The following is a list of normalized levels produced by a velocity “Level/Vel” of 32, offset of 0, and curve of 3:

[code type=markup]0.00006109667016452, // 1 0.00787401574803150 Factor: 128.87798511487434894
0.00024421929252065, // 2 0.01574803149606299 Factor: 64.48315910476921431
0.00053246166518723, // 3 0.02362204724409449 Factor: 44.36384586632738092
0.00097654239380771, // 4 0.03149606299212598 Factor: 32.25263254503197174
0.00150582368438364, // 5 0.03937007874015748 Factor: 26.14521152008066807
0.00222391879398856, // 6 0.04724409448818898 Factor: 21.24362392003423139
0.00301164736876728, // 7 0.05511811023622047 Factor: 18.30164806405646871
0.00390616957523084, // 8 0.06299212598425197 Factor: 16.12631627251598587
0.00485040605851320, // 9 0.07086614173228346 Factor: 14.61035238645692047
0.00602346212567200, // 10 0.07874015748031496 Factor: 13.07224248073617723
0.00748057586206146, // 11 0.08661417322834646 Factor: 11.57854352732648096
0.00889584256409166, // 12 0.09448818897637795 Factor: 10.62161209527048022
0.01013183657092679, // 13 0.10236220472440945 Factor: 10.10302564671609815
0.01204675686320656, // 14 0.11023622047244094 Factor: 9.15069688250507696
0.01372147517826418, // 15 0.11811023622047244 Factor: 8.60769229882568787
0.01562501307719824, // 16 0.12598425196850394 Factor: 8.06298537774372903
0.01779168512818332, // 17 0.13385826771653545 Factor: 7.52364190081659068
0.01940162423405281, // 18 0.14173228346456693 Factor: 7.30517619322846024
0.02209473197727739, // 19 0.14960629921259844 Factor: 6.77112984970608167
0.02409368111455057, // 20 0.15748031496062992 Factor: 6.53616664933466751
0.02744295035652836, // 21 0.16535433070866143 Factor: 6.02538460917798258
0.02992247083638329, // 22 0.17322834645669291 Factor: 5.78923937812185496
0.03263851075443674, // 23 0.18110236220472442 Factor: 5.54873240287491054
0.03558353764450409, // 24 0.18897637795275590 Factor: 5.31078106512952353
0.03880308107996817, // 25 0.19685039370078741 Factor: 5.07306090707343582
0.04232794047811744, // 26 0.20472440944881889 Factor: 4.83662581113901968
0.04418946395455479, // 27 0.21259842519685040 Factor: 4.81106594584379454
0.04818719484096369, // 28 0.22047244094488189 Factor: 4.57533254783819388
0.05255133836022229, // 29 0.22834645669291340 Factor: 4.34520725481191228
0.05488590071305673, // 30 0.23622047244094488 Factor: 4.30384614941284394
0.05984494167276657, // 31 0.24409448818897639 Factor: 4.07878228913130680
0.06250005230879295, // 32 0.25196850393700787 Factor: 4.03149268887186452
0.06814571940826954, // 33 0.25984251968503935 Factor: 3.81304243232491658
0.07116690790087074, // 34 0.26771653543307089 Factor: 3.76181210241670927
0.07431028973380097, // 35 0.27559055118110237 Factor: 3.70864589773960418
0.08105469256741432, // 36 0.28346456692913385 Factor: 3.49720118540172642
0.08465571356809742, // 37 0.29133858267716534 Factor: 3.44145209339959468
0.08837892790910958, // 38 0.29921259842519687 Factor: 3.38556492485304084
0.09231572951349140, // 39 0.30708661417322836 Factor: 3.32648201765387608
0.09637455707006483, // 40 0.31496062992125984 Factor: 3.26808900083744858
0.10510250933230714, // 41 0.32283464566929132 Factor: 3.07161691685753269
0.10977180142611345, // 42 0.33070866141732286 Factor: 3.01269230458899129
0.11462404875413847, // 43 0.33858267716535434 Factor: 2.95385375796307237
0.11968988334553314, // 44 0.34645669291338582 Factor: 2.89461968906092748
0.12499993722944847, // 45 0.35433070866141730 Factor: 2.83464709275022964
0.13055421040588444, // 46 0.36220472440944884 Factor: 2.77436264432512925
0.13629143881653907, // 47 0.37007874015748032 Factor: 2.71534839877683476
0.14233398318987892, // 48 0.37795275590551181 Factor: 2.65539365536695859
0.14862057946760193, // 49 0.38582677165354329 Factor: 2.59605212841772248
0.15521232431987270, // 50 0.39370078740157483 Factor: 2.53653045353671791
0.16210938513482864, // 51 0.40157480314960631 Factor: 2.47718417299288962
0.16931142713619485, // 52 0.40944881889763779 Factor: 2.41831768725376905
0.17675785581821915, // 53 0.41732283464566927 Factor: 2.36098606601593630
0.17675785581821915, // 54 0.42519685039370081 Factor: 2.40553297292189727
0.18463129163884537, // 55 0.43307086614173229 Factor: 2.34559842103502181
0.19274894675199222, // 56 0.44094488188976377 Factor: 2.28766428725093007
0.20129394378001583, // 57 0.44881889763779526 Factor: 2.22966915551263245
0.21020501866461427, // 58 0.45669291338582679 Factor: 2.17260708753337717
0.21020501866461427, // 59 0.46456692913385828 Factor: 2.21006583042188343
0.21954343546408947, // 60 0.47244094488188976 Factor: 2.15192471541316710
0.22924809750827693, // 61 0.48031496062992124 Factor: 2.09517533995055105
0.23937993407920372, // 62 0.48818897637795278 Factor: 2.03938971850675488
0.25000004184703434, // 63 0.49606299212598426 Factor: 1.98425163636375168
0.25000004184703434, // 64 0.50393700787401574 Factor: 2.01574769408381105
