Curvature

The easiest to use, yet most advanced compressor in the world

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Features

  • Unique compression curves completely unavailable in other plugins
  • World's first compressor to use the Black-Scholes model
  • Incredibly easy to use main page, just click stuff
  • Advanced page has extreme control over the algorithms
  • Themes: global or instance based. User theme slots.
  • Fast and intuitive side chain EQ with external side chain input
  • Side chain EQ able to be applied to the main out
  • Oversampling option (all paths)
  • More algorithms coming soon (upwards compression, extremely unique resonant and weird creative stuff never seen elsewhere)
  • Lifetime free upgrades

Compatibility & download

Curvature works with all major DAWs on:

  • Mac - VST3 & AU - AAX coming soon
  • Linux - VST3
  • Windows - VST3

USER MANUAL & FEATURE OVERVIEW

THE MAIN PAGE

This is where most people should hang out. Simply click an algorithm and try out one of the presets (# buttons). There are eight different presets per algorithm. If you find something you like as a starting point, you can nudge the attack and release times (A and R buttons) and adjust the input gain to fine-tune.

There are no ratio, threshold, or knee knobs on the main screen — those aren't necessary to get a decent compressor sound. Just like with an 1176, to hit the threshold harder, simply crank up the input gain. And similar to New York-style compression, aim for an exaggerated version of what you're after, then dial it back using the MIX knob to blend in the clean signal.

The two buttons marked with the infinity sign are feedback on (FB) and feedback off (FF). Many presets include feedback — sometimes even full-on screaming feedback. If you're looking for sounds without it, simply hit FF. It will be completely disconnected from the circuit for all presets until you turn it back on.

GAIN STRUCTURE IS EVERYTHING

Increasing the input gain causes the output gain to be automatically reduced, and vice versa. Unlike most plugins which fool you into thinking the compression sounds better, just because it gets louder when you add more, Curvature behaves in a much more honest way. Once you start hitting gain reduction, Curvature does exactly that: it reduces the gain. Contrary to lay belief, (regular downwards) compression doesn't make stuff louder, it actually turns stuff down. Then you adjust the gain back up to compensate. But how the gain is compensated is extremely important.

Many, if not most compressor plugins on the market, apply automatic gain makeup based on the threshold. But this is a psychoacoustic sleight of hand. Why? Well unless the amount of gain reduction is exactly equivalent to the amount of make-up gain applied, which is rarely the case, the loudness will likely increase the more compression is applied, instead of staying approximately constant. This is problematic because, when presented with two sounds, and one is slightly louder, the louder one will generally be preferred. So using this kind of gain compensation makes your ears more gullible, fooling you into thinking the compression sounds good.

The way Curvature works is importantly different. Increasing the input gain, decreases the output gain in a 1:1 relationship, yielding zero difference in loudness until you start hitting gain reduction. At which point, the gain reduction starts to compound with the negative gain compensation and the result is that the overall loudness becomes quieter the more compression you apply. This makes your ears more skeptical. Meaning, the compression has to be genuinely good for you to prefer it.

Adjusting the output gain does not change the input level, maintaining the amount of compression. If you want to adjust the input gain independently, just hold the SHIFT key.

Note: feedback for the side chain path happens pre-output gain, so adjusting the output knob doesn't mess with your compression level. But feedback on the main out is post output gain knob. This means, given that you control your gain structure elsewhere in your session, you can push the feedback by cranking up the output gain and really make Curvature feed back and scream. The alpha knob will determine whether that is low frequency feedback or high frequency. Cranking the output gain will also drive harder into the saturation ceiling, as that comes last in the chain. However, the clean signal you can dial back in with the MIX knob stays untouched, unaffected and ignores the output gain knob. Resultantly, if you are creating a complex blend of distortion and feedback and the output level really matters, you need to make sure your audio is hitting Curvature at a hot enough level if you want to use the mix knob. Otherwise, the clean signal will be comparatively wimpy, making it harder to balance. Gain structure is one of the most important aspects of audio engineering, and to get the most out of Curvature, you have to know what's going on with your levels in your session.

THE EXPERT PAGE

The presets on the main page change most of the knobs on the expert page to quickly dial in a sound — without needing to understand or even look at this page. But a couple of things here are actually pretty straightforward. STEREO LINK is an important control for stereo compressors. It is not affected by the presets on the main page and it should mostly be left on max, or some amount above 50%, so compression is applied equally to both channels, avoiding imbalances in the stereo image. Unless you want imbalance, then turn the knob down. Another case where you should definitely set this knob to zero is when using Delta Expose.

