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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