There is a sound synthesis technique called Frequency Modulation wherein an oscillator (such as a sine wave), has it's frequency modulated by another oscillator to produce a more complex sound. Eg, when the second oscillator is high, the frequency of the first oscillator becomes faster. However, in practice hardly any real musical synthesizers perform real FM synthesis. Instead they use a technique popularized by the Yamaha DX7, and do what's called Phase Modulation instead. Please explain how Phase Modulation works, and why it's used over real Frequency Modulation in most FM synthesizers.
Phase Modulation (PM) is a sound synthesis technique that is closely related to Frequency Modulation (FM) synthesis, but with some key differences. In PM, instead of modulating the frequency of the carrier oscillator, the phase of the oscillator is modulated by a modulating oscillator. The amount of phase modulation is directly proportional to the amplitude of the modulating oscillator, and the result is a sound with a complex waveform that can be shaped by adjusting the parameters of the modulating oscillator.

The main reason why PM is used over real FM in most FM synthesizers is due to the simplicity of the synthesis process. PM is much easier to implement than true FM synthesis, which requires a more complex algorithm to calculate the frequency modulation. PM can be implemented in a much simpler way by using a lookup table to determine the phase shift caused by the modulating oscillator. This makes PM more efficient, and thus more practical for real-time synthesis.

Another advantage of PM is that it provides a greater degree of control over the resulting sound. In FM synthesis, the frequency modulation can cause unpredictable sidebands to appear in the resulting waveform. In PM, the sidebands are more predictable, and can be controlled by adjusting the parameters of the modulating oscillator. This allows for greater precision when shaping the sound, and makes it easier to achieve the desired result.

Finally, PM has been popularized by the Yamaha DX7 synthesizer, which used a form of PM synthesis known as "linear frequency modulation" (LFM). LFM is a specific form of PM in which the modulating oscillator is also a sine wave, but with a frequency that is allowed to vary linearly over time. This technique was used extensively in the DX7, and became synonymous with the sound of FM synthesis in the 1980s.

In summary, while PM and FM are closely related synthesis techniques, PM is generally preferred in modern synthesizers due to its simplicity, greater control over the resulting sound, and its association with the iconic sounds of the Yamaha DX7.
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### Instruction:

There is a sound synthesis technique called Frequency Modulation wherein an oscillator (such as a sine wave), has it's frequency modulated by another oscillator to produce a more complex sound. Eg, when the second oscillator is high, the frequency of the first oscillator becomes faster. However, in practice hardly any real musical synthesizers perform real FM synthesis. Instead they use a technique popularized by the Yamaha DX7, and do what's called Phase Modulation instead. Please explain how Phase Modulation works, and why it's used over real Frequency Modulation in most FM synthesizers.

### Response:

Phase Modulation (PM) is a sound synthesis technique that is closely related to Frequency Modulation (FM) synthesis, but with some key differences. In PM, instead of modulating the frequency of the carrier oscillator, the phase of the oscillator is modulated by a modulating oscillator. The amount of phase modulation is directly proportional to the amplitude of the modulating oscillator, and the result is a sound with a complex waveform that can be shaped by adjusting the parameters of the modulating oscillator.

The main reason why PM is used over real FM in most FM synthesizers is due to the simplicity of the synthesis process. PM is much easier to implement than true FM synthesis, which requires a more complex algorithm to calculate the frequency modulation. PM can be implemented in a much simpler way by using a lookup table to determine the phase shift caused by the modulating oscillator. This makes PM more efficient, and thus more practical for real-time synthesis.

Another advantage of PM is that it provides a greater degree of control over the resulting sound. In FM synthesis, the frequency modulation can cause unpredictable sidebands to appear in the resulting waveform. In PM, the sidebands are more predictable, and can be controlled by adjusting the parameters of the modulating oscillator. This allows for greater precision when shaping the sound, and makes it easier to achieve the desired result.

Finally, PM has been popularized by the Yamaha DX7 synthesizer, which used a form of PM synthesis known as "linear frequency modulation" (LFM). LFM is a specific form of PM in which the modulating oscillator is also a sine wave, but with a frequency that is allowed to vary linearly over time. This technique was used extensively in the DX7, and became synonymous with the sound of FM synthesis in the 1980s.

In summary, while PM and FM are closely related synthesis techniques, PM is generally preferred in modern synthesizers due to its simplicity, greater control over the resulting sound, and its association with the iconic sounds of the Yamaha DX7.
