**Thoughts about Electronic Music**

Additive sound synthesis is the oldest method of making synthetic instruments; this is how an acoustic organ produces tones with its pipes and stops. The organ dates back many centuries to the Romans and also Medieval Europe. The construction of church organ in the Middle Ages was that ages space program. Of course for electronic music additve synthesis is done on electronic keyboards or via a computer program by adding sine waveforms produced by oscillators. Here is an amplitude output which is graphed as

y = a sine( ft) + b sine( 2ft) + c sine( 3ft) + d sine( 4ft) + ... etc

where the a,b,c,...s are the amplitudes of the oscillator sine wave output, t is time and f is 2 times phi times the fundamental of the tone being produced. Each sine term in the above sum is like the output of one organ pipe. With different amplitudes for enough added sine waves, for example, one could get a "stringy" sounding ramp waveform.

However, large acoustic pipe organs with many pipes are very exspensive; some can cost around $200,000; also even on a modern personal computer programs that can add a large mumber of waveforms still use large amounts of memory.

So around 1967 John Chowning and his students at Stanford University created a new technique to create synthetic sounds by using frequency modulation(FM) much like FM radio does to produce a broadcast. By 1983 they produced the famous DX7 electronic keyboard which used this technique.

Here is one mathematical function which could be used for this type of modulation technique:

y = A*cos[( 2*phi* fc*t) + I + K*cos(2*phi*fm*t)] where A and K are amplitudes and t is time and fc represents the carrier wave frequency; fm represents modulating wave frequency. The " * " means multiply and " I " is the phase shift.

FM synthesis produces excellent percussive sounds and with proper filtering other excellent sounds as well. In my opinion it is unfortunate that sampling keyboards and sampling computer progrqams have almost completely replaced FM synthesis

There are other types of electronic applications such as sound processing and algorithmic copmposition used in electronic music.

Vocoder, see http://en.wikipedia.org/wiki/Vocoder, and granulations, see

http://www.sfu.ca/~truax/gran.html or

http://en.wikipedia.org/wiki/Granular_synthesis , are interestiong techniques which as far as I know are unique to electronic music. Also synthetic reverberation both as hardware and software has been created for many types of actual reverberation.

A good website to begin learning about algorithmic composition is http://ccrma-www.stanford.edu/~blackrse/algorithm.html .

Also Fractals can be used in electronic music or composition. There are web sites listed below in" Some related web sites" for fractal information.

Personally, over the years I have collected a folder full of adopted formulas from various sources. I have used these transformed formulas for sound or music creation. I often transform these formulas from computer graphics programs which generate fractal graphic designs. To do this effectively one needs skills in algebra and some knowledge of a sound processing computer system which uses some programing language; I use the Kyma sound processing system which uses Script (Small Talk).

Then I use the arithmetic of modular numbers to a base such as 12, 18,24, etc. to get the set of tones in a particular range from the numbers the fractal formulas are generating.

My personal musical creed:

To create a music which is instrumentally expressive and which uses mainly electronic instrumental technology and which is also based on contempory acoustcal knowledge and mathematics.