Due: At the start of class, Thursday, October 18


Submit: SC file with SynthDef's as needed for all exercises, plus SC statements as your answers for the problems. Do NOT submit audio files, just one SC file with your code.

Problem 1

A harmonic sound has harmonics or harmonic partials with frequencies that are related as whole-number multiples. Our perception fuses all partials of a harmonic sound into a single pitch at the fundamental frequency.

Show this using an altered version of SynthDef \oscili_1c that you create called \oscili_1d. You should change the envelope (Line.kr) to have a steady value of 1.0. Write a SC statement for your oscili_1d that will create a sound with a fundamental frequency of 440 Hz and the first 9 harmonic partials (fundamental + 9 harmonics = 10 partials total). Use a fixed amplitude of 0.05 for each partial and a duration of 5 seconds.

Problem 2

In the region of approximately 20 Hz to 2 kHz the fusion of harmonic partials into the sensation of a single pitch operates even when the fundamental frequency is absent. Show this by using \oscili_1d from Problem 3, and write a SC statement that will play the same harmonic sound from the previous problem but now with durations proportional to the number of partials: partial 1 will be 1 second long, partial 10 will be 10 seconds long. All partials (notes) should start together at time 0 so that you will gradually lose the fundamental, then lose the second partial, then the third, and so on. Question: How many partials do you have to take out to lose the perception of the fundamental?

Problem 3

When two sinusoidal tones reach our ears, our ability to discriminate between the frequency of each tone depends on the difference between those frequencies. Closely tuned pure tones (within 10 to 15 Hz difference) will result in a beating sensation.

To demonstrate this, write SC statements for oscili_1d that will play seven separate pairs of tones with frequency differences of: 3, 5, 7, 9, 11, 13, and 15 Hz respectively. Use the frequency of middle C on the piano as the stationary reference frequency for the experiment. Each tone pair (middle C plus the higher tone) should last three seconds.

Problem 4

Repeat problem 3 now with frequency differences of: 15, 17, 19, 21, 23, 25, and 27 Hz respectively. Use the same reference frequency (middle C).

Question: How do you perceive these sets of pairs? How do explain this?

Problem 5

"Make your own equal-loudness test."

Fletcher-Munson Curves (p. 43 in Dodge) show equal loudness profiles for sinusoidal tones of different frequencies. Those curves are the result of an experiment consisting of giving a subject a sinusoidal reference tone at 1 kHz at a reference intensity level and askingÊ the subject to compare it to a tone of the same intensity but with a differentÊ frequency. The subject is asked to change the level of the second tone until it seems that both tones have "equal loudness." By repeating this test along a range of frequencies, one of the curves in the graph can be drawn.

Make the same experiment using SuperCollider and your \oscili_1d.Ê Write a SC statements that will playÊ for you 2 tones to compare: 1) a reference sinusoid at 1 kHz, amplitude 0.25, and duration of 2 seconds, 2) a comparison tone using the same duration and amplitude but a different frequency. Then, adjust the amplitude of the second tone until you perceive both tones with equal loudness.

When you are done with testing and adjusting one frequency, move on to a new frequency, again starting at amplitude 0.25.

Use the following test frequencies, in this order: 500, 2000, 300, 4000, 100, 8000.

Here is the firs pair of SC statements for your test:


// reference tone at 1KHz
s.sendMsg(\s_new, \oscili_1d, -1, 0, 1, \dur, 2, \freq, 1000, \amp, 0.25);
// comparison tone at 500Hz, allow half a second between playback
s.sendMsg(\s_new, \oscili_1d, -1, 0, 1, \dur, 2, \freq, 500, \amp, 0.25);



You should take the test in this frequency order and wearing headphones if possible. Don't change the output volume to the headphones one you've started the test, or you will invalidate your results.

When done, write down a table showing the test frequencies and your chosen amplitudes expressed in dB, using 0.25 as the reference value for the scale. (That is, a value of 0.25 would be recorded as 0 dB.) Your chart would look something like:

frequency ---> amp in dB
500 ---> your dB
2000 ---> your dB
300 ---> your dB
4000 ---> your dB
100 ---> your dB
8000 ---> your dB

Upload your assigment in 461 Dropbox.