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310 7-limit linear temperaments in the u-v plane

🔗Gene Ward Smith <gwsmith@svpal.org>

2/11/2004 1:27:15 PM

Below I list the wedgie, u and v for the 310 temperaments on my list of
32000-odd possibles for which u>-2 and v>-2. Here if C is the
complexity and E is the error, I set x=ln(C) and y=ln(E). Then u=4-x-y
and v=12-4x-y. It would in my view be very useful to see a plot of this.

The first coordinate of the pair, which I have given as [u, v], is
unforgiving of error. The second is unforgiving of complexity. I could
have sorted the list according to either, but instead used
g = 2/3 u + 1/3 v. This is a goodness measure of the infamous log-flat
variety; we have g = 20/3 - 2x - y, so exp(-g) = K (E C^2) where K =
exp(-20/3).

[18, 27, 18, 1, -22, -34] [3.629230331, .575465612]
[37, 46, 75, -13, 15, 45] [3.406220860, -1.874710583]
[22, -5, 3, -59, -57, 21] [2.714891805, -.970728663]
[19, 19, 57, -14, 37, 79] [2.908019068, -1.601883155]
[4, -32, -15, -60, -35, 55] [2.722577966, -1.258540154]
[1, -8, 39, -15, 59, 113] [2.633249246, -1.257146728]
[1, 4, 10, 4, 13, 12] [1.005097996, 1.609665600]
[6, -7, -2, -25, -20, 15] [1.411065061, .2629785497]
[16, 2, 5, -34, -37, 6] [1.736866439, -.585529481]
[1, 4, -2, 4, -6, -16] [.363511386, 2.141744135]
[0, 5, 0, 8, 0, -14] [.152491081, 2.548674345]
[5, 1, 12, -10, 5, 25] [1.012524503, .7830372729]
[2, 3, 1, 0, -4, -6] [-.205382324, 3.133144155]
[0, 0, 3, 0, 5, 7] [-.589897843, 3.859219804]
[2, 1, 3, -3, -1, 4] [-.308576499, 3.236590508]
[2, -4, -4, -11, -12, 2] [.524469574, 1.498444023]
[7, 9, 13, -2, 1, 5] [.8521893702, .8383344292]
[6, 5, 22, -6, 18, 37] [1.398998141, -.2728789107]
[0, 2, 2, 3, 3, -1] [-.666311581, 3.828729871]
[0, 0, 2, 0, 3, 5] [-1.114694760, 4.583757375]
[4, 4, 4, -3, -5, -2] [.160875338, 1.953852436]
[1, -8, -14, -15, -25, -10] [1.080908962, .5026039173e-1]
[7, -3, 8, -21, -7, 27] [1.060730636, .7657743908e-1]
[2, 25, 13, 35, 15, -40] [1.630631612, -1.092923122]
[1, -1, 3, -4, 2, 10] [-.297159006, 2.756450471]
[1, 2, 1, 1, -1, -3] [-.933260604, 3.972326987]
[1, 1, 0, -1, -3, -3] [-1.067288298, 4.222744655]
[1, 2, 3, 1, 2, 1] [-.742852499, 3.554638596]
[5, 13, -17, 9, -41, -76] [1.646019337, -1.276833941]
[3, 0, 6, -7, 1, 14] [.113185821, 1.762756409]
[13, 14, 35, -8, 19, 42] [1.661188320, -1.374233657]
[1, -1, -2, -4, -6, -2] [-.540654341, 2.936334354]
[1, -1, 0, -4, -3, 3] [-.872793868, 3.560962162]
[3, 0, -6, -7, -18, -14] [.426316706, .940456192]
[1, 4, 3, 4, 2, -4] [-.374818183, 2.471764627]
[4, 2, 2, -6, -8, -1] [-.74238576e-1, 1.810219121]
[2, 1, -1, -3, -7, -5] [-.475239786, 2.576382050]
[2, 8, 1, 8, -4, -20] [.283811920, 1.034875923]
[4, -3, 2, -14, -8, 13] [.345586529, .859876933]
