		  33.32461855    237.1  [-15  12,  -2 -1  1 >      5845851 : 5734400
		  33.34436251    237.3  [-37  11,   9  2 -2 >  1.69535E+13 : 1.66301E+13
		  33.34733541    237.3  [ 12  -2,  -5  1  0 >        28672 : 28125
		  33.39493301    237.6  [-12  -1,   8 -3  1 >      4296875 : 4214784
		  33.41764987    237.8  [ 15 -15,   5 -1  0 >    102400000 : 100442349
		  33.47341244    238.2  [-16  14,  -6  4 -1 >  11483908569 : 11264000000
		  33.5083395     238.4  [ 62 -13, -10 -4 -2 >  4.61169E+18 : 4.52328E+18
		  33.52101003    238.5  [-40  15,   7  0  0 >  1.12101E+12 : 1.09951E+12
		  33.52398294    238.6  [  9   2,  -7 -1  2 >       557568 : 546875
		  33.5437269     238.7  [-13   1,   4  2 -1 >        91875 : 90112
		  33.5466998     238.7  [ 36 -12, -10  1  1 >   5.2914E+12 : 5.18985E+12
		  33.56644376    238.9  [ 14 -13,   1  4 -2 >    196689920 : 192913083
		  33.5942974     239.1  [ 12 -11,   3 -3  2 >     61952000 : 60761421
		  33.72037442    239.9  [-16   5,   2  0  1 >        66825 : 65536
		  33.74309128    240.1  [ 11  -9,  -1  2  0 >       100352 : 98415
		  33.91973881    241.4  [  8  -5,  -3  0  2 >        30976 : 30375
		  33.93948277    241.5  [-14  -6,   8  3 -1 >    133984375 : 131383296

		  34.00745553    242.0  [  6  10,  -4 -2 -2 >      3779136 : 3705625
		  34.04581583    242.3  [-20  11,  -4  3  1 >    668375631 : 655360000
		  34.07776999    242.5  [  9  -3,   6 -4 -2 >      8000000 : 7844067
		  34.09341343    242.6  [-44  12,   9 -1  2 >  1.25594E+14 : 1.23145E+14
		  34.11613029    242.8  [-17  -2,   6  1  1 >      1203125 : 1179648
		  34.18410305    243.2  [  3  14,  -6 -4  0 >     38263752 : 37515625
		  34.20681991    243.4  [ 30   0,  -9 -2 -1 >   1073741824 : 1052734375
		  34.24220732    243.7  [-45  14,   5  4  0 >  3.58872E+13 : 3.51844E+13
		  34.24518022    243.7  [  4   1,  -9  3  2 >      1992144 : 1953125
		  34.27713437    243.9  [ 33 -13,   1 -4 -1 >  42949672960 : 42107664753
		  34.31549468    244.2  [  7 -12,   1  1  2 >       542080 : 531441
		  34.4032114     244.8  [  5   3,   0 -1 -2 >          864 : 847
		  34.4415717     245.1  [-21   4,   0  4  1 >      2139291 : 2097152
		  34.47352586    245.3  [  8 -10,  10 -3 -2 >   2500000000 : 2450710647
		  34.51188616    245.6  [-18  -9,  10  2  1 >   5263671875 : 5159780352
		  34.57985892    246.1  [  2   7,  -2 -3  0 >         8748 : 8575
		  34.60257578    246.2  [ 29  -7,  -5 -1 -1 >    536870912 : 526246875
		  34.64093609    246.5  [  3  -6,  -5  4  2 >      2324168 : 2278125
		  34.72865281    247.1  [  1   9,  -6  2 -2 >      1928934 : 1890625
		  34.7762504     247.5  [-23  10,   7 -2 -1 >   4613203125 : 4521459712
		  34.77922331    247.5  [ 26  -3,  -7 -3  1 >    738197504 : 723515625
		  34.79896727    247.6  [  4  -4,   4  0 -2 >        10000 : 9801
		  34.81461071    247.7  [-49  11,   7  3  2 >  5.74385E+14 : 5.6295E+14
		  34.90530033    248.4  [ -2  13,  -8  0  0 >      1594323 : 1562500
		  34.95289793    248.7  [-26  14,   5 -4  1 >  1.64415E+11 : 1.61128E+11
		  34.97561479    248.9  [  1   0,   2 -2  0 >           50 : 49              small biseptimal-comma, tritonic diesis, decatonic comma [Erlich]
		  34.99833165    249.0  [ 28 -14,  -1  0 -1 >    268435456 : 263063295

		  35.12440868    249.9  [  0   2,  -2  3 -2 >         3087 : 3025
		  35.15226231    250.1  [ -2   4,   0 -4  2 >         9801 : 9604
		  35.17497918    250.3  [ 25 -10,  -3 -2  1 >    369098752 : 361675125
		  35.19472314    250.4  [  3 -11,   8  1 -2 >     21875000 : 21434787
		  35.3010562     251.2  [ -3   6,  -4  1  0 >         5103 : 5000
		  35.32377307    251.4  [ 24  -8,  -7  3 -1 >   5754585088 : 5638359375
		  35.3486538     251.5  [-27   7,   9 -3  1 >  46986328125 : 46036680704
		  35.37137066    251.7  [  0  -7,   6 -1  0 >        15625 : 15309
		  35.46206028    252.3  [ 47  -5,  -9 -4 -2 >  1.40737E+14 : 1.37884E+14
		  35.47770373    252.5  [ -6  10,  -6 -1  2 >      7144929 : 7000000
		  35.49744769    252.6  [-28   9,   5  2 -1 >   3013959375 : 2952790016
		  35.50042059    252.6  [ 21  -4,  -9  1  1 >    161480704 : 158203125
		  35.52016455    252.8  [ -1  -5,   2  4 -2 >        60025 : 58806
		  35.54801819    253.0  [ -3  -3,   4 -3  2 >        75625 : 74088
		  35.62649761    253.5  [ -7  12, -10  4  0 >   1275989841 : 1250000000
		  35.67409521    253.9  [-31  13,   3  0  1 >   2192194125 : 2147483648
		  35.69681207    254.0  [ -4  -1,   0  2  0 >           49 : 48              large biseptimal-comma, slendro diesis
		  35.71952894    254.2  [ 23 -15,  -3  4 -1 >  20141047808 : 19729747125
		  35.76712653    254.5  [ -1 -14,  10  0  0 >      9765625 : 9565938
		  35.85781615    255.2  [ 46 -12,  -5 -3 -2 >  7.03687E+13 : 6.89262E+13
		  35.8734596     255.3  [ -7   3,  -2  0  2 >         3267 : 3200
		  35.89320356    255.4  [-29   2,   9  3 -1 >   6029296875 : 5905580032
		  35.89617646    255.4  [ 20 -11,  -5  2  1 >    565182464 : 553584375
		  35.94377406    255.8  [ -4 -10,   8 -2  2 >     47265625 : 46294416

		  36.03149077    256.4  [ -6   5,   7 -4 -2 >     18984375 : 18593344
		  36.06985108    256.7  [-32   6,   7  1  1 >   4385390625 : 4294967296
		  36.09256794    256.8  [ -5  -8,   4  3  0 >       214375 : 209952
		  36.1605407     257.3  [ 15   8,  -8 -2 -1 >    214990848 : 210546875
		  36.19890101    257.6  [-11   9,  -8  3  2 >    816903549 : 800000000
		  36.23085516    257.8  [ 18  -5,   2 -4 -1 >      6553600 : 6417873
		  36.26921547    258.1  [ -8  -4,   2  1  2 >        21175 : 20736
		  36.33718822    258.6  [ 12  12, -10 -4  1 >  23944605696 : 23447265625
		  36.35693219    258.7  [-10  11,   1 -1 -2 >       885735 : 867328
		  36.39529249    259.0  [-36  12,   1  4  1 >  70179441255 : 68719476736
		  36.43021955    259.2  [ 42 -15,  -3 -4  0 >  4.39805E+12 : 4.30647E+12
		  36.48832381    259.6  [ -6 -15,   8  4  0 >    937890625 : 918330048
		  36.53357971    260.0  [-13  15,  -1 -3  0 >     14348907 : 14049280
		  36.55629657    260.1  [ 14   1,  -4 -1 -1 >        49152 : 48125
		  36.57901344    260.3  [ 41 -13,  -7  1 -2 >  1.53932E+13 : 1.50713E+13
		  36.59465688    260.4  [-12   2,  -4  4  2 >      2614689 : 2560000
		  36.62661103    260.6  [ 17 -12,   6 -3 -1 >   2048000000 : 2005126893
		  36.66497134    260.9  [ -9 -11,   6  2  2 >     92640625 : 90699264
		  36.7329441     261.4  [ 11   5,  -6 -3  1 >      5474304 : 5359375
		  36.75268806    261.5  [-11   4,   5  0 -2 >       253125 : 247808
		  36.75566096    261.5  [ 38  -9,  -9 -1  0 >  2.74878E+11 : 2.69104E+11
		  36.88173798    262.4  [ 10   7, -10  2 -1 >    109734912 : 107421875
		  36.92933558    262.8  [-14   8,   3 -2  0 >       820125 : 802816
		  36.95205244    262.9  [ 13  -6,   0  0 -1 >         8192 : 8019

