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.

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.

The first digital pitch shifter: Lexicon Varispeech

When I was planning my “editorial calendar” for the next few weeks, I had planned on discussing the Eventide H910 Harmonizer as the “first digital pitch shifter.” I even described the H910 as such in an earlier blog post. However, it turns out I was wrong. The Lee article that I discussed in my previous post describes what is probably the first commercially available pitch shifter, the Lexicon Varispeech:

The Lexicon Varispeech was introduced in 1972, a good 3 years before the H910.  The Lexicon Pro website makes only passing mention of the device, describing it as a “Lexicon product for the language instruction market.” Fortunately, the Obsoletetechnology blog has a nice overview of the device, including photos, gutshots, and sound examples. The following image is taken directly from the aforementioned blog post, which you really should read:

Interestingly enough, for a device that was marketed as being used for speech and time compression, the Varispeech 27Y has a feedback knob. This is solely for use as a special effect, and was prominently featured on the H910 and H949 harmonizers of later years. I am uncertain if this was in the 1972 Varispeech, or if the 27Y was the original Lexicon model or a later version. If anyone has any info, please contact me.

Chris Walla of Death Cab for Cutie describes his use of the Lexicon Varispeech in an EQ Mag interview, where he also notes the incongruity of the feedback knob on a device used for time compression and expansion:

There was a lot of speech pathology research developed at Lexicon that was cross-purposed into pro audio. The Varispeech was originally intended to help stroke victims and people with speech disorders. The idea was that you could slow down a conversation at regular pitch but keep pitch where it was so that people could practice figuring out how to reconnect their mouth and their brain.

There was this weird period where [Lexicon was] screwing around with it; I got one that had a feedback knob, which as far as I can tell is completely useless for speech pathology, but it makes everything sound like Doctor Who, which is awesome.

It sounds great under the snare drum, and Tegan’s vocals run through it on ‘The Cure’ when she does the ‘Oh, uh oh, uh oh’ thing. The Varispeech is a really cool chorus-y, flange-y thing if you set it up that way. But it’s a speaker destroyer, too. It’s an old [’70s] effect, and Lexicon wasn’t worried about being sued by guys who were like, ‘You blew up my guitar amp, dude!’