钢琴声音的敲击和两级衰减
我正在研究数学建模的钢琴合成器。现在我正在使用基于模态的方法，其中声音是由指数衰减正弦曲线（谐波）的总和形成的。
现在我可以计算正弦曲线的频率（当然，考虑到不和谐性）。对于初始振幅值，我使用从真实钢琴样本获得的数据，因为现在更容易。我不关心相位，只关心喷射。
我主要关心的是衰减率。为了模拟跳动和两级衰减，我使用大约相同频率的 2 或 3 个指数（取决于特定音符的弦数）。
对于 3 根弦的情况，理论表明其中一个指数会衰减得更快，而两个指数会以大约相同的速率衰减，但由于频率的细微差别，它们会产生跳动。
文献中描述了这种方法，但没有给出获取实际值的算法。
目前，我使用自己创建的简单公式，它们根本不基于任何物理原理，但经过大量试验和错误后会产生不错的声音。
我的问题是：是否有一种方法可以基于更物理的方法来计算这些衰减率？
关键时刻 - 方法应该在合成本身发生之前产生衰减率的值，因此基于构建带有反馈的系统来重现这种行为的方法对我来说不起作用。
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.
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如果您使用多个重叠模式（轻微失谐）合成弦乐分音，并且以相同的相位开始分音，您自然会得到 2 阶段衰减 - 首先当您的分音同步时声音很大，然后导致快速衰减让你的偏音异相。
If you synth your string partials with multiple overlapped modes (with slight detuning), and you start your partials with the same phase, you'll naturally get 2 stage decay - loud at first as your partials are in sync, then a quick decay caused by having your partials go out of phase.