		  37.07812947    263.8  [-15  10,  -1  3 -2 >     20253807 : 19824640
		  37.1059831     264.0  [-17  12,   1 -4  2 >    321521805 : 314703872
		  37.12869997    264.2  [ 10  -2,  -2 -2  1 >        11264 : 11025
		  37.14844393    264.3  [-12  -3,   9  1 -2 >     13671875 : 13381632
		  37.19901443    264.7  [ 13 -15,   8 -4  1 >  35200000000 : 34451725707
		  37.25477699    265.1  [-18  14,  -3  1  0 >     33480783 : 32768000
		  37.27749385    265.3  [  9   0,  -6  3 -1 >       175616 : 171875
		  37.30237459    265.4  [-42  15,  10 -3  1 >  1.54139E+15 : 1.50853E+15
		  37.32509145    265.6  [-15   1,   7 -1  0 >       234375 : 229376
		  37.32806435    265.6  [ 34 -12,  -7 -2  2 >  2.07876E+12 : 2.03442E+12
		  37.34780831    265.8  [ 12 -13,   4  1 -1 >     17920000 : 17537553
		  37.41578107    266.2  [ 32   3,  -8 -4 -2 >  1.15964E+11 : 1.13485E+11
		  37.45414138    266.5  [  6   4,  -8  1  1 >       399168 : 390625
		  37.47388534    266.7  [-16   3,   3  4 -2 >      8103375 : 7929856
		  37.50173897    266.9  [-18   5,   5 -3  2 >     91884375 : 89915392
		  37.52445584    267.0  [  9  -9,   2 -1  1 >       140800 : 137781
		  37.65053286    267.9  [-19   7,   1  2  0 >       535815 : 524288
		  37.67324972    268.1  [  8  -7,  -2  4 -1 >       614656 : 601425
		  37.81153694    269.1  [ 31  -4,  -4 -3 -2 >   2147483648 : 2101089375
		  37.82718038    269.2  [-22  11,  -1  0  2 >     21434787 : 20971520
		  37.84692434    269.3  [-44  10,  10  3 -1 >  1.97791E+14 : 1.93514E+14
		  37.84989725    269.3  [  5  -3,  -4  2  1 >        17248 : 16875
		  37.89749484    269.7  [-19  -2,   9 -2  2 >    236328125 : 231211008
		  37.98521156    270.3  [-21  13,   8 -4 -2 >  6.22782E+11 : 6.09267E+11

		  38.01090133    270.5  [ 55 -14,  -9 -3 -1 >  3.60288E+16 : 3.52464E+16
		  38.02357187    270.6  [-47  14,   8  1  1 >  1.43863E+14 : 1.40737E+14
		  38.04628873    270.7  [-20   0,   5  3  0 >      1071875 : 1048576
		  38.04926163    270.8  [ 29 -13,  -9  2  2 >  3.18311E+12 : 3.11391E+12
		  38.13697835    271.4  [ 27   2, -10  0 -2 >   1207959552 : 1181640625
		  38.18457595    271.7  [  3   3,   3 -4 -1 >        27000 : 26411
		  38.20729281    271.9  [ 30 -11,   0 -2 -2 >   1073741824 : 1050304563
		  38.22293625    272.0  [-23   4,   3  1  2 >      8575875 : 8388608
		  38.24565312    272.1  [  4 -10,   0  3  1 >        60368 : 59049
		  38.38394034    273.1  [ 27  -7,  -2 -4  0 >    134217728 : 131274675
		  38.4420446     273.5  [-21  -7,   9  4  0 >   4689453125 : 4586471424
		  38.51001736    274.0  [ -1   9,  -3 -1 -1 >        19683 : 19250
		  38.53273422    274.2  [ 26  -5,  -6  1 -2 >    469762048 : 459421875
		  38.54837767    274.3  [-27  10,  -3  4  2 >  17154974529 : 16777216000
		  38.58033182    274.5  [  2  -4,   7 -3 -1 >       312500 : 305613
		  38.61869213    274.8  [-24  -3,   7  2  2 >    463203125 : 452984832
		  38.68666488    275.3  [ -4  13,  -5 -3  1 >     17537553 : 17150000
		  38.70640884    275.4  [-26  12,   6  0 -2 >   8303765625 : 8120172544
		  38.70938175    275.4  [ 23  -1,  -8 -1  0 >      8388608 : 8203125
		  38.70967742    275.5  [1/31  0,   0  0  0 >                               1/31-edo (diminished-2nd)
		  38.77969621    275.9  [ 26 -14,   2 -3  0 >   1677721600 : 1640558367
		  38.83545877    276.3  [ -5  15,  -9  2 -1 >    703096443 : 687500000
		  38.88602927    276.7  [ 20   3, -10 -3  2 >   3425697792 : 3349609375
		  38.90577323    276.8  [ -2   2,   1  0 -1 >           45 : 44
		  38.92849009    277.0  [ 25 -12,  -2  2 -2 >   1644167168 : 1607609025

		  39.08242075    278.1  [ -5   6,  -1 -2  1 >         8019 : 7840
		  39.10216471    278.2  [-27   5,  10  1 -2 >  16611328125 : 16240345088
		  39.10513762    278.3  [ 22  -8,  -4  0  0 >      4194304 : 4100625
		  39.15273521    278.6  [ -2  -7,   9 -4  1 >     21484375 : 21003948
		  39.23121464    279.2  [ -6   8,  -5  3 -1 >      2250423 : 2200000
		  39.27881224    279.5  [-30   9,   8 -1  0 >   7688671875 : 7516192768
		  39.28178514    279.5  [ 19  -4,  -6 -2  2 >     63438848 : 62015625
		  39.3015291     279.7  [ -3  -5,   5  1 -1 >        21875 : 21384
		  39.36950186    280.1  [ 17  11,  -7 -4 -2 >  23219011584 : 22696953125
		  39.40786216    280.4  [ -9  12,  -7  1  1 >     40920957 : 40000000
		  39.42760613    280.6  [-31  11,   4  4 -2 >  2.65831E+11 : 2.59846E+11
		  39.43057903    280.6  [ 18  -2, -10  3  0 >     89915392 : 87890625
		  39.45545976    280.8  [-33  13,   6 -3  2 >  3.01427E+12 : 2.94635E+12
		  39.47817662    280.9  [ -6  -1,   3 -1  1 >         1375 : 1344
		  39.50089349    281.1  [ 21 -15,   0  1  0 >     14680064 : 14348907
		  39.60425365    281.8  [-34  15,   2  2  0 >  17577411075 : 17179869184
		  39.62697051    282.0  [ -7   1,  -1  4 -1 >         7203 : 7040
		  39.67754101    282.3  [ 18 -11,  -2 -1  2 >     31719424 : 31000725
		  39.69728497    282.5  [ -4 -12,   9  2 -1 >     95703125 : 93533616
		  39.76525773    283.0  [ 16   4,  -3 -3 -2 >      5308416 : 5187875
		  39.80361804    283.2  [-10   5,  -3  2  1 >       130977 : 128000
		  39.8263349     283.4  [ 17  -9,  -6  4  0 >    314703872 : 307546875
		  39.85121563    283.6  [-34   6,  10 -2  2 >  8.61416E+11 : 8.41814E+11
		  39.8739325     283.7  [ -7  -8,   7  0  1 >       859375 : 839808
		  39.96462212    284.4  [ 40  -6,  -8 -3 -1 >  1.09951E+12 : 1.07442E+12

		  40.00000952    284.6  [-35   8,   6  3  0 >  35162859375 : 34359738368
		  40.00298242    284.7  [ 14  -5,  -8  2  2 >     97140736 : 94921875
		  40.09069914    285.3  [ 12  10,  -9  0 -2 >    241864704 : 236328125
		  40.13829674    285.6  [-12  11,   4 -4 -1 >    110716875 : 108179456
		  40.1610136     285.8  [ 15  -3,   1 -2 -2 >       163840 : 160083
		  40.17665704    285.9  [-38  12,   4  1  2 >  2.81332E+11 : 2.74878E+11
		  40.19937391    286.1  [-11  -2,   1  3  1 >        18865 : 18432
		  40.33766112    287.0  [ 12   1,  -1 -4  0 >        12288 : 12005
		  40.36037799    287.2  [ 39 -13,  -4 -2 -1 >  5.49756E+11 : 5.37088E+11
		  40.39576539    287.4  [-36   1,  10  4  0 >  70341796875 : 68719476736
		  40.39873829    287.5  [ 13 -12,  -4  3  2 >    339992576 : 332150625
		  40.48645501    288.1  [ 11   3,  -5  1 -2 >       387072 : 378125
		  40.53405261    288.4  [-13   4,   8 -3 -1 >     31640625 : 30908416
		  40.53702551    288.5  [ 36  -9,  -6 -4  1 >  7.55914E+11 : 7.3842E+11
		  40.55676947    288.6  [ 14 -10,   5 -1 -2 >     51200000 : 50014503
		  40.57241291    288.7  [-39   5,   8  2  2 >  5.62792E+11 : 5.49756E+11
		  40.59512978    288.9  [-12  -9,   5  4  1 >     82534375 : 80621568
		  40.66310253    289.4  [  8   7,  -7 -1  0 >       559872 : 546875
		  40.6858194     289.5  [ 35  -7, -10  1 -1 >  2.40518E+11 : 2.34932E+11
		  40.73341699    289.9  [ 11  -6,   3 -3  0 >       256000 : 250047
		  40.83975006    290.6  [  5  11,  -9 -3  2 >    685913184 : 669921875
		  40.85949402    290.7  [-17  10,   2  0 -1 >      1476225 : 1441792
		  40.88221088    290.9  [ 10  -4,  -1  2 -2 >        50176 : 49005

		  41.03614154    292.0  [-20  14,   0 -2  1 >     52612659 : 51380224
		  41.05885841    292.2  [  7   0,  -3  0  0 >          128 : 125             enharmonic-diesis, great diesis [Ellis], minor diesis [Rameau]
		  41.08157527    292.3  [ 34 -14,  -6  2 -1 >  8.41814E+11 : 8.22073E+11
		  41.106456      292.5  [-17   1,  10 -4  1 >    322265625 : 314703872
		  41.12917287    292.7  [ 10 -13,   7 -2  0 >     80000000 : 78121827
		  41.23550593    293.4  [  4   4,  -5 -2  2 >       156816 : 153125
		  41.25524989    293.6  [-18   3,   6  1 -1 >      2953125 : 2883584
		  41.25822279    293.6  [ 31 -10,  -8  0  1 >  23622320128 : 23066015625
		  41.27796675    293.7  [  9 -11,   3  3 -2 >     21952000 : 21434787
		  41.30582039    293.9  [  7  -9,   5 -4  2 >     48400000 : 47258883
		  41.38429982    294.5  [  3   6,  -9  3  0 >      2000376 : 1953125
		  41.43189741    294.8  [-21   7,   4 -1  1 >     15035625 : 14680064
		  41.45461428    295.0  [  6  -7,   1  1  0 >         2240 : 2187
		  41.5806913     295.9  [-22   9,   0  4 -1 >     47258883 : 46137344
		  41.6312618     296.2  [  3  -3,  -1 -1  2 >          968 : 945
		  41.65100576    296.4  [-19  -4,  10  2 -1 >    478515625 : 467140608
		  41.71897852    296.9  [  1  12,  -2 -3 -2 >      1062882 : 1037575
		  41.75733882    297.1  [-25  13,  -2  2  1 >    859340097 : 838860800
		  41.78005569    297.3  [  2  -1,  -5  4  0 >         9604 : 9375
		  41.82765328    297.6  [-22   0,   8  0  1 >      4296875 : 4194304
		  41.85037015    297.8  [  5 -14,   5  2  0 >      4900000 : 4782969
		  41.9183429     298.3  [ 25   2,  -7 -3 -1 >    301989888 : 294765625
		  41.94105977    298.4  [ 52 -12, -10 -1 -2 >   4.5036E+15 : 4.39581E+15
		  41.95670321    298.6  [ -1   3,  -7  2  2 >       160083 : 156250
		  41.97942007    298.7  [ 26 -11, -10  4  1 >  1.77241E+12 : 1.72995E+12