At the bottom, there's a chart showing the input signal (peak) and the gain reduction (blue), which is pretty standard. Less common, though, is the green line — it shows the internal slew signal of the sidechain path.

Feedback has two knobs: Alpha (EQ emphasis) and Beta (amount). This can easily self-oscillate. Next to feedback is Ceiling, a gentle saturation distortion that acts as a limiter to prevent things from getting too loud — while also adding intentional grit and vibe. The lower the ceiling, the earlier you hit saturation.

ACTUAL KNOB FUNCTIONS

Apart from attack and release, which are self-evident, there are four remaining knobs on the expert page. On one hand, it's very simple: just turn them and listen to what happens. But for those who want to dig deeper and really understand what’s going on inside the compression algorithms, these four knobs are key.

The easiest to understand is Theta. This knob is, for all intents and purposes, the ratio knob. It’s not labeled as ratio because some algorithms, especially the upcoming ones, use dynamic ratios. In those cases, this knob influences the computation of the ratio and doesn’t constitute it in of itself.

Not all algorithms use all of the knobs, and in such cases, they are replaced by an X.

Where Kappa is available, it generally has something to do with the curvature of the attack phase. Gamma, where available often influences the calculation of Kappa. Lambda, when available, often influences the curvature of the release phase.

This is a bit oversimplified and there are exceptions to this. The following table describes more precisely what the knobs do per algorithm:

Algorithm
Kappa
Gamma
Lambda
Theta
Classic
RMS style attack shaping
Ratio
Log2
Convexity of attack
Rate of Kappa scaling
Concavity of release
Ratio
Linear
Deviation from linearity (attack)
Makes the gain reduction apex convex
Deviation from linearity (release)
Ratio
Lin Log
Deviation from linearity (attack)
Makes the gain reduction apex convex
Ratio
Log Lin
Deviation from linearity (release)
Ratio
Analog
RMS style attack shaping
Ratio
Chaos
Flutter interval
Resonance / feedback
Amount of chaos
Ratio

The world's first Black Scholes Compressor

Meet Curvature's crown jewel: the Black Scholes algorithm. It's highly likely that this is the first audio compressor ever made using the Black-Scholes-Merton option pricing model. After scouring the internet, there's literally zero evidence anyone has tried this before.

Does it work? Yes. Shockingly well. It's probably not going to become a go-to mastering compressor but for creative work on individual elements in the mix, it sounds incredibly unique. When set up correctly, it can do quirky things that no other compressor currently available can do.

WTF is Black-Scholes?

Nerd answer: The Black-Scholes-Merton options pricing model is a parabolic partial differential equation derived under the assumption that the underlying asset follows a geometric Brownian motion, implying log-normal price dynamics with the discounted asset price evolving as a martingale under the risk-neutral measure.

Translation: It's the math that options traders on Wall Street use to make or lose millions of dollars every day in the stock market. It's also a particularly beautiful bit of math which won the Nobel Prize. Well, Fisher Black passed away two years before the award but Robert Merton and Myron Scholes both received the Nobel prize.

Stolen from financial mathematics

Stock options are basically fancy gambling contracts. You're betting on where a stock price will be at some future date. The option's value doesn't just depend on the current stock price though. It's a complex dance between multiple variables:

  • Stock price (is Apple at $90 or $120?)
  • Strike price (what price did you bet on?)
  • Time to expiration (Options contracts lose value over time)
  • Volatility (how wildly is the stock price bouncing around?)
  • Exposure (how much money are you risking?)

The closer you get to expiration, the more dramatic the value swings become. High volatility means more uncertainty, so option sellers demand higher prices to cover their risk. The Black-Scholes model crunches all this chaos into a single valuation.

Now here's the cool part - audio compression has extremely similar moving parts. It's almost identical:

Finance
Audio
Stock price
Input signal level
Expiration date
Compressor time constants
Strike price
Threshold
Exposure
Compression ratio/strength
Volatility
Signal dynamics

The Result?

