Inharmonicity table for <Hurdy> low string

  • Fundamental frequency:= 55 Hz (A). midi note: 33
  • Calculated for a string factor B= 1.256182E-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 (0.0112375 kg/m)
  • r = string radius (1.4mm)
  • 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: 45.04    Plato-Harmonic: 45          Dif= 4  cent    Dif= .28 Hz
Partial nr.: 3              real partial note: 52.12    Plato-Harmonic: 52.02       Dif= 10  cent    Dif= .93 Hz
Partial nr.: 4              real partial note: 57.17    Plato-Harmonic: 57          Dif= 17  cent    Dif= 2.2 Hz
Partial nr.: 5              real partial note: 61.13    Plato-Harmonic: 60.86       Dif= 27  cent    Dif= 4.28 Hz
Partial nr.: 6              real partial note: 64.4     Plato-Harmonic: 64.02       Dif= 38  cent    Dif= 7.38 Hz
Partial nr.: 7              real partial note: 67.21    Plato-Harmonic: 66.69       Dif= 52  cent    Dif= 11.67 Hz
Partial nr.: 8              real partial note: 69.67    Plato-Harmonic: 69          Dif= 67  cent    Dif= 17.35 Hz
Partial nr.: 9              real partial note: 71.88    Plato-Harmonic: 71.04       Dif= 84  cent    Dif= 24.57 Hz
Partial nr.: 10             real partial note: 73.89    Plato-Harmonic: 72.86       Dif= 102  cent    Dif= 33.52 Hz
Partial nr.: 11             real partial note: 75.74    Plato-Harmonic: 74.51       Dif= 122  cent    Dif= 44.35 Hz
Partial nr.: 12             real partial note: 77.46    Plato-Harmonic: 76.02       Dif= 144  cent    Dif= 57.21 Hz
Partial nr.: 13             real partial note: 79.07    Plato-Harmonic: 77.41       Dif= 167  cent    Dif= 72.25 Hz
Partial nr.: 14             real partial note: 80.59    Plato-Harmonic: 78.69       Dif= 191  cent    Dif= 89.58 Hz
Partial nr.: 15             real partial note: 82.04    Plato-Harmonic: 79.88       Dif= 215  cent    Dif= 109.34 Hz
Partial nr.: 16             real partial note: 83.41    Plato-Harmonic: 81          Dif= 241  cent    Dif= 131.65 Hz
Partial nr.: 17             real partial note: 84.73    Plato-Harmonic: 82.05       Dif= 268  cent    Dif= 156.6 Hz
Partial nr.: 18             real partial note: 85.99    Plato-Harmonic: 83.04       Dif= 296  cent    Dif= 184.31 Hz
Partial nr.: 19             real partial note: 87.21    Plato-Harmonic: 83.98       Dif= 324  cent    Dif= 214.86 Hz
Partial nr.: 20             real partial note: 88.39    Plato-Harmonic: 84.86       Dif= 352  cent    Dif= 248.33 Hz
Partial nr.: 21             real partial note: 89.52    Plato-Harmonic: 85.71       Dif= 382  cent    Dif= 284.81 Hz
Partial nr.: 22             real partial note: 90.62    Plato-Harmonic: 86.51       Dif= 411  cent    Dif= 324.36 Hz
Partial nr.: 23             real partial note: 91.69    Plato-Harmonic: 87.28       Dif= 441  cent    Dif= 367.06 Hz
Partial nr.: 24             real partial note: 92.73    Plato-Harmonic: 88.02       Dif= 471  cent    Dif= 412.95 Hz
Partial nr.: 25             real partial note: 93.74    Plato-Harmonic: 88.73       Dif= 502  cent    Dif= 462.11 Hz
Partial nr.: 26             real partial note: 94.73    Plato-Harmonic: 89.41       Dif= 532  cent    Dif= 514.58 Hz
Partial nr.: 27             real partial note: 95.69    Plato-Harmonic: 90.06       Dif= 563  cent    Dif= 570.4 Hz
Partial nr.: 28             real partial note: 96.62    Plato-Harmonic: 90.69       Dif= 593  cent    Dif= 629.62 Hz
Partial nr.: 29             real partial note: 97.54    Plato-Harmonic: 91.3        Dif= 624  cent    Dif= 692.28 Hz
Partial nr.: 30             real partial note: 98.43    Plato-Harmonic: 91.88       Dif= 655  cent    Dif= 758.41 Hz
Partial nr.: 31             real partial note: 99.3     Plato-Harmonic: 92.45       Dif= 685  cent    Dif= 828.05 Hz
Partial nr.: 32             real partial note: 100.16   Plato-Harmonic: 93          Dif= 716  cent    Dif= 901.23 Hz
