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Introduction:
Audio signals describe pressure variations on the ear that are perceived as sound.
We focus on periodic audio signals, that is, on tones.
A pure tone can be written
as a cosinusoidal signal of amplitude a > 0,
frequency wo > 0, and phase angle
q:
x(t) = a cos(wot +
q)
The frequency wo is in
units of radians/second, and
wo/2p
is the frequency in Hertz.
The perceived loudness of a tone is proportional to a0.6.
The pitch of a pure tone is logarithmically related to the frequency.
Perceptually, tones separated by an octave (factor of 2 in frequency) are very
similar. For the purpose of Western music, the octave is subdivided into 12 notes,
equally spaced on a logarithmic scale. The ordering of notes in the octave beginning
with 220 Hz is shown in the following table. Click on the waveform to listen to
the corresponding tone.
| Note | Frequency (Hz) |
|---|
| A | 220 = 220 … 20/12 |
|---|
| A# | 233 = 220 … 21/12 |
|---|
| B | 247 = 220 … 22/12 |
|---|
| C | 262 = 220 … 23/12 |
|---|
| C# | 277 = 220 … 24/12 |
|---|
| D | 294 = 220 … 25/12 |
|---|
| D# | 311 = 220 … 26/12 |
|---|
| E | 330 = 220 … 27/12 |
|---|
| F | 349 = 220 … 28/12 |
|---|
| F# | 370 = 220 … 29/12 |
|---|
| G | 392 = 220 … 210/12 |
|---|
| G# | 415 = 220 … 211/12 |
|---|
| A | 440 = 220 … 212/12 |
|---|
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Demonstration prepared by Kevin Rosenbaum
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