# Synthesis Theory I: Assignment 1

Choose one of the following exercises. Do more than one exercise for extra credit.

Exercise 1:

Write a short piece or compositional study (less than 5 minutes) which is generated solely by additive synthesis. You may use any program to generate the piece. Write a 1-2 page analysis/description of your piece.

Exercise 2:

Plot the loudness at which sound is barely audible for a range of frequencies from 20 to 20,000 Hz. Use at least 20 frequencies: 40, 100, 200, 500, 1000, 2000, 3000, 4000, 5000, 6000, 8000, 10000, 12000, 15000, 16000, 17000, 18000, 19000, 20000. Compare your plot to the Fletcher-Munsen equal-loudness curves around 0-10 dBSPL/phons. Plot the loudness in decibels: 20 * log10(amplitude)

Exercise 3:

Experiment with sound masking (which is the fundamental principle used in MPEG audio compression). Choose a frequency (e.g. 1000 Hz) and set it to a moderately loud volume. Play a second sinewave (say 1100 Hz) at the same loudness and at the same time as the first sinewave. Can you hear both sinewaves? (I hope so.) Reduce the volume of the second sinewave until you cannot hear it sounding with the first sinewave. Plot the loudness at which the second sinewave "disappears". Plot the masking loudness of about 20 frequencies for the same first sinewave. Compare to this sample plot.

Exercise 4:

Synthesize timbres for various instruments from frequency data collected by Carl Seashore in the book Psychology of Music (Call number: ML3830.S4P8 1967 on reserve in the library starting Tuesday afternoon for 350.867). Have several people listen to your instrument syntheses and identify the instruments (don't tell them what it is before they hear it, of course). Which timbres were easy or difficult to identify? Write a 1-2 page analysis of the results.
Here are some example data from the Psychology of Music:

Partial Content of the Bassoon (page 184)
Pitch dynamic Partials as percentage
of total energy
normalized
amplitude/partial
decibels/partial
C5 (523 Hz) forte 87 9 4 0.932 0.3 0.2 -0.604 -10.457 -13.979
C5 (523 Hz) piano 96 4 0.979 0.2 -0.177 -13.979
G4 (392 Hz) forte 41 50 4 5 0.64 0.707 0.2 0.223 -3.872 -3.01 -13.979 -13.01
G4 (392 Hz) piano 84 14 1 1 0.916 0.374 0.1 0.1 -0.757 -8.538 -20 -20
E4 (329 Hz) forte 40 29 25 5 0.632 0.538 0.5 0.223 -3.979 -5.376 -6.02 -13.01
E4 (329 Hz) piano 71 22 7 1 0.842 0.469 0.264 0.1 -1.487 -6.575 -11.549 -20
C4 (262 Hz) forte 2 96 1 0 1 0.141 0.979 0.1 0 0.1 -16.989 -0.177 -20 -inf -20
C4 (262 Hz) piano 5 95 0.223 0.974 -13.01 -0.222
G3 (194 Hz) forte 1 88 10 1 0.1 0.938 0.316 0.1 -20 -0.555 -9.999 -20
G3 (194 Hz) piano 1 79 19 1 0.1 0.888 0.435 0.1 -20 -1.023 -7.212 -20
E3 (163 Hz) forte 0 10 87 2 0 1 0 0.316 0.932 0.141 0 0.1 -inf -9.999 -0.604 -16.989 -inf -20
E3 (163 Hz) piano 0 12 86 1 0 1 0 0.346 0.927 0.1 0 0.1 -inf -9.208 -0.655 -20 -inf -20
C3 (130 Hz) forte 0 8 58 23 10 0 0 0 1 0 0.282 0.761 0.479 0.316 0 0 0 0.1 -inf -10.969 -2.365 -6.382 -9.999 -inf -inf -inf -20
C3 (130 Hz) piano 4 14 52 29 1 0.2 0.374 0.721 0.538 0.1 -13.979 -8.538 -2.839 -5.376 -20
G2 (97 Hz) forte 1 1 7 25 59 7 0.1 0.1 0.264 0.5 0.768 0.264 -20 -20 -11.549 -6.02 -2.291 -11.549
G2 (97 Hz) piano 2 2 4 62 25 5 0.141 0.141 0.2 0.787 0.5 0.223 -16.989 -16.989 -13.979 -2.076 -6.02 -13.01
E2 (82 Hz) forte 2 0 9 6 9 49 23 1 0 0 1 0 0 1 0.141 0 0.3 0.244 0.3 0.7 0.479 0.1 0 0 0.1 0 0 0.1 -16.989 -inf -10.457 -12.218 -10.457 -3.098 -6.382 -20 -inf -inf -20 -inf -inf -20
E2 (82 Hz) piano 11 3 2 16 4 42 2 1 16 1 0.331 0.173 0.141 0.4 0.2 0.648 0.141 0.1 0.4 0.1 -9.586 -15.228 -16.989 -7.958 -13.979 -3.767 -16.989 -20 -7.958 -20
Data for cut/paste: all energy data all amplitude data all decibel data
PERL program to convert from energy: to amplitudes to decibels

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