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node3.html
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<!DOCTYPE HTML>
<script type="text/javascript" src="https://www.maths.nottingham.ac.uk/plp/pmadw/LaTeXMathML.js">
</script>
<!--Converted with LaTeX2HTML 2021 (Released January 1, 2021) -->
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<head>
<title>Introduction</title>
<meta name="description" content="Intro">
<meta name="keywords" content="clarinet project">
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<h2 id="results">Results and Discussion</h2>
<p><img src="./images/media/image38.png" alt="Chart Description automatically
generated" class="center" width="50%">
<center><strong>Figure 11:</strong> The top figure is the implemented clarinet model in MATLAB;
the middle figure is the model implemented in the stk toolkit; the
bottom figure is a frequency response comparison between the two
implementations.</center>
</p>
<p>
Matlab version <br>
<audio controls>
<source src="./sounds/clarinetmatlab.wav" type="audio/wav">
Your browser does not support the audio element.
</audio>
</p>
<p>
Stk version <br>
<audio controls>
<source src="./sounds/clarinetdemo.wav" type="audio/wav">
Your browser does not support the audio element.
</audio>
</p>
<p>To obtain the resulting clarinet model, the parameter values used are:</p>
<p><img src="./images/media/image39.png" alt="Text Description automatically generated with medium
confidence" class="center" width="50%">
<center><strong>Figure 12:</strong>With these results the generated sound approaches that of an actual
clarinet. </center>
</p>
<p>To obtain a more natural sound, an envelope is applied to the mouth
pressure values ramping it from 0 to
$\mu H\left( 2\pi f_{r} \right)^{2}$ in approximately 100 milliseconds.
Noise and vibrato are also added for similar reasons.</p>
<p>By changing the variables $H,\mu$ it affects the rate at which the
resulting pressure will ramp but beware that it will also affect the
upper harmonics of the sound. Reducing $H$ will reduce $u_{0}$ which
leads to a reduction of $p_{\Delta}$ which results in a removal of
energy in the higher harmonics due too the reed filter. Inversely,
increasing the reed's dynamic mass per area will have the same effect as
$H$ as it affects the numerator of the filter,
$\frac{4z^{- 1}}{\mu_{r}}$.</p>
<p>To have the clarinet model play non-integer-based frequencies and
compare it properly with the stk toolkit version, I implemented an
interpolated delay line.</p>
<p>With some tunning of the note's frequency, I was able to line up the
sounds rather well resulting in:</p>
<p><img src="./images/media/image40.png" alt="Graphical user interface, application, table, Excel Description
automatically generated" class="center" width="50%"></p>
<center> <strong>Figure 13:</strong>
Frequency response between the tuned matlab and stk model</center>
<p>
As we can see in figure 11 and 12, the frequency responses resemble, however
the resulting sounds differ in their amplitude envelope. The amplitude
variation in the stk model is most likely due to the applied reverb, a
ramped down envelope, and the difference in reed models. When attempting
to apply a downwards ramping envelope on the mouth pressure in my model,
it created issues with the filters returning imaginary numbers and blowing up the values. Hence
why there is only an envelope on the upwards motion.
</p>
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<address>
<table>
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<td>
<a href="http://www.mcgill.ca/"><img src="./images/mcgill.gif" alt="McGill" width="150"
border="0"></a>
</td>
<td>
</td>
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<tr>
<td>
Made by Maxwell Gentili-Morin.
</td>
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</address>
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