0.26110842081176888, // 65 0.51181102362204722 Factor: 1.96014752044710194
0.27258304502121561, // 66 0.51968503937007871 Factor: 1.90652004540352360
0.27258304502121561, // 67 0.52755905511811019 Factor: 1.93540671275812248
0.28466796637975783, // 68 0.53543307086614178 Factor: 1.88090383921826243
0.29724115893520386, // 69 0.54330708661417326 Factor: 1.82783262102880495
0.29724115893520386, // 70 0.55118110236220474 Factor: 1.85432294886980209
0.31042481602788285, // 71 0.55905511811023623 Factor: 1.80093565090498764
0.32421877026965729, // 72 0.56692913385826771 Factor: 1.74860059270086321
0.32421877026965729, // 73 0.57480314960629919 Factor: 1.77288671204393067
0.33862302166052716, // 74 0.58267716535433067 Factor: 1.72072519611047037
0.35351554424830089, // 75 0.59055118110236215 Factor: 1.67050979995259574
0.35351554424830089, // 76 0.59842519685039375 Factor: 1.69278326395196399
0.36926275066582814, // 77 0.60629921259842523 Factor: 1.64191815043675526
0.36926275066582814, // 78 0.61417322834645671 Factor: 1.66324176278008973
0.38549806089212185, // 79 0.62204724409448819 Factor: 1.61361964481726017
0.40258788756003167, // 80 0.62992125984251968 Factor: 1.56468010913167199
0.40258788756003167, // 81 0.63779527559055116 Factor: 1.58423861049581793
0.42041020471736595, // 82 0.64566929133858264 Factor: 1.53580784694000050
0.42041020471736595, // 83 0.65354330708661412 Factor: 1.55453721092707364
0.43908687092817894, // 84 0.66141732283464572 Factor: 1.50634730078921719
0.43908687092817894, // 85 0.66929133858267720 Factor: 1.52428000675099340
0.45849602762841640, // 86 0.67716535433070868 Factor: 1.47692741817931439
0.45849602762841640, // 87 0.68503937007874016 Factor: 1.49410099280930653
0.47875970077026997, // 88 0.69291338582677164 Factor: 1.44730933850938737
0.49999991630593127, // 89 0.70078740157480313 Factor: 1.40157503775664138
0.49999991630593127, // 90 0.70866141732283461 Factor: 1.41732307188873841
0.52221684162353776, // 91 0.71653543307086609 Factor: 1.37210326431297136
0.52221684162353776, // 92 0.72440944881889768 Factor: 1.38718132216256462
0.54516592265429376, // 93 0.73228346456692917 Factor: 1.34323044441516259
0.54516592265429376, // 94 0.74015748031496065 Factor: 1.35767378252715365
0.56933593275951566, // 95 0.74803149606299213 Factor: 1.31386665239510969
0.56933593275951566, // 96 0.75590551181102361 Factor: 1.32769682768347930
0.59448231787040773, // 97 0.76377952755905509 Factor: 1.28478090028836278
0.59448231787040773, // 98 0.77165354330708658 Factor: 1.29802606420886124
0.59448231787040773, // 99 0.77952755905511806 Factor: 1.31127122812935992
0.62084963205576571, // 100 0.78740157480314965 Factor: 1.26826454289083634
0.62084963205576571, // 101 0.79527559055118113 Factor: 1.28094718831974475
0.64843754053931457, // 102 0.80314960629921262 Factor: 1.23859208649644481
0.64843754053931457, // 103 0.81102362204724410 Factor: 1.25073514616797854
0.67724604332105431, // 104 0.81889763779527558 Factor: 1.20915824591546572
0.67724604332105431, // 105 0.82677165354330706 Factor: 1.22078476751080678
0.70703125588473925, // 106 0.83464566929133854 Factor: 1.18049331248716838
0.70703125588473925, // 107 0.84251968503937003 Factor: 1.19163004185025478
0.70703125588473925, // 108 0.85039370078740162 Factor: 1.20276677121334141
0.73852533394351894, // 109 0.85826771653543310 Factor: 1.16213713611220792
0.73852533394351894, // 110 0.86614173228346458 Factor: 1.17279894470039325
0.77099612178424370, // 111 0.87401574803149606 Factor: 1.13361886439693582
0.77099612178424370, // 112 0.88188976377952755 Factor: 1.14383164695907058
0.80517577512006333, // 113 0.88976377952755903 Factor: 1.10505532707424337
0.80517577512006333, // 114 0.89763779527559051 Factor: 1.11483457775631623
0.80517577512006333, // 115 0.90551181102362199 Factor: 1.12461382843838931
0.84082024204659445, // 116 0.91338582677165359 Factor: 1.08630332750842351
0.84082024204659445, // 117 0.92125984251968507 Factor: 1.09566801136625469
0.87817374185635788, // 118 0.92913385826771655 Factor: 1.05802965174480712
0.87817374185635788, // 119 0.93700787401574803 Factor: 1.06699600472569545
0.87817374185635788, // 120 0.94488188976377951 Factor: 1.07596235770658355
0.91699205525683281, // 121 0.95275590551181100 Factor: 1.03900126511451774
0.91699205525683281, // 122 0.96062992125984248 Factor: 1.04758805242951358
0.95751940154053994, // 123 0.96850393700787396 Factor: 1.01147186725371951
0.95751940154053994, // 124 0.97637795275590555 Factor: 1.01969521576797750
0.95751940154053994, // 125 0.98425196850393704 Factor: 1.02791856428223527
1.00000000000000000, // 126 0.99212598425196852 Factor: 0.99212598425196852
1.00000000000000000, // 127 1.00000000000000000 Factor: 1.00000000000000000[/code]
Only the left-most value is relevant here, and the integer following “// ” is the velocity that produced the given level.

