Inharmonicity table for <Hurdy> low string

  • Fundamental frequency:= 55 Hz (A). midi note: 33 (force 230 N)
  • Calculated for a string factor B= 1.442045E-3
  • Formula: f(n) = n .f(0). SQR( 1 + B.n^2)
  • with: B = E.mu.(Pi.r)^2 / (4.p.T.L^2)
  • E= Youngs modulus for the string material (2E11 Pa)
  • mu = mass per length (0.0129 kg/m)
  • r = string radius 0.75mm (diameter 1.5mm)
  • p = density of the string material (7.3kg/l)
  • T = string tension in Newton (calculated using Taylors law with measured frequency)
  • L = string length in meter (1.215m)
Partial nr.: 1              real partial note: 33       Plato-Harmonic: 33          Dif= 0  cent    Dif= 0 Hz
Partial nr.: 2              real partial note: 45.05    Plato-Harmonic: 45          Dif= 5  cent    Dif= .32 Hz
Partial nr.: 3              real partial note: 52.13    Plato-Harmonic: 52.02       Dif= 11  cent    Dif= 1.07 Hz
Partial nr.: 4              real partial note: 57.2     Plato-Harmonic: 57          Dif= 20  cent    Dif= 2.52 Hz
Partial nr.: 5              real partial note: 61.17    Plato-Harmonic: 60.86       Dif= 31  cent    Dif= 4.91 Hz
Partial nr.: 6              real partial note: 64.46    Plato-Harmonic: 64.02       Dif= 44  cent    Dif= 8.46 Hz
Partial nr.: 7              real partial note: 67.28    Plato-Harmonic: 66.69       Dif= 59  cent    Dif= 13.37 Hz
Partial nr.: 8              real partial note: 69.76    Plato-Harmonic: 69          Dif= 76  cent    Dif= 19.86 Hz
Partial nr.: 9              real partial note: 72       Plato-Harmonic: 71.04       Dif= 96  cent    Dif= 28.11 Hz
Partial nr.: 10             real partial note: 74.03    Plato-Harmonic: 72.86       Dif= 117  cent    Dif= 38.32 Hz
Partial nr.: 11             real partial note: 75.91    Plato-Harmonic: 74.51       Dif= 139  cent    Dif= 50.66 Hz
Partial nr.: 12             real partial note: 77.65    Plato-Harmonic: 76.02       Dif= 163  cent    Dif= 65.3 Hz
Partial nr.: 13             real partial note: 79.29    Plato-Harmonic: 77.41       Dif= 189  cent    Dif= 82.38 Hz
Partial nr.: 14             real partial note: 80.84    Plato-Harmonic: 78.69       Dif= 215  cent    Dif= 102.05 Hz
Partial nr.: 15             real partial note: 82.32    Plato-Harmonic: 79.88       Dif= 243  cent    Dif= 124.45 Hz
Partial nr.: 16             real partial note: 83.72    Plato-Harmonic: 81          Dif= 272  cent    Dif= 149.7 Hz
Partial nr.: 17             real partial note: 85.07    Plato-Harmonic: 82.05       Dif= 302  cent    Dif= 177.91 Hz
Partial nr.: 18             real partial note: 86.36    Plato-Harmonic: 83.04       Dif= 332  cent    Dif= 209.18 Hz
Partial nr.: 19             real partial note: 87.6     Plato-Harmonic: 83.98       Dif= 363  cent    Dif= 243.61 Hz
Partial nr.: 20             real partial note: 88.81    Plato-Harmonic: 84.86       Dif= 394  cent    Dif= 281.29 Hz
Partial nr.: 21             real partial note: 89.97    Plato-Harmonic: 85.71       Dif= 426  cent    Dif= 322.29 Hz
Partial nr.: 22             real partial note: 91.1     Plato-Harmonic: 86.51       Dif= 458  cent    Dif= 366.7 Hz
Partial nr.: 23             real partial note: 92.19    Plato-Harmonic: 87.28       Dif= 491  cent    Dif= 414.57 Hz
Partial nr.: 24             real partial note: 93.25    Plato-Harmonic: 88.02       Dif= 523  cent    Dif= 465.96 Hz
Partial nr.: 25             real partial note: 94.29    Plato-Harmonic: 88.73       Dif= 556  cent    Dif= 520.94 Hz
Partial nr.: 26             real partial note: 95.3     Plato-Harmonic: 89.41       Dif= 589  cent    Dif= 579.56 Hz
Partial nr.: 27             real partial note: 96.28    Plato-Harmonic: 90.06       Dif= 622  cent    Dif= 641.84 Hz
Partial nr.: 28             real partial note: 97.24    Plato-Harmonic: 90.69       Dif= 655  cent    Dif= 707.85 Hz
Partial nr.: 29             real partial note: 98.17    Plato-Harmonic: 91.3        Dif= 688  cent    Dif= 777.62 Hz
