ValhallaUberMod: The MOD Parameters

ValhallaÜberMod allows the user to dial in different chorus, ensemble, and glitch shifting modulations through the use of the MOD controls. By clicking on the MOD button at the upper right of the GUI, the 5 modulation parameters can be viewed and adjusted:

The MOD parameters:

  • MOD SlowRate controls the slower delay modulation LFOs, with the value represented in Hertz. Depending on the Mode being used, this will control the speed of anywhere from 1 to 16 LFOs.
    • In modes with multiple LFOs, the modulation rate varies for each LFO, so the SlowRate value maps to the cycle speed of the slow LFO with the highest frequency – all the other LFOs will be somewhat slower.
  • MOD SlowDepth controls the modulation depth of the slow LFOs. This is more of a scale than an absolute value, and is used to balance the slow and fast LFO depths (which are both scaled by the high level DEPTH control).
    • The MOD SlowDepth also depends on the MOD OverMod setting, which acts as a control to set the slow LFO depth beyond reasonable bounds – see below.
  • MOD VibRate controls the faster delay modulation LFOs, with the value represented in Hertz. Depending on the Mode being used, this will control the speed of anywhere from 1 to 32 LFOs.
    • In modes with multiple LFOs, the modulation rate varies for each LFO, so the VibRate value maps to the cycle speed of the fast/vibrato LFO with the highest frequency – all the other vibrato LFOs will be somewhat slower.
    •  For most applications, the MOD VibRate should be used to add vibrato to a chorus, with the main detuning generated by the MOD SlowRate and MOD SlowDepth controls. However, this is just a suggestion – the fast LFOs can generate cool chorus effects by themselves.
  • MOD VibDepth controls the modulation depth of the faster LFOs. This is more of a scale than an absolute value, and is used to balance the slow and fast LFO depths (which are both scaled by the high level DEPTH control).
    • The MOD VibDepth setting doesn’t get as deep as the SlowDepth control, as LFOs running at faster frequencies cause more pitch change than slower LFOs.
    • In addition, the MOD VibDepth isn’t affected by the setting of MOD OverMod.
  • MOD OverMod. Acts as a scale on MOD SlowDepth. At the default OverMod setting (1X), the slow LFOs are optimized for creating chorusing and detuning effects. For higher settings of OverMod, the detuning gets deeper and deeper, until it moves into the realm of pitch shifting and backwards delays.
    • The modulation depth established by MOD SlowDepth and MOD OverMod is also scaled by the high level DEPTH slider.
    • The pitch shifting is not the controlled type found in ValhallaShimmer. The amount of pitch bend depends on the interconnections between MOD SlowRate, MOD SlowDepth, MOD OverMod, and the DEPTH slider. A better name for this would be “glitch shifting.” I just threw up a little in my mouth as I typed this, but it is the most descriptive phrase I can think of for the OverMod artifacts.

ValhallaShimmer Tips and Tricks: Shimmering

ValhallaShimmer was designed to get a variety of big reverb sounds, with the option of adding pitch shifted feedback to the decay. The “Shimmer” in the title refers to the classic shimmer effect, as used by U2, Brian Eno, Daniel Lanois, Coldplay, etc. There are a few presets that ship with ValhallaShimmer which reproduce this effect, but if you want to dial in your own version, here’s some tips:

  • Use the mediumStereo or bigStereo reverb modes for the smoothest shimmer sounds. The mono reverb mode will have a stronger sense of pitch shifting in the feedback signal, while the other modes have a gentler onset of the pitch shifting.
  • Set the Feedback control for the desired amount of pitch shift in the output signal, and then use the Size control to dial in the decay.
  • The Pitch control should be at +12 semitones.
  • Diffusion works best at around 0.9 for reverberant sounds. If you set Diffusion < 0.5, it will sound closer to a pitch shifted echo, which is another cool sound.
  • The different pitch shift modes have different levels of “smoothness”:
    • The single and dual pitch shift modes have more noisiness in their decay. This is better for emulating the orchestral sounds as heard in “Deep Blue Day.”
    • The singleReverse and dualReverse pitch shift modes are much smoother, and are better for organ-esque sounds.
  • colorMode should be set to dark. This produces a natural roll-off of high frequencies, which eliminates almost all of the aliasing noise in the feedback path of the pitch shifter.
  • Set the modDepth control to a fairly low value at first, as the pitch shifting provides its own random modulation to the signal.