		  42.02701767    299.1  [  2 -10,   3  0  2 >        60500 : 59049
		  42.11473439    299.7  [  0   5,   2 -2 -2 >         6075 : 5929
		  42.15309469    300.0  [-26   6,   2  3  1 >     68762925 : 67108864
		  42.29138191    300.9  [ -3   9,   0 -4  0 >        19683 : 19208
		  42.31409878    301.1  [ 24  -5,  -3 -2 -1 >     16777216 : 16372125
		  42.35245908    301.4  [ -2  -4,  -3  3  2 >        41503 : 40500
		  42.4401758     302.0  [ -4  11,  -4  1 -2 >      1240029 : 1210000
		  42.4877734     302.3  [-28  12,   9 -3 -1 >  1.03797E+12 : 1.01281E+12
		  42.4907463     302.4  [ 21  -1,  -5 -4  1 >     23068672 : 22509375
		  42.51049026    302.5  [ -1  -2,   6 -1 -2 >        15625 : 15246
		  42.51346316    302.5  [ 48 -15,  -8 -2  0 >  2.81475E+14 : 2.74647E+14
		  42.5261337     302.6  [-54  13,   9  2  2 >  1.84624E+16 : 1.80144E+16
		  42.54885056    302.8  [-27  -1,   6  4  1 >    412671875 : 402653184
		  42.61682332    303.3  [ -7  15,  -6 -1  0 >     14348907 : 14000000
		  42.63954019    303.4  [ 20   1,  -9  1 -1 >     22020096 : 21484375
		  42.68713778    303.8  [ -4   2,   4 -3  0 >         5625 : 5488
		  42.69011069    303.8  [ 45 -11, -10 -4  2 >  4.25731E+15 : 4.15361E+15
		  42.70985465    303.9  [ 23 -12,   1 -1 -1 >     41943040 : 40920957
		  42.74821495    304.2  [ -3 -11,   1  4  2 >      1452605 : 1417176
		  42.83593167    304.8  [ -5   4,   0  2 -2 >         3969 : 3872
		  42.88650217    305.2  [ 20  -8,  -1 -3  1 >     11534336 : 11252115
		  42.90624613    305.3  [ -2  -9,  10  0 -2 >      9765625 : 9526572

		  43.01257919    306.1  [ -8   8,  -2  0  0 >         6561 : 6400
		  43.03529606    306.2  [ 19  -6,  -5  2 -1 >     25690112 : 25059375
		  43.08289365    306.6  [ -5  -5,   8 -2  0 >       390625 : 381024
		  43.18922672    307.3  [-11  12,  -4 -2  2 >     64304361 : 62720000
		  43.20897068    307.5  [-33  11,   7  1 -1 >  96877265625 : 94489280512
		  43.21194358    307.5  [ 16  -2,  -7  0  1 >       720896 : 703125
		  43.23168754    307.6  [ -6  -3,   4  3 -2 >       214375 : 209088
		  43.25954118    307.8  [ -8  -1,   6 -4  2 >      1890625 : 1843968
		  43.28225804    308.0  [ 19 -15,   3 -2  1 >    720896000 : 703096443
		  43.3380206     308.4  [-12  14,  -8  3  0 >   1640558367 : 1600000000
		  43.3856182     308.7  [-36  15,   5 -1  1 >  4.93244E+11 : 4.81036E+11
		  43.40833506    308.9  [ -9   1,   2  1  0 >          525 : 512
		  43.43105193    309.0  [ 18 -13,  -1  3 -1 >     89915392 : 87687765
		  43.56933915    310.0  [ 41 -10,  -3 -4 -2 >  2.19902E+12 : 2.14437E+12
		  43.58498259    310.1  [-12   5,   0 -1  2 >        29403 : 28672
		  43.60769945    310.3  [ 15  -9,  -3  1  1 >      2523136 : 2460375
		  43.62744341    310.4  [ -7 -10,   8  4 -2 >    937890625 : 914550912
		  43.6363636     310.5  [2/55  0,   0  0  0 >                                2/55-edo
		  43.65529705    310.6  [ -9  -8,  10 -3  2 >   1181640625 : 1152216576
		  43.73377647    311.2  [-13   7,  -4  4  0 >      5250987 : 5120000
		  43.78137407    311.5  [-37   8,   9  0  1 >  1.40959E+11 : 1.37439E+11
		  43.80409093    311.7  [-10  -6,   6  2  0 >       765625 : 746496
		  43.87206369    312.2  [ 10  10,  -6 -3 -1 >     60466176 : 58953125
		  43.89478056    312.3  [ 37  -4,  -9 -1 -2 >  1.37439E+11 : 1.33998E+11
		  43.910424      312.5  [-16  11,  -6  2  2 >   1050304563 : 1024000000
		  43.93314086    312.6  [ 11  -3,  -9  4  1 >     54089728 : 52734375
		  43.98073846    313.0  [-13  -2,   4  0  2 >        75625 : 73728

		  44.06845518    313.6  [-15  13,   3 -2 -2 >    199290375 : 194281472
		  44.10681548    313.9  [-41  14,   3  3  1 >  2.25577E+12 : 2.19902E+12
		  44.19984681    314.5  [-11 -13,  10  3  0 >   3349609375 : 3265173504
		  44.26781956    315.0  [  9   3,  -2 -2 -1 >        13824 : 13475
		  44.29053643    315.2  [ 36 -11,  -5  0 -2 >  68719476736 : 66983709375
		  44.30617987    315.3  [-17   4,  -2  3  2 >      3361743 : 3276800
		  44.33813402    315.5  [ 12 -10,   8 -4 -1 >   1600000000 : 1559543139
		  44.37649433    315.8  [-14  -9,   8  1  2 >    330859375 : 322486272
		  44.44446709    316.3  [  6   7,  -4 -4  1 >      1539648 : 1500625
		  44.46421105    316.4  [-16   6,   7 -1 -2 >     56953125 : 55508992
		  44.46718395    316.4  [ 33  -7,  -7 -2  0 >   8589934592 : 8372109375
		  44.50257135    316.7  [-42   7,   7  4  1 >  4.51257E+12 : 4.39805E+12
		  44.59326097    317.3  [  5   9,  -8  1 -1 >      4408992 : 4296875
		  44.64085857    317.7  [-19  10,   5 -3  0 >    184528125 : 179830784
		  44.64383147    317.7  [ 30  -3,  -9 -4  2 >  1.29923E+11 : 1.26615E+11
		  44.66357543    317.8  [  8  -4,   2 -1 -1 >         6400 : 6237
		  44.70193574    318.1  [-18  -3,   2  4  2 >      7263025 : 7077888
		  44.7699085     318.6  [  2  13, -10 -1  1 >     70150212 : 68359375
		  44.78965246    318.7  [-20  12,   1  2 -2 >    130203045 : 126877696
		  44.84022296    319.1  [  5   0,   0 -3  1 >          352 : 343
		  44.86293982    319.2  [ 32 -14,  -3 -1  0 >   4294967296 : 4185097875
		  44.98901684    320.1  [  4   2,  -4  2 -1 >         7056 : 6875

		  45.01173371    320.3  [ 31 -12,  -7  4 -2 >  5.15611E+12 : 5.02378E+12
		  45.03661444    320.5  [-20   3,   9 -2  0 >     52734375 : 51380224
		  45.03958734    320.5  [ 29 -10,  -5 -3  2 >  64961380352 : 63293146875
		  45.0593313     320.6  [  7 -11,   6  0 -1 >      2000000 : 1948617
		  45.16566437    321.4  [  1   6,  -6  0  1 >        16038 : 15625
		  45.18540833    321.5  [-21   5,   5  3 -2 >    260465625 : 253755392
		  45.18838123    321.6  [ 28  -8,  -9  2  0 >  13153337344 : 12814453125
		  45.21326196    321.7  [-23   7,   7 -4  2 >  20673984375 : 20141047808
		  45.23597883    321.9  [  4  -7,   4 -2  1 >       110000 : 107163
		  45.28301887    322.2  [2/53  0,   0  0  0 >                               2/53-edo (JI diminished-2nd, great diesis = ~128:125)
		  45.36205585    322.8  [-24   9,   3  1  0 >     17222625 : 16777216
		  45.38477272    323.0  [  3  -5,   0  3 -1 >         2744 : 2673
		  45.52305993    323.9  [ 26  -2,  -2 -4 -2 >     67108864 : 65367225
		  45.53870338    324.0  [-27  13,   1 -1  2 >    964565415 : 939524096
		  45.56142024    324.2  [  0  -1,  -2  1  1 >           77 : 75
		  45.5811642     324.3  [-22  -2,   9  4 -2 >   4689453125 : 4567597056
		  45.5841371     324.4  [ 27 -15,  -5  3  0 >  46036680704 : 44840334375
		  45.6317347     324.7  [  3 -14,   8 -1  1 >     34375000 : 33480783
		  45.68749726    325.1  [-28  15,  -3  4  0 >  34451725707 : 33554432000
		  45.72242432    325.4  [ 50 -12,  -7 -4 -1 >   1.1259E+15 : 1.09655E+15
		  45.75781172    325.6  [-25   2,   7  2  0 >     34453125 : 33554432
		  45.76078463    325.6  [ 24 -11,  -7  1  2 >  14210301952 : 13839609375
		  45.78052859    325.8  [  2 -12,   4  4 -1 >      6002500 : 5845851
		  45.84850134    326.3  [ 22   4,  -8 -1 -2 >    339738624 : 330859375
		  45.88686165    326.5  [ -4   5,  -8  4  1 >      6417873 : 6250000
		  45.9188158     326.8  [ 25  -9,   2 -3 -2 >    838860800 : 816903549
		  45.93445925    326.9  [-28   6,   5  0  2 >    275653125 : 268435456
		  45.95717611    327.0  [ -1  -8,   2  2  1 >        13475 : 13122

