# Synthesis Theory (Spring Term)

## Final Exam: May 7th (Tuesday), 2-3:20 pm

- Frequencey Modulation (sub-audio rate) (3.2.14)
- Periodic Vibrato (3.2.15)
- Random Vibrato (3.2.16)
- Exponential envelopes (3.2.8)
- Karplus-Strong Algorithm (3.4.5)
- Frequencey Modulation (a la Chowning) (3.5.1)
- Non-linear waveshaping - Chebyshev polynominal (3.5.4)

- Spectrum measurements (2.3)
- Digital filters (2.4)
- Bandlimited excitation sources (3.4.2)
- Time-varying digital filters (3.4.1)
- Formant (vowel) synthesis (3.4.6)

### Assignment #16 - Due: Apr. 18

Write a csound program using subtractive synthesis techinique (buzz & reson),
to imitate the first four notes in Handel's Messiah Hallelujah chorus.
Assume your choir has about 4-10 singers to a part (i.e. use chorus
effect, such as different attack time, pitch variance, and different vibrato.
Please have the sound file ready to play on the 314 computer.
Optionally, add some reverb (assume this is performed in a live church).

### Assignment #15 - Due: Mar. 28

Write an FFT program That accepts sound file as input and variable N.

### Assignment #14 - Due: Feb. 22

1. Show that if modulation frequency is N x carrier frequency and if
N is an even number, the resulting FM spectrum contains only odd numbered
harmonics.
2. If modulation frequency is 3 x carrier frequency, then what is missing
in the resulting FM spectrum.

3. Find the 10th element (T_{9}) in Chebychev's polynomial.

4. Prove that FM is a non-linear system.

### Assignment #13 - Due: Feb. 13

Use FM instruments (brass, woodwind, soprano and pecussion) to orchestrate
the music on p.191 or something similar.

### Assignment #12 - Due: Feb. 6

Use exponential curve envelope function and Karplus-Strong Algorithm to create a 10 sec. piece.

### Assignment #11 - Due: Jan 25

Produce using C, one second, single note (sine wave) with amplitude envelope, tremolo, and enveloped random vibrato.

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