MATRIXSYNTH: theory


Showing posts with label theory. Show all posts
Showing posts with label theory. Show all posts

Thursday, May 16, 2019

Wavehole Approach to Granular Synthesis Using Xenakis Screens


For those interested, see here.

See here for previous posts featuring Xenakis and granular synthesis.

What or rather who is Xenakis? Via Wikipedia: Iannis Xenakis - "Xenakis pioneered the use of mathematical models in music such as applications of set theory, stochastic processes and game theory and was also an important influence on the development of electronic and computer music. He integrated music with architecture, designing music for pre-existing spaces, and designing spaces to be integrated with specific music compositions and performances."

From the site linked above:

"The wavehole approach to organising acoustic particles is an adaptation of the Xenakis screen. In Formalized Music Xenakis discusses various methods with which to organise grains of sound. A Xenakian screen is not unlike Gabor’s Matrix (1946). The representation is musical and interpreted differently from the theoretical signals presented in Gabor’s communications literature. The Xenakis screen (Fig.1), is a two dimensional grid which, exists in one moment of time."

If you look below you will see an image of multiple Xenakis Screens over time. The screens remind me of a mix of wavetable and granular synthesis. In a wavetable you have a table of multiple waveforms you can morph through. In granular synthesis you typically have a sample or audio you can morph through and manipulate over time either grabbing a "slice" of the audio or particular "grains" within a slice or slices of audio - almost like a hybrid of additive and subtractive synthesis but working with a given audio sample.

"Each cell of the screen grid, houses a silence or grain event. Thus, each screen can have, depending on its resolution, a sparse or dense population of grains. The population is referred to as a cloud. Each occupied cell has a frequency ∆F and gain ∆G parameter. A Xenakis cloud is the grouped grain topology in one screen at a given moment in ∆t as in Fig.2."

Monday, January 07, 2008

Continuous Signal Processing: The Fourier Series


via AH regarding the following question:

"Does anyone know the formula for calculating the resulting harmonics the formula for calculating the resulting harmonics of a pulse wave when the pulse width is varied? In other words, a square wave (or pulse wave with 50% duty cycle) has only the odd-numbered harmonics present; how do you determine the harmonics present when the duty cycle is 25%, or any other value?"

Dave Manley followed up with a link to this site.
"This brings us to the last member of the Fourier transform family: the Fourier series. The time domain signal used in the Fourier series is periodic and continuous. Figure 13-10 shows several examples of continuous waveforms that repeat themselves from negative to positive infinity."

Update: also see this Synth Secrets article on Sound on Sound.
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