Instead of engaging with the synth in realtime and constructing rich (if inaccurate) mental models, I found myself laboriously transcribing its output and endlessly scrutinizing waveforms in an attempt to discern the underlying mathematical models; this felt wrong. Yet, without such tools I wouldn't be able to explain at all what's happening under the hood of Phase.
This is the slippery slope at which I find myself: should I return to synths previously discussed and apply the same mechanical scrutiny? Looking at the waveforms would make the shape of Digital's main and sub oscillators perfectly clear, but using the computer screen to do a job best suited to my ears seems like a perversion of the OP-1 spirit.
For now, I will avoid re-examining previous synths "under the microscope" in preference for an approach more akin to taste-testing them. With Phase I will have to rely somewhat on the clinical results, and even then I'm afraid you will find many gaps and unknowns; as usual, there will be a forum thread linked at the bottom of this post, so if you have any insights or corrections, please let me know!
The manual (from which the above diagram is taken) classifies Phase's type as "Phase Distortion"; phase distortion synthesis is, like FM, a form of synthesis whose basis is inherently digital and whose popular roots lie in a series of digital keyboards introduced in the 80s (in this case, Casio's CZ series).
Here are a few helpful introductory links into PD synthesis:
http://www.electricdruid.net/index.php?page=info.pdsynthesis
http://en.wikipedia.org/wiki/Phase_distortion_synthesis
http://www.algomusic.net/PDSynthesis.html
The basic idea, if I may inaccurately attempt an overview, is that a "playhead" scans across a sampled waveform -- in this case a sine wave. During each period of the wave, the playhead is sped up/slowed down as it sweeps from left to right; this causes the result to be a sine wave which is by turns compressed/stretched (respectively), "distorting" its shape. (You might remember this playhead as the "phase accumulator" lurking inside of Dr. Wave; indeed, there are several similarities between that synth and Phase, although the end results are quite different.)
The exact ways in which the playhead's speed varies is specified by a phase distortion function, which is typically (or at least, historically) in the form of a set of line segments describing the playhead's position in the sampled wave at each instant in time. (Please refer to the above links for a more thorough treatment of PD; I would only be paraphrasing them -- and poorly at that -- were I to attempt to say any more on the subject.)
The graphical interface for Phase is akin to an interactive diagram -- a wonderful tip of the hat to the mathematical/geometric basis underpinning this method of synthesis.
Blue ("Phase Shift"), Green ("Distortion Amount"):
I'm discussing both of these parameters together, because they both seem to control the phase distortion function.TE have grouped their graphics together, suggesting perhaps that these parameters are properly considered a pair.
Visually, both Blue and Green are represented quite simply: a pair of correspondingly coloured sinusoidal shapes which slide left/right as the controls are rotated CCW/CW.
Unfortunately, it's proven impossible for me to reverse-engineer the exact way in which these two parameters alter the shape of the PD function -- the above websites typically show this function as a sort of upside-down "V" made of two linear segments. In the case of Phase, the PD function seems to be more complex. Moreover, I suspect that Blue and Green interact with each other somehow: they may be moving a single point around a 2-dimensional parameter space, rather than moving two unrelated 1-dimensional points.
So, please forgive me for the relative lack of solid information and useful description in this section. What can be said about Blue and Green?
With all parameters at minimum (fully CCW), Phase produces a pure sine wave. Turning Blue CW from here results in the sine wave being increasingly "squished" to the left -- this is analogous to the "pulsewidth" behaviour of Dr. Wave's White parameter, adding high harmonics as the sine is compressed into a single very skinny sine-shaped pulse/burst.
Starting again with all parameters at min, turning Green CW has a different effect on the sine wave: the second half of the wave is stretched out horizontally. With continued CW movement this broad U bifurcates, becoming finally a doubled UU shape when Green is fully CW. Aurally, this adds some high-frequency content as well as reinforcing the bass end, rounding out the sound.
When both parameters are combined, the results are complex and difficult to both predict and describe. I'm trying to avoid merely posting pictures of the resulting single-cycle waveforms as I think this sort of minutia is perhaps going too far.
