Inharmonicity table for <Hurdy> high string
- Fundamental frequency:= 146.83 Hz (D). midi note: 50
- Calculated for a string factor B= 4.33465E-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 (0.003848451 kg/m)
- r = string radius (0.35mm)
- 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= .03 Hz Partial nr.: 3 real partial note: 69.02 Plato-Harmonic: 69.02 Dif= 0 cent Dif= .09 Hz Partial nr.: 4 real partial note: 74.01 Plato-Harmonic: 74 Dif= 1 cent Dif= .2 Hz Partial nr.: 5 real partial note: 77.87 Plato-Harmonic: 77.86 Dif= 1 cent Dif= .4 Hz Partial nr.: 6 real partial note: 81.03 Plato-Harmonic: 81.02 Dif= 1 cent Dif= .69 Hz Partial nr.: 7 real partial note: 83.71 Plato-Harmonic: 83.69 Dif= 2 cent Dif= 1.09 Hz Partial nr.: 8 real partial note: 86.02 Plato-Harmonic: 86 Dif= 2 cent Dif= 1.63 Hz Partial nr.: 9 real partial note: 88.07 Plato-Harmonic: 88.04 Dif= 3 cent Dif= 2.32 Hz Partial nr.: 10 real partial note: 89.9 Plato-Harmonic: 89.86 Dif= 4 cent Dif= 3.18 Hz Partial nr.: 11 real partial note: 91.56 Plato-Harmonic: 91.51 Dif= 5 cent Dif= 4.23 Hz Partial nr.: 12 real partial note: 93.07 Plato-Harmonic: 93.02 Dif= 5 cent Dif= 5.49 Hz Partial nr.: 13 real partial note: 94.47 Plato-Harmonic: 94.41 Dif= 6 cent Dif= 6.98 Hz Partial nr.: 14 real partial note: 95.76 Plato-Harmonic: 95.69 Dif= 7 cent Dif= 8.71 Hz Partial nr.: 15 real partial note: 96.97 Plato-Harmonic: 96.88 Dif= 8 cent Dif= 10.71 Hz Partial nr.: 16 real partial note: 98.1 Plato-Harmonic: 98 Dif= 10 cent Dif= 13 Hz Partial nr.: 17 real partial note: 99.16 Plato-Harmonic: 99.05 Dif= 11 cent Dif= 15.59 Hz Partial nr.: 18 real partial note: 100.16 Plato-Harmonic: 100.04 Dif= 12 cent Dif= 18.49 Hz Partial nr.: 19 real partial note: 101.11 Plato-Harmonic: 100.98 Dif= 13 cent Dif= 21.74 Hz Partial nr.: 20 real partial note: 102.01 Plato-Harmonic: 101.86 Dif= 15 cent Dif= 25.35 Hz Partial nr.: 21 real partial note: 102.87 Plato-Harmonic: 102.71 Dif= 16 cent Dif= 29.33 Hz Partial nr.: 22 real partial note: 103.69 Plato-Harmonic: 103.51 Dif= 18 cent Dif= 33.71 Hz Partial nr.: 23 real partial note: 104.48 Plato-Harmonic: 104.28 Dif= 20 cent Dif= 38.5 Hz Partial nr.: 24 real partial note: 105.23 Plato-Harmonic: 105.02 Dif= 21 cent Dif= 43.72 Hz Partial nr.: 25 real partial note: 105.96 Plato-Harmonic: 105.73 Dif= 23 cent Dif= 49.39 Hz Partial nr.: 26 real partial note: 106.66 Plato-Harmonic: 106.41 Dif= 25 cent Dif= 55.53 Hz Partial nr.: 27 real partial note: 107.33 Plato-Harmonic: 107.06 Dif= 27 cent Dif= 62.15 Hz Partial nr.: 28 real partial note: 107.98 Plato-Harmonic: 107.69 Dif= 29 cent Dif= 69.27 Hz Partial nr.: 29 real partial note: 108.61 Plato-Harmonic: 108.3 Dif= 31 cent Dif= 76.92 Hz Partial nr.: 30 real partial note: 109.21 Plato-Harmonic: 108.88 Dif= 33 cent Dif= 85.1 Hz Partial nr.: 31 real partial note: 109.8 Plato-Harmonic: 109.45 Dif= 35 cent Dif= 93.84 Hz Partial nr.: 32 real partial note: 110.38 Plato-Harmonic: 110 Dif= 38 cent Dif= 103.15 Hz Partial nr.: 33 real partial note: 110.93 Plato-Harmonic: 110.53 Dif= 40 cent Dif= 113.04 Hz Partial nr.: 34 real partial note: 111.47 Plato-Harmonic: 111.05 Dif= 42 cent Dif= 123.55 Hz Partial nr.: 35 real partial note: 112 Plato-Harmonic: 111.55 Dif= 45 cent Dif= 134.68 Hz Partial nr.: 36 real partial note: 112.51 Plato-Harmonic: 112.04 Dif= 47 cent Dif= 146.45 Hz Partial nr.: 37 real partial note: 113.01 Plato-Harmonic: 112.51 Dif= 50 cent Dif= 158.87 Hz Partial nr.: 38 real partial note: 113.5 Plato-Harmonic: 112.98 Dif= 53 cent Dif= 171.97 Hz Partial nr.: 39 real partial note: 113.98 Plato-Harmonic: 113.42 Dif= 55 cent Dif= 185.76 Hz Partial nr.: 40 real partial note: 114.44 Plato-Harmonic: 113.86 Dif= 58 cent Dif= 200.26 Hz Partial nr.: 41 real partial note: 114.9 Plato-Harmonic: 114.29 Dif= 61 cent Dif= 215.47 Hz Partial nr.: 42 real partial note: 115.35 Plato-Harmonic: 114.71 Dif= 64 cent Dif= 231.43 Hz Partial nr.: 43 real partial note: 115.78 Plato-Harmonic: 115.12 Dif= 67 cent Dif= 248.14 Hz Partial nr.: 44 real partial note: 116.21 Plato-Harmonic: 115.51 Dif= 70 cent Dif= 265.62 Hz Partial nr.: 45 real partial note: 116.63 Plato-Harmonic: 115.9 Dif= 73 cent Dif= 283.89 Hz Partial nr.: 46 real partial note: 117.04 Plato-Harmonic: 116.28 Dif= 76 cent Dif= 302.96 Hz Partial nr.: 47 real partial note: 117.45 Plato-Harmonic: 116.66 Dif= 79 cent Dif= 322.85 Hz Partial nr.: 48 real partial note: 117.84 Plato-Harmonic: 117.02 Dif= 82 cent Dif= 343.57 Hz Partial nr.: 49 real partial note: 118.23 Plato-Harmonic: 117.38 Dif= 86 cent Dif= 365.13 Hz Partial nr.: 50 real partial note: 118.62 Plato-Harmonic: 117.73 Dif= 89 cent Dif= 387.56 Hz Partial nr.: 51 real partial note: 118.99 Plato-Harmonic: 118.07 Dif= 92 cent Dif= 410.87 Hz Partial nr.: 52 real partial note: 119.36 Plato-Harmonic: 118.41 Dif= 96 cent Dif= 435.07 Hz Partial nr.: 53 real partial note: 119.73 Plato-Harmonic: 118.74 Dif= 99 cent Dif= 460.17 Hz Partial nr.: 54 real partial note: 120.09 Plato-Harmonic: 119.06 Dif= 103 cent Dif= 486.2 Hz
Note: Partials higher than 32 are not implemented in the firmware for the <Hurdy> robot.
dr.Godfried-Willem Raes, 29.02.2008
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