a DCO is not a digital oscillator

I keep hearing and seeing people referring to DCOs as digital oscillators, which is not correct, and a sad insult to DCOs in my opinion as a lover of DCO synths. So I decided to fight misinformation by making a post here explaining the actual difference between VCOs, DCOs and digital oscillators.
Analog vs. digital, actually
What do the words analog and digital even mean? Their meanings are more general than some people realize. Analog means continuously changing, like a circuit in which potentials (voltages) and current flow are always present and always changing.
Digital refers to any system in which there are two states (which can be thought of as 1 and 0, high state and low state, or on and off) and the outputs can only switch immediately between them, with no slopes transitioning between them gradually.
VCOs – Voltage Controlled Oscillators
Most synth people are probably familiar with the idea behind a VCO (voltage controlled oscillator). The frequency is controlled by the amount of control voltage being put in, following the basic rule of electricity that a higher applied voltage yields a higher frequency. The most important sonic characteristic of a VCO is the fact that it is typically somewhat unstable.
A VCO will always be experiencing slight fluctuations in temperature which change the behavior of its components. And since it will always be sharing a power supply with other circuits (the other parts of the synth), there will be slight fluctuations in the voltage it can use due to the changing voltage and current needs of its neighboring circuits. These factors lead to slight fluctuations in the frequency of the oscillator’s output. This can show up as pitch drifts over the span of minutes or seconds, warbles or tiny irregularities in the waveform.

T represents the period (amount of time it takes for a full cycle) at the the target frequency (e.g., 440hz for A4).
In this graph, the VCO is oscillating at the correct frequency in the long run, but there are slight short-term fluctuations in its frequency (first too fast, then too slow).
Digital Oscillators
A digital oscillator is very different. A digital oscillator has a processor or other digital data source spitting out a series of discrete values, each value represented by a series of 1s and 0s, at a standardized time interval to create an approximation of a continuous waveform.

This is an exaggerated depiction of a digitally generated waveform, though many years ago there were digital oscillators this crude. Digital oscillators designed decades ago sounded gnarly or noisy, or just sounded different from analog oscillators because of all the information they naturally had to leave out. But we’ve finally gotten to the point that digital oscillators designed today can have such a high resolution (resolution represented on this graph by the number of “steps” making up each “triangle wave”) that they don’t sound any different from analog waveforms.
DCOs – Digitally Controlled Oscillators
Some people describe DCOs as “somewhere in between” VCOs and digital oscillators or “hybrid digital/analog oscillators” but I take exception even to those characterizations. DCOs are true analog oscillators that are just synced to a digital clock source. The part of the DCO that is doing the oscillating is analog– producing an analog waveform! They were invented in the 80s as a way to avoid the pitch instability of VCOs. A DCO’s digital clock source can produce the exact correct frequency for each note, ensuring that the oscillator is perfectly in tune across all notes. (I should probably mention that because a DCO is an analog oscillator, it is still very difficult for it to produce a perfectly symmetrical triangle wave like the one shown in the graph, and the same goes for a VCO. I just used triangle waves because they’re easy to draw in MS Paint.)

Some people prefer VCOs because their pitch drifts and variations can make a synth sound more colorful and naturalistic. Some people are excessively sensitive to intonation and can’t stand very unstable VCOs. I’ll stand by DCOs until the end.
Thanks for reading, especially if you are just a casual synth user– you are now one step closer to being a synth nerd.