# 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