ValhallaShimmer: a bit of history

ValhallaShimmer has its roots in the earliest digital reverberation algorithms, as described by Mannfred Schroeder in 1961. Schroeder, in his earliest AES paper on the subject, described a “colorless” reverberator, based upon cascaded diffusor (allpass) delays. At the time, the computation power available on the mainframe computers Schroeder was using limited the complexity of his algorithms.

In 2006, I experimented with extending Schroeder’s early reverberator structure to much higher orders. I was expecting that using much larger numbers of cascading diffusors would increase the echo density of the algorithm. It did, but it had a really weird effect: As the number of diffusors increased, the reverb decay started to sound less and less like a “real” acoustic space, and more and more like some weird spooky backwards thing.

It turned out that I had run into an artifact of what is known as the Central Limit Theorem. Without getting into the messy scientific details, the effective result was that, as the number N of cascaded diffusors increased, the attack and decay characteristics of the reverb changed from an exponential decay towards a bell, or Gaussian, curve. In other words, the reverb would slowly fade in, and then slowly fade out.

This wasn’t what I was expecting. More importantly, it sounded cool. Add some randomized modulation to each of the diffusors, and the result was an ethereal, ghostly soundscape.

The pitch shifting Eno trick was one that I had first tried back in 2004. The pitch shifter I used at the time produced decent results. Later on, I conducted research into early pitch shifting techniques (as detailed in earlier blog posts) and developed a simple yet effective algorithm for pitch shifting. The goal was to generate similar artifacts to what a “de-glitched” pitch shifter would produce in a feedback loop with a reverberator, but without performing the costly autocorrelation analysis that the deglitching pitch shifters used. The result was a pitch shifting algorithm that added noise and texture to the feedback loop. It was an attempt to avoid metallic colorations (and emulate what a deglitching pitch shifter sounds like when it is freaking out), but it also sounded like a huge orchestra warming up.

When I started work on ValhallaShimmer in the spring of 2010, I knew that I wanted to combine the results of the cascaded diffusor experiments with the pitch shifted feedback as used by Brian Eno, Daniel Lanois, U2 et al. In order to put these into plugin form, I had to perform extensive optimization on the basic building blocks, as my early experiments used up far too much of the CPU. After a few months of work, I had a framework that brought the CPU consumption down by a factor of 10 to 20 from my 2006 experiments.

The original version of ValhallaShimmer had a single reverb algorithm, the one currently labeled as “mono.” Testing the plugin with material recorded with stereo miking techniques quickly pointed out that true stereo algorithms were necessary. The resulting algorithms (bigStereo, mediumStereo, smallStereo) were designed to get different perceived room “sizes,” although most of the sounds fall in the range between pretty big and huge.

During the optimization process, I found that one of my CPU-reducing tricks resulting in a lot of high frequency loss. Instead of looking at this as a technical shortcoming, I listened to the results. The optimized code sounded “warm,” and much closer to an ancient digital reverb with a low sampling rate and steep anti-aliasing filters. So I left it in as the “color” mode, so the user can choose between the original “bright” mode for modern reverb sounds, and the “dark” mode for that warm vintage sound.

Looking back at the history of ValhallaShimmer, it just struck me that most of what makes this an original algorithm was embracing the weird little artifacts that I came across while experimenting with various digital signal processing techniques. The cascaded diffusors didn’t behave in the manner I was expecting, but they sounded great. The pitch shifting artifacts added some grainy texture to the reverb decay, that sounded like a string orchestra section, even though the original goal was to get rid of metallic coloration. My optimization techniques darkened the overall tone, and helped me to realize that dark is often a good thing for a reverb. Happy accidents.

Introducing ValhallaShimmer

I am happy to announce my first commercial plugin, ValhallaShimmer:

ValhallaShimmer is an algorithmic reverberation plugin. It is designed to produce BIG sounds, from concert halls, to the Taj Mahal, to the halls of Valhalla.

There are several reverberation modes available, to allow the user to dial in the preferred initial sound. By adjusting the Feedback, Diffusion and Size controls, the attack, sustain and decay of the reverb signal can be fine tuned. The modulation controls can be set to produce subtle mode thickening, glistening string ensemble-esque decays, and the distinctive random modulation of the older Lexicon hall algorithms. Two tone controls and the Color Mode selector allow the timbre to be adjusted from bright and glistening to a more natural dark decay, similar to that produced by air absorption in large spaces.

