Good time!
Some time ago I was interested in the question of the reasons for the frequency shift of some overtones from the values predicted by the inharmonicity. Philip replied that the reason was the inharmonicity of the strings and the impedance of the deck. At that moment I did not understand how the impedance is involved in frequency biases. Now again became interesting mechanism for this. Schematically, well and simply the reason for this is shown in this video:
https://www.youtube.com/watch?v=4Lv72JbXRf8&t=158s
Now more understandable. It becomes clear the reason for the complexity of tuning the unison in double entwined strings. The associated vibrations of the strings, the deck and the bridge lead to a shift in the antinodes of some frequencies. Phantom frequencies, additional beats in the sound of even one string are possible.
In this regard, some questions have arisen:
What is the quantitative relationship between the impedance and the change in the oscillation frequency? What changes in impedance will lead to noticeable changes in frequency?
In Pianoteq, critical impedance values (0.3-3.0) can
[should?] lead to any noticeable frequency shifts of overtones? . Or is the effect insignificant and elusive in the range of values that Pianoteq allows?
If there is a change in impedance, a shift of a certain frequency, is there a relationship with the point of impact of the hammer in the simulation?
Full rebuild — string tension — can be linked to this?
Can anyone recommend literature or detailed research in this area?
Upd..
If you know the exact parameters of the string, then measuring the frequency can be judged on the properties of the impedance at the point of contact with the string of the bridge? So find out about the characteristics of the bridge and deck at certain points?
Last edited by scherbakov.al (13-04-2019 10:36)