		  46.02514887    327.5  [ 19   8, -10 -3  0 >   3439853568 : 3349609375
		  46.22154035    328.9  [ -6  11,  -1 -2 -1 >       177147 : 172480
		  46.24425721    329.1  [ 21  -3,  -4  0 -2 >      2097152 : 2041875
		  46.25990066    329.2  [-32  12,  -1  3  2 >  22056395823 : 21474836480
		  46.29185481    329.4  [ -3  -2,   9 -4 -1 >      1953125 : 1901592
		  46.33021512    329.7  [-29  -1,   9  1  2 >   1654296875 : 1610612736
		  46.35293198    329.8  [ -2 -15,   6  3  1 >     58953125 : 57395628
		  46.39818787    330.2  [ -9  15,  -3 -4  1 >    157837977 : 153664000
		  46.41793184    330.3  [-31  14,   8 -1 -2 >  1.86835E+12 : 1.81892E+12
		  46.42090474    330.3  [ 18   1,  -6 -2  0 >       786432 : 765625
		  46.4436216     330.5  [ 45 -13,  -9  0 -1 >  3.51844E+13 : 3.4253E+13
		  46.45629214    330.6  [-57  15,   8  4  1 >  1.48035E+17 : 1.44115E+17
		  46.4912192     330.8  [ 21 -12,   4 -4  0 >   1310720000 : 1275989841
		  46.56969863    331.4  [ 17   3, -10  3 -2 >   1213857792 : 1181640625
		  46.59755226    331.6  [ 15   5,  -8 -4  2 >    963477504 : 937890625
		  46.61729622    331.7  [ -7   4,   3 -1 -1 >        10125 : 9856
		  46.64001309    331.9  [ 20 -10,   0  1 -2 >      7340032 : 7144929
		  46.65565653    332.0  [-33   5,   3  4  2 >   8824575375 : 8589934592
		  46.79394375    333.0  [-10   8,   1 -3  1 >       360855 : 351232
		  46.81666061    333.1  [ 17  -6,  -2 -1  0 >       131072 : 127575
		  46.94273763    334.0  [-11  10,  -3  2 -1 >      2893401 : 2816000
		  46.9654545     334.2  [ 16  -4,  -6  4 -2 >    157351936 : 153140625
		  46.99033523    334.4  [-35  11,  10 -2  0 >  1.72995E+12 : 1.68363E+12
		  46.99330813    334.4  [ 14  -2,  -4 -3  2 >      1982464 : 1929375

		  47.01305209    334.5  [ -8  -3,   7  0 -1 >        78125 : 76032
		  47.11938516    335.3  [-14  14,  -5  0  1 >     52612659 : 51200000
		  47.13912912    335.4  [-36  13,   6  3 -2 >  8.54457E+12 : 8.31506E+12
		  47.14210202    335.5  [ 13   0,  -8  2  0 >       401408 : 390625
		  47.16698275    335.6  [-38  15,   8 -4  2 >   6.7821E+14 : 6.59982E+14
		  47.18969962    335.8  [-11   1,   5 -2  1 >       103125 : 100352
		  47.21241648    336.0  [ 16 -13,   2  0  0 >      1638400 : 1594323
		  47.31874954    336.7  [ 10   4, -10  0  2 >     10036224 : 9765625
		  47.3384935     336.9  [-12   3,   1  3 -1 >        46305 : 45056
		  47.389064      337.2  [ 13  -9,   0 -2  2 >       991232 : 964467
		  47.47678072    337.8  [ 11   6,  -1 -4 -2 >      1492992 : 1452605
		  47.51514103    338.1  [-15   7,  -1  1  1 >       168399 : 163840
		  47.53488499    338.3  [-37   6,  10  4 -2 >  1.70931E+13 : 1.66301E+13
		  47.53785789    338.3  [ 12  -7,  -4  3  0 >      1404928 : 1366875
		  47.58545549    338.6  [-12  -6,   9 -1  1 >     21484375 : 20901888
		  47.67614511    339.3  [ 35  -4,  -6 -4 -1 >  34359738368 : 33426421875
		  47.71153251    339.5  [-40  10,   8  2  0 >  1.13023E+12 : 1.09951E+12
		  47.71450541    339.5  [  9  -3,  -6  1  2 >       433664 : 421875
		  47.73424937    339.7  [-13  -4,   5  4 -1 >      7503125 : 7299072
		  47.80222213    340.2  [  7  12,  -7 -1 -2 >     68024448 : 66171875
		  47.84058244    340.4  [-19  13,  -7  4  1 >  42107664753 : 40960000000
		  47.87253659    340.7  [ 10  -1,   3 -3 -2 >       128000 : 124509
		  47.88818003    340.8  [-43  14,   6  0  2 >   9.0428E+12 : 8.79609E+12
		  47.9108969     340.9  [-16   0,   3  2  1 >        67375 : 65536
		  47.93361376    341.1  [ 11 -14,   0  4  0 >      4917248 : 4782969

		  48.07190098    342.1  [ 34 -11,  -2 -3 -1 >  17179869184 : 16709390775
		  48.11026128    342.3  [  8 -10,  -2  2  2 >      1517824 : 1476225
		  48.197978      343.0  [  6   5,  -3  0 -2 >        15552 : 15125
		  48.2455756     343.3  [-18   6,  10 -4 -1 >   7119140625 : 6923485184
		  48.26829246    343.5  [  9  -8,   7 -2 -2 >     40000000 : 38900169
		  48.2839359     343.6  [-44   7,  10  1  2 >  1.80897E+13 : 1.75922E+13
		  48.30665277    343.7  [-17  -7,   7  3  1 >    294765625 : 286654464
		  48.37462553    344.2  [  3   9,  -5 -2  0 >       157464 : 153125
		  48.39734239    344.4  [ 30  -5,  -8  0 -1 >   1073741824 : 1044140625
		  48.44493999    344.7  [  6  -4,   5 -4  0 >       200000 : 194481
		  48.52341941    345.3  [  2  11,  -9  3 -2 >    243045684 : 236328125
		  48.55127305    345.5  [  0  13,  -7 -4  2 >    192913083 : 187578125
		  48.57101701    345.6  [-22  12,   4 -1 -1 >    332150625 : 322961408
		  48.57398991    345.6  [ 27  -1, -10 -2  1 >   1476395008 : 1435546875
		  48.59373387    345.8  [  5  -2,   1  1 -2 >         1120 : 1089
		  48.60937732    345.9  [-48  13,   4  4  2 >   2.8949E+14 : 2.81475E+14
		  48.64430437    346.1  [ 30 -14,   0 -4  1 >  11811160064 : 11483908569
		  48.7703814     347.0  [  2   2,  -1 -1  0 >           36 : 35              septimal-diesis
		  48.79309826    347.2  [ 29 -12,  -4  1 -1 >   3758096384 : 3653656875
		  48.84069586    347.5  [  5 -11,   9 -3  0 >     62500000 : 60761421
		  48.91917528    348.1  [  1   4,  -5  4 -2 >       388962 : 378125
		  48.94702892    348.3  [ -1   6,  -3 -3  2 >        88209 : 85750
		  48.96677288    348.4  [-23   5,   8  0 -1 >     94921875 : 92274688
		  48.96974578    348.5  [ 26  -8,  -6 -1  1 >    738197504 : 717609375
		  48.98948974    348.6  [  4  -9,   5  2 -2 >      2450000 : 2381643

		  49.09582281    349.4  [ -2   8,  -7  2  0 >       321489 : 312500
		  49.11853967    349.5  [ 25  -6, -10  4 -1 >  80564191232 : 78310546875
		  49.1434204     349.7  [-26   9,   6 -2  1 >   3383015625 : 3288334336
		  49.16613727    349.9  [  1  -5,   3  0  0 >          250 : 243             maximal-diesis, major diesis [Rameau]
		  49.27247033    350.6  [ -5  12,  -9  0  2 >     64304361 : 62500000
		  49.29221429    350.8  [-27  11,   2  3 -1 >   1519035525 : 1476395008
		  49.34278479    351.1  [ -2  -1,   1 -2  2 >          605 : 588
		  49.36550165    351.3  [ 25 -15,  -2  0  1 >    369098752 : 358722675
		  49.43050151    351.7  [ -4  14,   0 -4 -2 >      4782969 : 4648336
		  49.46886181    352.0  [-30  15,   0  1  1 >   1104865839 : 1073741824
		  49.49157868    352.2  [ -3   1,  -3  3  0 >         1029 : 1000
		  49.53917627    352.5  [-27   2,  10 -1  1 >    966796875 : 939524096
		  49.56189314    352.7  [  0 -12,   7  1  0 >       546875 : 531441
		  49.6298659     353.2  [ 20   4,  -5 -4 -1 >     84934656 : 82534375
		  49.65258276    353.3  [ 47 -10,  -8 -2 -2 >  1.40737E+14 : 1.36758E+14
		  49.6682262     353.4  [ -6   5,  -5  1  2 >       205821 : 200000
		  49.68797016    353.6  [-28   4,   6  4 -1 >   3038765625 : 2952790016
		  49.69094306    353.6  [ 21  -9,  -8  3  1 >   7912554496 : 7688671875
		  49.73854066    353.9  [ -3  -8,   5 -1  2 >       378125 : 367416
		  49.82625738    354.6  [ -5   7,   4 -3 -2 >      1366875 : 1328096
		  49.82923028    354.6  [ 44  -6, -10 -4  0 >  1.75922E+13 : 1.70931E+13
		  49.86461769    354.8  [-31   8,   4  2  1 >   2210236875 : 2147483648
		  49.88733455    355.0  [ -4  -6,   1  4  0 >        12005 : 11664