In addition, ValhallaShimmer has the ability to pitch shift the feedback signal. There are 3 pitch shift modes available:

  • Single, where the feedback is shifted up or down by the Shift value.
  • Dual, where the feedback is shifted both up and down (in parallel) by the Shift value.
  • Bypass, which turns off the pitch shifting (useful for “standard” reverb sounds).

By setting the Shift amount to +12 semitones, and the Feedback to 0.5 or greater, the classic “shimmer” sound is produced, as heard on Eno / Lanois productions for U2 and others. I have discussed the “shimmer” effect in great (excruciating?) detail in earlier blog posts, and applied the research to the architecture of ValhallaShimmer. The resulting algorithms allow for the classic shimmer effects to be generated with ease, as well as a variety of pitch shifted, evolving ambiences.

ValhallaShimmer is the end result of several years of research, and is highly optimized:

  • The core pitch shifting algorithm uses randomization to avoid the comb filtering artifacts that can be heard in simpler pitch shifters.
  • The code has been optimized for SIMD processors, in order to allow the complex algorithm to run while using a small fraction of modern CPUs.
  • The reverberation algorithm has been designed to work in conjunction with the pitch shifting, to allow for high levels of feedback without compromising stability.
  • The algorithm works well with cascading multiple instances, both from a signal processing perspective and in terms of the low CPU consumption.

I will be posting more sound examples during the week (earlier examples can be heard here and here). For now, here’s a sound file that showcases the use of ValhallaShimmer for deep ambient sounds. The example uses 4 instances of Shimmer in series, with pitch shifting on 3 of the instances (+/- 12 semitones, +/- 7 semitones, and +/- 5 semitones).

ValhallaShimmer has been released for OSX (AU, VST, RTAS) and Windows (VST). 64-bit Audio Units, 64-bit Windows VST, and Windows RTAS will be coming soon.

Another clip from my upcoming plugin

The following clip shows some of the different modes of my upcoming plugin, ValhallaShimmer:


A brief summary of what is going on:

  • The clip begins with harp recorded in a fairly echo free environment
  • At 0:24, the mix control on the plugin is set to about halfway. The plugin is currently producing a fairly large reverb sound.
  • At 0:48, the feedback control on the plugin is turned up. This results in a much longer reverb sound. It is kinda subtle in this context.
  • At 1:13, the Pitch Mode of the plugin is set to “single,” with the pitch shift set at +12 semitones. This produces the classic “shimmer” sound that I have talked about in earlier blog posts, and that featured heavily in Eno / Lanois productions and many classic U2 tracks.
  • At 1:38, the harp loop ends, and the “shimmer” reverb decays away. Notice that the reverb increases in pitch as it decays.

In the next few days, I’ll be going into more details about the upcoming plugin. For now, I’m burning the midnight oil in front of the compiler.

Feedback, anti-feedback, and complexity in time-varying systems

“For my birthday I got a humidifier and a dehumidifier. I put them in the same room and let them fight it out.” – Stephen Wright

When I was researching the Eventide H910 Harmonizer, I found it curious that the box had controls for both feedback and something called “anti-feedback.” The service manual explains the anti-feedback control as follows:

Increasing clockwise rotation of the ANTI-FEEDBACK control progressively adds a small up and down frequency shift to the output signal, which serves to decrease the effect of room resonance peaks on the signal which ultimately re-arrives at the microphone.

In modern terms, I would call this a chorus effect, with a triangle wave modulator. Pretty simple. However, it is interesting to see how such a simple process can have a significant effect in a PA system – by turning on the Anti-Feedback control, you can increase the gain of a microphone being fed into the H910.

The idea of using a time-varying system, such as pitch shifting, delay modulation, or frequency shifting, to increase the maximum gain of a system before oscillation occurs, dates back many decades. In 1962, Manfred Schroeder (of digital reverb fame) published an article in the AES Journal about using frequency shifting as a method of increasing the gain of a PA system by up to 6 dB. A picture tells a thousand words, especially if it has a bunch of words attached to it:

Schroeder also discusses what happens if the gain is turned up beyond the feedback suppression limits of the frequency shifter:

For example, when using the frequency shifter, an excessive gain announces itself by a faint but easily recognizable “growl” or “chirp.” When this sound is heard, the operator decreases the gain by one or two decibels and the system continues to operate without the audience having heard any adverse effect.