Partial nr.: 33             real partial note: 100.99   Plato-Harmonic: 93.53       Dif= 746  cent    Dif= 977.97 Hz
Partial nr.: 34             real partial note: 101.81   Plato-Harmonic: 94.05       Dif= 776  cent    Dif= 1058.29 Hz
Partial nr.: 35             real partial note: 102.62   Plato-Harmonic: 94.55       Dif= 806  cent    Dif= 1142.23 Hz
Partial nr.: 36             real partial note: 103.4    Plato-Harmonic: 95.04       Dif= 836  cent    Dif= 1229.81 Hz
Partial nr.: 37             real partial note: 104.17   Plato-Harmonic: 95.51       Dif= 866  cent    Dif= 1321.03 Hz
Partial nr.: 38             real partial note: 104.93   Plato-Harmonic: 95.98       Dif= 896  cent    Dif= 1415.93 Hz
Partial nr.: 39             real partial note: 105.67   Plato-Harmonic: 96.42       Dif= 925  cent    Dif= 1514.51 Hz
Partial nr.: 40             real partial note: 106.4    Plato-Harmonic: 96.86       Dif= 954  cent    Dif= 1616.79 Hz
Partial nr.: 41             real partial note: 107.12   Plato-Harmonic: 97.29       Dif= 983  cent    Dif= 1722.78 Hz
Partial nr.: 42             real partial note: 107.82   Plato-Harmonic: 97.71       Dif= 1011  cent    Dif= 1832.51 Hz
Partial nr.: 43             real partial note: 108.51   Plato-Harmonic: 98.12       Dif= 1039  cent    Dif= 1945.97 Hz
Partial nr.: 44             real partial note: 109.19   Plato-Harmonic: 98.51       Dif= 1067  cent    Dif= 2063.19 Hz
Partial nr.: 45             real partial note: 109.85   Plato-Harmonic: 98.9        Dif= 1095  cent    Dif= 2184.16 Hz
Partial nr.: 46             real partial note: 110.51   Plato-Harmonic: 99.28       Dif= 1123  cent    Dif= 2308.91 Hz
Partial nr.: 47             real partial note: 111.15   Plato-Harmonic: 99.66       Dif= 1150  cent    Dif= 2437.43 Hz
Partial nr.: 48             real partial note: 111.79   Plato-Harmonic: 100.02      Dif= 1177  cent    Dif= 2569.73 Hz
Partial nr.: 49             real partial note: 112.41   Plato-Harmonic: 100.38      Dif= 1203  cent    Dif= 2705.83 Hz
Partial nr.: 50             real partial note: 113.03   Plato-Harmonic: 100.73      Dif= 1230  cent    Dif= 2845.73 Hz
Partial nr.: 51             real partial note: 113.63   Plato-Harmonic: 101.07      Dif= 1256  cent    Dif= 2989.43 Hz
Partial nr.: 52             real partial note: 114.22   Plato-Harmonic: 101.41      Dif= 1282  cent    Dif= 3136.95 Hz
Partial nr.: 53             real partial note: 114.81   Plato-Harmonic: 101.74      Dif= 1307  cent    Dif= 3288.28 Hz
Partial nr.: 54             real partial note: 115.39   Plato-Harmonic: 102.06      Dif= 1333  cent    Dif= 3443.43 Hz
Partial nr.: 55             real partial note: 115.95   Plato-Harmonic: 102.38      Dif= 1358  cent    Dif= 3602.41 Hz
Partial nr.: 56             real partial note: 116.51   Plato-Harmonic: 102.69      Dif= 1383  cent    Dif= 3765.22 Hz
Partial nr.: 57             real partial note: 117.07   Plato-Harmonic: 102.99      Dif= 1407  cent    Dif= 3931.86 Hz
Partial nr.: 58             real partial note: 117.61   Plato-Harmonic: 103.3       Dif= 1431  cent    Dif= 4102.34 Hz
Partial nr.: 59             real partial note: 118.15   Plato-Harmonic: 103.59      Dif= 1455  cent    Dif= 4276.66 Hz
Partial nr.: 60             real partial note: 118.67   Plato-Harmonic: 103.88      Dif= 1479  cent    Dif= 4454.83 Hz
Partial nr.: 61             real partial note: 119.2    Plato-Harmonic: 104.17      Dif= 1503  cent    Dif= 4636.84 Hz
Partial nr.: 62             real partial note: 119.71   Plato-Harmonic: 104.45      Dif= 1526  cent    Dif= 4822.7 Hz
Partial nr.: 63             real partial note: 120.22   Plato-Harmonic: 104.73      Dif= 1549  cent    Dif= 5012.42 Hz

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

dr.Godfried-Willem Raes, 29.02.2008
Back to <Hurdy>