![]() ![]() A fundamental frequency (blue) with 2nd harmonic (red) and 3rd harmonic (green) Taken together, this is referred to as the ‘harmonic series’. The second harmonic is 2x the fundamental frequency, the third harmonic 3x and so on, ad -infinitum. Each ‘stop’ in this mathematical series is given a number: the fundamental frequency is also the first harmonic because it is 1x the fundamental frequency. There is a special category of partials called harmonics – and these are partials whose frequency is a multiple of the fundamental frequency: twice the fundamental frequency, three times the fundamental, four times and so on. Most algorithms also provide the facility for one operator to be fed back to an earlier point in the algorithm’s chain. Operators connected only to other operators are called ‘modulators’ and their output is not directly audible. Operators connected to the output are called ‘carriers’ – these are the operators that you actually hear. This DX7 algorithm consists entirely of carriers, with no modulators The algorithm chosen for an FM patch has a huge impact on the resulting sound and it very much determines the type of sound a patch can produce – piano, strings, organ, or whatever. The specific routing of these connections is referred to as an algorithm. ![]() Operators are connected either to other operators, or to the synth’s output. The simple waveforms an operator can produce also depends on the FM implementation, but for the purposes of this discussion, we’ll stick with sine-wave operators, as these are common to all implementations. Operators are essentially just oscillators and the number available per-voice depends on the particular FM implementation six-operator and four-operator are the most common variants. The simple waveforms in an FM synth are produced by something called an ‘operator’. This is how FM works: it modulates the frequency of one waveform with another, and in so doing creates complexity in the resulting waveform. If the vibrato rate were to be increased sufficiently, we would perceive timbral rather than pitch changes in the resulting sound. This modulates the pitch of the note at a frequency that’s independent of the note’s frequency, changing its waveform accordingly. When playing a single note on our imaginary guitar, you can add vibrato with your left hand. When playing a chord on this guitar, each note of the chord would be a partial of the resulting waveform changing notes would change the partial content and thus the timbre of the sound produced. The difference between modulation and simply mixing sine waves together is easiest to understand using the analogy of an imaginary guitar whose strings produce sine waves. Rather, it uses one simple waveform to modulate the frequency of another, with the result then being used to modulate another simple waveform, which in turn can modulate another, and so on. ![]() But FM doesn’t just mix together those simple waveforms (although it can). A sine wave is a pure tone comprised of just a fundamental frequency Modulate not mixįM synthesis harnesses this principle in order to generate complex waveforms from much simpler waveforms. Taken to its logical conclusion, this means that all waveforms are made up of a stack of partials with differing frequencies and amplitudes. Technically, each of these sine wave components is referred to as a partial. Similarly, if you were to isolate any one overtone, it too would be a sine wave. If you were to remove all of the overtones from a waveform, so that all that was left was the fundamental frequency, you would have a sine wave in other words, a sine wave is a pure tone with no overtones. Let ’s break things down for you… Partial to partials Now that you ’ve got some insight on the origins of FM synthesis, it ’s time to understand how it works.
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