This works well for gain increases up to a certain limit, but what happens when the gain is increased well beyond that point? The answer can be found in ValhallaFreqEcho. As the feedback gain is pushed beyond a certain level, the plugin will enter into a self-oscillating region, but one that has a huge amount of complexity. By controlling the shift frequency, delay, tone controls, and feedback gain, a variety of constantly evolving patterns can be produced. The overt goal of ValhallaFreqEcho is to get those chirps and growls that Schroeder described.

The Eno/Lanois “shimmer” sound works along similar principles. Pitch shifting, in and of itself, is a useful way of avoiding oscillation, as it pushes the feedback energy into regions that are above or below the original energy in frequency. However, if you turn the feedback gain up high enough, the system will start to self-oscillate, but in a highly chaotic manner. Keeping the gain just below self-oscillation will result in a sound that slowly evolves into a huge orchestral wash, that fades away into tinkling high octaves.

From a DSP developer’s perspective, delay modulation, frequency shifting, and pitch shifting all fall under the category of time-varying systems. Conventional digital signal processing theory concerns itself with linear, time-invariant (LTI) systems. Once time-variation is introduced, conventional LTI theory falls apart. There has been some research performed on what time-variation will do in otherwise linear systems, but there is no simple answer.

In some systems, time variation will make a simple system become unstable, such that its output amplitude grows out of bounds. Reverb developers call that “blowing up,” as that is the best way to describe the sound that comes out of the speakers. However, in the systems described above, time-variation serves to make a system more stable, in that it allows for the feedback gain to be increased. The onset of oscillation in such systems is something that is usually avoided in academic DSP, but in musical audio it is an area rich for exploration.

In my next post, I will look at an early digital reverb in which the entire theory of operation was based upon the increased gain obtainable through time-variation.

Shimmer: Modulation, auto-correlation, and decorrelation

In my previous post, I discussed the Eno/Lanois shimmer sound, and how it is based around a pitch shifter and a digital reverb placed in a global feedback loop. It is worth exploring what is going on in this signal chain at the micro level, and how a fairly simple signal routing can create such a complex sound.

The AMS pitch shifter used by Eno and Lanois used a de-glitching board in its architecture, to find the ideal points for splicing together the time-scaled waveform chunks. This presumably worked in a similar manner to the H949 de-glitching card, in that autocorrelation was used to find the most similar segments of the waveform, and the delay time of one of the channels was adjusted for an ideal splice. It is also possible that the auto-correlation would trigger a new splice, such that the rate between splices was a function of the periodicity of the input signal.

Auto-correlation works well for determining splicing points, assuming that the input signal has a certain degree of correlation. A single sustained guitar note, for example, can have a high auto-correlation factor after the initial attack. But what happens when the signal to be shifted has a very low auto-correlation factor? Such a signal is said to be decorrelated; that is, the auto-correlation or cross-correlation is said to be greatly reduced compared to the original signal.

In the audio world, decorrelation often refers to randomization of the phases of the signal while preserving the frequencies, or to a time-varying process to slightly shift the frequencies of a signal to prevent feedback. Both of these processes are present, to a large extent, within time varying reverbs such as the Lexicon 224 and EMT250 used by Eno and Lanois.

The Lexicon 224 Concert Hall algorithm is made up of a number of allpass delays, which preserve the input frequencies while completely scrambling the phase response. In addition, the Concert Hall algorithm uses time varying delays inside of the recursive delay network, which increased the perceived modal density of the reverb, and also impart a beautiful chorusing to the reverb decay. This lushness from time-varying delay lines is very prominent in 1980′s Eno/Lanois productions – in addition to the Concert Hall algorithm and EMT250, they made use of the multi-voice chorus algorithms in the Lexicon units, as well as the Symphonic preset in the Yamaha SPX-90.

So, what happens when a pitch shifter that uses auto-correlation to find the ideal splicing points is put into a feedback loop with a reverb that is highly decorrelated and time-varying? The answer: chaos. The pitch shifter will NOT be able to find ideal splicing points, as the phase of the reverb output is continually being scrambled.