A compressor which takes into account the dynamic range of the input signal and responds in a dynamic and unique way, much more dramatically than typical "program dependent" compressors. Applying essentially identical signal processing techniques found in quantitative finance to audio opens up a completely new sound of compression that has literally never been heard before. Yes it is a bit experimental, unpredictable and slightly CPU hungry, but that's part of the fun of the algorithm.

Academic paper

For anyone with a background in finance or mathematics, I wrote a paper on the topic which goes into more technical detail on the inner workings. Although the actual implementation used in Curvature will remain proprietary, and more complex than just the Black Scholes model, since there is also GARCH-esque volatility forecasting in there two, the mini paper details the mappings.

THE ALGORITHMS

Unlike many compressor plugins, having multiple "algorithms" doesn't just mean there's actually just one main piece of code inside with some tweaking of the internal constants. As you can see with Curvature, you have access to the internal constants anyway, and with the help of Delta Expose, it's obvious to see that each algorithm is actually doing something unique. At the time of release, there are 8 different algorithms and here's what they do:

Algorithm
Characteristic
Classic
This is one of the most basic and widely used compression algorithms in the industry. Some large percentage of compressor plugins do something identical or very similar to this, regardless of the flowery adjectives they use in their marketing materials. If you check this out in Delta Expose, you will see a convex attack and concave release. This is the hallmark of bog standard compression code and so many plugins just do this. But in addition, there is RMS shaping isolated to the attack phase, so the release stays constant. This classic algorithm alone is more flexible and potentially better sounding than many of the overpriced SSL style bus compressor plugins on the market which have fancy analogue style graphics but a limited selection of time constants and no RMS.
Log2
This is a significantly more refined and powerful version of the idea behind Versatile Compressor. With the Kappa and Gamma knobs, you can dial in an impressive amount of attack curve shapes. From a ruler flat linear attack, to linear with a small convex apex, to a larger apex, to extremely rounded. The release can also be shaped from a standard concave behaviour, to a slight S curve, completely independently of the attack phase. This algorithm alone, when intelligently used, can create many, if not most, compression flavours.
Linear
Linear style compressors are less common as they can sound aggressive, choppy, digital, unrefined or otherwise not as musical or analogue sounding as the classic convex-concave style ubiquitous in compressor plugins. TDR Molot has a couple of modes which tend towards almost linear behaviour, and this is one of the better sounding compressor plugins out there. So although linear can sound bad, the key is in the implementation, particularly whether the apexes are rounded or hard. With gamma on minimum, you get a ruler straight line with a totally sharp apex, which is a pretty harsh sound. But with the gamma knob turned up, you round off the apex, creating a sound which is still very aggressive, but much more natural.
Lin Log
Same as the linear algorithm but with a concave release
Log Lin
Same as the linear algorithm but with a classic convex attack
Analog
This algorithm creates very smooth S shaped attack and release curves. But the attack time significantly influences the release time.
Chaos
It is difficult to explain what is happening here. The algorithm is especially creative, weird and unintuitive. The majority of the weirdness is found with input signals around the threshold with minimal gain reduction. In fact, the more gain reduction, the less strong the effect. Putting the stereo link on minimum can introduce extreme stereo image instability around the threshold level depending on the settings. This one is definitely better suited to individual sounds for creative processing. Also, turning down the mix knob will cause the signal to phase cancel, further increasing the effect, until the delta is reached.
Money / Black-Scholes
The knobs STRIKE and EXPIRATION directly determine the strike price and expiration date fed into the black scholes model. EXPOSURE scales the output from the generalized autoregressive conditional heteroskedasticity model since this is, given the fictional context, rough functionally akin to increasing the portfolio allocation to a given asset. In english this means that turning up the EXPOSURE knob causes more compression. VOLATILITY scales the relative influence of the alpha and beta coefficients of the GARCH model. In english this means turning up the knob produces a more erratic sound with more sensitivity to recent signal dynamic. This interacts with the time values of the compressor.

THE SIDE CHAIN PAGE

Curvature comes equipped not only with an external side chain input but also the ability to apply various instant filter settings, regardless of whether the source is internal or external. The external side chain path (EXT) can only be activated if there is actually a side chain input set up. For example, in reaper increase the track channels to 4.

