FM synthesis (frequency modulation synthesis) is a method of sound synthesis that uses one or more modulating oscillators to manipulate the frequency of one or more carrier oscillators. The modulating oscillator is used to modulate the frequency of the carrier oscillator, resulting in the creation of new harmonic content.

The sound is created by using a modulating oscillator to modulate the frequency of a carrier oscillator. As the frequency of the modulating oscillator changes, the frequency of the carrier oscillator is modulated, which creates new harmonic content in the resulting sound. By changing the frequency, amplitude, and phase of the modulating oscillator, a wide range of different sounds can be created, from simple bell-like tones to complex and evolving textures.

One of the advantages of FM is its ability to create complex and evolving sounds using a relatively simple synthesis engine. With careful parameter adjustment, sound designers and music producers can create a wide range of sounds, from warm and mellow to harsh and metallic.

FM synthesis was popularized in the 1980s with the introduction of the Yamaha DX7 synthesizer, which used FM synthesis to create a wide range of sounds, from realistic pianos and brass to experimental and avant-garde textures. Today, FM synthesis remains a popular method of sound synthesis, used in both hardware and software synthesizers, as well as in sound design and audio production more broadly.

Ratio refers to the relationship between the frequency of the modulating oscillator and the frequency of the carrier oscillator. The modulating oscillator is used to modulate the frequency of the carrier oscillator, which results in the creation of new harmonic content.

The ratio between the modulating oscillator and the carrier oscillator determines the type of harmonics that are produced. When the ratio is low (i.e., less than 1), the modulating oscillator has a lower frequency than the carrier oscillator, and the resulting harmonics are mostly odd-numbered harmonics. When the ratio is high (i.e., greater than 1), the modulating oscillator has a higher frequency than the carrier oscillator, and the resulting harmonics are mostly even-numbered harmonics. When the ratio is exactly 1, no new harmonics are produced.

The ratio can greatly affect the sound produced by the synthesis engine. By adjusting the ratio, sound designers and music producers can create a wide variety of sounds, from bell-like tones to harsh, metallic sounds.

Index refers to the strength of the modulation signal that is applied to the carrier frequency. The index determines the amplitude of the modulating signal, and thus, the amount of frequency deviation that is introduced to the carrier signal. A higher index value results in a more pronounced effect on the carrier frequency, resulting in more complex and harmonically rich sounds.

This parameter is typically expressed as a ratio or a percentage. For example, an index value of 1 would mean that the amplitude of the modulating signal is equal to the amplitude of the carrier signal, resulting in a symmetrical waveform. An index value of 2 would mean that the amplitude of the modulating signal is twice the amplitude of the carrier signal, resulting in a more complex waveform with more harmonic content.

The index parameter can greatly affect the timbre and character of the resulting sound. By adjusting the index, sound designers and music producers can create a wide variety of sounds, from smooth and mellow tones to harsh and metallic textures.

Sidebands refer to the additional frequency components that are produced when a signal is modulated by another signal. In the context of FM (frequency modulation) synthesis, sidebands are the additional frequency components that are produced when a modulating signal is applied to a carrier signal.

They are created when the modulating signal causes the frequency of the carrier signal to deviate from its original frequency. As a result, new frequencies are produced that are offset from the original carrier frequency by the frequency of the modulating signal. These new frequencies are known as sidebands and are positioned above and below the carrier frequency in the frequency spectrum.

The number and intensity of the sidebands depend on the strength and frequency of the modulating signal. As the modulation depth (i.e., the degree to which the carrier frequency is modulated) increases, the number and intensity of the sidebands also increase, resulting in a more complex and harmonically rich sound.

By adjusting the frequency and intensity of the modulating signal, sound designers and music producers can create a wide range of sounds, from smooth and mellow to harsh and metallic textures.

Control Rate & Autorate In the context of sound synthesis, control rate and audio rate refer to the rate at which signals are processed by a synthesizer.

Control rate, also known as the modulation rate, is the rate at which control signals, such as envelopes, LFOs (low-frequency oscillators), and other modulators, are processed by a synthesizer. Control rate signals typically have a much lower frequency range than audio signals, typically ranging from a few hertz up to a few kilohertz.

Autorate, on the other hand, refers to the automatic adjustment of control signals to match the frequency of the audio signal. This is commonly used in dynamic filter or EQ (equalization) effects, where the cutoff or center frequency of the filter is automatically adjusted based on the frequency content of the audio signal.

Audio rate, as the name suggests, is the rate at which audio signals are processed by a synthesizer. Audio rate signals typically have a much higher frequency range than control rate signals, ranging from around 20 Hz to 20 kHz, which covers the range of human hearing.

To summarize, control rate refers to the rate at which control signals are processed, while audio rate refers to the rate at which audio signals are processed. Autorate is a specific technique that adjusts control signals to match the frequency of the audio signal, and is commonly used in dynamic effects.