Instructions | Deliverables | Walkthrough | References

Detailed Instructions

You can do this lab in any programming language, however, you MUST create your own musical notes using a low-level cosine function. If you use any music synthesis API, you will receive no credit for the lab.

Following instructions assume you're using python.

  1. Create a program lab2.py
  2. Find a song that contains at least 6 notes. For each note, figure out its frequency, duration, and starttime. To compute frequency, you might find this table to be useful. To compute duration and starttime, I recommend that you choose a tempo (in beats per minute or bpm), then compute the duration of a quarter note as quarternote=Fs*60/bpm, then compute the duration and starttime of every note with respect to quarternote. Finally, create lists to hold these pieces of information:
    frequencies=[freq1,freq2,...]
    durations=[dur1,dur2,...]
    starttimes=[stt1,stt2,...]
     where you would replace freq1 by a number, and so on.
  3. Create a numpy array long enough to hold all of your notes. songaudio=np.zeros(durations[-1]+starttimes[-1]).
  4. For each note: calculate sample values, and add them to songaudio at the right times. Something like
    for notenum in range(0,len(frequencies)):
    for n in range(0,durations[notenum]):
    songaudio(starttimes[notenum]+n) += math.cos(2*pi*frequencies[notenum]*n/Fs)
  5. Convert your songaudio from floating point to 16-bit integer, using the np.ndarray.astype function. First you'll need to scale your values so they don't all get set to zero. The maximum possible 16-bit integer is +/-math.pow(2,15). If you've added together up to four notes, then your songaudio array already contains values up to +/-4, so you want to multiply by math.pow(2,13). So you should be able to do something like:
    wavframes = math.pow(2,13)*songaudio.astype('int16')
  6. Use wave to save the result to a wav file. For example,
    with wave.open('lab2.wav','wb') as f:
    f.setnchannels(1)
    f.setframerate(Fs)
    f.setsampwidth(2)
    f.writeframes(wavframes)
  7. Compute the energy spectrum of your song, as a function of pitch in semitones. For each pitch (A0 is pitch 0, A4 is pitch 48, and so on), add the power of the sinusoid (1/2, if the amplitude is 1), multiplied by the duration of the sinusoid.
  8. Compute the level spectrum = energy spectrum in decibels. To do this, you'll need to calculate 10*math.log10 only of the pitches that have a nonzero energy spectrum. log10(0) is undefined, so if any pitch has a zero energy spectrum, leave its level spectrum also at zero (or at -60, or at some other small value which is lower than the levels of all nonzero energies)
  9. Use matplotlib.pyplot.stem to create an image showing the level (in decibels) as a function of pitch (in semitones). Use matplotlib.pyplot.xlabel to label the X axis, matplotlib.pyplot.ylabel to label the Y axis, and matplotlib.pyplot.savefigure to save the image file.

Deliverables

By 1/31/2017 23:59, upload to compass the following things:

  1. A wav file containing your song.
  2. An image file showing the energy spectrum of the song, as a function of log frequency. Abscissa should be labeled in semitones over A0 (12*math.log2(f/27.5)). Ordinate should be labeled in decibels below most powerful note (10*math.log10(power*duration)).
  3. A program that creates the song, and the figure. If not python, provide a comment specifying how to run it.

Walkthrough

Here is a video walkthrough of lab 2.

References