Any waveform (even complex), can be produced by adding sinus waveforms together. A sinus waveform is a wave that contains only one frequency and no further frequencies, ie no overtones or subtones. This sinus waveform can act as a base in a more complex waveform.
As an example, we may create a voice "aaaa" just by adding sinuses with different frequencies toghether.

A sinus waveform (alone, or in a more complex waveform) with the lowest frequency may be called the base frequency, or the fundamental frequency. To add sinus waveforms we have to add them in multiples to this base frequency, ie the additional frequencies has to be the double, triple etc, of the base frequency. Lets call the base sinus frequency sinus 1, and each multiple sinus 2, 3 etc. The frequency of the sinus 2 is exactly one octave above sinus 1 (1 octave = 12 semitones). Hence, sinus 3 is two octaves above sinus 1, one octave over sinus 2 and so forth. So the frequency doubles up between each octave frequency, sinus 2, 4, 8, 16, 32 etc.
To create a complex waveform we have to add several sinus waveforms together. In fourier synthesis, the minimum interval between each tone, as stated, is one octave. (Basically so, since it is possible to create effects by (slight) detuning. However, this is another story.)

To create a complex waveform like a voice, more than 50-100 sinuses are seldom needed, otherwise you would most often and unnecessarily exceed the audible 20KHz range. For a simple sound like a church organ tone you may need only 2-3 sinuses but a complex sound like a voice may require 50 sinuses. A sound like a sawtooth waveform may need 100 sinuses to obtain sufficient or full brilliance, if the base frequency is low. Otherwise, if the base frequency is higher, we need a less number of sinuses to create a sawtooth waveform since the highest sinuses of the sum waveform would exceed the 20KHz range anyway.

If we want to emulate a lowpass filter on a sawtooth waveform (or any other wafeform as well) then we would modulate the amplitude of the highest sinuses. Accordingly, to emulate a resonant filter shape, we would emphasize the sinuses around the "cutoff" frequency.
Consequently, thinking of other filter types, as of emulating a highpass filter, the amplitudes of the lowest sinuses are modulated.
To produce fm synthesis alike sounds we need perhaps 2-20 sinuses although it is more complex to emulate a changing fm waveform.

Now lets look at some examples using my program "box":
You can see the resulting waveform to the right bottom at each picture. At the right, the middle window, shows which sinuses are activated with the lowest frequency to the left. (At the left side the sinus editor but this is not important here.)

Here we see a single sinus waveform.


Here we have activated sinus 1 & 2 and as you can see, the resulting waveform, where sinus 1 & 2 are added together.


Here we have activated the sinuses 1, 2, 4, 8, 16, 32. This sounds like an organ.


To emulate a voice, an "aaaa", although not fully accurate, we need the following parameters:


A sawtooth waveform looks like this:


And a filtered square with only a few overtones:


Here are some examples to listen at, all of them made through fourier synthesis.

1. sinus1.mp3 - Fm synthesis type sound.

In my my latest cd the melodies are very happily calming. It is clearing up your mood actively, and releasing and energizing you.     (Unlike many new age type music, that may obscure the mind in a distorting and passive way.)

After a lot of work in developing my own programs related to fourier synthesis, sequencing and composing, I think that my music indeed brings positive strength to its listeners. This is also a part of my personal goals, in bringing a positive meaning into this world of sadness and egoism.
Buy my cd - ordering.

Info, text and images: Olof Hasvén
Support and editing:    Dick Palmé

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Fourier composing is a new way of creating msuic through a pure instrumentational build up, using sinus waveforms in order to create more complex sounds. This way of making music is of a new kind and is called fourier syntethic music or fourier synthesis music.

Fourierkomponering är ett nytt sätt att skapa musik på genom en ren instrumentaionsuppbyggnad, genom att använda sinustoner för att åstadkomma mer komplexa vågformer.
Detta sätt att skapa musik är av ett nytt sätt och kallas fouriersyntetisk musik eller fouriersyntesmusik. Till skillnad mot att använda en synt eller flera syntar så kan man i en pc med dedikerade program åstadkomma mer eftersom det blir bättre överblick och detta gör att arbetet går anabbare. Inte heller har man i ett dedikerat program ett antal onödiga parametrar utan det är enkelheten som eftersträvas, för att få in tid till att skapa fram tydlighet i musiken i avseende på melodi och ljudbild.