		  50.02562177    356.0  [ 19  -3,  -1 -3 -1 >       524288 : 509355
		  50.06398207    356.2  [ -7  -2,  -1  2  2 >         5929 : 5760
		  50.13429653    356.7  [ -4 -15,   9  0  2 >    236328125 : 229582512
		  50.15169879    356.9  [ -9  13,  -2  0 -2 >      1594323 : 1548800
		  50.22201325    357.4  [ -6   0,   8 -2 -2 >       390625 : 379456
		  50.22498615    357.4  [ 43 -13,  -6 -3  0 >  8.79609E+12 : 8.54457E+12
		  50.26037356    357.6  [-32   1,   8  3  1 >   4421484375 : 4294967296
		  50.35106318    358.3  [ 15   3,  -7  0 -1 >       884736 : 859375
		  50.37378004    358.5  [ 42 -11, -10  2 -2 >  2.15504E+14 : 2.09324E+14
		  50.39866077    358.6  [ -9   4,   6 -4  0 >      1265625 : 1229312
		  50.42137764    358.8  [ 18 -10,   3 -2 -1 >     32768000 : 31827411
		  50.45973794    359.1  [ -8  -9,   3  3  2 >      5187875 : 5038848
		  50.5277107     359.5  [ 12   7,  -9 -2  1 >     98537472 : 95703125
		  50.54745466    359.7  [-10   6,   2  1 -2 >       127575 : 123904
		  50.59802516    360.0  [ 15  -6,   1 -4  1 >      1802240 : 1750329
		  50.72410218    360.9  [-13  10,   0 -1  0 >        59049 : 57344
		  50.74681905    361.1  [ 14  -4,  -3  1 -1 >       114688 : 111375
		  50.79441664    361.4  [-10  -3,  10 -3  0 >      9765625 : 9483264
		  50.87289607    362.0  [-14  12,  -4  4 -2 >   1275989841 : 1239040000
		  50.90074971    362.2  [-16  14,  -2 -3  2 >    578739249 : 561971200
		  50.92049367    362.3  [-38  13,   9  0 -1 >  3.11391E+12 : 3.02366E+12
		  50.92346657    362.4  [ 11   0,  -5 -1  1 >        22528 : 21875
		  50.94321053    362.5  [-11  -1,   6  2 -2 >       765625 : 743424
		  50.94618344    362.5  [ 38 -14,  -8  1  0 >  1.92415E+12 : 1.86835E+12
		  50.99378103    362.9  [ 14 -13,   5 -3  1 >    563200000 : 546852789

		  51.07226046    363.4  [ 10   2,  -9  4 -1 >     22127616 : 21484375
		  51.11985806    363.8  [-14   3,   4  0  0 >        16875 : 16384    negri
		  51.12283096    363.8  [ 35 -10, -10 -1  2 >  4.15753E+12 : 4.03655E+12
		  51.14257492    363.9  [ 13 -11,   1  2 -1 >      2007040 : 1948617
		  51.29650558    365.0  [-17   7,   2 -2  2 >      6615675 : 6422528
		  51.31922244    365.2  [ 10  -7,  -1  0  1 >        11264 : 10935
		  51.3389664     365.3  [-12  -8,  10  3 -2 >   3349609375 : 3251736576
		  51.44529947    366.1  [-18   9,  -2  3  0 >      6751269 : 6553600
		  51.51561393    366.6  [-15  -4,   8  1  0 >      2734375 : 2654208
		  51.58358668    367.1  [  5  12,  -4 -4 -1 >     17006112 : 16506875
		  51.60630355    367.2  [ 32  -2,  -7 -2 -2 >   4294967296 : 4168828125
		  51.62194699    367.3  [-21  13,  -4  1  2 >   1350391581 : 1310720000
		  51.64169095    367.5  [-43  12,   7  4 -1 >  9.96867E+13 : 9.6757E+13
		  51.64466385    367.5  [  6  -1,  -7  3  1 >       241472 : 234375
		  51.67661801    367.7  [ 35 -15,   3 -4 -2 >  4.29497E+12 : 4.16866E+12
		  51.69226145    367.8  [-18   0,   6 -1  2 >      1890625 : 1835008
		  51.71497831    368.0  [  9 -14,   3  1  1 >      4928000 : 4782969
		  51.77997817    368.5  [-20  15,   5 -3 -2 >  44840334375 : 43519049728
		  51.78295107    368.5  [ 29   2,  -9 -4  0 >   4831838208 : 4689453125
		  51.84105534    368.9  [-19   2,   2  4  0 >       540225 : 524288
		  51.97934255    369.9  [  4   5,   0 -3 -1 >         3888 : 3773

		  52.00205942    370.0  [ 31  -9,  -3 -1 -2 >   2147483648 : 2083937625
		  52.01770286    370.1  [-22   6,   0  2  2 >      4322241 : 4194304
		  52.04041972    370.3  [  5  -8,  -3  4  1 >       845152 : 820125
		  52.08801732    370.6  [-19  -7,  10  0  2 >   1181640625 : 1146617856
		  52.1739130     371.3  [1/23  0,   0  0  0 >                               2/46-edo
		  52.17573404    371.3  [-21   8,   9 -2 -2 >  12814453125 : 12434014208
		  52.17870694    371.3  [ 28  -5,  -5 -3  0 >    268435456 : 260465625
		  52.21409434    371.5  [-47   9,   9  3  1 >  1.45047E+14 : 1.40737E+14
		  52.30478397    372.2  [  0  11,  -6  0 -1 >       177147 : 171875
		  52.32750083    372.4  [ 27  -3,  -9  2 -2 >   6576668672 : 6380859375
		  52.35238156    372.5  [-24  12,   7 -4  0 >  41518828125 : 40282095616
		  52.37509843    372.7  [  3  -2,   4 -2 -1 >         5000 : 4851
		  52.37807133    372.7  [ 52 -15, -10 -3  1 >  4.95396E+16 : 4.80632E+16
		  52.41345873    373.0  [-23  -1,   4  3  2 >     25939375 : 25165824
		  52.48143149    373.4  [ -3  15,  -8 -2  1 >    157837977 : 153125000
		  52.50117545    373.6  [-25  14,   3  1 -2 >   4185097875 : 4060086272
		  52.55174595    373.9  [  0   2,   2 -4  1 >         2475 : 2401
		  52.57446281    374.1  [ 27 -12,  -1 -2  0 >    134217728 : 130203045
		  52.70053984    375.0  [ -1   4,  -2  1 -1 >          567 : 550
		  52.7232567     375.2  [ 26 -10,  -5  3 -2 >  23018340352 : 22327903125
		  52.75111034    375.4  [ 24  -8,  -3 -4  2 >   2030043136 : 1969120125
		  52.7708543     375.5  [  2  -9,   8 -1 -1 >      1562500 : 1515591
		  52.8092146     375.8  [-24  -8,   8  4  2 >  1.13485E+11 : 1.10075E+11
		  52.87718736    376.3  [ -4   8,  -4 -1  1 >        72171 : 70000
		  52.89693132    376.4  [-26   7,   7  2 -2 >   8372109375 : 8120172544
		  52.89990422    376.4  [ 23  -6,  -7  1  0 >     58720256 : 56953125
		  52.94750182    376.8  [ -1  -5,   6 -3  1 >       171875 : 166698

		  53.02598125    377.3  [ -5  10,  -8  4 -1 >    141776649 : 137500000
		  53.07357884    377.7  [-29  11,   5  0  0 >    553584375 : 536870912
		  53.07655175    377.7  [ 20  -2,  -9 -1  2 >    126877696 : 123046875
		  53.09629571    377.8  [ -2  -3,   2  2 -1 >         1225 : 1188
		  53.14686621    378.2  [ 23 -15,   1 -3  2 >   5075107840 : 4921675101
		  53.16426846    378.3  [ 18  13, -10 -3 -2 >  4.17942E+11 : 4.05303E+11
		  53.20262877    378.6  [ -8  14, -10  2  1 >   2578020291 : 2500000000
		  53.25022637    378.9  [-32  15,   3 -2  2 >  2.17027E+11 : 2.10453E+11
		  53.27294323    379.1  [ -5   1,   0  0  1 >           33 : 32             undecimal-diesis
		  53.29566009    379.2  [ 22 -13,  -3  2  0 >    205520896 : 199290375
		  53.34325769    379.6  [ -2 -12,  10 -2  1 >    107421875 : 104162436
		  53.46933471    380.5  [-30   4,   9  1  0 >   1107421875 : 1073741824
		  53.47230762    380.5  [ 19  -9,  -5  0  2 >     63438848 : 61509375
		  53.49205158    380.6  [ -3 -10,   6  3 -1 >      5359375 : 5196312
		  53.56002434    381.1  [ 17   6,  -6 -2 -2 >     95551488 : 92640625
		  53.59838464    381.4  [ -9   7,  -6  3  1 >      8251551 : 8000000
		  53.6303388     381.6  [ 20  -7,   4 -4 -2 >    655360000 : 635369427
		  53.64598224    381.7  [-33   8,   7 -1  2 >  62021953125 : 60129542144
		  53.6686991     381.9  [ -6  -6,   4  1  1 >        48125 : 46656
		  53.73667186    382.4  [ 14  10,  -8 -4  0 >    967458816 : 937890625
		  53.79477612    382.8  [-34  10,   3  4  0 >  17722081125 : 17179869184
		  53.93306334    383.8  [-11  13,   1 -3 -1 >      7971615 : 7727104
		  53.95578021    383.9  [ 16  -1,  -2 -1 -2 >        65536 : 63525
		  53.97142365    384.1  [-37  14,   1  2  2 >  1.41791E+11 : 1.37439E+11
		  53.99414051    384.2  [-10   0,  -2  4  1 >        26411 : 25600

