<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html> <body text="#000000" bgcolor="#FFFFFF" link="#0000EE" vlink="#551A8B" alink="#FF0000">   Stephen Birkett wrote: <blockquote TYPE=CITE>  The topic of this thread has rankled everytime I saw it come up. Finally someone has spotted the error. The art in this design issue is how to achieve a desirable impedance *mis-match* between soundboard and bridge.  This is far from impedance matching, since that situation would have zero sustain, all energy being rapidly passed from bridge to soundboard. Stephen  </blockquote> Hmmm.. lets see.. I had used the expression "impedance matching" because this is what was used in the article by Klaus Wogram (included as one of the 5 Lectures on the Acoustics of the Piano). I didnt think that this refered to matching the impedance of the strings to the impedance of the board in such a way that these were equal. But I think I see how this idea might easily get started and thereby your point is taken. Re-reading the  article I tried to see if I could infer this idea from it, and couldnt really. Correct me if I am wrong, but it seems to me that Wogram  relates the soundboard impedance to the strings, in the sense that the strings represent a Force applied to the board. he states         "The vibration energy of the string is transfered to the soundboard, transformed from mechanical to acoustic energy, and radiated as airborne sound. The rate at which this energy flow takes place is determined by the soundboard (the consumer) in relation to the properties of the string (the source). In engineering terms this relationship is referred to as "impedance matching" The loading exerted by the soundboard on the string can be expressed by means of its input impedance Z, which is defined as the excitation force F, divided by the resulting velocity v, at the point of excitation." He goes on to say     "A high value of the input impedance means that a large force must be expended in order to achieve a certain volume" This part of his discussion seems to be from the perspective of describing some positive attributes of a good soundboard, and not of any "matching" to the strings, above and beyond the general statement above. In the section he entitles The Influence of String Tension , there is a description of what effects raising and lowering of string tension has on the soundboards' impedance curve and its resonant frequencies. Again this seems to me to be in the perspective of analysing the characteristics of the soundboard itself. Where he does specifically define "matching" between the strings and the board he states (in the section entitled Decay Of Piano Tone     "Hence, a good match between the string and the soundboard is found when the input impedance is high and the phase angle is positive" He demonstrates in this section how the tension of the string can be "matched" to the input impedance of the board to accomplish this. (tho no method by which to design a scale in this manner is given) But again, this section seems to be mostly concerned with the soundboard itself. From the same section:     "Consequently, one characteristic of a high quality soundboard is that the impedance curve exhibits as few dips as possible, avoiding sharp zigzaging. In addition the overall level of the impedance curve should be high enough to ensure sufficient reflexion of the string energy at the bridge, resulting in long decay time" The point being that a soundboard that Does have an impedance curve with large dips and sharp zigzaging will have strong resonances at these dips, and suck the energy from any string that has partial frequencies that correspond to these resonant frequencies., (regardless of its tension, string impedance etc) The final section on the Modal analysys of soundboards seems to go in the same general direction, but taken a step further. By demonstrating that the soundboard actually behaves like it was several interdependant boards, vibrating in seperate sections (the number of which depends on the resonance mode) in opposite phases which each other (with the exception of the first mode). This creates nodelines between the sections for any given mode which do not move much and hence represent high values of input impedance at those points on the board which lie along that nodal line. If these points are directly under the bridge then strings delivering their energy at these points will meet high impedance, and this will result in long decay time. (too long perhaps) Sections of the board away from these nodelines behave in the opposite manner. The jist of all this again seems to point in the direction soundboard itself. In this case more in the direction of how to identify and adjust problem areas in the impedance characteristics of the board. This is part of my understanding of the Wogram article, and I would greatly appreciate hearing where I am mistaken and where I am not. In anycase I do not see any direct correlation to how one would go about "matching" string impedance to soundboard impedance in this article. If I were to jump to conclusions I would be tempted to think that a stringing scale should, ideally, be designed after knowing the impedance properties of the soundboard so as to be strong enough to drive the board, within tension parameters allowed for the construction of the instrument as a whole, and with a smooth as possible inharmonicity curve. How to go about this is something I would also appreciate very much hearing about. For those of you in the know, please understand I am just opening these doors, and need direction and your input, even if that be only suggestions for further readings.  For all such help I would be very gratefull. Richard Brekne I.C.P.T.G.  N.P.T.F. Bergen, Norway </body> </html>