prompter: 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.
assistant: Phase modulation (PM) is a technique similar to frequency modulation (FM) that is used in digital synthesizers. In PM, instead of modulating the frequency of an oscillator, the phase of an oscillator is modulated by another oscillator. When the modulating oscillator is at a high point, it causes the phase of the carrier oscillator to shift forward, resulting in a higher pitch. Conversely, when the modulating oscillator is at a low point, it causes the phase of the carrier oscillator to shift backward, resulting in a lower pitch.

One reason why PM is used instead of real FM in most digital synthesizers is that PM is computationally more efficient. FM synthesis requires complex algorithms that involve exponential functions and can be computationally expensive. In contrast, PM can be implemented with simple multiplication and addition operations, making it much faster and easier to implement in hardware and software.

Another reason why PM is preferred over FM is that it allows for more control over the harmonics and timbre of the synthesized sound. In FM, the number and amplitude of the harmonics that are generated can be difficult to predict and control. In PM, however, the phase of the carrier oscillator can be shifted by precise amounts, allowing for greater control over the harmonics and the resulting timbre of the sound.

In addition, PM is more forgiving in terms of tuning and stability. In FM, the oscillators must be precisely tuned and stable to produce a clean and stable sound. In PM, small tuning errors or instability in the oscillators can produce interesting and desirable harmonics and modulation effects.

Finally, the popularity of the Yamaha DX7 and its use of PM played a significant role in the widespread adoption of PM over FM in digital synthesizers. The DX7 was a groundbreaking instrument that popularized digital synthesis in the 1980s, and its use of PM paved the way for other digital synthesizers that used similar techniques. As a result, PM became the de facto standard for digital synthesis and is still widely used today.
prompter: How to make procedural animations in Unreal Engine 5?
assistant: To make procedural animations in Unreal Engine 5, you can use a combination of Blueprints and animation blueprints. Here are the general steps you can follow:

1.    Create a new Blueprint actor for your procedural animation.
2.    Create the animations you want to use as your base in a separate animation Blueprint.
3.    Add a Skeletal Mesh component to your procedural animation Blueprint actor and set it to use the base animations you created.
4.    In the Blueprint graph, you can use a combination of math and logic nodes to manipulate the transform of the Skeletal Mesh component to create your procedural animation.
5.    To update the animation at runtime, you can use the Event Tick node to continuously update the Skeletal Mesh component's transform.

Here are some specific examples of what you can do:

*    You can use math nodes to generate smooth sine waves to make the Skeletal Mesh component move back and forth or up and down.
*    You can use a timeline node to animate the Skeletal Mesh component moving from one location to another over a set period of time.
*    You can use a random number generator to create a randomized animation, such as randomly moving the arms of a character.
*    You can use logic nodes to create conditional animations, such as having a character change their walking animation speed based on whether they're on a flat surface or a slope.

These are just a few examples, but with the power of Blueprint scripting and the flexibility of the Unreal Engine, the possibilities for procedural animation are endless.