Why are so many levels simply duplicated? This same table is used regardless of the offset and Level/Vel settings; if offset is 1 then simply move all the levels up 1 line in the list, remove the top 0.00006109667016452, and insert another 1.00000000000000000 at the bottom. If Level/Vel is 33, simply remove the 0.00006109667016452 at the top (note velocity 1 produces no sound).

So basically the Yamaha MONTAGE has this internal table of velocity mappings that is referenced when you press a key.
Why do any of the levels have to be duplicates? Why wouldn’t one just use 127 unique values? This is such a waste of velocity levels.

The levels after the velocity integer (0.00787401574803150 on the first line) are the levels I actually want it to generate.
These levels are simply a linear mapping from 1/127 (= 0.00787401574803150) to 127/127(= 1.00000000000000000).

1. Can we get an update that actually uses all 127 levels, regardless of the curve? All curves have these same redundancies, wasting a lot of the available note-velocity resolution.
2. Can we get an update that provides a linear curve? These numbers were generated using curve #3, which is the roundest curve on the system, yet in reality it is just a slightly linearized exponential curve.
   
   Curve #2, which is displayed as a linear image on the machine, is actually a completely exponential curve, except with a bunch of duplicate values as above.
   Can we get curve #5, such that it actually is truly linear (the values in my table can be used as a reference)?

   Thank you,
   Anne