A handy feature which you may find a use case for more than you expect, is to be able to assign the same EQ setting to the main output as is applied to the side chain path. This is applied by hitting the MAIN button

FEEDBACK BEHAVIOUR

When the external side chain input is selected (EXT), the side chain path takes the external signal directly without any feedback. In normal internal operation, the side chain path is determined by the feedback button on the main page (∞). When FB is selected, not only is the feedback permitted/engaged on the main output, but Curvature also uses the main output signal for the side chain input, regardless of the position of the feedback knob on the expert page. This is feed-back compression which is more wild and interesting sounding than modern feed-forward compression.

When FF is selected, not only is feedback no longer permitted on the main out, but it also changes the detector circuit behaviour. Curvature will then feed the side chain path from a paralleled version of the input signal when the feedback knob on the expert page is on minimum. This is feed-forward behaviour which is modern, standard, clean and less exciting than feedback. But there's a twist... increasing the feedback knob on the expert page when in FF mode (or having it changed as part of selecting a new preset with the # button), will result in the output signal being fed back into the side chain detector path, and on max it will be entirely feedback style. This way, you can dial in arbitrary amounts of feedback compression whilst avoiding squealing or ringing in your actual audio.

FACTORY THEMES

There are two scopes of themes: global, where you simply select your favourite theme and stick with that, and instance based, where every plugin instance can have a different theme. Curvature remembers the theme you have selected for each plugin instance, so you can use the different themes as a quick visual cue for different sounds.

USER THEMES

In addition to the 8 factory themes, there is the possibility to add your own custom theme. First, locate the folder where the curvature settings and preset files are located. For example, on Mac this is:

~/Library/Application Support/AP Mastering/

Now add your custom theme background images in this filename format: user1_main.png, user2_main.png etc. Right now the only page which you can have a custom theme for is the main page. This is the image file for the main background image:

ADVANCED STUFF

HIDDEN CONTROLS

There are a couple of hidden controls not accessable from the interface. This is because, for almost all users, these settings should just be left as they are. But for full details for anyone who wants to know the exact behaviour of the plugin, perhaps when running it through plugin doctor or something, these parameters are hidden and accessible from the parameter list view or automation lane view, depending on your DAW:

Filter DC - After getting some early initial feedback from White Sea Studios (he was the first engineer to see the plugin), he noticed that when using feedback, he was getting DC errors from his sensitive RME converters. Looking into this, it was not a case of the plugin generating DC itself but rather, the feedback knob significantly amplified any DC that might have been present in the source material. So I simply added a butterworth high pass at 20Hz which kills all DC. In case anyone cares, this uses a state variable topology whereas all the other filters in Curvature are vanilla biquads. So although this DC offset filter can be completely ignored and forgotten, anyone who happens to want to turn it off for some special reason, can do so.

Filter Ultrasonics - The feedback knob can cause some really cool squealing which is cool. However, what is not cool is a gigantic resonance near nyquist which causes the passband to choke and tweeters to explode. This is why, even when oversampling is turned off, if you are analysing the plugin using plugin doctor or Bertom EQ analyser, you will see an IIR low pass round 20kHz. This has nothing to do with antialiasing. The antialiasing uses a FIR lowpass. This additional lowpass is specifically to prevent ultrasonic feedback. If you disable feedback, and for some special reason also do not want an IIR low pass in the circuit, you can disable it with the hidden parameter. However, I recommend leaving this on because the plugin does exhibit instability in ultrasonic frequencies when using feedback without this filter.

Internal trim - this is used for (very approximately) gain matching the presets after hearing more excellent feedback from White Sea Studios. Note that this is overwritten every time you select a preset so there is zero utility in touching this control and it can also be ignored.

PRESET HACKING

The presets are supposed to be curated, quick starting points to save having to spend time learning how to use the expert screen. They are not intended to replace the plugin preset system built into your DAW. If you want to save and load presets, use the normal method for managing presets built into your DAW. Just like a piece of hardware that says "DO NOT OPEN, NO USER SERVICEABLE PARTS INSIDE", this makes me want to open it up and see what exactly is in side. In this spirit, the presets are NOT USER EDITABLE. The XML file where they are all stored is, for example on Mac, here:

~/Library/Application Support/AP Mastering/Curvature.presets

If you want to reset back to factory defaults, simply delete the file and it will be regenerated with the factory settings next time you load Curvature. Note that if Curvature encounters a presets file with an incorrect format, it will override it with the factory defaults on launch without any warning or confirmation. So if you are putting effort into editing these presets, make sure to copy the file to another directory as backup.