[10, 9, 7, -9, -17, -9] [.8297942242, -.2058606098]
[6, 5, 3, -6, -12, -7] [.322424097, .767227201]
[2, 1, 6, -3, 4, 11] [-.218755495, 1.845931213]
[1, 9, -2, 12, -6, -30] [.4535440254, .4454275914]
[2, 8, 8, 8, 7, -4] [.245867248, .811824633]
[0, 0, 7, 0, 11, 16] [-.248247752, 1.739146134]
[9, 5, -3, -13, -30, -21] [.8424961778, -.4842422682]
[1, -3, -4, -7, -9, -1] [-.280612685, 1.704441303]
[6, 10, 10, 2, -1, -5] [.287044794, .548744901]
[3, 17, -1, 20, -10, -50] [.8955276833, -.7518398037]
[12, 34, 20, 26, -2, -49] [1.462830432, -1.914845007]
[24, 32, 40, -5, -4, 3] [1.483539340, -1.995207689]
[0, 0, 4, 0, 6, 9] [-.922056519, 2.805750119]
[15, -2, -5, -38, -50, -6] [1.191031885, -1.439618129]
[8, 18, 11, 10, -5, -25] [.8374157707, -.7456108813]
[3, 12, -1, 12, -10, -36] [.5552853406, -.1895850224]
[0, 0, 5, 0, 8, 12] [-.677810269, 2.251962805]
[0, 12, 24, 19, 38, 22] [1.055447382, -1.226619823]
[0, 0, 12, 0, 19, 28] [.178510293, .520800106]
[1, 4, -9, 4, -17, -32] [.3364294610, .1379787620]
[3, -12, -30, -26, -56, -36] [1.323782432, -1.954253378]
[2, 6, 6, 5, 4, -3] [-.291711764, 1.217976987]
[2, -1, 1, -6, -4, 5] [-.787640236, 2.183807521]
[8, 13, 23, 2, 14, 17] [.7514403927, -.9215592083]
[2, -4, -16, -11, -31, -26] [.6436652400, -.7139691630]
[2, -2, 1, -8, -4, 8] [-.562262654, 1.696035879]
[3, 5, 9, 1, 6, 7] [-.181870640, .926592561]
[2, 1, -4, -3, -12, -12] [-.349909310, 1.240369407]
[3, -24, -1, -45, -10, 65] [1.109082908, -1.726264787]
[1, -1, 1, -4, -1, 5] [-1.257426652, 2.987275426]
[12, -2, 20, -31, -2, 52] [.9685827999, -1.466539439]
[11, 13, 17, -5, -4, 3] [.5451289967, -.6327346883]
[3, 5, -6, 1, -18, -28] [.176167209, .93101647e-1]
[12, 22, -4, 7, -40, -71] [1.168736181, -1.916947188]
[6, 0, 0, -14, -17, 0] [-.144103110, .552331535]
[11, 18, 5, 3, -23, -39] [.7393125860, -1.304148322]
[2, -2, -2, -8, -9, 1] [-.648390366, 1.435403570]
[17, 6, 15, -30, -24, 18] [.9225671470, -1.740042662]
[4, 16, 9, 16, 3, -24] [.4104041316, -.7691098524]
[4, 21, -3, 24, -16, -66] [.8279921578, -1.650503107]
[1, -3, -2, -7, -6, 4] [-.796717686, 1.588083020]
[3, 5, 1, 1, -7, -12] [-.580823747, 1.147950612]
[12, 10, -9, -12, -48, -49] [.9283293931, -1.875845700]
[8, 6, 6, -9, -13, -3] [.68663257e-1, -.172409567]
[5, -11, -12, -29, -33, 3] [.6475907742, -1.340799742]
[6, -2, -2, -17, -20, 1] [-.2200063e-2, -.50795881e-1]
[3, 12, 11, 12, 9, -8] [.1733958065, -.4114685585]
[1, 4, 5, 4, 5, 0] [-.842313783, 1.614549170]
[6, 0, 3, -14, -12, 7] [-.186135940, .253731850]
[2, -9, -4, -19, -12, 16] [.110765143, -.367098214]
[9, 10, -3, -5, -30, -35] [.4841383122, -1.114817471]
[3, 2, 4, -4, -2, 4] [-.878126390, 1.586446158]
[4, -8, 14, -22, 11, 55] [.5972396400, -1.382584001]
