Granularsynthesis

The Granularsynthesis is an innovative approach for the representation and gereation of musical signals. The basic idea is that a sound can be viewed as a (possibly overlapping) sequence of elementar accoustic elements. This accoustic elementar elements are called Grains. The Granularsynthesis builds complex and dynamic events with a large amount of Grains. The attributes and the distribution of the Grains in time define the characteristic of the sound.

This approach implicates a particlemodel for sounds. The single particles, the Grains, last a short moment which aproximates the smallest duration at which duration, frequency and amplitude of an accoustic event still can be distincted (typically a couple of milliseconds). A Grain therefore builds kind of a basic building block for soundobjects.

The basic idea for a Quantum- or a Granular-representation of sounds was set in a series of publications of the British Dude Physicist Dennis Gabor. In his imagination every sound can be formed by a matching combination of thousands of elementar soundgrains. This hypothesis was later mathematically proved by Bastiaans. The Grain is a specifically matching representation for sounds because it combines information in the timedomain (starting time, duration, shape of the Grain-envelope, shape of the waveform in the Grain) with information in the frequency domain (period of the waveform in the Grain, spectrum of the waveform). This is contradistinctious to representations on sample-level, which don't contain any information about the frequencydomain and abstract Fouriermethods which assume that the sounds are sums of indefinately long sinewaves.

Parameter of a Grain

A Grain is defined by following parameters:

• duration of the Grain
• waveform in the Grain
• envelope of the Grain (e.g. Gaussian, Trapezoid, Pulse)

Figure 1.2: Composition of a Grain

Organisation of the Grains

There are several different approaches for the organisation of the Grains. A possible method is to analyse a sampled sound. The collected data of the analys can be changed and finally the according sound will be produced in a synthesis-step (Analysis-Resynthesis).

Other methods only consist of a synthesis-step.

I only present a single method, the Asynchronous Granularsyntheis. There are other studied approaches for the Granularsynthesis, if you are interestd check the links to literature in the detailed documentation.

Asynchronous Granularsynthesis

In the Asynchronous Granularsynthesis (AGS), Grains are spread probabilisitcally in regions on the frequency/time-plane. This regions are called clouds and build the units with which a compser can work.

Figure 1.3: An AGS-cloud

A cloud is defined by following parameters:

• starting time and duration of the cloud
• duration of the Grains
• density of the Grains
• frequencyband of the cloud, usually defined by a lower and upper limiting frequency
• amplitude-envelope of the claud
• waveform(s) in the Grains
• spatial distribution of the cloud (e.g. stereo)

The duration of the Grains can be set to an absolute value in milliseconds, defined depending on the frequency of the Grain or randomly distributed between two absolute values.

The density of the Grains specifies the number of Grains per unit of time. If the density is small, only a few Grains are put into the cloud at random points (asynchronous distribution in the timedomain - that's where the name comes from). If the density is high, the Grains overlap and create rich & complex spectras.

The waveform(s) of the Grains is a very powerfull cloudparameter. You can take e.g. simple sinewaves, sinewaves with their harmonics, a pulse or excerpts of sampled audio material. It's possible to use mixes of different waveformes or a transition from one waveform to another one. Cumulus uses sinewavs with an adjustable set of harmonics. This allows setting the exact frequency of the Grain!

Following picture shows the parameters which are used in Cumulus to define a cloud: