The process for this is very similar to the last post that I made on kick drums. This being the case, i'm going to boradly outline what you need to do to make a snare drum in a synthesizer (Operator, packaged with Ableton, is what I am using) rather than giving you detailed instuctions and screenshots like I did last time. From reading my last post on kickdrums, and by downloading the free instrument rack that i'm providing and reverse engineering it, you should easily be able to get an idea of the process involved.
Disclaimer: Synthesized snare drums sound nowhere near as good as synthesized kick drums. Simply put they lack any flavour or authenticity. Use them as scaffolding for a real snare drum sample, with the real sample providing much needed character.
Step 1: Tune a sine wave to your desired key and applying a volume envelope to it so the attack time is instentaneous and the decay time is to your liking.
Step 2: Repeat the same process with another layer of white or looped noise. Once you've done this, make sure all the oscillators are summing together / in parallel rather than in a series (see my earlier blog post on kick drum sounds for instructions on this).
Step 3: Now pass the two oscillators entirely through a pitch envelope and set it up to your taste, generally I like the sound to start an octave above the sustain level and drop from there, but this is up to you and will often depend on the type of snare you want and the genre of music you are making.
Step 4: If needed add a sub oscillator in, that is another sine wave that's one octave below our first sine wave. You may want to have this oscillator less loud than the other two, or else you snare might sound to bottom heavy.
Step 5: Add compression, saturation, EQ, Reverb and any other effects processing that you like, and you're done. Now you have a good starting point for a snare that you can tune to whatever frequency suits.
Grab the Ableton Instrument rack that I made using this technique for free here. Hope this has been at least somewhat useful, i'll be back with another article next week.