User Manual

Sound in Our World
unnerving and unpleasant. Most electronic
speech processing systems being developed
use some form of speech prediction filters.
Take a piece of string or rope roughly 4 feet
long and tie one end of it to a chair or other
piece of furniture. Swing the other end up and
down so that you have a cyclic pattern, as
shown:
Now swing it three times as fast (three times
the frequency), to produce this pattern:
Now try to swing it five times as fast (five times
the frequency), to produce this pattern:
Since the later patterns are frequency
multiples of the first, we refer to them as
overtones (the music term) or harmonics (the
electronics term) and the original pattern is
called the fundamental. If you could combine
all three of the above patterns onto the string
then you would get a pattern, which looks like
this:
This combined pattern (a single fundamental
with overtones) is called a tone (and a pure
tone is a single fundamental with no
overtones). Notice that each pattern is more
difficult to produce than the one before it, with
the combined pattern being quite complicated.
And also notice that the more complicated
patterns are much more interesting and
pleasing to look at than the simpler ones. Well
the same thing applies to sound waves.
Complex patterns that have many overtones
for each fundamental are more pleasant to
listen to than simple patterns. If many
overtones were combined together, the results
would approximate a square wave shape.
All traditional music instruments use this
principle, with the instrument shapes and
materials perfected through the years to
produce many overtones for each fundamental
chord or key that is played by the user. Grand
pianos sound better than upright pianos since
their larger shape enables them to produce
more overtones, especially at lower
frequencies. Concert halls sound better than
small rooms because they are designed for
best overtone performance and to take
advantage of the fact that sound waves can
reflect off walls to produce different overtone
relationships between both of your ears. The
same thing applies to stereo sound. You may
have heard the term acoustics; this is the
science of designing rooms for best sound
effects.
A commonly used musical scale (which
measures pitch) will now be introduced. This
scale is called the equal temperament scale,
expressed in hertz. You might think of this as
a conversion table between the artistic and
scientific worlds since it expresses pitch in
terms of frequency. Each overtone (overtone
0 being the fundamental) is divided into 12
semitones: C, C# (“C-flat”), D, D#, E, F, F#, G,
G#, A, A#, and B. The semitones increase by
the ratio 12:2, or 1.05946. Musical notes
(tones) are the measure of pitch and are
expressed using both the semitone and the
overtone, such as A3, G#4, D6, A#1, and E2.
(frequency in hertz and rounded off)
-13-
Overtone C C# D D# E F
0 16.4 17.3 18.4 19.4 20.6 21.8
1 32.7 34.6 36.7 38.9 41.2 45.7
2 65.4 69.3 73.4 77.8 82.4 87.3
3 130 139 147 156 165 175
4 262 278 294 311 330 349
5 523 554 587 622 659 698
6 1047 1109 1174 1245 1319 1397
7 2093 2217 2344 2489 2637 2794
8 4186 4435 4698 4978 5274 5588
9 8372 8870 9397 9956 10548 11175
Overtone F# G G# A A# B
0 23.1 24.5 26.0 27.5 29.1 30.9
1 46.2 49.0 51.9 55.0 58.3 61.7
2 92.5 98.0 104 110 117 123
3 185 196 208 220 233 247
4 370 392 415 440 466 494
5 740 784 831 880 932 988
6 1480 1568 1661 1760 1865 1976
7 2960 3136 3322 3520 3729 3951
8 5920 6271 6645 7040 7459 7902
9 11840 12542 13290 14080 14917 15804