[1, -8, -2, -15, -6, 18] [-.167272250, .143772795]
[6, 10, 3, 2, -12, -21] [.4101414e-2, -.242117955]
[13, 19, 23, 0, 0, 0] [.4556158489, -1.149903551]
[1, -3, 5, -7, 5, 20] [-.474868918, .678598615]
[5, 3, 7, -7, -3, 8] [-.383860087, .493175395]
[8, 1, 18, -17, 6, 39] [.4064523106, -1.107722833]
[3, 0, -3, -7, -13, -7] [-.584010116, .871684734]
[12, 10, 25, -12, 6, 30] [.6281053654, -1.574944233]
[2, 3, 6, 0, 4, 6] [-.906409329, 1.473314402]
[3, 0, 9, -7, 6, 21] [-.333176615, .321368661]
[3, -7, -8, -18, -21, 1] [.71689763e-1, -.518553272]
[1, -3, 3, -7, 2, 15] [-.762855535, 1.135262755]
[1, -1, -5, -4, -11, -9] [-.745754672, 1.098651594]
[6, -12, 10, -33, -1, 57] [.6101417586, -1.638299992]
[2, -6, 1, -14, -4, 19] [-.348997990, .241608334]
[1, -13, -2, -23, -6, 32] [.1433815335, -.7600710565]
[3, -5, -6, -15, -18, 0] [-.167754823, -.149512117]
[1, 6, 5, 7, 5, -5] [-.655893330, .823648016]
[2, 8, -11, 8, -23, -48] [.3204117006, -1.129079582]
[5, 8, 2, 1, -11, -18] [-.285071625, .62437310e-1]
[0, 0, 19, 0, 30, 44] [.1665485838, -.8594312212]
[2, 5, 3, 3, -1, -7] [-.961974750, 1.377881885]
[5, 1, -7, -10, -25, -19] [.826121e-3, -.556383277]
[5, 8, 14, 1, 8, 10] [-.142165912, -.304220656]
[7, 9, 32, -2, 31, 49] [.6797859680, -1.962055240]
[8, 1, -13, -17, -43, -33] [.5073592316, -1.641189793]
[3, 5, 16, 1, 17, 23] [-.23980789e-1, -.587567616]
[11, -6, 10, -35, -15, 40] [.5818775046, -1.825094348]
[4, 2, 9, -6, 3, 15] [-.516138894, .237011021]
[3, 2, -1, -4, -10, -8] [-.903474981, .983810996]
[3, 7, -1, 4, -10, -22] [-.467662952, .84355164e-1]
[4, -8, -20, -22, -43, -24] [.5251916022, -1.910857084]
[14, 11, 9, -15, -25, -10] [.3765010353, -1.620633894]
[4, 4, 0, -3, -11, -11] [-.737971277, .597488784]
[0, 0, 5, 0, 8, 11] [-1.299404555, 1.716508494]
[8, -11, -6, -36, -32, 17] [.4773026098, -1.873039923]
[4, 9, 26, 5, 30, 35] [.3885253755, -1.726927868]
[4, 9, 19, 5, 19, 19] [.938231575e-1, -1.139670180]
[5, -4, -10, -18, -30, -12] [.903299045e-1, -1.171003260]
[2, 13, 1, 16, -4, -34] [-.129567301, -.746767354]
[6, 7, 5, -3, -9, -8] [-.481343559, -.93481826e-1]
[1, 7, 3, 9, 2, -13] [-.760448506, .453124399]
[0, 0, 8, 0, 13, 19] [-.867601868, .647228967]
[3, 12, 18, 12, 20, 8] [.730840107e-1, -1.261518978]
[0, 5, 10, 8, 16, 9] [-.492128352, -.155852317]
[11, 6, 15, -16, -7, 18] [.1122979282, -1.365027872]
[1, -6, 3, -12, 2, 24] [-.594540504, .32941526e-1]
[9, -2, 14, -24, -3, 38] [.1476387417, -1.454725281]
[6, 0, 15, -14, 7, 35] [-.67879467e-1, -1.036328496]
[4, 2, 5, -6, -3, 6] [-.930494064, .687971897]
[0, 5, -5, 8, -8, -26] [-.582128162, -.10439184e-1]
[4, 9, -8, 5, -24, -44] [.527903825e-1, -1.321161350]
[2, -4, 8, -11, 7, 30] [-.366759238, -.490652025]
