Acoustics

Sound is the perception of vibration of our eardrums.
The Minim package is a user-contributed audio library in the processing library for playing, manipulating, and synthesizing sound.
A musical note is a wave that oscillates at a certain frequency.
We will use concert A, the A above middle C, as a reference note.
Concert A (also known as A440, A4, Stuttgart pitch) has been standardized to oscillate at a frequency of 440 times per second (Hz).
When you double or halve the frequency, you move up or down one octave on the scale. E.g., 880 Hz is one octave above concert A; 110 Hz is three octaves below concert A.

Acoustics, continued

A newborn baby can hear sound waves of frequency between 20 to 20,000 Hz. People lose the ability to hear the high-frequency sounds as they grow older.
The sin function repeats itself once every \(2\pi\) units, so if we measure \(t\) in seconds and plot \(\sin(2\pi t \times 440)\), we get a curve that oscillates 440 times per second.
The amplitude of the wave determines what we perceive as volume. We'll plot our curves between –1.0 and +1.0 and assume the devices that record and play sound will scale as appropriate.
When a guitar string is plugged, the string vibrates, producing a sine wave that is the prominent part of the sound that you hear and recognize as a note.
There are 12 notes on the chromatic scale, evenly spaced on a (base 2) logarithmic scale. For any given note, we get the \(i\)th note above it by multiplying its frequency by \(2^{i/12}\).

For digital sound, we represent a curve by sampling it at regular intervals.
We will use the commonly used sampling rate of 44,100 samples per second.
For concert A, that rate corresponds to plotting each cycle of the sine wave by sampling it at about 100 points.
We represent sound as an array of real numbers between –1.0 and +1.0.