History[ edit ] By the midth century, frequency modulation FM , a means of carrying sound, had been understood for decades and was being used to broadcast radio transmissions. Patent 4,,  is actually based on phase modulation , but the results end up being equivalent mathematically as both are essentially a special case of QAM. Several other models by Yamaha provided variations and evolutions of FM synthesis during that decade. Casio developed a related form of synthesis called phase distortion synthesis , used in its CZ range of synthesizers. It had a similar but slightly differently derived sound quality to the DX series. His , and dual oscillator modules had a specific FM control voltage input,  and the model Music Easel had a modulation oscillator hard-wired to allow FM as well as AM of the primary oscillator.
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Yamaha bought the patent from Chowning and began producing digital synthesizer prototypes in the late seventies. The Carrier Frequency is most related to the pitch or the fundamental frequency and is usually controllable with a keyboard or other MIDI input. For any given Modulator frequency, it is the Modulation Index and, therefore, the amplitude of the Modulator that determines the amplitude of each of the components in the spectrum of the output signal.
So even in the case of simple FM, the addition of envelopes to alter the amplitude of the Modulator and the Carrier can drastically effect the resulting timbre. At the heart of the method is the concept of sideband frequencies. These are sum and difference tones that are generated during frequency modulation. So below is an example of simple sinusoidal FM where fc is the carrier frequency, and fm is the modulating frequency. Russ More complex FM systems can have several operators that are interconnected in various ways.
The DX series had six operators which could be connected in up to 32 configurations that could include, multiple carriers, multiple modulators, multiple modulator and carrier pairs, feedback systems, stacked and additive systems and combinations.
Below are 8 examples and more can be found at the link below. Each number represents an Operator connected in various ways. Image Source Adding the use of wave shapes other than sine waves and combining and routing operators functioning as multiple carriers and modulators enables the creation incredibly complex sonorities at relatively low computational cost in terms of current CPUs.
The relationship between the frequency of the Carrier and the Modulator need not be harmonically related, which introduces another source of timbral variety and the ability to create rich dissonant textures.
Below are some examples and descriptions of the how they were generated. Variations in Modulation Frequency.
Introduction to FM Synthesis
That year, a big batch of inexpensive, low parts count synth kits showed up at my doorstep after a long wait. My own take on the EFM diode filter, finished, tests working. My only EFM unbuilt kit that still has the all the parts NOS in bag, circa ! Still have sommore EFM, over 15 years old, unbuilt.
Frequency modulation synthesis
Electronics For Music- EFM