Basic Sound Library
Following is based on “Musical Notation for Computers”, which
one can find on the same site, next to this presentation.
To construct a
composition, a Music/sound Composer needs a Sound Library – a group of patterns
of sound, which we call “sound-images”.
There are three groups of
sounds-images.
One is a group of “musical tones” –
periodic vibrations of steady level of intensity.
The other group consists of patterns
of sound intensity rump-up to a musical tone or fade-out from a musical tone.
The third group consists of
patterns of transitions from one musical tone to another musical tone.
Parallel lines of coordinated in
time execution produce various accords.
Note, that “parallel execution”
does not mean “parallel computing”. A computer program produces a sound file
with digitized presentation of changing in time sound. For each time point of digital
presentation of sound, the program walks through all lines of “parallel
execution” and adds corresponding values of sound intensity.
Following Sound Patterns
are simple enough that they do not distract a Composer with unexpected sound
phenomena and allow him to focus on the structure of the “message”. When the composition
is ready, the Library of these Sound Patterns could be replaced with another,
more sophisticated one.
Pure musical tones are
all of the form:
a*sin(f*t)
where
a – intensity of the sound (amplitude),
f – frequency of sound vibration,
t – time from the beginning of the
musical phrase(!).
Such definition
sometimes requires air pressure caused by the sound in the beginning of the
musical tone to be more than zero. Fortunately, we have transitional sounds,
which could be used to bring air pressure to desirable level. A Composer specifies types of transitional
sounds and the program computes their parameters.
To specify a harmonious
accord, we need:
“leading frequency” F,
“leading intensity” A,
group of pairs (g,n),
where:
g – real number,
n – natural
number (1,2,3..).
Each component of the accord is a
sound of the form:
A*g*sin(F*n*t).
We divide components of
the accord into two groups:
·
“main” group of high value of intensity coefficient A*g
·
“timbre” group of low value
of intensity coefficient A*g.
Most often, we use the “main group”
consisting of only one component, and when we use the “main group” with many
components, we define values of intensity in the way, that there is a leading
component with the value of intensity detectably larger, than others.
Transitional sounds are not
periodic and we create them with “modulation functions” by applying these
functions to existing periodic sounds as follows.
Transitional sound from a tone to a
silence is created first by extending the tone in time beyond its interval forward
and next by multiplying it by a smooth modulation function, which is moving in
time from value “one” to value “zero”.
Transitional sound from a silence
to a tone is created by extending the tone in time beyond its interval backward
and next by multiplying it by a smooth modulation function moving in time from
value “zero” to value “one”.
Transition from one tone to another
tone is done as a combination of these two methods:
-
a tone in the front is extended backward and
modulated into silence
-
a following tone is extended forward and modulated
into silence
-
after that, these
two sounds are added up.
Alexander Liss 12/29/2019