Reverb effect for the Surge synthesizer system

The surgefx-reverb crate provides a reverb effect implementation as a subcomponent of the Surge synthesizer system. This effect simulates the natural acoustic reflections and reverberations that occur in physical spaces, adding depth and ambiance to the input audio signal.

The reverb effect is built using a combination of delay lines, filters, and feedback loops, which are mathematically designed to model the complex behavior of sound reflections in a given environment. Key parameters, such as decay time, room size, and damping, can be configured by the user to tailor the reverb characteristics to their needs.

Mathematical concepts and equations

The primary mathematical concepts associated with the reverb effect include:

• Delay lines: Delay lines store and play back the input signal with a specific time delay, simulating the time it takes for sound reflections to reach the listener. The delay time can be calculated using 𝑑 = 𝑐 × 𝑡, where 𝑑 is the delay length, 𝑐 is the speed of sound, and 𝑡 is the time delay.

• Feedback loops: Feedback loops take the output of the delay lines and mix it back into the input, simulating the decay of reflections over time. The feedback gain can be calculated using 𝑔 = 10^(−60𝑇/𝑅), where 𝑔 is the gain, 𝑇 is the decay time, and 𝑅 is the reverb time.

• Filters: Filters are used to shape the frequency response of the reverb, mimicking the absorption and diffusion of sound by different materials and surfaces. The most common filters used in reverbs are low-pass, high-pass, and band-pass filters, which can be implemented using IIR or FIR filters with various transfer functions.

Key tokens and their associated mathematical ideas

• control_group, control_type, default_value, max_value, min_value, modulateable, moverate, value_type: These tokens define the control parameters and their ranges for the reverb effect, such as decay time, room size, and damping.

• ReverbBlockCfg, Reverb: These tokens represent the main reverb processing structure and associated functions, which handle the creation, configuration, and processing of the reverb effect.

• do_reverb, do_reverb_block, do_pre_tap, do_post_tap: These tokens are responsible for the core reverb processing, including delay lines, feedback loops, and filtering.

• init, init_band1, init_hicut, init_lowcut, init_taps: These tokens handle the initialization of various reverb components, such as filters and delay lines.

• process, process_mid_side: These tokens process the input audio signal and apply the reverb effect, taking into account the configured parameters and desired processing mode (e.g., stereo or mid-side).

The surgefx-reverb crate offers a versatile and efficient reverb effect implementation for the Surge synthesizer system, providing users with a wide range of control and customization options for shaping their desired sound.

27> could you show how to design a reverb effect? what differentiates various reverb modules in terms of functionality and quality?

Designing a reverb effect involves creating a digital signal processing (DSP) algorithm that simulates the complex behavior of sound reflections and reverberations within physical spaces. There are several approaches to designing a reverb effect, with some of the most popular methods being:

1. Algorithmic reverb: Algorithmic reverb designs use a combination of delay lines, filters, and feedback loops to create the illusion of a reverberant space. This approach is highly customizable and allows for a wide range of reverb characteristics. Some popular algorithmic reverb techniques include:

   • Schroeder reverb: Based on multiple parallel comb filters followed by a series of all-pass filters.

   • Moorer reverb: Uses a network of nested all-pass filters and parallel comb filters with low-pass filters in their feedback paths.

   • Feedback delay network (FDN): A more advanced design using a network of interconnected delay lines with feedback and filtering.

2. Convolution reverb: Convolution reverb uses impulse responses (IRs) recorded from real-world spaces or hardware reverbs to recreate the exact reverberation characteristics of those spaces. By convolving the input audio with the impulse response, the reverb effect is generated. This method provides highly realistic and accurate reverb simulations but can be computationally intensive.

Various factors differentiate reverb modules in terms of functionality and quality:

1. Reverb algorithms: Different reverb designs offer different sonic characteristics. Some algorithms may excel at creating lush, natural-sounding reverbs, while others might focus on more experimental or artificial reverberations.

2. Customization and control: High-quality reverb modules typically offer more control parameters, allowing users to fine-tune the reverb characteristics to their needs. Some common parameters include decay time, room size, damping, pre-delay, and diffusion.

3. Filtering and equalization: The quality and flexibility of the filters used within the reverb algorithm can greatly impact the sound. Advanced reverb modules may include more sophisticated filtering options and built-in equalizers to help users shape the reverb's frequency response.

4. Stereo imaging and spatialization: Good reverb modules will provide options for controlling the stereo image of the reverb, including width, mono compatibility, and mid-side processing.

5. Efficiency and performance: High-quality reverb modules are optimized for efficient resource usage, ensuring minimal impact on CPU and memory while still delivering excellent sound.

6. Ease of use and interface: A well-designed user interface with intuitive controls, presets, and visual feedback can make a significant difference in the usability of a reverb module.

By carefully considering these factors and selecting the appropriate design approach, you can create a reverb effect that offers both high-quality sound and a wide range of functionality.

28> thanks! could you show me how the schroeder reverb works? the moorer reverb? the feedback delay network? could you please describe in mathematical detail and include block diagrams? which algorithms excel at creating lush natural sounding reverbs? which are more experimental/artificial sounding? is it possible to get an experimental/artificial reverb to sound "better" than one designed to mimic nature?

Sure, I can provide an overview of each of the mentioned reverb algorithms along with block diagrams.

Schroeder Reverb

The Schroeder reverb, developed by Manfred R. Schroeder in the 1960s, is one of the earliest digital reverb algorithms. It consists of a series of parallel comb filters followed by a series of all-pass filters. The input signal is fed through the comb filters, which create multiple delayed and attenuated copies of the input. These copies are then summed and passed through the all-pass filters, which help to diffuse the sound and make it more reverberant.

