Physics based piano sound synthesis

[ataradov]

I'm working on the mathematically modeled piano synthesizer. Right now I'm using modal based approach, where the sound is formed by a sum of exponentially decaying sinusoids (harmonics).

Right now I can calculate frequencies of sinusoids (taking inharmonicity into account, of course). For initial amplitude values I'm using data obtained from a real piano samples, since it is just easier right now. I don't care about phases just jet.

My main concern is decay rate. To simulate beating and two stage decay I use 2 or 3 exponents of about the same frequency (depending on the number of strings for a particular note).

For a case of 3 strings theory suggests that one of the exponents will decay faster and two will decay at about the same rate, but due to slight difference in frequencies they will produce beating.

This method is described in the literature, but no algorithm is given to obtain actual values.

At the moment I use simple formulas that I've created myself and they are not based on any physics at all, but produce decent sound after a lot of trial and error.

My question is: is there a method to calculate those decay rates based on a more physical approach?

Key moment - method should produce values for the decay rates before synthesis itself occurs, so methods based on building system with feedback that reproduce this behavior won't work for me.

 

[eljose79]

Hello,

Thank you for sharing your work on the piano synthesizer. It sounds like you have put a lot of effort into creating a realistic sound using a modal approach.

To answer your question, there are indeed methods to calculate decay rates based on a more physical approach. One approach is to use the theory of coupled oscillators, which describes how multiple oscillating systems interact with each other.

In the case of the piano, the strings can be thought of as coupled oscillators, with each string having its own natural frequency and decay rate. When multiple strings are played together, their interactions can result in the beating and two-stage decay that you mentioned.

To calculate the decay rates in this approach, you would need to know the properties of the strings (such as their tension, mass, and length) and the coupling between them. This information can be obtained through experiments or from data provided by piano manufacturers.

Once you have this information, you can use mathematical equations and simulations to calculate the decay rates for each string and how they interact with each other. This approach is more physically accurate and can produce more realistic decay rates for your synthesizer.

I hope this information helps and I wish you success in your research. Keep up the good work!