The pitch shifter HAS to splice, whether or not it is a perfect situation, so it will pick the best possible match, but this will probably be a fairly random location each time. The result will be random delays for each new splicing point, or random sizing of the grain windows, depending on how the auto-correlation is used within the pitch shifter. This randomization will cause the sidebands of the input signal to be spread out, such that an individual sinusoid would be turned into a band of frequencies centered around the original (that has been shifted up by an octave).

Add in the additional octaves produced by the feedback, the random sideband spread caused by the modulation within the reverb, and harmonics that are created by analog nonlinearities in the feedback path, and the result is a HUGE amount of sonic complexity generated from a simple system. Put a sine wave into this type of feedback system, and the output can approach near orchestral levels of thickness.

In this light, it is interesting to think about Eno’s use of the DX7 around this time. The DX7 can produce chaotic sounds through the use of cascaded FM, but it can also produce gentle, minimalist textures through the use of parallel operators (sine oscillators). A simple DX7 patch with several parallel sine oscillators and a low FM index may produce a fairly boring sound on its own, but would create an enormous yet controllable sound when fed into a complex feedback loop of digital processing.

Coming up: more on the topic of generating complexity through simple systems with feedback applied to them, both from a technical and creative perspective.

Eno/Lanois Shimmer Sound: How it is made

The basic foundation of the Brian Eno / Daniel Lanois shimmer sound is fairly simple: Create a feedback loop, incorporating a pitch shifter set to +1 octave, and a reverb with a fairly long decay time. By controlling the gain and equalization of the feedback loop, and the lengths of the various delays within the loop, the temporal evolution of the sound can be altered from steel drum-esque sounds to the slow attack “string pads” hear on many of the Eno/Lanois tracks. This is the same technique used by ValhallaShimmer, with the reverberation, pitch shifting and feedback all incorporated within the same plugin.

Kevin Killen, answering a question about the signal flow on the U2 song “4th of July” on Gearslutz, described the signal path as follows:

The delay and modulation was derived from the AMS 1580. On its fader return , some hi frequencies were rolled off, then it was fed into a 224 Hall setting, probably 5 seconds but with a rolloff in the top and bottom. This return may have been equalised also. We may have added a second delay but then the delays have to be timed to the track as the net effect is blurring the chord progression…Our last tweak would be to play with the sends on all of the returns to the point that its almost recirculating out of control, which in turn is creating a layer upon layer effect.

The AMS DMX 15-80s was a digital delay / sampler / pitch shifter that was in common use in Britain in the early 1980′s. Eno and Lanois have both sung the praises of this unit, and Wendy Carlos has said that the AMS unit had “perhaps the least audible artifacts to pitch shifting available at that time.”

David Kulka has written that the AMS DMX had an optional de-glitch card installed, which worked on a similar principle to the auto-correlation deglitcher in the H949. His post is worth quoting:

Harmonizers, at least the early ones, had to electronically “splice” sections of the waveform in order to accomplish pitch change. When the out and in points had different voltage levels, a small DC pop could be heard at each transition. The result was a sort of low level crackle, more obvious with certain kinds of program material, and more audible at extreme pitch change settings.

The Eventide H910 exhibited this, along with the early AMS Harmonizers. Both Eventide (on the H949) and AMS partially resolved this by adding “de-glitch” cards. The circuitry on this card added a “smart” algorithm to pitch change, adjusting the transitions to better match voltages at the in and out points.

The “224 Hall setting” that Killen refers to is the Concert Hall algorithm in the Lexicon 224. This algorithm has a fairly low initial echo density, that builds to a higher density as the decay evolves. The Concert Hall algorithm is also distinguished by its high degree of modulation. The resulting sound is not a terribly accurate simulation of a real concert hall, but rather a lush and spatially expansive reverb that is still sought after more than 30 years after its introduction.

Other accounts of the “shimmer” sound refer to different reverbs being used, such as the EMT250. In addition, modulated delay lines, such as the Lexicon Prime Time, have been used by Lanois at different times. The common elements always seem to be the pitch shifter, a modulated reverb and/or a modulated delay line, and feedback and equalization generated via an analog mixer. In my next post, I will analyze the contributions of these elements to the shimmer sound, and will discuss how the various components respond in a feedback situation.

