The class project for Com Sci 295 is an open project. It is open in two senses.

1. There are no restrictions on how you accomplish project work. You are encouraged to collaborate, share work, use ideas that you hear from others, find information in books and articles or figure out for yourself, whatever works. I will evaluate your project work entirely from your presentation of the insights that you gain. You may present the work of others, as well as your own, but you must explain what it means. Of course, you must acknowledge the source of each idea that you use. You must share your own work freely with the class.
   
   
2. You may change the definition of the project. I will provide a default work schedule, but you are at liberty to vary any parts of it that you like. In order to get useful credit toward a grade, though, you must be able to demonstrate the materials that you develop. I will provide a sound-capable Linux system with all of the software that comes up in class. If you want any other facilities, you must take the initiative to arrange them for the final interview. If you make serious changes in the standard project, it's a good idea to discuss them with me, to make sure that I will appreciate their value in the final interview.

The goal of the project is to evaluate intuitively the quality of several common models for synthesizing sound, by simulating a small number of musical instruments with some of those models, interpolating between the qualities of instruments using the Loris tool library, and listening carefully to the results. With each synthesis model, the idea is to discover its natural good and bad qualities. So, there's no point in trying to perfect the instrument simulation with each model. Rather, we want to find the best simulation that uses the model in an intuitively natural fashion.

I haven't updated beyond this point. The remainder reflects the spring 2002 project. [O'D]

We will simulate the sound of the trumpet using 4 or 5 different synthesis models. In each case, we will create a simulation that can play individual notes of a second or two at a moderate articulation and dynamic, for each pitch of the chromatic scale over the normal range of the instrument. The 5 types of synthesis are:

1. Hacking around with a recorded sample using sound editors, such as MixView, DAP, snd. (Accomplish by Monday 9 April 2002)
   
   
2. Wavetable synthesis, using a single sampled period of sound, playing it at various speeds to produce different pitches, and using a single amplitude envelope for the articulation. (Accomplish by Thursday 18 April 2002)
   
   
3. Additive sinusoidal synthesis with a single amplitude envelope. This will sound just like step 2, but prepare us for step 4. (Accomplish by Thursday 25 April 2002)
   
   
4. Additive sinusoidal synthesis with a separate amplitude envelope for each partial. (Have a working start by Monday 6 May 2002)
   
   
5. Pass the results of step 4 through a broadband filter to eliminate the chipmunk effect.
   
   
6. (Maybe we'll get this far) Adding a bit of randomness to the results of 5, to make them more lifelike.

You should accomplish step 1 by Monday, 9 April 2002.

1. Choose one recorded trumpet note.
   
   
2. Use waveform editors, such as MixView, DAP, and snd, to produce a short sequence of notes with different lengths and pitches. Make sure that you include some notes near each end of the instrument's normal range---you might even decide to go beyond that range. You can produce a scale, an arpeggio, or a short musical piece according to your own taste. I had my best results using DAP's ``Resample Non Time'' feature to create different pitches, cut & paste to shorten/lengthen notes, ``Amp Ramp'' to smooth out the joints. You might enjoy trying the ``Resample Time'' feature to shift pitches and control lengths. But that's a rather sophisticated feature, and I'd like you to also observe what can/cannot be accomplished with primitive editing.
   
   
3. Try creating some waveforms freehand. You can do this by starting with no sound file in DAP, setting the ``Edit'' button on the right upper side of the window, pushing values around with the mouse, then playing with the ``Loop'' feature. This probably won't work very well. The interesting thing is to observe that it doesn't work.
   
   
4. Listen and critique. This is the most important part. Describe as clearly as you can the qualities of trumpet sound that are captured by your simulation, and those that are not.

• Recorded notes from the McGill CD.
  
  
• Snd manual
  
  
• MXV manual
  
  
• DAP features

You should accomplish Step 2 by Thursday 18 April.

1. Take a low recorded trumpet note from the McGill recordings. Inspect it and listen to it with DAP (the ``Loop'' function is especially helpful) and any other tools that you like. Find a region in the middle of the note that seems to represent the overall quality of the sustained portion of the sound reasonably well.
   
   
2. Save a single period from the chosen region as a separate file, and make it into a wavetable in Csound. Unfortunately, CSound only uses wavetables containing numbers of samples that are powers of two. Use DAP's ``Resample Time'' function, specifying ``Frame'' units to resample up to the next higher power of two.
   
   
3. Create a Csound amplitude envelope for the trumpet note. You may do this intuitively by eye, or you may use software tools.
   
   
4. Use Csound to play simulated trumpet scales, arpeggios, songs, or whatever.
   
   
5. Listen and critique. This is the most important part. Describe as clearly as you can the qualities of trumpet sound that are captured by your simulation, and those that are not.