[6, -12, -2, -33, -20, 29] [.2396727699, -1.711253700]
[4, 9, -15, 5, -35, -60] [.3295592714, -1.891195103]
[10, 2, 2, -20, -25, -1] [-.135958369, -.983381730]
[4, 2, -1, -6, -13, -8] [-.840404798, .399233499]
[9, 0, 9, -21, -11, 21] [-.88241812e-1, -1.117777876]
[3, -19, -1, -37, -10, 51] [.3203051393, -1.938482989]
[2, -6, -6, -14, -15, 3] [-.490643293, -.324972878]
[2, -11, 1, -22, -4, 33] [-.208605058, -.928487618]
[4, 7, 2, 2, -8, -15] [-.729973553, .105553053]
[10, 14, 14, -1, -6, -7] [-.130239572, -1.120392559]
[6, 5, 7, -6, -6, 2] [-.669182904, -.52572019e-1]
[10, 2, 5, -20, -20, 6] [-.144935409, -1.102210677]
[13, 9, 1, -16, -35, -23] [.2040258001, -1.811428592]
[4, 4, -8, -3, -24, -30] [-.250244066, -.905880539]
[0, 12, 12, 19, 19, -6] [-.153602558, -1.110036858]
[4, 11, 2, 8, -8, -26] [-.392976455, -.698339145]
[0, 0, 10, 0, 16, 23] [-.798950098, .94142260e-1]
[0, 0, 9, 0, 14, 21] [-.910594332, .312296123]
[10, 7, 5, -12, -20, -8] [-.171649456, -1.172003014]
[0, 5, 5, 8, 8, -2] [-1.069386426, .613463954]
[4, 4, 16, -3, 14, 26] [-.293166681, -.946892724]
[3, -7, 11, -18, 9, 45] [-.613254898e-1, -1.420879511]
[5, -6, 7, -21, -3, 33] [-.203779439, -1.141852673]
[4, 14, 14, 13, 11, -7] [-.159713909, -1.238289909]
[4, -8, 2, -22, -8, 27] [-.264479353, -1.033889617]
[9, -7, 4, -32, -19, 29] [.1269925897, -1.819072876]
[2, -4, 18, -11, 23, 53] [.546965533e-1, -1.683034542]
[3, 10, 9, 9, 6, -7] [-.543080986, -.518248827]
[1, 9, 3, 12, 2, -18] [-.712851570, -.179354638]
[5, -4, 2, -18, -11, 16] [-.469100176, -.673676890]
[3, -2, 1, -10, -7, 8] [-1.050697330, .484233616]
[2, -4, 6, -11, 4, 25] [-.655813167, -.314681978]
[4, -1, 9, -11, 3, 24] [-.608340692, -.417591882]
[6, 3, 5, -9, -9, 3] [-.746637222, -.147651739]
[5, 1, -10, -10, -30, -26] [-.200994740, -1.276223819]
[6, 3, 1, -9, -15, -6] [-.729419044, -.226572839]
[9, 0, -3, -21, -30, -7] [-.221482197, -1.248814995]
[7, 4, 10, -10, -4, 12] [-.513527003, -.669199578]
[9, 15, 19, 3, 5, 2] [-.181219698, -1.336445983]
[9, 17, 14, 6, -3, -15] [-.128303853, -1.481158664]
[1, 4, -21, 4, -36, -60] [.934456477e-1, -1.926243230]
[2, 8, 13, 8, 15, 8] [-.469057709, -.807412748]
[8, 8, 4, -6, -16, -13] [-.407897003, -.931833274]
[7, 2, 15, -13, 4, 29] [-.279250412, -1.190689962]
[5, 18, 17, 17, 13, -11] [.146447901e-1, -1.781586163]
[7, 4, -2, -10, -23, -16] [-.407040381, -.940462937]
[6, 12, 12, 5, 2, -6] [-.485397722, -.795045536]
[2, 13, -4, 16, -12, -46] [-.149758098, -1.475182572]
[8, 13, 4, 2, -16, -27] [-.245101239, -1.284705873]
[5, 20, 0, 20, -14, -56] [.1050152716, -1.990665292]
[1, -6, -2, -12, -6, 12] [-.925443902, .55637649e-1]
[3, -3, 1, -12, -7, 11] [-.957172730, .116395575]
[13, 14, 16, -8, -11, -2] [-.586887779e-1, -1.701323570]
