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.

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.

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.

Early pitch shifting: The Eventide H910 Harmonizer

In 1975, Eventide came out with their first Harmonizer, the H910:

Designed by Anthony Agnello (later of Princeton Digital), this was a digital variant of the rotary tape head pitch shifters that I discussed earlier. Like the Lexicon Varispeech that preceded it, the H910 would be what I would label a 2-tap pitch shifter, in that there were 2 pitch shifted signals, with crossfading between the 2 signals. The H910 appears to use a fairly simple triangle wave crossfading, which means that the 2 different delayed signals will be present to a greater or lesser extent in the output at virtually all times.

So, why did the H910 become identified with pitch shifting, and the term “Harmonizer” become almost as generic as “Xerox” (at least in recording circles), while the Lexicon Varispeech faded into relative obscurity? I don’t know. If I had to guess, it has something to do with marketing. The Varispeech was described in the literature as a way of time correcting speech, while the Harmonizer was sold from the get-go as something to generate musical harmonies. Let’s face it, Harmonizer is a great name.

Whatever the reason, the Harmonizer quickly made its way into recording studios around the world. Tony Visconti famously described the H910 to David Bowie and Brian Eno: “It fucks with the fabric of time!” Visconti used the H910 while recording Bowie’s “Low,” where it was used to create a snare drum sound that descended downwards, with the amount of pitch bend determined by how hard Dennis Davis hit the snare:

The snare sound also has some sort of gating on it, but you can clearly hear the Harmonizer on the first snare hits. The H910 was set to a downshift setting of around -1 semitone, and the feedback was turned up to get the quick delays that shoot down in pitch.

One of my personal favorite examples of harmonizer (ab)use is “Duck Stab” by The Residents. Practically every song on this record uses harmonizer feedback, either for generating a detuned chorus on the vocal, or a minor third transposition with feedback to create “dimished” harmonies. Enjoy the following super creepy video while listening to the nifty pitch shifting tricks.

Pitch Shifters, pre-digital

When I was doing research on pitch shifting for my analysis of the Eno/Lanois “shimmer” effect, I had presumed that I would start with the first commercially available digital pitch shifter, the Eventide H910 Harmonizer. However, it is worth exploring the analog pitch changing devices that predated the H910 by several decades.

In a 1966 Journal of the Audio Engineering Society article, William Marlens traces the history of analog pitch and time changing devices, with the earliest patents dating back to the 1920′s. The basic idea of all of the patents was to record the audio signal onto some moving medium (tape, wire, film, etc.), and then use a rotating playback head, where the read heads would be moving at a different rate as the recording head:

The rotary playback head has 2, 4 or more read heads. By adjusting the rate of the rotation relative to the tape motion, the pitch of the signal can be raised or lowered. Time expansion / compression can be achieved by speeding up or slowing down the rate of the tape, while keeping the tape heads moving past the tape at a rate that is identical to the original recording rate. As a given tape head comes into contact and is rotated away from the tape, the output signal from that given head will fade in and out, which results in a natural cross-fading of pitch shifted segments.

It is hard to track down audio examples of these early time/pitch changers. Stockhausen made use of one for Hymnen, and other European electronic music studios had similar devices on hand, but the most common use in the US seemed to be shortening audio for commercials to fit a given length. Strangely enough, the Beach Boys seem to have made use of a rotary head pitch shifter on a few songs. Listen to the vocals in “She’s Going Bald” off 1967′s Smiley Smile, starting at 0:51, to hear the characteristic formant shift and warbly sound of a cross-fading pitch shifter.

The Beach Boys also used a fixed rotary speed to add a metallic effect to the drums on “Do It Again.” It is most obvious on the intro:

Wendy Carlos has a detailed blog post about her experiences with the Eltro “Information Rate Changer.” Carlos describes how this 1960′s rotary tape head device was used for the voice of HAL 9000 in “2001″ (Carlos wasn’t involved with 2001, but had the story relayed to her by Stanley Kubrick). Apparently the Eltro was used on HAL’s voice throughout the film, but the effect is most obvious in the “death” scene. At 3:06, you can hear the voice start to warble more, presumably as the signal’s pitch was shifted further downwards:

One of Carlos’ experiments involved recording a signal onto an Ampex tape deck, using the Eltro to play back the signal, and sending some of the pitch shifted signal to the record head of the Ampex. This resulted in a pitch shifted tape delay loop, where each repeat was higher (or lower) in pitch. This pitch shifted feedback, in digital form, is a crucial component of the Eno/Lanois shimmer effect. It seems that Wendy Carlos was exploring similar realms a few decades earlier.