• Recorded notes from the McGill CD.
  
  
• Csound manual
  
  
• Trivial Csound example for you to modify
  
  
• Discussion of a similar project step from 1996, 1999, and 2000, and 2001.
  
  
• My own preliminary work on the horn
  
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  • I used MixView (mxv, but if I were doing it now, I'd use DAP) to select a 726-sample period from a low horn note, resampled it to 1024 samples (using the phony sample rate 44100*1024/726=62201), and saved it as a wav file. Then, I used the ``GEN01'' routine in Csound to read it in as a wave table, and played a 3-octave scale. Here are my files:
    
    
    • horn_sample_1.orc
      
      
    • horn_sample_1.sco
      
      
    • horn_period_1024.wav (temporarily missing---I'll retrieve it soon)

• Compare different amplitude envelopes. In particular, try more and less accurate envelopes, using more and less break points.
  
  
• Study a number of different trumpet notes, and consider how much the envelope shape depends on the pitch of the note. Experiment with CSound instrument definitions that adjust the envelope depending on the pitch.
  
  
• Try wavetables taken from recorded notes at different pitches.

You should do this step quickly, by Thursday 25 April. It won't produce much in the way of interesting new sounds---it's mostly just a programming step to position you for step 4, which has the most interesting listening exercises.

1. Choose one period from a recording of a trumpet note, and find its sinusoidal components by taking a Fourier Transform. Lots of different software tools will do a Fourier Transform for you, but I found Scilab to be most convenient. You may also try out data from the SHARC database.
   
   
2. Construct a simulation of the trumpet in Csound by additive synthesis, adding up some reasonable number of the partials analyzed by the Fourier Transform above. Ignore the phase of the partials, and use only the amplitude information in the magnitude of the Fourier Transform. Use a single envelope to control the attack, sustain, and decay of each note, just as you did in step 1. Add more partials until you can't hear the difference.
   
   
3. Improve the simulation to avoid aliasing, by omitting partials above about 20,000 Hz. This requires a conditional form, since the actual frequency of a partial depends on the pitch of the note.
   
   
4. Add phase information.
   
   
5. Listen and critique. Given the same recorded period and the same amplitude envelope, the results of this step should sound almost the same as the results of step 1. You may be able to hear some differences due to
   
   
   1. omission of some partials,
      
      
   2. approximation of the amplitudes of partials,
      
      
   3. omission and approximation of the phase of partials,
      
      
   4. aliasing in the wavetable synthesis, which is avoided in the additive synthesis.
   
   
   You should also look at the waveforms resulting from different styles of additive synthesis, and correlate the visible differences with the audible differences.

Here is my preliminary work with the horn from 1999. You should be able to update it with trumpet data.

1. My Csound score file, adsyn_horn.sco.
   
   
2. My recorded period, horn_period_1.wav. Since the Fourier Transform function in Scilab does not require the number of samples to be a power of 2, I did not resample the period.
   
   
3. A transcript of my Scilab session to compute partial amplitudes and phases from my horn period. I defined special functions plot_spectrum and arg to help. They are in the file fourier_demo.sci", $GLOBALS["OD_ROOT_URL_PATH"] . "/Scholar/Work_in_progress/Digital_Sound_Modelling/Scilab_demos/fourier_demo.sci") . " "; ?> described with the .
   
   
4. My Csound orchestra file, adsyn_horn_1.orc, performing additive synthesis with 18 partials. The higher partials appear to be so small that they probably don't have much audible impact. I ignored the phase information, and used only the magnitudes from the Fourier Transform.
   
   
5. My Csound orchestra file, adsyn_horn_2.orc, with conditional code to avoid aliasing problems.
   
   
6. My Csound orchestra file, adsyn_horn_3.orc, using the measured phase of each partial

I structured the Csound orchestra files fairly carefully for convenient experimentation with different variations. I normalized the size of the envelope kenv to 1, so that the amplitude value from the note is mentioned only once. To avoid scaling the amplitude of each individual partial, I divided by the sum of all the partial amplitudes (391.34) in the final calculuation of aout. You should be able to do lots of interesting experiments just by changing the numbers in my orchestra files, and possibly adding or deleting lines to handle more or fewer partials, but without changing the basic structure in any way.

This step is the most complicated and labor intensive in the project. You should have a basic structure to work with by Monday 6 May. Then you can spend another 1-2 weeks refining and experimenting.

1. Study the recorded trumpet notes, especially the attack portion of each note, both by listening and by looking at plots of the waveforms. Try to identify a few interesting notes and some characteristics of those notes to try to reproduce by additive synthesis.
   
   
2. Perform time-frequency analysis of one or more interesting notes. Since the trumpet notes are highly periodic, and they are played with very little variation in pitch, you can get pretty good results by taking discrete Fourier transforms of individual periods, using the Scilab functions that I designed.
   
