How Does String Tension Affect Audio Output Amplitude in Synthesizers?

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Discussion Overview

The discussion centers on the relationship between string tension and audio output amplitude in synthesizers, particularly in the context of a guitar/piano synthesizer design. Participants explore how tension changes upon excitation of the string and its impact on sound characteristics, including pitch and inharmonicity.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant proposes that the increase in string tension upon plucking should correlate directly with the amplitude of the audio output signal, suggesting a potential linear relationship.
  • Another participant considers the tension increase as potential energy that rapidly decays back to baseline after the string is plucked, questioning how this decay could be modeled based on various physical properties of the string.
  • A third participant challenges the initial claim regarding inharmonicity, suggesting it may not be significantly affected by the force of plucking.
  • A participant provides a reference to a paper that discusses related issues, indicating that further reading may be beneficial for understanding the topic.
  • Another participant emphasizes the need for more data points to validate the proposed theory regarding tension and amplitude relationship.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between string tension and audio output amplitude, with no consensus reached on the nature of this relationship or the influence of plucking force on inharmonicity.

Contextual Notes

Participants note the complexity of modeling the relationship due to factors such as string diameter, tension, and linear mass, which remain unresolved in the discussion.

mikejm
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I am working on a guitar/piano synthesizer for my own interest. When a string is plucked or struck, tension increases causing a slight pitch bend and change in the inharmonicity. This change then settles as the note quiets down. Thus it is important to model how the tension rises above baseline when a note is struck and evolves.

I have put a lot of thought into it and my presumption is that the tension increase from excitation must vary in some fairly direct manner with the amplitude of the total audio output signal of the string.

Let's say a string has a resting tension of 70 N with a resting audio signal output of amplitude 0. Let's say you then calibrate the simulation so an output amplitude of 1 corresponds to a tension increase to 72 N. Would there be a linear relationship between the tension and the amplitude changes, so that at an output of 0.5 there would be 71 N tension expected?

If not, how would the relationship likely work?

Thanks.
 
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Now I'm actually thinking of it from a different perspective.

The tension that is increased at the point of plucking or striking a string is the potential energy that then creates the audio output, right?

So actually the tension should decay very rapidly back to the baseline as the sound "explodes" from plucking it.

I wonder if there's any way to model how quickly the tension would decay based on things like string diameter, tension, linear mass, etc.
 
Did you really mean inharmonicity? I would have guessed that wouldn't be significantly influenced by how hard you pluck a string.
 
http://www2.eng.cam.ac.uk/~jw12/JW%20PDFs/Guitar_II.pdf

That paper discusses the issues you ask about. I found it with an Internet search for "plucked string design".
 
And you would need significantly more than a single data point to test your theory.
 

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