		  54.02609467    384.4  [ 19 -14,   8 -3 -2 >    2.048E+11 : 1.98508E+11
		  54.06445497    384.7  [ -7 -13,   8  2  1 >    210546875 : 204073344
		  54.13242773    385.2  [ 13   3,  -4 -3  0 >       221184 : 214375
		  54.15514459    385.4  [ 40 -11,  -7 -1 -1 >  1.09951E+12 : 1.06565E+12
		  54.1935049     385.6  [ 14 -10,  -7  4  2 >   4759896064 : 4613203125
		  54.28122162    386.3  [ 12   5,  -8  2 -2 >     48771072 : 47265625
		  54.32881921    386.6  [-12   6,   5 -2 -1 >      2278125 : 2207744
		  54.33179212    386.6  [ 37  -7,  -9 -3  1 >  1.51183E+12 : 1.46512E+12
		  54.35153608    386.8  [ 15  -8,   2  0 -2 >       819200 : 793881
		  54.36717952    386.9  [-38   7,   5  3  2 >  2.83647E+11 : 2.74878E+11
		  54.45786914    387.5  [  9   9, -10  0  0 >     10077696 : 9765625
		  54.50546674    387.9  [-15  10,   3 -4  1 >     81192375 : 78675968
		  54.5281836     388.0  [ 12  -4,   0 -2  0 >         4096 : 3969
		  54.5454545     388.1  [1/22  0,   0  0  0 >                            1/22-edo
		  54.65426062    388.9  [-16  12,  -1  1 -1 >      3720087 : 3604480
		  54.67697749    389.1  [ 11  -2,  -4  3 -2 >       702464 : 680625
		  54.70483112    389.3  [  9   0,  -2 -4  2 >        61952 : 60025
		  54.72457508    389.4  [-13  -1,   9 -1 -1 >      1953125 : 1892352
		  54.72754799    389.4  [ 36 -14,  -5 -2  1 >  7.55914E+11 : 7.32392E+11
		  54.74729195    389.6  [ 14 -15,   6  1 -2 >   1792000000 : 1736217747
		  54.76293539    389.7  [-39   0,   9  4  2 >  5.67424E+11 : 5.49756E+11
		  54.85065211    390.3  [-41  15,   8  2 -2 >  2.74647E+14 : 2.66082E+14
		  54.85362501    390.3  [  8   2,  -6  1  0 >        16128 : 15625
		  54.87634187    390.5  [ 35 -12,  -9  3 -1 >  1.17854E+13 : 1.14177E+13
		  54.90122261    390.7  [-16   3,   7 -3  1 >     23203125 : 22478848
		  54.92393947    390.8  [ 11 -11,   4 -1  0 >      1280000 : 1240029

		  55.03027253    391.6  [  5   6,  -8 -1  2 >      2822688 : 2734375
		  55.05001649    391.7  [-17   5,   3  2 -1 >      1488375 : 1441792
		  55.07273336    391.9  [ 10  -9,   0  4 -2 >      2458624 : 2381643
		  55.10058699    392.1  [  8  -7,   2 -3  2 >       774400 : 750141
		  55.22666402    393.0  [-20   9,   1  0  1 >      1082565 : 1048576
		  55.24938088    393.1  [  7  -5,  -2  2  0 >         6272 : 6075
		  55.4230555     394.4  [-45  12,  10  1  0 >   3.6329E+13 : 3.51844E+13
		  55.4260284     394.4  [  4  -1,  -4  0  2 >         1936 : 1875
		  55.44577237    394.5  [-18  -2,   7  3 -1 >     26796875 : 25952256
		  55.44874527    394.6  [ 31 -15,  -7  2  1 >  1.15749E+12 : 1.12101E+12
		  55.49634286    394.9  [  7 -14,   6 -2  2 >    242000000 : 234365481
		  55.51374512    395.0  [  2  14,  -5 -2 -2 >     19131876 : 18528125
		  55.55210543    395.3  [-24  15,  -5  3  1 >  54138426111 : 52428800000
		  55.58405958    395.5  [  5   1,   5 -4 -2 >       300000 : 290521
		  55.62241989    395.8  [-21   2,   5  1  1 >      2165625 : 2097152
		  55.64513675    396.0  [  6 -12,   2  3  0 >       548800 : 531441
		  55.71310951    396.4  [ 26   4, -10 -2 -1 >   5435817984 : 5263671875
		  55.75146982    396.7  [  0   5, -10  3  2 >     10085229 : 9765625
		  55.78342397    396.9  [ 29  -9,   0 -4 -1 >    536870912 : 519847713
		  55.82178428    397.2  [  3  -8,   0  1  2 >         6776 : 6561
		  55.90950099    397.8  [  1   7,  -1 -1 -2 >         4374 : 4235
		  55.9478613     398.1  [-25   8,  -1  4  1 >    173282571 : 167772160
		  55.97981545    398.3  [  4  -6,   9 -3 -2 >     31250000 : 30255687

		  56.01817576    398.6  [-22  -5,   9  2  1 >   1052734375 : 1019215872
		  56.08614852    399.1  [ -2  11,  -3 -3  0 >       177147 : 171500
		  56.10886538    399.3  [ 25  -3,  -6 -1 -1 >     33554432 : 32484375
		  56.14722569    399.5  [ -1  -2,  -6  4  2 >       290521 : 281250
		  56.21754015    400.0  [  2 -15,   4  2  2 >     14822500 : 14348907
		  56.2349424     400.2  [ -3  13,  -7  2 -2 >     78121827 : 75625000
		  56.28254       400.5  [-27  14,   6 -2 -1 >  74733890625 : 72343355392
		  56.2855129     400.5  [ 22   1,  -8 -3  1 >    138412032 : 133984375
		  56.30525686    400.7  [  0   0,   3  0 -2 >          125 : 121
		  56.32090031    400.8  [-53  15,   6  3  2 >  9.30504E+15 : 9.0072E+15
		  56.48190439    401.9  [ -3   4,   1 -2  0 >          405 : 392
		  56.50462125    402.1  [ 24 -10,  -2  0 -1 >     16777216 : 16238475
		  56.63069828    403.0  [ -4   6,  -3  3 -2 >       250047 : 242000
		  56.65855191    403.2  [ -6   8,  -1 -4  2 >       793881 : 768320
		  56.67829587    403.3  [-28   7,  10 -1 -1 >  21357421875 : 20669530112
		  56.68126877    403.3  [ 21  -6,  -4 -2  1 >     23068672 : 22325625
		  56.70101274    403.5  [ -1  -7,   7  1 -2 >       546875 : 529254
		  56.71665618    403.6  [-54   8,  10  4  2 >  1.86143E+16 : 1.80144E+16
		  56.8073458     404.2  [ -7  10,  -5  1  0 >       413343 : 400000
		  56.83006266    404.4  [ 20  -4,  -8  3 -1 >    359661568 : 348046875
		  56.8549434     404.6  [-31  11,   8 -3  1 >  7.61179E+11 : 7.36587E+11
		  56.87766026    404.7  [ -4  -3,   5 -1  0 >         3125 : 3024
		  56.96834988    405.4  [ 43  -1, -10 -4 -2 >  8.79609E+12 : 8.51136E+12
		  56.98399332    405.5  [-10  14,  -7 -1  2 >    578739249 : 560000000

		  57.00373728    405.6  [-32  13,   4  2 -1 >  48826141875 : 47244640256
		  57.00671019    405.7  [ 17   0, -10  1  1 >     10092544 : 9765625
		  57.02645415    405.8  [ -5  -1,   1  4 -2 >        12005 : 11616
		  57.05430778    406.0  [ -7   1,   3 -3  2 >        45375 : 43904
		  57.07702465    406.2  [ 20 -13,   0 -1  1 >     11534336 : 11160261
		  57.20310167    407.0  [ -8   3,  -1  2  0 >         1323 : 1280
		  57.22581853    407.2  [ 19 -11,  -4  4 -1 >   1258815488 : 1217885625
		  57.27341613    407.5  [ -5 -10,   9  0  0 >      1953125 : 1889568
		  57.36410575    408.2  [ 42  -8,  -6 -3 -2 >  4.39805E+12 : 4.25471E+12
		  57.37974919    408.3  [-11   7,  -3  0  2 >       264627 : 256000
		  57.39949315    408.4  [-33   6,   8  3 -1 >  97674609375 : 94489280512
		  57.40246606    408.5  [ 16  -7,  -6  2  1 >     35323904 : 34171875
		  57.45006365    408.8  [ -8  -6,   7 -2  2 >      9453125 : 9144576
		  57.53778037    409.4  [-10   9,   6 -4 -2 >    307546875 : 297493504
		  57.57614068    409.7  [-36  10,   6  1  1 >  71043328125 : 68719476736
		  57.59885754    409.9  [ -9  -4,   3  3  0 >        42875 : 41472
		  57.6668303     410.3  [ 11  12,  -9 -2 -1 >   1088391168 : 1052734375
		  57.7051906     410.6  [-15  13,  -9  3  2 >  66169187469 : 64000000000
		  57.73714476    410.8  [ 14  -1,   1 -4 -1 >        81920 : 79233
		  57.75986162    411.0  [ 41 -15,  -2 -2 -2 >  2.19902E+12 : 2.12687E+12
		  57.77550506    411.1  [-12   0,   1  1  2 >         4235 : 4096
		  57.79822193    411.3  [ 15 -14,  -2  3  1 >    123633664 : 119574225
		  57.86322178    411.7  [-14  15,   0 -1 -2 >     14348907 : 13877248
		  57.93353624    412.2  [-11   2,  10 -3 -2 >     87890625 : 84998144
		  57.93650914    412.3  [ 38 -11,  -4 -4  0 >  2.74878E+11 : 2.65831E+11
		  57.97189655    412.5  [-37   3,  10  2  1 >  1.42119E+11 : 1.37439E+11
		  57.99461341    412.7  [-10 -11,   7  4  0 >    187578125 : 181398528