Partial nr.: 30             real partial note: 99.08    Plato-Harmonic: 91.88       Dif= 720  cent    Dif= 851.17 Hz
Partial nr.: 31             real partial note: 99.98    Plato-Harmonic: 92.45       Dif= 753  cent    Dif= 928.55 Hz
Partial nr.: 32             real partial note: 100.85   Plato-Harmonic: 93          Dif= 785  cent    Dif= 1009.78 Hz
Partial nr.: 33             real partial note: 101.7    Plato-Harmonic: 93.53       Dif= 817  cent    Dif= 1094.89 Hz
Partial nr.: 34             real partial note: 102.54   Plato-Harmonic: 94.05       Dif= 849  cent    Dif= 1183.89 Hz
Partial nr.: 35             real partial note: 103.36   Plato-Harmonic: 94.55       Dif= 881  cent    Dif= 1276.82 Hz
Partial nr.: 36             real partial note: 104.16   Plato-Harmonic: 95.04       Dif= 912  cent    Dif= 1373.68 Hz
Partial nr.: 37             real partial note: 104.95   Plato-Harmonic: 95.51       Dif= 943  cent    Dif= 1474.51 Hz
Partial nr.: 38             real partial note: 105.72   Plato-Harmonic: 95.98       Dif= 974  cent    Dif= 1579.31 Hz
Partial nr.: 39             real partial note: 106.48   Plato-Harmonic: 96.42       Dif= 1005  cent    Dif= 1688.1 Hz
Partial nr.: 40             real partial note: 107.22   Plato-Harmonic: 96.86       Dif= 1035  cent    Dif= 1800.9 Hz
Partial nr.: 41             real partial note: 107.94   Plato-Harmonic: 97.29       Dif= 1065  cent    Dif= 1917.71 Hz
Partial nr.: 42             real partial note: 108.66   Plato-Harmonic: 97.71       Dif= 1095  cent    Dif= 2038.55 Hz
Partial nr.: 43             real partial note: 109.36   Plato-Harmonic: 98.12       Dif= 1125  cent    Dif= 2163.43 Hz
Partial nr.: 44             real partial note: 110.05   Plato-Harmonic: 98.51       Dif= 1154  cent    Dif= 2292.36 Hz
Partial nr.: 45             real partial note: 110.73   Plato-Harmonic: 98.9        Dif= 1183  cent    Dif= 2425.34 Hz
Partial nr.: 46             real partial note: 111.39   Plato-Harmonic: 99.28       Dif= 1211  cent    Dif= 2562.39 Hz
Partial nr.: 47             real partial note: 112.05   Plato-Harmonic: 99.66       Dif= 1239  cent    Dif= 2703.51 Hz
Partial nr.: 48             real partial note: 112.69   Plato-Harmonic: 100.02      Dif= 1267  cent    Dif= 2848.71 Hz
Partial nr.: 49             real partial note: 113.32   Plato-Harmonic: 100.38      Dif= 1295  cent    Dif= 2997.99 Hz
Partial nr.: 50             real partial note: 113.95   Plato-Harmonic: 100.73      Dif= 1322  cent    Dif= 3151.37 Hz
Partial nr.: 51             real partial note: 114.56   Plato-Harmonic: 101.07      Dif= 1349  cent    Dif= 3308.84 Hz
Partial nr.: 52             real partial note: 115.16   Plato-Harmonic: 101.41      Dif= 1376  cent    Dif= 3470.42 Hz
Partial nr.: 53             real partial note: 115.75   Plato-Harmonic: 101.74      Dif= 1402  cent    Dif= 3636.1 Hz
Partial nr.: 54             real partial note: 116.34   Plato-Harmonic: 102.06      Dif= 1428  cent    Dif= 3805.9 Hz
Partial nr.: 55             real partial note: 116.91   Plato-Harmonic: 102.38      Dif= 1454  cent    Dif= 3979.81 Hz
Partial nr.: 56             real partial note: 117.48   Plato-Harmonic: 102.69      Dif= 1479  cent    Dif= 4157.84 Hz
Partial nr.: 57             real partial note: 118.04   Plato-Harmonic: 102.99      Dif= 1504  cent    Dif= 4339.99 Hz
Partial nr.: 58             real partial note: 118.59   Plato-Harmonic: 103.3       Dif= 1529  cent    Dif= 4526.27 Hz
Partial nr.: 59             real partial note: 119.13   Plato-Harmonic: 103.59      Dif= 1554  cent    Dif= 4716.67 Hz
Partial nr.: 60             real partial note: 119.66   Plato-Harmonic: 103.88      Dif= 1578  cent    Dif= 4911.21 Hz
Partial nr.: 61             real partial note: 120.19   Plato-Harmonic: 104.17      Dif= 1602  cent    Dif= 5109.88 Hz

Note: In the firmware for the <Hurdy> robot, partials higher than 32 are not implemented.

dr.Godfried-Willem Raes, 03.03.2008
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