Inharmonicity table for <Hurdy> high string

  • Fundamental frequency:= 146.83 Hz (D). midi note: 50 Force: 265N
  • Calculated for a string factor B= 3.184641E-5
  • 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 (0.002064 kg/m)
  • r = string radius (0.30mm), diameter 0.6mm
  • p = density of the string material (7.3 kg/l)
  • T = string tension in Newton (calculated using Taylors law)
  • L = string length in meter (1.220 m)



Partial nr.: 1              real partial note: 50       Plato-Harmonic: 50          Dif= 0  cent    Dif= 0 Hz
Partial nr.: 2              real partial note: 62       Plato-Harmonic: 62          Dif= 0  cent    Dif= .02 Hz
Partial nr.: 3              real partial note: 69.02    Plato-Harmonic: 69.02       Dif= 0  cent    Dif= .06 Hz
Partial nr.: 4              real partial note: 74       Plato-Harmonic: 74          Dif= 0  cent    Dif= .15 Hz
Partial nr.: 5              real partial note: 77.87    Plato-Harmonic: 77.86       Dif= 1  cent    Dif= .29 Hz
Partial nr.: 6              real partial note: 81.03    Plato-Harmonic: 81.02       Dif= 1  cent    Dif= .5 Hz
Partial nr.: 7              real partial note: 83.7     Plato-Harmonic: 83.69       Dif= 1  cent    Dif= .8 Hz
Partial nr.: 8              real partial note: 86.02    Plato-Harmonic: 86          Dif= 2  cent    Dif= 1.2 Hz
Partial nr.: 9              real partial note: 88.06    Plato-Harmonic: 88.04       Dif= 2  cent    Dif= 1.7 Hz
Partial nr.: 10             real partial note: 89.89    Plato-Harmonic: 89.86       Dif= 3  cent    Dif= 2.34 Hz
Partial nr.: 11             real partial note: 91.55    Plato-Harmonic: 91.51       Dif= 3  cent    Dif= 3.11 Hz
Partial nr.: 12             real partial note: 93.06    Plato-Harmonic: 93.02       Dif= 4  cent    Dif= 4.04 Hz
Partial nr.: 13             real partial note: 94.45    Plato-Harmonic: 94.41       Dif= 5  cent    Dif= 5.13 Hz
Partial nr.: 14             real partial note: 95.74    Plato-Harmonic: 95.69       Dif= 5  cent    Dif= 6.41 Hz
Partial nr.: 15             real partial note: 96.94    Plato-Harmonic: 96.88       Dif= 6  cent    Dif= 7.88 Hz
Partial nr.: 16             real partial note: 98.07    Plato-Harmonic: 98          Dif= 7  cent    Dif= 9.56 Hz
Partial nr.: 17             real partial note: 99.13    Plato-Harmonic: 99.05       Dif= 8  cent    Dif= 11.46 Hz
Partial nr.: 18             real partial note: 100.13   Plato-Harmonic: 100.04      Dif= 9  cent    Dif= 13.6 Hz
Partial nr.: 19             real partial note: 101.07   Plato-Harmonic: 100.98      Dif= 10  cent    Dif= 15.99 Hz
Partial nr.: 20             real partial note: 101.97   Plato-Harmonic: 101.86      Dif= 11  cent    Dif= 18.65 Hz
Partial nr.: 21             real partial note: 102.83   Plato-Harmonic: 102.71      Dif= 12  cent    Dif= 21.58 Hz
Partial nr.: 22             real partial note: 103.65   Plato-Harmonic: 103.51      Dif= 13  cent    Dif= 24.8 Hz
Partial nr.: 23             real partial note: 104.43   Plato-Harmonic: 104.28      Dif= 14  cent    Dif= 28.33 Hz
Partial nr.: 24             real partial note: 105.18   Plato-Harmonic: 105.02      Dif= 16  cent    Dif= 32.17 Hz
Partial nr.: 25             real partial note: 105.9    Plato-Harmonic: 105.73      Dif= 17  cent    Dif= 36.35 Hz
Partial nr.: 26             real partial note: 106.59   Plato-Harmonic: 106.41      Dif= 18  cent    Dif= 40.87 Hz
Partial nr.: 27             real partial note: 107.26   Plato-Harmonic: 107.06      Dif= 20  cent    Dif= 45.76 Hz
Partial nr.: 28             real partial note: 107.9    Plato-Harmonic: 107.69      Dif= 21  cent    Dif= 51.01 Hz
Partial nr.: 29             real partial note: 108.52   Plato-Harmonic: 108.3       Dif= 23  cent    Dif= 56.65 Hz
Partial nr.: 30             real partial note: 109.13   Plato-Harmonic: 108.88      Dif= 24  cent    Dif= 62.68 Hz
Partial nr.: 31             real partial note: 109.71   Plato-Harmonic: 109.45      Dif= 26  cent    Dif= 69.13 Hz
Partial nr.: 32             real partial note: 110.28   Plato-Harmonic: 110         Dif= 28  cent    Dif= 76 Hz
Partial nr.: 33             real partial note: 110.83   Plato-Harmonic: 110.53      Dif= 30  cent    Dif= 83.31 Hz
Partial nr.: 34             real partial note: 111.36   Plato-Harmonic: 111.05      Dif= 31  cent    Dif= 91.06 Hz
Partial nr.: 35             real partial note: 111.88   Plato-Harmonic: 111.55      Dif= 33  cent    Dif= 99.28 Hz
Partial nr.: 36             real partial note: 112.39   Plato-Harmonic: 112.04      Dif= 35  cent    Dif= 107.98 Hz
Partial nr.: 37             real partial note: 112.88   Plato-Harmonic: 112.51      Dif= 37  cent    Dif= 117.17 Hz
Partial nr.: 38             real partial note: 113.36   Plato-Harmonic: 112.98      Dif= 39  cent    Dif= 126.85 Hz
Partial nr.: 39             real partial note: 113.83   Plato-Harmonic: 113.42      Dif= 41  cent    Dif= 137.05 Hz
Partial nr.: 40             real partial note: 114.29   Plato-Harmonic: 113.86      Dif= 43  cent    Dif= 147.78 Hz
Partial nr.: 41             real partial note: 114.74   Plato-Harmonic: 114.29      Dif= 45  cent    Dif= 159.04 Hz
Partial nr.: 42             real partial note: 115.18   Plato-Harmonic: 114.71      Dif= 47  cent    Dif= 170.85 Hz
Partial nr.: 43             real partial note: 115.61   Plato-Harmonic: 115.12      Dif= 50  cent    Dif= 183.23 Hz
Partial nr.: 44             real partial note: 116.03   Plato-Harmonic: 115.51      Dif= 52  cent    Dif= 196.19 Hz
Partial nr.: 45             real partial note: 116.44   Plato-Harmonic: 115.9       Dif= 54  cent    Dif= 209.73 Hz
Partial nr.: 46             real partial note: 116.85   Plato-Harmonic: 116.28      Dif= 56  cent    Dif= 223.87 Hz
Partial nr.: 47             real partial note: 117.24   Plato-Harmonic: 116.66      Dif= 59  cent    Dif= 238.62 Hz
Partial nr.: 48             real partial note: 117.63   Plato-Harmonic: 117.02      Dif= 61  cent    Dif= 253.99 Hz
Partial nr.: 49             real partial note: 118.01   Plato-Harmonic: 117.38      Dif= 64  cent    Dif= 270 Hz
Partial nr.: 50             real partial note: 118.39   Plato-Harmonic: 117.73      Dif= 66  cent    Dif= 286.66 Hz
Partial nr.: 51             real partial note: 118.76   Plato-Harmonic: 118.07      Dif= 69  cent    Dif= 303.97 Hz
Partial nr.: 52             real partial note: 119.12   Plato-Harmonic: 118.41      Dif= 72  cent    Dif= 321.96 Hz
Partial nr.: 53             real partial note: 119.48   Plato-Harmonic: 118.74      Dif= 74  cent    Dif= 340.63 Hz
Partial nr.: 54             real partial note: 119.83   Plato-Harmonic: 119.06      Dif= 77  cent    Dif= 359.99 Hz
Partial nr.: 55             real partial note: 120.17   Plato-Harmonic: 119.38      Dif= 80  cent    Dif= 380.05 Hz

Note: Partials higher than 32 are not implemented in the firmware for the <Hurdy> robot.

dr.Godfried-Willem Raes, 03.03.2008
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