(I'll actually refer to it as Dr. Wave rather than Dr Wave from now on, because whether or not this was the intended nomenclature, I think "Doctor Wave" is an awesome name)
Anyway: we have now reached the third method of synthesis currently available in the OP-1, the Dr. Wave engine. This is definitely one of my favorites, and very likely my absolute favorite -- it's got range, it's got personality, and it's really fun and easy to use.
The gorgeous manual (from which the above image is cribbed) describes Dr. Wave thusly: "Frequency Domain Synthesis".
I have absolutely no idea what this means!
Moreover, I suspect that this is pure jargon which might refer to the implementation details of the synth; this isn't very useful because digital synthesis terminology is vague and seems confused -- possibly because much of it was decided by marketers rather than engineers. For example, PD and FM synthesis are more or less the same thing, as least as far as I can tell; "Frequency Domain" could mean basically anything.
(Upon further reflection: this probably suggests that a Fast Fourier Transform is happening and thus the oscillator shape and filter action are occurring in FFT-land. But still: it could be anything from additive synthesis to filtering)
Does this matter? Probably not; "Dr. Wave" is all the terminology you really need.
My personal conclusion -- and I would stress here that you should probably take TE's word over mine on this matter -- is that Dr. Wave employs what this informative and interesting webpage refers to as "direct digital synthesis".
At least, this theory seems to partially explain some of the behaviours and controls found inside Dr. Wave. It might be far off the mark though; the basic idea of an index/phase accumulator that sweeps across a sampled waveform can no doubt be applied in many different ways and doesn't in itself require a single particular approach to synthesis.
Let's just forget about what's actually happening and discuss things in empirical, phenomenological terms: what does it sound like Dr. Wave is doing?
My best guess is that a digital waveform (an array of samples) is generated, using a variably-shaped oscillator (continuously morphable between sawtooth->square->triangle) passed through a fixed-resonance lowpass/highpass filter. Possibly it's this initial step which occurs in the frequency domain; regardless, this is just the beginning of the synthesis process.
The generated array of samples is then scanned/resampled at a variable samplerate (i.e skipping some of the samples) and speed (i.e sweeping through the array in a variable amount of time) to generate a final waveform, which can then be doubled; the duplicate wave's pitch is modulated by an LFO to produce a detuning/phasing/chorus effect.
So: Waveform -> Filter -> Resample -> Chorus
Visually, this is both one of the most interesting, as well as one of the most practical, functional, and (for lack of a better term) "grokkable" of the current OP-1 synth engines. It displays the output of the resampling step: a waveform which is (more or less) the literal depiction of what you're hearing. (I say "more or less" because I suspect that the Orange/Chorus parameter is being visualized metaphorically rather than directly; nevertheless this is an eminently useable and powerful synth in terms of graphical feedback.)
The waveform is visibly made up of discrete samples, each represented as a horizontal line; when the sampling rate is high enough these horizontal spans are so short that they create the illusion of a single smooth curved waveform, while a low sampling rate causes the waveform to degenerate and break up into low-resolution stepped edges.
Finally, Dr. Wave is also notable for having most of its parameters (all but Orange) being continuously variable, either cyclical/wrapping or mirroring, so that there is no true "minimum" or "maximum" setting. This makes it a bit challenging to accurately describe them, so please bear with me! :)
Blue ("Wave Type & Length"):
This single parameter affects two different internal processes, each at opposite ends of the signal chain: the shape of the waveform that's run through the filter, and the sample rate that is used to resample the resulting filtered wave.
When turning the control, you can see immediately the result of your movement: the waveform will morph from one shape to another, and possibly become "coarser" as the sample rate is decreased -- visually this looks like obvious stepping rather than a smooth wave, as each sample is extended horizontally to make up for their diminishing numbers; the waveform gets visibly chunky.
As with most of the parameters in Dr. Wave, Blue is wrapped/cyclical, so that if you turn constantly in a particular direction you eventually end up where you started. A single period of this cycle looks like sawtooth -> square -> triangle (and then back to sawtooth) when rotating the encoder CW.
Coupled with this continuous morphing of waveshapes is control over the samplerate reduction (henceforth SRR).
When rotating CW, there are three full periods of saw->sqr->tri before the control wraps around to where you started and the cycle repeats; what differs in each of the three rotations is the amount of SRR applied.
The first CW "lap" through the waveforms (saw->square->tri) is at full samplerate with no SRR applied. The second time through sees SRR introduced during the saw->square transition, and increasing as the waveform morphs through square into triangle. The amount of SRR applied reaches a maximum directly between the second and third lap through the waveforms: the transition from the end of the 2nd lap (triangle) to the start of the 3rd (sawtooth) is when SRR is at its maximum value and the waveform is at its most coarse, with only 2 or 3 samples spanning the entire screen. Continued CW movement from there through to the end of the third lap results in SRR gradually reducing in intensity until it's completely absent by the end of that final third saw->square->tri rotation.