		  58.06258617    413.2  [ 10   5,  -5 -1 -1 >       248832 : 240625
		  58.08530303    413.3  [ 37  -9,  -8  1 -2 >  9.62073E+11 : 9.30329E+11
		  58.10094647    413.4  [-16   6,  -5  4  2 >    211789809 : 204800000
		  58.13290063    413.7  [ 13  -8,   5 -3 -1 >     25600000 : 24754653
		  58.17126093    413.9  [-13  -7,   5  2  2 >     18528125 : 17915904
		  58.23923369    414.4  [  7   9,  -7 -3  1 >     27713664 : 26796875
		  58.25897765    414.6  [-15   8,   4  0 -2 >      4100625 : 3964928
		  58.26195056    414.6  [ 34  -5, -10 -1  0 >  17179869184 : 16611328125
		  58.43562518    415.8  [-18  12,   2 -2  0 >     13286025 : 12845056
		  58.45834204    416.0  [  9  -2,  -1  0 -1 >          512 : 495
		  58.5286565     416.5  [ 12 -15,   9 -2 -1 >   8000000000 : 7734060873
		  58.5365854     416.5  [2/41  0,   0  0  0 >                                2/41-edo
		  58.5670168     416.8  [-14 -14,   9  3  2 >  81060546875 : 78364164096
		  58.58441906    416.9  [-19  14,  -2  3 -2 >   1640558367 : 1585971200
		  58.63498956    417.2  [  6   2,  -3 -2  1 >         6336 : 6125
		  58.65473352    417.4  [-16   1,   8  1 -2 >      8203125 : 7929856
		  58.65770643    417.4  [ 33 -12,  -6  0  0 >   8589934592 : 8303765625
		  58.70530402    417.7  [  9 -11,   7 -4  1 >    440000000 : 425329947
		  58.78378345    418.3  [  5   4,  -7  3 -1 >       889056 : 859375
		  58.83138105    418.6  [-19   5,   6 -1  0 >      3796875 : 3670016
		  58.83435395    418.7  [ 30  -8,  -8 -2  2 >  1.29923E+11 : 1.25582E+11
		  58.85409791    418.8  [  8  -9,   3  1 -1 >       224000 : 216513
		  58.92207067    419.3  [ 28   7,  -9 -4 -2 >  5.87068E+11 : 5.67424E+11
		  58.96043097    419.6  [  2   8,  -9  1  1 >      2020788 : 1953125
		  58.98017493    419.7  [-20   7,   2  4 -2 >    131274675 : 126877696

		  59.00802857    419.9  [-22   9,   4 -3  2 >   1488526875 : 1438646272
		  59.03074543    420.1  [  5  -5,   1 -1  1 >         1760 : 1701
		  59.15682246    421.0  [-23  11,   0  2  0 >      8680203 : 8388608
		  59.17953932    421.1  [  4  -3,  -3  4 -1 >        38416 : 37125
		  59.22713692    421.5  [-20  -2,  10  0  0 >      9765625 : 9437184
		  59.23010982    421.5  [ 29 -15,  -4 -1  2 >  64961380352 : 62776468125
		  59.31782654    422.1  [ 27   0,  -5 -3 -2 >    134217728 : 129696875
		  59.33346998    422.2  [-26  15,  -2  0  2 >   1736217747 : 1677721600
		  59.35321394    422.3  [-48  14,   9  3 -1 >  3.20422E+15 : 3.09622E+15
		  59.35618684    422.4  [  1   1,  -5  2  1 >         3234 : 3125
		  59.37890371    422.5  [ 28 -13,  -8  4  0 >  6.44514E+11 : 6.22782E+11
		  59.40378444    422.7  [-23   2,   8 -2  2 >    425390625 : 411041792
		  59.4265013     422.9  [  4 -12,   5  0  1 >       550000 : 531441
		  59.51719093    423.5  [ 51 -10, -10 -3 -1 >   2.2518E+15 : 2.1757E+15
		  59.55257833    423.8  [-24   4,   4  3  0 >     17364375 : 16777216
		  59.55555123    423.8  [ 25  -9, -10  2  2 >  1.98944E+11 : 1.92217E+11
		  59.69086555    424.8  [ -1   7,   2 -4 -1 >        54675 : 52822
		  59.71358241    424.9  [ 26  -7,  -1 -2 -2 >     67108864 : 64833615
		  59.72922585    425.0  [-27   8,   2  1  2 >    138929175 : 134217728
		  59.75194271    425.2  [  0  -6,  -1  3  1 >         3773 : 3645
		  59.89022993    426.2  [ 23  -3,  -3 -4  0 >      8388608 : 8103375
		  59.9483342     426.6  [-25  -3,   8  4  0 >    937890625 : 905969664

		  60.01630696    427.1  [ -5  13,  -4 -1 -1 >      1594323 : 1540000
		  60.03902382    427.2  [ 22  -1,  -7  1 -2 >     29360128 : 28359375
		  60.05466726    427.3  [-31  14,  -4  4  2 >  1.38955E+12 : 1.34218E+12
		  60.08662142    427.6  [ -2   0,   6 -3 -1 >        15625 : 15092
		  60.08959432    427.6  [ 47 -13,  -8 -4  1 >  1.54811E+15 : 1.4953E+15
		  60.10933828    427.7  [ 25 -14,   3 -1 -2 >   4194304000 : 4051174743
		  60.12498172    427.8  [-28   1,   6  2  2 >    277921875 : 268435456
		  60.14769859    428.0  [ -1 -13,   3  4  1 >      3301375 : 3188646
		  60.21567134    428.5  [ 19   3,  -9 -1  0 >     14155776 : 13671875
		  60.2859858     429.0  [ 22 -10,   1 -3  0 >     20971520 : 20253807
		  60.41206283    429.9  [ -6   6,   0  0 -1 >          729 : 704
		  60.43477969    430.0  [ 21  -8,  -3  2 -2 >    102760448 : 99235125
		  60.48237729    430.4  [ -3  -7,  10 -2 -1 >      9765625 : 9430344
		  60.52073759    430.7  [-29  -6,  10  3  2 >  4.05303E+11 : 3.91379E+11
		  60.58871035    431.1  [ -9  10,  -2 -2  1 >       649539 : 627200
		  60.60845431    431.3  [-31   9,   9  1 -2 >  2.69104E+11 : 2.59846E+11
		  60.61142721    431.3  [ 18  -4,  -5  0  0 >       262144 : 253125
		  60.65902481    431.6  [ -6  -3,   8 -4  1 >      4296875 : 4148928
		  60.73750424    432.2  [-10  12,  -6  3 -1 >    182284263 : 176000000
		  60.78510183    432.5  [-34  13,   7 -1  0 >  1.24556E+11 : 1.20259E+11
		  60.78807474    432.6  [ 15   0,  -7 -2  2 >      3964928 : 3828125
		  60.8078187     432.7  [ -7  -1,   4  1 -1 >         4375 : 4224
		  60.8107916     432.7  [ 42 -14, -10  0  1 >  4.83785E+13 : 4.67087E+13
		  60.83053556    432.9  [ 20 -15,   1  3 -2 >   1798307840 : 1736217747
		  60.8583892     433.1  [ 18 -13,   3 -4  2 >   3964928000 : 3827969523
		  60.87579146    433.2  [ 13  15,  -8 -4 -2 >  1.17546E+11 : 1.13485E+11
		  60.93389572    433.6  [-35  15,   3  4 -2 >  4.30647E+12 : 4.15753E+12
		  60.98446622    434.0  [-10   3,   2 -1  1 >         7425 : 7168

		  61.00718309    434.1  [ 17 -11,  -1  1  0 >       917504 : 885735
		  61.13326011    435.0  [-11   5,  -2  4 -1 >       583443 : 563200
		  61.18383061    435.4  [ 14  -7,  -3 -1  2 >      1982464 : 1913625
		  61.20357457    435.5  [ -8  -8,   8  2 -1 >     19140625 : 18475776
		  61.27154733    436.0  [ 12   8,  -4 -3 -2 >     26873856 : 25939375
		  61.30990763    436.3  [-14   9,  -4  2  1 >     10609137 : 10240000
		  61.3326245     436.4  [ 13  -5,  -7  4  0 >     19668992 : 18984375
		  61.35750523    436.6  [-38  10,   9 -2  2 >  1.39549E+13 : 1.3469E+13
		  61.38022209    436.8  [-11  -4,   6  0  1 >       171875 : 165888
		  61.47091171    437.4  [ 36  -2,  -9 -3 -1 >  68719476736 : 66322265625
		  61.50629912    437.7  [-39  12,   5  3  0 >  5.69638E+11 : 5.49756E+11
		  61.50927202    437.7  [ 10  -1,  -9  2  2 >      6071296 : 5859375
		  61.57958648    438.2  [ 13 -14,   1  0  2 >      4956160 : 4782969
		  61.59698874    438.3  [  8  14, -10  0 -2 >   1224440064 : 1181640625
		  61.64458633    438.7  [-16  15,   3 -4 -1 >   1793613375 : 1730871296
		  61.6673032     438.8  [ 11   1,   0 -2 -2 >         6144 : 5929
		  61.7056635     439.1  [-15   2,   0  3  1 >        33957 : 32768
		  61.73761766    439.3  [ 14 -12,  10 -4 -2 >      1.6E+11 : 1.54395E+11
		  61.77597796    439.6  [-12 -11,  10  1  1 >    751953125 : 725594112
		  61.84395072    440.1  [  8   5,  -2 -4  0 >        62208 : 60025
		  61.86666758    440.2  [ 35  -9,  -5 -2 -1 >  34359738368 : 33153553125
		  61.90205499    440.5  [-40   5,   9  4  0 >  1.13954E+12 : 1.09951E+12
		  61.90502789    440.5  [  9  -8,  -5  3  2 >     21249536 : 20503125
		  61.99274461    441.1  [  7   7,  -6  1 -2 >      1959552 : 1890625