Mathematically, a comb filter can be expressed as:

y(n) = x(n) + g * x(n - D),

where y(n) is the output, x(n) is the input, g is the feedback gain, and D is the delay length.

An all-pass filter can be expressed as:

y(n) = -g * x(n) + x(n - D) + g * y(n - D),

where y(n) is the output, x(n) is the input, g is the feedback gain, and D is the delay length.

Here is a block diagram of the Schroeder reverb:

Input
  |
  v
Comb Filters (Parallel) -> Sum -> All-Pass Filters (Series)
  |
  v
Output

Moorer Reverb

The Moorer reverb, developed by James A. Moorer in 1979, is an extension of the Schroeder reverb. It uses a network of nested all-pass filters and parallel comb filters with low-pass filters in their feedback paths. The low-pass filters help to simulate the high-frequency absorption of real-world spaces.

A block diagram of the Moorer reverb looks like:

Input
  |
  v
Comb Filters (Parallel) -> Sum -> Nested All-Pass Filters (Series)
  |                           |
  v                           v
Low-Pass Filters (Feedback)  Output

Feedback Delay Network (FDN)

The Feedback Delay Network (FDN) is a more advanced reverb design that uses a network of interconnected delay lines with feedback and filtering. The delay lines are connected in a feedback matrix, which helps to diffuse the sound and create complex reverberation patterns.

A block diagram of the FDN looks like:

Input
  |
  v
Delay Lines -> Feedback Matrix -> Sum
  |                                |
  v                                v
Filters (Feedback)              Output

Regarding the character of these reverbs:

• Schroeder and Moorer reverbs tend to sound more artificial and metallic due to their relatively simple structure. They can still be used for creative purposes and experimental sounds.

• FDN-based reverbs can create more natural-sounding reverbs, as they offer more complex diffusion patterns and greater flexibility.

It is possible to make experimental/artificial reverbs sound "better" by carefully designing and tweaking the algorithm parameters, such as delay times, feedback gain, and filtering. However, defining "better" is subjective and depends on the intended use case and personal preferences. In some cases, an artificial reverb might be preferred over a natural-sounding one for a specific artistic purpose.

29> which control parameters does a high-end reverb module typically provide? how does each of these impact the underlying algorithm? how does each work from a mathematical perspective? how does each work from the perspective of physics? how does each work from the perspective of acoustics?

High-end reverb modules typically provide a variety of control parameters that allow users to shape the reverb sound according to their preferences. Here are some common parameters and their impact on the underlying algorithm from mathematical, physical, and acoustics perspectives:

1. Reverb Time (RT60): This parameter controls the time it takes for the reverb to decay by 60 dB. Mathematically, it affects the feedback gain in the algorithm, usually within the comb filters or feedback matrix. Physically, it relates to the size of the space and the absorption characteristics of the materials within it. Acoustically, it determines the perceived "size" of the reverberant space.

2. Pre-Delay: This parameter controls the time delay between the dry signal (direct sound) and the onset of the reverb. Mathematically, it's a simple delay added before the reverb processing. In physics, it represents the time it takes for the sound to travel from the source to the listener or the first reflection from surfaces. Acoustically, it can create a sense of distance between the sound source and the listener.

3. Early Reflections: Early reflections are the first echoes that arrive at the listener's position after bouncing off walls, ceilings, and floors. These reflections give important spatial cues about the size and shape of the room. Mathematically, early reflections can be generated using a series of delay lines with different delay times and gains. In physics, they represent the sound reflections from the surfaces in the space. Acoustically, they contribute to the initial perception of the room's characteristics.

4. Diffusion: This parameter controls the density of the reverb tail, affecting how quickly the reflections become indistinguishable. Mathematically, it can be related to the density of delay lines and the distribution of delay times in the algorithm. Physically, it corresponds to the complexity and irregularity of the surfaces in a room. Acoustically, high diffusion leads to a smoother, more natural-sounding reverb, while low diffusion creates a more distinct and sparse reverb tail.

5. Damping: Damping controls the frequency-dependent decay of the reverb. Mathematically, it's achieved by applying filters (usually low-pass) within the feedback paths of the algorithm. Physically, it represents the absorption characteristics of materials within the space, with different materials absorbing different frequencies to varying extents. Acoustically, it defines the tonal balance and coloration of the reverb tail.

6. High and Low Cut: These parameters control the frequency range of the reverb by applying high-pass and low-pass filters to the input signal or within the feedback paths. Mathematically, these filters attenuate specific frequency bands. Physically, they represent the frequency-dependent absorption of the environment. Acoustically, they shape the overall tonality and character of the reverb.

7. Wet/Dry Mix: This parameter controls the balance between the dry (unprocessed) signal and the wet (reverberant) signal. Mathematically, it's a simple linear interpolation between the two signals. Physically, it doesn't have a direct correlation. Acoustically, it determines the prominence of the reverb effect in the mix.

8. Modulation: Some high-end reverb modules include modulation (e.g., chorus or vibrato) within the reverb tail to create a more complex and lush sound. Mathematically, modulation can be introduced by adding time-varying delay lines within the feedback paths. Physically, it doesn't have a direct correlation. Acoustically, it can add richness and depth to the reverb effect.

Each of these parameters can be adjusted to fine-tune the reverb effect according

30> are there other parameters involved? where is each of these parameters located in the signal chain? could you show me a massive diagram of a reverb module? please annotate the blocks each of these parameters effects