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 – 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:
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