		  62.0403422     441.5  [-17   8,   7 -3 -1 >    512578125 : 494534656
		  62.04331511    441.5  [ 32  -5,  -7 -4  1 >  47244640256 : 45581484375
		  62.06305907    441.6  [ 10  -6,   4 -1 -2 >       640000 : 617463
		  62.07870251    441.7  [-43   9,   7  2  2 >  9.11723E+12 : 8.79609E+12
		  62.10141937    441.9  [-16  -5,   4  4  1 >     16506875 : 15925248
		  62.16939213    442.4  [  4  11,  -8 -1  0 >      2834352 : 2734375
		  62.23970659    442.9  [  7  -2,   2 -3  0 >         3200 : 3087
		  62.30078376    443.3  [  8 -15,  -1  4  2 >     74373376 : 71744535
		  62.34603965    443.6  [  1  15, -10 -3  2 >   3472435494 : 3349609375
		  62.36578362    443.8  [-21  14,   1  0 -1 >     23914845 : 23068672
		  62.38850048    443.9  [  6   0,  -2  2 -2 >         3136 : 3025
		  62.43907098    444.3  [ 31 -12,  -3 -3  1 >  23622320128 : 22785532875
		  62.45881494    444.4  [  9 -13,   8  0 -2 >    200000000 : 192913083
		  62.565148      445.2  [  3   4,  -4  0  0 >          648 : 625
		  62.58786487    445.4  [ 30 -10,  -7  2 -1 >  52613349376 : 50745234375
		  62.6127456     445.5  [-21   5,   9 -4  1 >   5220703125 : 5035261952
		  62.63546246    445.7  [  6  -9,   6 -2  0 >      1000000 : 964467
		  62.74179553    446.5  [  0   8,  -6 -2  2 >       793881 : 765625
		  62.76153949    446.6  [-22   7,   5  1 -1 >     47840625 : 46137344
		  62.76451239    446.6  [ 27  -6,  -9  0  1 >   1476395008 : 1423828125
		  62.78425635    446.8  [  5  -7,   2  3 -2 >       274400 : 264627
		  62.81210999    447.0  [  3  -5,   4 -4  2 >       605000 : 583443
		  62.89058941    447.5  [ -1  10, -10  3  0 >     20253807 : 19531250
		  62.93818701    447.9  [-25  11,   3 -1  1 >    243577125 : 234881024
		  62.96090387    448.0  [  2  -3,   0  1  0 >           28 : 27

		  63.0869809     448.9  [-26  13,  -1  4 -1 >   3827969523 : 3690987520
		  63.12190795    449.2  [ 52 -14,  -5 -4 -2 >   4.5036E+15 : 4.34235E+15
		  63.1375514     449.3  [ -1   1,  -2 -1  2 >          363 : 350
		  63.15729536    449.4  [-23   0,   9  2 -1 >     95703125 : 92274688
		  63.15789474    449.4  [1/19  0,   0  0  0 >                               1/19-edo (augmented-prime, chromatic-semitone)
		  63.16026826    449.4  [ 26 -13,  -5  1  1 >   5167382528 : 4982259375
		  63.18001222    449.6  [  4 -14,   6  4 -2 >    600250000 : 578739249
		  63.20786586    449.8  [  2 -12,   8 -3  2 >    189062500 : 182284263
		  63.28634528    450.3  [ -2   3,  -6  4  0 >        64827 : 62500
		  63.33394288    450.7  [-26   4,   7  0  1 >     69609375 : 67108864
		  63.35665974    450.8  [  1 -10,   4  2  0 >        61250 : 59049
		  63.4246325     451.3  [ 21   6,  -8 -3 -1 >   1528823808 : 1473828125
		  63.46299281    451.6  [ -5   7,  -8  2  2 >     12966723 : 12500000
		  63.53330727    452.1  [ -2  -6,   2  0  2 >         3025 : 2916
		  63.62102399    452.7  [ -4   9,   1 -2 -2 >        98415 : 94864
		  63.65938429    453.0  [-30  10,   1  3  1 >   1113959385 : 1073741824
		  63.79767151    454.0  [ -7  13,  -1 -4  0 >      1594323 : 1536640
		  63.82038837    454.1  [ 20  -1,  -4 -2 -1 >      1048576 : 1010625
		  63.84310524    454.3  [ 47 -15,  -7  0 -2 >  1.40737E+14 : 1.35642E+14
		  63.85577577    454.4  [-55  13,  10  4  0 >  3.73825E+16 : 3.60288E+16
		  63.85874868    454.4  [ -6   0,  -4  3  2 >        41503 : 40000
		  63.89070283    454.6  [ 23 -14,   6 -4 -1 >  1.31072E+11 : 1.26323E+11
		  63.92906314    454.9  [ -3 -13,   6  1  2 >     13234375 : 12754584
		  63.9464654     455.0  [ -8  15,  -5  1 -2 >    100442349 : 96800000
		  63.9970359     455.4  [ 17   3,  -6 -4  1 >     38928384 : 37515625

		  64.01677986    455.5  [ -5   2,   5 -1 -2 >        28125 : 27104
		  64.01975276    455.6  [ 44 -11,  -9 -2  0 >  1.75922E+13 : 1.69535E+13
		  64.05514016    455.8  [-31   3,   5  4  1 >   2228428125 : 2147483648
		  64.14582978    456.5  [ 16   5, -10  1 -1 >    111476736 : 107421875
		  64.19342738    456.8  [ -8   6,   3 -3  0 >        91125 : 87808
		  64.21614424    457.0  [ 19  -8,   0 -1 -1 >       524288 : 505197
		  64.25450455    457.2  [ -7  -7,   0  4  2 >       290521 : 279936
		  64.34222127    457.8  [ -9   8,  -1  2 -2 >       321489 : 309760
		  64.39279177    458.2  [ 16  -4,  -2 -3  1 >       720896 : 694575
		  64.41253573    458.3  [ -6  -5,   9  0 -2 >      1953125 : 1881792
		  64.51886879    459.1  [-12  12,  -3  0  0 >       531441 : 512000
		  64.54158565    459.3  [ 15  -2,  -6  2 -1 >      1605632 : 1546875
		  64.56646639    459.4  [-36  13,  10 -4  1 >  1.71265E+14 : 1.64995E+14
		  64.58918325    459.6  [ -9  -1,   7 -2  0 >        78125 : 75264
		  64.59215615    459.6  [ 40 -14,  -7 -3  2 >  1.33041E+14 : 1.28169E+14
		  64.61190011    459.8  [ 18 -15,   4  0 -1 >    163840000 : 157837977
		  64.71526027    460.5  [-37  15,   6  1 -1 >  1.56941E+12 : 1.51183E+12
		  64.71823318    460.5  [ 12   2,  -8  0  1 >       405504 : 390625
		  64.73797714    460.7  [-10   1,   3  3 -2 >       128625 : 123904
		  64.76583077    460.9  [-12   3,   5 -4  2 >     10209375 : 9834496
		  64.78854764    461.0  [ 15 -11,   2 -2  1 >      9011200 : 8680203
		  64.91462466    461.9  [-13   5,   1  1  0 >         8505 : 8192
		  64.93734152    462.1  [ 14  -9,  -2  3 -1 >      5619712 : 5412825

		  65.07562874    463.1  [ 37  -6,  -4 -4 -2 >  1.37439E+11 : 1.32369E+11
		  65.09127218    463.2  [-16   9,  -1 -1  2 >      2381643 : 2293760
		  65.11101614    463.3  [-38   8,  10  2 -1 >  3.13954E+12 : 3.02366E+12
		  65.11398905    463.3  [ 11  -5,  -4  1  1 >       157696 : 151875
		  65.13373301    463.5  [-11  -6,   7  4 -2 >    187578125 : 180652032
		  65.16158664    463.7  [-13  -4,   9 -3  2 >    236328125 : 227598336
		  65.24006607    464.2  [-17  11,  -5  4  0 >    425329947 : 409600000
		  65.28766367    464.6  [-41  12,   8  0  1 >  2.28354E+12 : 2.19902E+12
		  65.31038053    464.7  [-14  -2,   5  2  0 >       153125 : 147456
		  65.31335343    464.8  [ 35 -15,  -9  1  2 >  2.91027E+13 : 2.80252E+13
		  65.37835329    465.2  [  6  14,  -7 -3 -1 >    306110016 : 294765625
		  65.40107015    465.4  [ 33   0, -10 -1 -2 >   8589934592 : 8271484375
		  65.41671359    465.5  [-20  15,  -7  2  2 >  85074669603 : 81920000000
		  65.43943046    465.7  [  7   1, -10  4  1 >     10141824 : 9765625
		  65.4545455     465.8  [3/55  0,   0  0  0 >                                3/55-edo
		  65.47138461    465.9  [ 36 -13,   0 -3 -2 >  68719476736 : 66169187469
		  65.48702805    466.0  [-17   2,   3  0  2 >       136125 : 131072
		  65.50974492    466.2  [ 10 -12,   0  2  1 >       551936 : 531441
		  65.7061364     467.6  [-15  -9,   9  3  0 >    669921875 : 644972544
		  65.77410916    468.0  [  5   7,  -3 -2 -1 >        69984 : 67375
		  65.79682602    468.2  [ 32  -7,  -6  0 -2 >   4294967296 : 4134796875
		  65.81246947    468.3  [-21   8,  -3  3  2 >    272301183 : 262144000
		  65.84442362    468.5  [  8  -6,   7 -4 -1 >     20000000 : 19253619
		  65.88278393    468.8  [-18  -5,   7  1  2 >     66171875 : 63700992
		  65.95075668    469.3  [  2  11,  -5 -4  1 >      7794468 : 7503125
		  65.97050064    469.4  [-20  10,   6 -1 -2 >    922640625 : 888143872
		  65.97347355    469.5  [ 29  -3,  -8 -2  0 >    536870912 : 516796875

		  66.00886095    469.7  [-46  11,   6  4  1 >  7.31036E+13 : 7.03687E+13
		  66.09955057    470.4  [  1  13,  -9  1 -1 >     22320522 : 21484375
		  66.14714817    470.7  [-23  14,   4 -3  0 >   2989355625 : 2877292544
		  66.15012107    470.7  [ 26   1, -10 -4  2 >  24360517632 : 23447265625
		  66.16986503    470.9  [  4   0,   1 -1 -1 >           80 : 77
		  66.19258189    471.0  [ 31 -14,  -2  1