Exercise 3

Readings:

Please read Chapter 3: Spectra from Miller Puckette's website.
Also, Chapter 2 from the Pierce book.

Exercises:

1) a) How many octaves above the fundamental is the 11th harmonic?
b) if the fundamental is 440 Hz, what is the frequency of this harmonic?
2) What is the closest equal temperament approximation to the interval between the 4th and 5th harmonic?
3) A low-pass filter has a frequency-dependent gain (as a ratio, not in dB) of
g(f) = 1/sqrt(1+(f/500Hz)) .
What is the gain, in dB, at 2000 Hz?
4) A virtuoso flautist, playing a perfect 1 kHz tone, generates only the first 3 odd harmonics with her instrument. At that very moment, a tugboat passes by and sounds its 55 Hz foghorn, containing the first 20 harmonics (even and odd).
a) What are the two harmonics closest in frequency to each other in this coincidence?
b) Are they within 10 Hz of each other?
c) Are they within a critical band?

Home Lab:

Critical bands and loudness. This project tries to investigate how loudnesses of clusters of sinusoids are perceived differently when they are spaced withing a critical band than otherwise. For this experiment you should try to set yourself up with a reasonable listening environment, either using headphones or playing through a stereo (but not your laptop speaker).

Start by connecting a single ``sinusoid" object with frequency 1000 Hz. to an ``switch" object (these objects are both in the Music 170 library).

Now make another version (in the same patch) with four sinusoids tuned to 960, 980, 1000, anad 1020 Hz.. Connect all four to th input of a second ``output" so that you can turn them on and off as a group, independently of the first one.

Make a third group of objects in the same way (or just duplicate the second group) but now set the frequencies to 500. 1000, 2000, and 4000.

Now, by turning them on and off (using the on/off control on the three output objects) equalize the outputs until all three are at a comfortable (reasonably soft) listening level. (If you have to push any of the output gains past about 90 dB, you should turn up your speaker instead. On my system I'm using gain values between 50 and 70.)

Now adjust the three output gains so that, as you turn them on one at a time, you judge them to have roughly equal loudnesses. Write down the three gain values you had to use to equalize them.

Since the four frequencies are roughly at the same level on the equal-loudness contour chart (Wikipedia is your friend), the different frequencies should be less a factor than the spacing. Is it in fact nearly true (or totally false) that in the close spacing example, you ended up adjusting the complex tone so that its power was roughly equal to the power of the single 1000 Hz. tone? Is that still true when the four frequencies are spread widely (500-4000)?