Hammond X66 Organ (three basic waveforms)

These are the three basic types of electrical waveforms which we find in many analog electronic organs. For best results, an instrument should make use of all three where necessary. Filtering circuits can transform both sawtooth and square waves into very good sine waves, and a clipping circuit can make a reasonably good square wave from a sine wave. For authentic duplication of various musical instrument sounds, each of the three types should be available in the instrument. Sawtooth waves that pass through suitable formant filters can yield good imitations of many woodwind, string and brass instruments. Sine waves used in additive harmonic synthesis are necessary for good imitation of various percussion voices such as chimes and bells of various types. Square waves are useful for creating a "hollow" woodwind tone such as the clarinet and they are also more easily filtered down into sine waves than sawtooth waves. In many tone generating systems, it's easier to start by generating square waves and then filtering them down to sine waves rather than to create sine waves directly.

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			Left, a *sawtooth wave*. It contains all harmonics, the amplitude of each is in-versely proportional to its ordinal number, that is, the second harmonic is 50% of the amplitude of the first or fundamental, the third harmonic's amplitude is 33.3% of that of the fundamental, etc. In a theoretically perfect sawtooth wave, the number of har-monics is infinite. In a real, practical saw-tooth, perhaps no more than 50 harmonics are present.
The three types of pri-mary waveforms used in most analog electronic or-gans. Right, upper. A *sine wave. The sine wave has no upper harmonics at all. The sinewave is actually the first harmonic by itself. As a sound wave, it is just a pure, characterless tone. Sine waves are used as individual harmonic pitches in the additive harmonic synthesis system. Right, lower.* A square wave. The theoretically perfect square wave contains an infinite number of odd numbered harmonics only, and like the sawtooth wave, the amplitudes of the individual harmonics are inversely proportional to their ordinal numbers. A practical square wave may have usually less than 50 harmonics. In analog electronic organs, the square wave is useful for imitating certain woodwind instruments like the clarinet whose tone has the odd harmonics emphasized. It is also easy to convert a square wave into a sine wave by simple filtering.


These are the three basic types of electrical waveforms which we find in many analog electronic organs. For best results, an instrument should make use of all three where necessary. Filtering circuits can transform both sawtooth and square waves into very good sine waves, and a clipping circuit can make a reasonably good square wave from a sine wave. For authentic duplication of various musical instrument sounds, each of the three types should be available in the instrument. Sawtooth waves that pass through suitable formant filters can yield good imitations of many woodwind, string and brass instruments. Sine waves used in additive harmonic synthesis are necessary for good imitation of various percussion voices such as chimes and bells of various types. Square waves are useful for creating a "hollow" woodwind tone such as the clarinet and they are also more easily filtered down into sine waves than sawtooth waves. In many tone generating systems, it's easier to start by generating square waves and then filtering them down to sine waves rather than to create sine waves directly.
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The Hammond X66 Organ