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Generalities and evolution
Generalities and evolution
Hammer pulse duration as a function of the period (string note) for different pianos (from Ref. [1]).
This figure summarizes the measurements of hammer force pulse duration performed on three historic and two modern pianos. The order of magnitude is similar for historic and modern pianos, regularly decreasing from 4-5 ms in the bass range (C1) to less than one ms in the upper treble (C7). The pulse duration is less than the period for the lowest four octaves. In contrast, it becomes larger than the period in the upper octave (C6 to C7).
Evolution of string length L and tension at rest T0 for the string A3, from 1819 (NS19) until today (STD).
Evolution of string diameter (Phi) and characteristic impedance (Zc) of pianos from 1819 until today.
These two figures show the evolution of some critical piano string parameters, between 1819 and today (1977). The example of string A3 is given. It can be seen that the tension is multiplied by a factor of 4 between 1819 and 1873, and only by an amount of 25 % during the following century. In comparison, the length of the strings is only slowly increasing. This leads to an increase is string's diameter and characteristic impedance Zc. This last parameter governs the degree of coupling betwen strings and soundboard.
Acronyms: NS19=N. Streicher (1819) ; CG28= C. Graf (1828) ; JBS36= J.B. Streicher (1836) ; JBS51=J.B. Streicher (1851) ; JBSS73 = J.B. Streicher and Son (1873). STD=Steinway D (1977).
Example of measured strings' data sheets
Example of measured strings' data sheets
Strings' data sheet for piano Nanette Streicher 1819.
Strings' data sheet for piano J.B. Streicher 1873.
W: wrapping.
Examples of hammer force pulses
Examples of hammer force pulses
Piano JBS73. String D#1.
Piano JBS51. String E2.
Piano GH05. String D3.
Piano JBS73. String C#5.
These figures show the typical shapes of hammer force pulses, as measured on different pianos. In the bass range, the hammer force shows clearly separated pulses (ex: D#1). As the notes are played up, then these pulses become closer and are mixed together (notes E2 and D3). In the upper range, only one pulse is seen, resulting from the aggreagtion of several incoming and outgoing waves on the string (C#5).
String velocity
String velocity
Non-contact measurements of string velocity.
Measured string velocity for three different attack level (p - mf - f). String A#2. Piano GH05. Y-axis: arbitrary unit.
For the experiments performed in this project, a dedicated electromagnetic non-contact measurements device was built in order to measure the string velocity (see the above left figure). Example of results are shown on the right figure for the string A#2 of the Gert Hecher piano (GH05), and for three different playing forces. With appropriate measuring location and filtering, the hammer force pulse can be reconstructed from measurements of the string velocity (see Ref. [1]).
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