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Advanced Audio Recording

Introduction to Quadratic residue diffusers

In modern studio design acoustic diffusers are used to control wall reflections and create a smoothed sound environment to make it easier for the mixing engineer to judge the true sound of a recording. Acoustic Diffusors make use of interence effects of super imposed partial waves as explaned here.

QRD - Sound Treatment

A common method of defining the wells' depth is to use the residue value of a division from the square of the coordinate and a prime figure.

quadratic residue equation with modulo

Quadratic residue calculated by modulo function.


QRD - Diffuser Examples

Two example configurations are shown below using dedicated offsets for the well number on order to optimize the height:

acoustic diffusers using quadratic residue equations 

Quadratic residue diffuser using 11 wells per period.


acoustic diffusers using quadratic residue equations using 13 wells

Quadratic residue diffuser using 13 wells per period.



Because of mathematical reasons the resulting well depths are fully symmetrical around a special number of well (here the 14th well with no13). Apart from the original definition given by Schröder, it is also possible to add an offset to obtain a zero value as either one or two well lengths and then leave them way by using the wall left and right from the diffuser, or move it into the middle. For more than one diffuser, the definition 2-13 should be built and placed with one well width in between to obtain an infinite pattern.

optimized placement of quadratic residue diffusers to fill wall completely

According to my investigations it should be of most advantage to completely fill the rear wall with diffusers that way that a modular pattern is repeated and size is optimized in order to create a pattern that is automatically mirrored by the wall. Reflections will reach a virtual diffuser which place and shape continues the given pattern for an ideal infinite diffuser. The same method may take effect regarding the wall and the top in a room.


Alternate Design

On the other hand mixing design frequencies might be an approach too.

Cinema 4D Model of an acoustic diffuser with two different elements

acoustic diffuser with two different elements


Conclusion and Summary

 Modified quadratic equations can be used to obtain optimized sound diffusers.


 See the former article about Diffuser Concepts

 See also other Diffusers

 You may also want to have a look at the article Studio Design  



© 2003 J.S.