Part 1: Single Note

For this section, a velocity recording of a single pluck on an electric guitar is used. This recording has been split apart into six components. Since the sum operation is analogous to the mix operation on a mixing board, the components may be summed together yielding the original pluck. The first five components correspond to the first, second, third, fourth, and fifth harmonics (sinusoidal components) of the pluck. The sixth component is the residual. It is the difference between the original pluck and the sum of the first five components. This ensures that summing all six components yields the original pluck recording. In an approximate sense, the residual component contains the 6th, 7th, 8th, etc... harmonics of the pluck as well as measurement noise.

1. Download the archive 2-1.zip, and extract the files included inside it. One of these is the laboratory patch 2-1.pd, which you should open in pd. The other files are audio files, which will be loaded automatically by the patch.

2. Ensure that the patch is not in editing mode, and check the ``compute audio'' box in the main pd window.

3. The volume adjustments are implemented using horizontal sliders to conserve space. This means that when a slider is placed fully to the left, the volume for the corresponding component should be zero. Fully to the right corresponds to a loud volume. Move the ``global volume reset'' slider so that it is about 25% to the right of the far left. Notice that this resets the volumes of the six channels below. Then click the light-beige ``START PLAYING'' button. Adjust the global volume reset slider until the volume is comfortable. The six components are being summed to produce the original pluck.

4. Check the ``LOOP ON'' box in the upper left-hand corner of the window. Now click the ``START PLAYING'' button so that the pluck will be played repeatedly. The spectrum should look similar to one shown in Figure 1.

   Figure 1: Example spectrum from patch 2-1.pd of part of a single note.

   

5. What is the fundamental frequency of the plucked string recording?

6. Try reducing the volume of the residual component. How does the sound change? Does it still sound like a real instrument?

7. Use the global volume reset to set the volumes for all of the channels to zero. Try increasing the volume of the first component, listen, and describe the sound. The first harmonic component is approximately an oscillator at the frequency $f_0$ whose amplitude is varied with time. Repeat the procedure for each of the other components. Describe how the residual component sounds.

8. Experiment with applying different volumes to the various components to see what kind of sounds you can produce.

9. What sets of volumes may you choose to make the note sound as if it had been played an octave higher on the guitar? Mathematically, this means that the new fundamental frequency is $2f_0$. To help you check your answer, we provide sound examples for an Eb4 note, and then a note an octave higher, which is called Eb5.

   Eb4 note on a piano vs Eb5 note on a piano (octave higher)

   Eb4 note on an electric guitar vs Eb5 note on an electric guitar (octave higher)