   
3. Synthesize scales of trumpet-like notes in Csound, using additive synthesis with separate amplitude envelope (programmed using linseg for different partials. Start with the minimum number of partials that produced reasonably satisfying results in step 2.
   
   
4. Try more vs. fewer partials, and different approximations to the amplitude envelopes, to discover how much audible difference such details produce. Try grouping several partials together with a single envelope.

1. My Csound score file, adsyn_horn.sco, the same as the one I used in step 3.
   
   
2. My recorded horn note, horn_mf_B2.wav.
   
   
3. A transcript of my Scilab session to compute time-frequency analyses from my trumpet note.
   
   
4. Scilab function definitions to help with your time-frequency analysis.
   
   
5. My Csound orchestra file, adsyn_horn_se_1.orc, performing additive synthesis with 6 partials, using a separate amplitude envelope for each partial, and leaving all the phases at the default.

1. Vary the frequencies of partials, as well as their amplitudes, in the early stages of the attack.
   
   
2. Add a small amount of noise at the initiation of the note.
   
   
3. Vary the decay characteristics of different partials.

Usually, the next recommended step is to add a filter to shape the spectra of notes at different pitches and eliminate the chipmunk effect. Many instruments have low notes that sound far too buzzy or nasal when shifted up to high pitches with the same relative strengths of different partials. To get a useful estimate of the right spectral profile for this filter, you need to compare spectra of several notes across the whole range of the trumpet. Greg Sandell's SHARC project has some average spectra that you can use for this purpose. You can compute your own averages using the FT function in Scilab. Or you can use some more sophisticated software that my Ph.D. student, Ilia Bisnovatyi, created. If you would like to work on a formant filter for the trumpet, please post questions and comments, and I will help you work out your methods in more detail. Since the chipmunk effect is not very dramatic in the trumpet, I expect a greater interest in the noise component.

In the best harmonic additive synthesis that we've achieved so far, we are still missing a certain high-frequency nasal or buzzy quality in some of the recorded notes. We have some indication that part of this quality can be produced by adding more of the higher harmonics. But some of those higher harmonics seem to stand out too much in the synthesized sound.

I suspect that there is a broadband noisy component to typical trumpet notes, derived physically from the hissing of air through the instrument. Such a noisy component might produce the buzzy quality that we've observed, and it might also soften the impact of higher partials by masking them.

Analyzing the noise component is a bit challenging. The basic idea is to take a very accurate harmonic synthesis, subtract it from the recorded note, and analyze the difference. If the harmonic synthesis is accurate enough, the remainder is essentially the noise component. Unfortunately, since the noise component is spread over a large range of frequencies, it can be perceptually loud even though it is numerically small. So the harmonic synthesis may need to be numerically accurate even beyond the requirements of perceptual accuracy.

I suggest that you take a substantial number of periods (perhaps 10, perhaps 100) from the sustain portion of a chosen trumpet note. Try to find a segment with very little amplitude or frequency variation. I think that there is very little frequency variation overall, but amplitude may be a problem. Set the endpoints of your segment carefully to get a precise integer number of periods.

Take a Fourier transform of your chosen segment, and find the peaks corresponding to harmonic partials. Zero them (or set them to some arbitrary very small value, in case division by 0 becomes a problem) by just reassigning their values in the spectrum vector. Look at the remaining part of the spectrum. If it has a fairly flat magnitude, and random-looking phase values, then you have a reasonable basis for estimating a noise component.

Complication: any amplitude modulation in the sequence of periods will spread out the harmonic peaks. You may have to remove a few frequency bins to each side of each peak in order to squelch the harmonic component. If the AM sidebands spread so far that they mask the noise component even halfway between harmonic peaks, then we'll have to try something more sophisticated. I'll reserve comment on that something until someone reports on an attempt with the simpler approach.

Why not analyze a single period, to avoid the AM sidebands? The analysis of a single period only provides the harmonic partials, and loses the indication of noise. Why not perform a higher frequency-resolution analysis of a single period, by padding with 0s? That gives you an analysis of a pulse containing a single period. The sharp turning on and off of that pulse amounts to a very severe sort of AM. Each harmonic partial generates a sinc-shaped spectral component, which will mask the evidence of a low-amplitude noise.

Variation: from a visual inspection of a trumpet recording, it appears that noise content might occur in very short pulses around the fundamental frequency. It makes sense that such pulses could result from turbulence in the air flowing through the reed, since the reed opens for one or a small number of very short pulses each period. It's not clear how best to try to analyze this possibility. You could select the apparent pulse regions by eyeball, and compute spectra. But they are so short that I'm not optimistic about getting useful results. You could work constructively: make a reasonable guess, compute such a sequence of pulses, and listen to the result.