Hopefully you can follow this -- as the control is endless, the designation "start" is obviously arbitrary and discussing things can be tricky without a fixed point of reference.
One notable aspect of SRR is that if you set it to a low rate (very steppy/chunky) and apply a bit of modulation to Blue, some very evil PWM-type ripping sounds can be had.
Green ("Filter"):
This parameter controls the cutoff of a lowpass/highpass filter with a fixed resonance peak (i.e resonance isn't adjustable).
As with Blue, Green is cyclical and will wrap around given sufficient rotation in a particular direction. As you rotate CW, the lowpass cutoff frequency sweeps upward from min (all waveforms are reduced to sine waves) to max (you can see the full sawtooth/square/triangle shape). Continuing to rotate CW from this point will begin sweeping a highpass filter's cutoff upward, from min (full waveform visible) to max (waveforms are completely filtered out and you're left with a flat line). Further CW movement from this point will then wrap around to begin the cycle anew: the lowpass cutoff will start to sweep upward.
(For those of you familiar with Elektron products, an analogy would be that initially, FLTF and FLTW both start at 0. As you rotate Green CW, FLTW is swept upwards to 127 while FLTF remains at 0; continuing CW from there results in FLTF sweeping up to 127 while FLTW stays at 127. Then both controls jump to 0 and the cycle repeats.)
Visually, you can see the waveform selected by Blue being filtered -- the resulting post-filter waveshape is what's drawn. This visualization is taken post-SRR so it can be a bit confusing/non-obvious unless you turn Blue until the wave is fine-grained and there's no obvious stepping: this will make the action of the filter obvious both visually and aurally.
When the filter control is near the start of its cycle (lowpass cutoff is low), the result will look like a sine wave regardless of the selected waveform -- the lowpass is rejecting all harmonics above the fundamental, leaving only a sine wave. As you move the control CW you can see the additional harmonics added -- bumps of decreasing size/increasing frequency -- until with lowpass cutoff fully raised you can see the pure sawtooth/square/triangle waveform.
Continuing CW from here, you can see the highpass's resonance peak distort the waveform, warping its initial sawtooth/square/triangle shape along a sine-shaped bulge: this is the resonance peak reinforcing the fundamental. Further CW movement will see the lower frequencies filtered out, with smaller and smaller high frequency waves remaining, which gradually reduce until you've left with an inaudible silent line. Turn CW from here to bring a sine wave out of this line -- you've wrapped around and the lowpass filter is sweeping up past the fundamental.
White ("Phase"):
(For a supplemental discussion of this parameter, please refer to this excellent blog post started by forum user BathHouse)
This control is very weird in a couple of ways. First of all, it is "mirrored": if you rotate CW for long enough, the parameter hits an internal extremum and then "reflects" off of this limit, moving in the other direction. This can be very confusing/disorienting, as it means that both CW and CCW turns can at different times produce the same change in sound -- which direction does what just depends on your previous movements.
To aid in explaining this control, I would recommend "zeroing" this parameter by rotating it CCW until a flat line appears on the right side of the display. If you have a flat region on the right side, and turning CCW causes this region to shrink rather than grow (i.e causes the waveform that's cramped into the left side to expand), then turn CW until the flat region extends to the left side of the screen and then starts to receed.
You should now be in a state where a CCW turn will cause the flat region to grow, extending further to the left, and a CW turn will cause it to shrink. To complete the process, rotate CW until the flat region disappears and you're left with a single cycle of the current waveform.
Okay, now we can begin talking about the strange creature that is Dr. Wave's White/Phase control!
This parameter is what made me think of the "Direct Digital Synthesis" article I linked to above. The naming in particular -- Phase -- suggests the phase accumulator described in that article: a "playhead" which scans through a sampled waveform.
My understanding of this control is as follows: from the "zeroed" position with a whole single cycle waveform visible, rotating in either direction will increase the rate at which the playhead sweeps through the sampled waveform. The difference between CW and CCW movement is that in one direction, the playhead is lifted after a single pass across the wave -- it only sweeps from start to end once -- while in the other direction it will wrap around and continue scanning through the wave until the end of the appropriate interval (this length of time is determined by the pitch of the note you're playing, i.e an A 440hz tone means that the playhead will be allowed to scan through the waveform repeatedly for 1/440th of a second before being reset to the start of the waveform).
If you've set things up properly, then turning CCW will produce the "scan once" behaviour while CW will "wrap around"; if this is backward, don't worry about it -- just mentally swap CW/CCW references in this text, or rotate CW until the parameter hits its minimum value and rebounds/mirrors.
(I really hope this is clear.. it's a tricky thing to talk about!)
