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>