Is this possible without generating a bunch of odd harmonics (like the classic fuzz pedal)?
Digital solutions which attempt to figure out what frequencies are in the source signal are slow to track changes particularly when there are multiple frequencies present.
Note that the input signal itself is the first harmonic. Presumably you want to keep that.
Anyway, you can do this, you just apply a polynomial to the input with whatever terms you want. If it only has even powers of x it will only generate even harmonics. It is hard to do with diodes and resistors, but easy with DSP. That said, if you want an analog filter any kind of unbalanced clipping -- something as simple as a single diode -- will generate more power in the even harmonics, but unless you design it carefully both will be present.
However, most instruments generate odd harmonics naturally. A simple distortion filter will not generally remove harmonics already present. To do this, you would need something that estimated the note you were playing and added in tunable notch filters to block the odd harmonics. That would indeed be slow to respond.
I found a youtube video where someone had run audio through a rectifier
Doesn't sound too good.
Is applying a polynomial in real-time something that be done with a 100 MHz microcontroller, or are DSPs realistically the only option?
Dug in deeper, and it really does look like there are not many easy analog ways outside of diode amplification of even octaves.
Note the circuit i linked was different to what your video showed, mine used a small amplitude so the diode was passing some signal but not clipping, his was full wave rectifying it.
First time i really looked in to it, but there is a lot of notes available on a guitar. The other way i was thinking was notch filtering the 3rd and 5th for each note, but I am assuming you want to subtract those harmonics in relation to the note you strum.
http://www.bryankimsey.com/popsicle/Guitar%20note%20frequencies.jpg
Then u would have latency on the effect of 1 base frequency, useless, maybe long sounds only.
This idea pops ups regularly in guitar forums, specifically ones for DIY effects pedals. The premise is that when clipping/overdriven, it is said valve amps produce even harmonics (as well as odd), where-as solid state distortion/overdrive is mostly odd harmonics, and this brings up the valves vs solid state debate for which people automatically assume valve = good, solidstate = bad, and makes for anice simple argument 'well, odd must be bad, and even must be good somehow!'.
Plenty of beloved guitar tones over the decades used combinations of both types of clipping. I don't believe there is anything inherently magical about even harmonics, although I oft see the repeated statement 'humans prefer even harmonic distortion to odd', which I suspect is entirely subjective. There is so much woo about it all that whilst much of it is based on fact, what exactly these things mean in terms of 'guitar tone' is anybody's guess.
You mention 'like a classic fuzz pedal', which I assume you mean the old fuzz face and clones, which used germanium transistors, didn't have much gain but were rather pleasant sounding and softer than modern fuzzes (mostly because of its low gain rather than the transistors).
Rather than start with DSP trying to boost specific harmonics, if your goal is to try and hear (and see) the difference such harmonic content can make to guitar 'tone', I would build several different clipping stages/amplifiers/fuzz boxes. Play a recorded guitar through them and record the output, then run an FFT on the input and output to see the difference in frequencies. I very much doubt you will find a specific harmonic boost that sounds 'awesome'.
Even harmonics are produced when the top half or bottom half of a signal is larger or smaller than the other half. It occurs with a vacuum tube or a transistor when there is no negative feedback to cancel the distortion. Some people like the even harmonics produced by a vacuum tube amplifier and call them "musical". They say a modern low distortion amplifier sounds "dead".
Odd harmonics are produced when both the top and bottom of the signal are squashed or expanded equally. It usually occurs when an amplifier is clipping.
In the video even harmonics are not clearly produced because the 'scope shows clipping that causes most of the fuzz sound.
The classic (used by Jimi Hendrix first in about 1966) "fuzz face" circuit produces even harmonics on low levels and both even and odd harmonics on high levels.
The fuzz pedals I've listened to all sound harsh to my ears so I hypothesised (correctly or incorrectly) that this is due to the odd harmonics that are mixed in with the even harmonics, hence my search for an even harmonic generator.