In terms of electronic music, when I'm picking a "bass" can I choose any instrument, including leads, and just set that instrument to be of lower frequency (lowering the octave) in order to create a bass. Does a bass just depend on frequency and not the type of instrument?
when I'm picking a "bass" can I choose any instrument..?
Yes, you can. However, you might find that not all instruments work well to your ears as 'bass' instruments.
When you see 'bass' in a synth patch name, it usually doesn't only refer to the instrument being low - because, as you say, you can usually play low notes with any sound in a synth. Instruments designated 'bass' often have certain characteristics that make them subjectively suitable for playing in a 'bass' role - such as:
- a strong fundamental when playing low frequency notes, giving a 'solid', bassy sound (in contrast to, say, the piano - whose low notes have weak fundamentals)
- a harmonic structure that makes the pitch of the notes easy to identify
- a harmonic structure that doesn't fill up the whole frequency range and leave no 'space' for other instruments
- a reasonably fast attack, suitable for the 'bass lines' found in many genres of music
Of course not all 'bass' instruments necessarily exhibit all these characteristics, but you would expect instruments labelled 'bass' to exhibit most of them. The labels we give to sounds aren't there to restrict you, but they can be useful!
Part of the confusion here appears to be that ‘bass’ is (a) the name of a range (~16-256 Hz), (b) the name of a specific instrument, the double bass (similar to a violin, but much bigger), (c) the name of a specific instrument, the bass guitar (bigger than the regular kind, cf. (d)), and (d) used in the names of a whole lot of instruments to denote that they are either deeper than the usual (bass violin) or fall into the range of (a). (There are also a bunch of perciformes, but those are unrelated etymologically.