Anyway, what does this control actually do, sound-wise? The closest thing I can compare it to is that CCW movement acts like a pulsewidth control, gradually increasing the high-frequency content while removing low-frequencies until you're left with (at the extreme value) a high buzzing sound. CW movement on the other hand behaves like oscillator sync in an analog or virtual analog synth.
Visually you can see both behaviours pretty clearly: the former (CCW movement) causes the waveform to be squished into the left side until nothing is left but a tiny vertical slice followed by flatness, while the latter (CW movement) causes the waveform to double, treble, and eventually multiply so many times that the display degenerates into a field of moire static.
This doesn't sound exactly like typical pulsewidth/sync, but these are the closest analogs I can think of to what's happening both visually and aurally. No pun intended :)
Orange ("Chorus"):
I'm going to take TE at their word here and assume that what's happening is that the output of the synth section (waveshape->filter->resample) is split into two, with one of the signals then undergoing pitch modulation by an LFO (either a sine or triangle, I can't tell which!). This brings the modulated signal in and out of phase with the unmodulated signal, creating a detuning type of effect.
Orange controls the rate of the modulation; the depth of the modulation is fixed.
The sound is quite striking, as the waves reinforce each other while in-phase and cancel each other out (almost completely) when out of phase, creating harsh sharp peaks and soft subtle valleys.This is definitely not a "chorus" effect as found in vintage analog synths!
Unlike the other Dr. Wave parameters, Orange isn't continuous -- there is a min/CCW limit and a max/CW limit which correspond to "off" (0hz if you prefer) and "fast" respectively. (I haven't bothered to time the rate of the LFO when Orange is set to max, but I would guess 1-2hz).
Visually, this parameter also differs from the previous three in that it seems to be depicted metaphorically/abstractly rather than literally/directly. The waveform displayed onscreen is pre-chorus, reflecting only the waveshape->filter->resample steps; the chorus effect is visualized as an invisible line which sweeps left to right through this waveshape, leaving each sample it passes mirrored/flipped vertically.
This visual sweep is synchronized with the pitch-modulating LFO so that one traversal of the screen from left to right corresponds with half of a cycle of the LFO (again, either a sine or triangle... I'm not positive which it is); I say half of a cycle rather than a full cycle, because from left to center to right, the phase offset between the pure and modulated signals seems to sweep from 0 (peak/in-phase) to almost 180 (valley/out of phase) back to 0 -- this single "bump" corresponds to half of a full sine or triangle cycle (which contain two bumps, one upwards and one downwards).
It sounds to me as though the chorus is applied after the sample rate reduction, but I'm not 100% sure of this -- possibly SRR happens after rather than before chorus. My only argument in defense of my position is that if chorus were after SRR, a very low samplerate would result in muffled/muddled audio with the chorus being lost (similar to how the resonant filter becomes much less obvious when the samplerate is chunky); since the chorus effect is always clear and present, it must therefore happen after SRR.
However, one unexplained but very interesting behaviour which calls into question my interpretation of this parameter is that at low samplerates (i.e when there's visible stepping of the waveform displayed), you can actually hear audible stepping as the visual chorus effect sweeps across the wave from sample to sample. I have no explanation for why this happens, and would be very interested in any theories you might have on this matter. This audible stepping can be a great source of shimmering pad sounds.
One final interesting aspect of the Orange parameter is that the modulation is retriggered/resync'd on keypress -- the LFO jumps back to the start of its cycle. (Obviously, when Legato mode is active and notes are played legato, no retriggering occurs.) This retriggering can be useful in many ways.
One useful side-effect of this retriggering is that Orange always creates a distinctive sweeping sound at the start of each note; since the rate of modulation can be very slow, this parameter can be used for long downward sweeps rather than just cyclical beating/detuned sounds.
Another important side-effect of the LFO retriggering at each keypress is that it tends to produce a small pop/click at the start of each note. This is intermittent and irregular; I would assume that what's happening is that the LFO is being forced to jump to zero (its starting point), and so depending on its previous value there is a discontinuity (vertical edge) of variable magnitude as it snaps down to zero, creating a bit of a click. This can be useful for percussive sounds.
Wrapping Up
Was that a hilarious pun referring to the cyclical nature of Dr. Wave's parameters? I'll never tell!
Ahem.
In summary, Dr. Wave might be my favorite of all the OP-1's wonderful synth engines. The combination of the variable waveshape and samplerate (Blue), the resonant lowpass/highpass filter (Green), the pulsewidth/sync (White) and finally the sweeping chorus (Orange) provide a huge amount of flexibility and range.
The graphics are amazingly functional and informative, while also being beautiful and fun to watch. Basically, it's just awesome!
Having said that, the next post will be an attempt to identify and address the least-awesome aspects of Dr. Wave. Are there any?! Stay tuned to find out :)
As usual, any comments, corrections, thoughts or ideas are invited and appreciated; just hit this forum thread and let the discussion begin! http://ohpeewon.com/discussion/229/op-101-dr.-wave
