Topic: vibration and synchronization
A musical instrument is full of vibrations. Vibrations do not exist by themselves, they are not separate. They are united and variously interconnected. They affect each other. When vibrations have a connection, synchronism begins to occur. Orderliness. In contrast to chaos. They are both present in vibrating structures. It is interesting to look at an extremely simplified version of this process. The simplest case is two coupled oscillators. This can be described by a system of differential equations. Or simulated using a simple electronic circuit.
Link to the plugin:
https://www.native-instruments.com/en/r...show/4417/
This is a strange attractor of Lorenz. When changing the parameters, you can notice that there are certain values at which synchronism occurs. In this case, a specific set of overtones is formed.
Two oscillators can be easily calculated with the speed of sound on a computer. But if there are many vibrations, then this becomes a difficult task for modeling on the fly. Nevertheless, in my opinion there are several interesting points that are inherent in the features of synchronization.
For examples, I used a synthesizer based on two chaotic coupled nonlinear oscillators. Modeled in REAKTOR by NI. Link:
https://www.native-instruments.com/en/r...show/6947/
One moment - how does the influence of the oscillators on each other sound? For example, when the oscillators are connected and their frequencies diverge a little. In such a situation, one oscillator pushes or pulls the phase of another. If you look at it with the help of figures I can see the appearance of a "hump" on flowing figures. This is a kind of “jerk”. There is an interesting article ..:
https://www.academia.edu/36559812/10.10...43-7_9.pdf
There is a derivative of acceleration. In other articles, I have not met such information about acceleration's acceleration.
On the spectrum, the interaction manifests itself as an additional frequency. Most likely a multiple of the fundamental frequencies of the oscillators (or not). But this is not a full-fledged vibration, but only an additional acceleration, an additional jerk in a certain place of the oscillator phase. Those. some part of the period of a higher frequency arising each time with the main frequency of the oscillator. Under certain conditions (the difference in the frequencies of the oscillators, the strength and phase of the action), this can be a stable state. Or movement towards a steady state. If the combination of parameters goes beyond some boundaries, then the oscillators go on to chaotic behavior.
During synchronization, both overtone and frequencies below the oscillator frequencies can occur. An additional low frequency may occur.
I had to add a little unevenness (which looks like an additional frequency on the spectrum), otherwise the oscillators lose stability and diverge.
Interestingly, the extra vibration is a little springy. And this "springiness" resembles the interaction between atoms.
Simulator for comparison:
https://phet.colorado.edu/sims/html/ato...ns_en.html
Для примера можно посмотреть на взаимодействие атомов кислорода. Очень наглядно.
If the connectedness and interaction of the oscillators generates additional frequencies, and the string has a number of overtones, then this may lead to a simulation of a higher overtone. Low frequencies may also occur. Those. synchronization of the fundamental frequency of the string will lead to amplitude modulation of the overtone with the velocity of the fundamental tone. Bass overtones are also possible. Maybe that's why the piano sound has some ripples on the amplitudes of the overtones.
What happens if multiple strings and interactions between them sound simultaneously? There will be the sound of a good piano. Living. What if you do not calculate all the interactions in direct time, but simply simulate the “sound of synchronization”. After all, many parameters are previously known. Frequencies and conditions of interaction are defined. Amplitudes and a little frequency change. Maybe this simplification makes some sense?
Interesting article. About modeling five connected oscillators:
http://journals.ioffe.ru/articles/viewPDF/44525
Thanks.
