of Microprocessors

18 MUSICAL ApPLICATIONS OF MICROPROCESSORS
-- "'"'- FEELING
120 .-/
120
100
/Xl
~ 80
-S w
:> w-'
60
>-
I-
iii
2
~ 40
~
20
o
V
110- ""'- .-/ .... --'}
/'
100-------- ../V ---'/.
---""--- /, " :/,
::--
* 90
(i)
~~ 1--- ~80
:J:
~~t:--:::----- ~ 70
----- /J;' .-
~t':: ~ :::~
----
~ 60
:> ~f-
~ ~ ::::~~ - UJ ..J 50
""-
~ ,~ (I)
.........................
- V
----
(I)
'-
~ 40 .I J
0
""",-~",
---~ V" -::::l30 )
~ 20
------ /J/' ~'J.
f-L,/J
"".J L-/.
) -~.
./
" ~, 9
,/
--JfI'
-....
./
"- ........... r-.... 10 --./ ,/ /
0--"
""'--
"'"
./ ,/ 1--
! I
"'" ..........
"'-- ~
20 50 100 500 1,000 5,000 10.000
FREQUENCY, (Hz)
*1 PHON, A UNIT OF LOUDNESS, IS NUMERICALLY EQUAL TO THE SOUND
PRESSURE LEVEL IN DECIBELS {dB} BASED ON A 1-I\H% REFERENCE.
Fig. 1-3. Loudness as a function of amplitude and frequency
amplitude level of 60 dB (relative to 10- 16 W/cm 2 in air) frequencies below
35 Hz would be too soft to be noticed. As frequency increases, loudness
Increases also up to about 800 Hz where it levels off to the comfortably loud
level of normal conversation. As frequency approaches the upper limit of
hearing, the apparent loudness again decreases.
The effect on pitch caused by an amplitude change IS much smaller.
Again the effect is greatest at the extremes of the frequency range. In particular,
the pitch of a low-frequency (l00 Hz) sine wave tone decreases as the
amplitude increases. The pitch shift effect is small enough to be ignored,
however, with more complex waveshapes.
The Mathematical Sine Shape
Before moving on to more complex waveshapes and other parameters,
we need to look more closely at the sine shape itself. Why is it the simplest
possible waveform and why is it so important? The name sine wave comes
from the sine trigonometric function. For right triangles, the sine of one of
the other angles is the ratio of the length of the side opposite the angle to the
length of the hypotenuse.
Figure 1-4A shows how this trigonometric ratio can be converted into
a sine wave shape. Assume that the crank, which represents the hypotenuse,
is one unit in length and that it is being turned counterclockwise at a