[5, 1, 9, -10, 0, 18] [-.775406912, -.296839099]
[3, 12, 6, 12, 1, -20] [-.531950950, -.802817614]
[0, 0, 15, 0, 24, 35] [-.513636132, -.851260538]
[4, 16, 21, 16, 22, 4] [-.78596493e-2, -1.873118974]
[4, 4, 12, -3, 8, 17] [-.679180114, -.540549884]
[8, -1, 4, -20, -16, 12] [-.444783364, -1.078038217]
[5, 6, -3, -2, -19, -24] [-.617424790, -.801516088]
[0, 10, 10, 16, 16, -5] [-.542587957, -.967067536]
[1, 14, -2, 20, -6, -44] [-.312833355, -1.432919432]
[6, 5, -12, -6, -36, -42] [-.950792365e-1, -1.912639830]
[1, -3, -11, -7, -20, -17] [-.673850885, -.767068718]
[1, 4, 22, 4, 32, 40] [-.1693814110, -1.778259566]
[0, 7, 7, 11, 11, -3] [-.943824367, -.252435548]
[5, 11, 7, 6, -3, -15] [-.680975735, -.803381348]
[2, 11, 6, 13, 4, -17] [-.688064282, -.847196060]
[0, 7, 14, 11, 22, 13] [-.524527117, -1.183832259]
[12, 0, 3, -28, -29, 7] [-.249740543, -1.763772806]
[3, 5, -13, 1, -29, -44] [-.346032864, -1.648490772]
[12, 10, 10, -12, -18, -5] [-.291080286, -1.763755419]
[2, -2, 4, -8, 1, 15] [-1.347075171, .323104394]
[9, 15, 4, 3, -19, -33] [-.295423014, -1.793259243]
[8, 8, 16, -6, 3, 15] [-.533863321, -1.335099102]
[3, 0, 21, -7, 25, 49] [-.273424726, -1.858509536]
[2, 6, -4, 5, -12, -26] [-.889032202, -.655693165]
[5, -9, -10, -26, -30, 2] [-.274449954, -1.895682348]
[0, 0, 22, 0, 35, 51] [-.326185152, -1.800558870]
[10, -5, 0, -31, -28, 14] [-.255187679, -1.950767071]
[7, 2, 18, -13, 9, 36] [-.379591474, -1.755590519]
[5, 6, 15, -2, 10, 18] [-.696144582, -1.130503207]
[0, 7, -7, 11, -11, -36] [-.709612161, -1.118256842]
[3, 0, -18, -7, -37, -42] [-.295882202, -1.948339436]
[7, 9, -6, -2, -29, -39] [-.358001449, -1.825655743]
[4, -1, 6, -11, -2, 17] [-1.104659762, -.335771190]
[9, 7, 11, -10, -8, 6] [-.622976626, -1.301922259]
[9, -2, -5, -24, -33, -6] [-.385338344, -1.815095725]
[8, 18, 18, 10, 6, -9] [-.338613285, -1.953887409]
[0, 5, 15, 8, 24, 21] [-.640548326, -1.358909077]
[0, 3, 6, 5, 10, 6] [-1.480169567, .298132908]
[0, 10, -5, 16, -8, -40] [-.645134209, -1.377252546]
[3, -14, -1, -29, -10, 37] [-.376708599, -1.921119003]
[3, 0, -9, -7, -23, -21] [-.841397568, -1.042826585]
[5, 3, -2, -7, -17, -13] [-1.022478254, -.688601470]
[2, -16, 1, -30, -4, 47] [-.368807442, -1.997698949]
[4, 6, 11, 0, 6, 9] [-1.115853383, -.508740081]
[2, -4, -6, -11, -15, -3] [-1.100447199, -.540671689]
[7, 11, 3, 1, -15, -24] [-.719265915, -1.313960440]
[8, -4, -4, -25, -29, 2] [-.512686428, -1.760131799]
[1, -3, 12, -7, 16, 36] [-.752771862, -1.290666263]
[10, 14, 22, -1, 7, 12] [-.426849901, -1.943606890]
[3, 10, -6, 9, -18, -42] [-.544035928, -1.716057489]
[2, -14, -4, -27, -12, 30] [-.463119391, -1.915165091]
[10, 12, 12, -4, -9, -6] [-.630242442, -1.584551407]
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