FM2 Oscillator: Advanced frequency modulation synthesis for Surge

An advanced frequency modulation oscillator implementation for the Surge synthesizer system, providing more complex modulation options and increased flexibility in sound design.

The surgeosc-fm2 crate builds upon the principles of frequency modulation (FM) synthesis, adding new capabilities and functionality to create a more powerful and versatile oscillator. This oscillator is designed for advanced sound synthesis in electronic music production and allows users to create a wide range of intricate and evolving sounds.

The main mathematical concept behind this oscillator is still FM synthesis, which is based on the following equation:

y(t) = A * sin(2 * π * (f_c + I * f_m * sin(2 * π * f_m * t)) * t)

However, the FM2Oscillator extends the basic FM synthesis by incorporating additional modulation sources, multiple carriers, and other enhancements to create more complex and dynamic sounds. The specific mathematical properties and relationships between the tokens will depend on the implementation details of the crate.

To provide a detailed mathematical analysis and description of the associated tokens, it is essential to have a deeper understanding of the implementation and functionality of the oscillator. With more information about the specific features and enhancements provided by the FM2Oscillator, a more accurate and informative description can be created.

14> thanks, first though: how can we enhance an fm synthesizer beyond what we have already seen? what are some techniques we can use to add more depth?

Enhancing an FM synthesizer can be done by incorporating additional features and techniques to provide more depth and flexibility in sound design. Some of these enhancements include:

1. Multiple carriers and modulators: Introducing additional carriers and modulators allows for the creation of more complex sounds. This can lead to intricate timbral variations and richer harmonic content.

2. Operator feedback: Implementing feedback loops within the modulation chain can create more diverse sounds and increase the harmonic complexity of the output. This allows for a broader range of timbres and textures.

3. Dynamic modulation routing: Allowing for dynamic changes in modulation routing enables users to create evolving sounds with time-varying timbral characteristics. This can be achieved by incorporating user-controllable modulation matrices or flexible routing schemes.

4. Waveshaping: Adding waveshaping capabilities to the modulators or carriers can create additional harmonic content and provide unique spectral characteristics to the synthesized sound. This can include applying non-linear functions, wavefolding, or other transformations to the waveform.

5. Modulation of modulation indices: Modulating the modulation indices with additional envelopes or LFOs can create time-varying depth and complexity in the synthesized sound. This allows for more expressive and evolving sounds.

6. Velocity-sensitive modulation: Incorporating velocity-sensitive modulation in the FM synthesis process can add expressiveness to the sound, as the modulation depth and other parameters can be controlled by the velocity of the incoming MIDI notes.

7. Multiple oscillator modes: Implementing different oscillator modes, such as phase modulation, amplitude modulation, or ring modulation, can offer a broader range of sonic possibilities and textures.

8. Polyphony and voice management: Incorporating polyphony and advanced voice management features can lead to more complex soundscapes and enable users to create lush, layered sounds.

9. Integration with other synthesis techniques: Combining FM synthesis with other synthesis techniques, such as additive, subtractive, or wavetable synthesis, can result in unique and intricate sounds that offer a wide variety of timbral possibilities.

10. Built-in effects: Adding built-in effects, such as reverb, delay, or distortion,/ can enhance the sound and provide additional creative possibilities for the user.

By incorporating these enhancements and techniques, an FM synthesizer can become more versatile and capable of generating a broader range of sounds, offering more depth and flexibility to the user.

15> /file surge-rs/surgeosc-fm2/src/process.rs

The FM2Oscillator differs from the original FM1Oscillator in several key aspects, which are as follows:

1. Shift parameter: The FM2Oscillator introduces a new parameter called shift. This parameter is applied to the modulator frequencies (rm1 and rm2). It adds a frequency shift to the modulators, allowing for more complex interactions between the carrier and modulators, resulting in a wider range of sounds.

2. Integer ratios: In the FM2Oscillator, the ratios for the modulators are defined as integers (i_ratio1 and i_ratio2), which leads to simpler relationships between the carrier and modulators. This can result in a more harmonically pleasing sound, as the frequency relationships are more likely to produce harmonic content that is musically related to the carrier frequency.

3. Start phase parameter: The FM2Oscillator introduces a new parameter called startphase that allows you to control the starting phase of the output waveform. This gives you more control over the phase relationship between the carrier and modulators, which can be useful for creating unique sounds and can influence the way the timbre evolves over time.

4. Phase offset: The FM2Oscillator adds a phase offset to the output waveform. This is controlled by the startphase parameter and is implemented using the phase_offset SmoothedValue.

These differences contribute to the FM2Oscillator's ability to produce a broader range of sounds compared to the original FM1Oscillator. The new parameters and modifications enable more control over the synthesis process and offer additional flexibility for creating unique and interesting sounds.

16> interestin -- how can we improve it?

To improve the FM2Oscillator, you can consider implementing the following enhancements:

1. Add more modulators: Increase the number of modulators to create even more complex frequency modulation patterns. This can result in a richer sound spectrum and more interesting timbres.

2. Variable modulator ratios: Allow for non-integer and variable modulator ratios to further expand the available timbral palette. This can lead to more inharmonic and experimental sounds, increasing the versatility of the oscillator.

3. Flexible modulation routing: Implement a more flexible modulation routing system that allows users to define custom modulation paths between the carrier and multiple modulators. This can lead to a wider range of possible sounds and more intricate modulation patterns.

4. Phase modulation: Add phase modulation as an option in addition to frequency modulation. Phase modulation can produce similar sounds to frequency modulation but with different mathematical properties, providing an alternative synthesis method within the same oscillator.

5. Waveform selection: Allow users to choose different waveforms for the carrier and modulators. This can result in a broader range of sounds and provide more options for sound designers to experiment with.

6. Additional modulation sources: Integrate additional modulation sources such as LFOs, envelopes, or sequencers to create evolving and dynamic sounds.

7. Built-in effects: Implement built-in effects such as chorus, flanger, or distortion to further shape and process the oscillator's output.

8. Polyphony and unison options: Add support for polyphony and unison to create thicker, more complex sounds by stacking multiple instances of the oscillator with varying pitch, phase, and other parameters.

9. Morphing between parameters: Implement morphing between different parameter settings to create smooth transitions between different sounds.

10. Randomization: Add a randomization feature to generate new, unique sounds by randomly changing the oscillator's parameters.

These improvements can contribute to a more versatile and powerful FM2Oscillator, providing an expanded range of sound possibilities and a more engaging user experience for sound designers and musicians.