Eno/Lanois Shimmer effect: Early examples

The collaboration of U2 with Brian Eno and David Lanois was the first introduction to a wide listening audience of the reverb with swelling octave overtones that has come to be referred to as “shimmer.” However, the effect was in use by Eno and Lanois for some time before it was featured on the 1984 album, “The Unforgettable Fire.”

My favorite example of the sound comes from the 1983 album, “Apollo: Atmospheres and Soundtracks” by Brian Eno, his brother Roger, and Daniel Lanois. It makes up the huge background pad in the song “Deep Blue Day:”

Similar octave-shifted reverb sounds can be heard all over the album. Not all of the songs use the feedback configuration of the reverb feeding into a pitch shifter and back into the reverb. In “An Ending (Ascent),” the main melody instrument has a delayed pitch shifted signal an octave above and below, but no feedback:

A more “shimmery” sound (i.e. more feedback) can be heard in the “Prophecy Theme” from the Dune soundtrack:

In the next post, we will examine the signal chain used to get these sounds.

Pitch Shifting: The H949, and “de-glitching”

In 1977, Eventide released the H949 Harmonizer:

The H949 built upon the harmonizing features of the H910, and added more memory (for longer delays), randomized delay, reversed delays, flanging, and a micropitch mode for small pitch shift intervals. However, from a DSP developer’s perspective, the most interesting feature was a new circuit board, the LU618 or “ALG-3″ board, that was an option for earlier H949s and was added as a standard mode to later units.

A somewhat technical review of the situation:

  • In the H910 and H949 pitch shift modes, information is being read into delay memory, and being read out at faster or slower rates, to change the pitch of the signal. Reading out of a delay line at a different rate than the data is written will quickly create a situation where the delay line runs out of samples to read.
  • In a modern delay line based around a circular buffer, if the read tap is moving through the buffer at a different rate than the write pointer, it will soon run into the write pointer, either by catching up to it or by being overtaken by it. Resetting the read tap to a different point avoids the issue of running out of memory or running into the write pointer, but this causes an audible popping sound as the read tap jumps instantaneously to some random point in the delay.
  • Pitch shifters deal with this artifact by fading the value of the read tap down to zero before making this jump, and then fading the volume back up again after the jump. In a 2-tap pitch shifter like the H910 and H949, the volume change can be viewed as a crossfade between the 2 read taps. This is directly analogous to what happens in the rotary head tape pitch shifters, as a given read head rotates away from the tape.
  • However, this crossfading is not without its problems. If the crossfading happens over too long of a time, the result is a metallic coloration of the sound, as the 2 read taps have a constant relative distance from each other that results in comb filtering. Having the crossfading take place over a shorter interval helps to reduce the comb filtering, but results in an audible “glitch,” as the phase differences between the 2 read taps causes cancellations in the frequency response that is heard as a volume drop during the crossfading period. This can be heard as a “stuttering” artifact in the pitch shifted sound.

The LU618 / ALG-3 board on the H949 works on eliminating this “glitch” artifact through a clever trick called autocorrelation. As described in an Eventide patent by Anthony Agnello, the ALG-3 board looks at the 2 delayed signals, and compares them to see where they share the most similarities – not just zero crossings, but true phase similarities. The H949 then calculates a delay offset, such that the new segment that is to be faded in is in phase alignment (or as close to phase alignment as possible) with the segment that is being faded out during the crossfade time. If the ALG-3 has calculated the delay offset correctly, the 2 segments that are being crossfaded between will be almost identical, which will result in the least cancellations in the frequency and amplitude response. Voila, glitch-free pitch shifting!

If only it were so easy. The H949 “de-glitcher,” and the de-glitching mode used in most time-domain pitch shifters that followed the H949, work well with signals that are as close to periodic as possible – i.e. a single monophonic musical line. Periodic signals have a high degree of autocorrelation, so the de-glitching hardware can usually find excellent splicing points. Voice can be de-glitched fairly, as can a monophonic guitar line. Once polyphonic signals (i.e. chords) enter the picture, it becomes harder and harder to find similar points to splice together. Noisy signals, like drums, will have almost no similar splice points (i.e. a very low autocorrelation value). In such a case, the de-glitcher will find the most similar points to splice together, but there is no guarantee that they will be in any way similar, so the result is more likely to have amplitude glitches.

Next week, we will discuss the various pitch shifting schemes and how they relate to the generation of the Eno/Lanois “shimmer” sound.