In general, both controls seem to add varying bands of higher-frequency content as they distort the sine wave. This is definitely not an intuitive set of controls; in fact, it's possibly the most inscrutable and confusing pair in all of the OP-1! I'm sorry I can't shed any more light onto them for now.
White ("Phase Filter"), Orange ("Phase Tilt"):
As with Blue/Green, I'm discussing these parameters in a pair, as they also seem to be two controls affecting a single process. Again, the way that TE have paired these two controls visually suggests that this is indeed the case.
Visually, White/Orange are illustrated in the same method as Green/Blue: each parameter is represented as a vector graphic which moves (up/down for White, left/right for Orange) to indicate its current position between the min/max bounds of that parameter. White is a horizontal line, while Orange is a connected chain of sinusoids of increasing frequency, tapering off to a flat line.
Synthesis-wise, these two parameters control a process very similar to that described in the section of the above-linked Wikepedia article titled "Simulating a resonant filter". The overall effect is more akin to increasingly powerful enveloped 2-op FM than to raising a lowpass filter's cutoff -- both add high frequencies, but the burble-y round nature of this sound is almost totally unlike the typical action of a filter.
Orange controls a process almost identical to the "sync" behaviour of Dr. Wave's White parameter: the speed of the "playhead" sweeping through the sampled wave is increased, and as the playhead passes the end of the wave it is wrapped around to the beginning. The main difference is that with Dr. Wave we were setting the constant speed of the playhead, while here we set the rate of increase of the playhead's speed -- the playhead is continuously accelerated from 1:1 to some maximum speed over the course of a single period, and Orange controls the rate of this acceleration.
Applied to a pure sine wave (i.e Blue/Green/White at minimum), the result matches the orange graphic onscreen: a sine wave of gradually increasing frequency. As indicated by the graphic, once the playhead's speed has surpassed some maximum limit (perhaps dictated by Nyquist or some other sampling/DSP-related constraint) the level drops to zero. This has the side-effect that increasing CW values of Orange cause this limit to be hit sooner and sooner, and we get another instance of "pulsewidth-esque" behaviour where a waveform is increasingly compressed towards the left, increasing the high-frequency content and removing the bass.
White controls the strength of an attenuation function -- in this case the downward volume ramp described by Figure 19d and steps (d) and (e) of the aforementioned Wikipedia article. As with Orange, White sets a rate rather than a level: turning White adjusts the slope of the ramp downward from horizontal (minimum/fully CCW) to sawtooth (maximum/fully CW). Since this ramping happens at audio rates -- once per period -- the result isn't perceived as a change in volume but rather a change in timbre.
The aural effect of this increasingly pronounced volume ramping varies depends on the values of the other parameters. Increasing values of White always result in somewhat of a drop in level, as you're introducing more and more attenuation.
When Orange is at low or minimum values, turning White CW results in the generation of some high-frequency sidebands: each cycle of the waveform is being shaped into an increasingly sharp decaying sawtooth shape, which makes it sound more like a sawtooth (it becomes a sinusoid with a sawtooth-shaped envelope).
When high values of Orange are dialed in, this subtle shaping effect is less perceptible; instead, increasing White in this context tends to "soften" the effect of Orange -- as illustrated in the Wikipedia article, the ramp controlled by White is reducing the amount of discontinuity found at the end of each cycle, which removes high frequencies.
Conclusion
I'm sorry I haven't been able to do a better job of explaining Phase to you; hopefully in the future, as more information is available I'll be able to rewrite this article to better communicate what's happening.
The general effect of Blue/Green/White is typically to generate bands of high-frequency content, but the way that these three parameters interact means that the results are highly unpredictable and the patterns/relationships of cause and effect are difficult if not impossible to ascertain.
In general, Phase sounds like what it is: a distorted sinusoid. This can range from round and subtle to shrill and buzzy, but the nature of the underlying sine-shaped source is always present to a certain extent. It's definitely very capable of bass, leads, evolving pads, and any manner of strange sweeping effects.
The next post will examine which aspects of Phase could best stand improvement or at least future scrutiny by TE; as you might imagine, the bewildering inscrutability of the controls is one very ripe low-hanging fruit.
As usual, there is a forum thread here where you can help share information about Phase, compare notes, or make corrections to this article: http://ohpeewon.com/discussion/234/op-101-phase
