2.2.6 Shape

As already suggested the envelopes do not need to be symmetrical. An isosceles triangle will give a different sonic result to that of a scalene triangle. The envelopes do not need to be linear. A more rounded envelope will result in less disturbance of the spectrum of the grain's content. The most common envelope shape used in granular synthesis is the Gaussian curve1(Gabor 1946: 435). It looks like a bell and is sometimes referred to as a bell shaped curve.
 

With all the parameters available for the envelope it is possible to create hundreds of different types of envelopes. These could be categorised into three basic shapes.

It must be noted that the shape is only a graphic representation of the function of the envelope.
 
 
 
2.2.6.1 Straight-lined
The straight-lined envelopes consist mainly of triangular and trapezium shaped envelopes. The Trapezium is the most common type of envelope because it is simple to make and has all the parameters that are needed. An attack, sustain and release. A triangular shape is even simpler to make, however, many applications require a sustain. Linear shapes are useful because they can be calculated more quickly, and achieve their purpose efficiently. (See fig 2.5)

 
Amplitude 
 Time
Amplitude 
   Time 

     Fig 2.5: Straight-lined envelopes - Triangular and Trapezium shaped.
 
 

2.2.6.2 Curved

Curved envelopes consist of the probability curves such as Gaussian, and Hanning, and also a large range of exponential shaped curves. These are more useful because they have more control over each part of the grain. FOF grains for example are designed by setting two exponential curves over a sine wave. One for the attack, and one for the decay. Because curves can be gradually sloped they are generally used to reduce spectral change induced by windowing. They can also be used for very steep inclines and declines, which is useful for introducing a large spectral change. (See fig 2.6)
 
Amplitude 
 Time 
Amplitude 
 Time 

     Fig 2.6: Curved shaped envelopes: Gaussian (bell) and exponential.
 
 

2.2.6.3 Complex

'Complex' Envelopes are still very new to the idea of granular synthesis. They consist of two envelopes. The first envelope is a sinusoidal type wave. Over the sinusoidal wave is placed another wave, any type of linear or exponential wave is adequate.
 
 
 
Amplitude 
   Time 

     Fig 2.7: Complex envelope shape
 

This type of envelope has, until recently, only been used with an analysis technique called Wavelet Transform (WT). This analysis process was developed by scientists at the University of Marseille in 1988 for physics and acoustic applications. (Boyer & Kronland-Martinet 1989: 51) The wavelet is very similar to a grain, but it's primary service has been analysis of magnitude of frequency, and phase. This analysis technique is used by windowing a sound sample with wavelets. (Roads 1996a: 581). Gordon Monro a mathematician at Sydney University has used Wavelets as a compositional tool. He suggested that this knowledge could be put into practice with granular synthesis. (Monro 1996) At the moment though it lies as a vast new area awaiting in-depth research.
 
 

1A probability curve was suggested by Dennis Gabor, but others have referred to it specifically as a gaussian probability curve. Whilst Gabor did not say gaussian, his mathematics and diagrams imply gaussian distribution. (Roads& Alexander 1996b: 3)