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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