Fixed and moveable Do are the two methods of solfeggio in ear training.
If you have no idea what sight singing is, never heard of solfeggio, just getting into ear training…. I highly recommend you begin with Moveable Do based ear training.
If you are a music dweeb, or perhaps have been practicing one of the two methods for some time and not sure why, then continue on…
There are two methods of Fixed Do, one with Chromatic Syllables such as Di & Te and another that uses just (Do, Re, Me, Fa, So, La, Ti, Do) where the voice must change pitch for chromatics. In Both these methods Do is always C.
Do is ALWAYS scale degree one. Moveable Do has several variations. Some systems use chromatic syllables and some do not. There is also moveable Do-La. This means any minor scale starts on La, major Starts on Do, and any mixolydian starts on Sol.
Which is better?
The answer is neither.
Both can be invaluable weapons in a musicians quiver. They excel in two different but equally important skills.
The relentless solfeggio argument is really the argument between relative and absolute pitch systems, in other words the perceptual vs. operational facets of music.
The entire theory is based upon the moving tonal center, thus exceling in the perceptual, relative side. It is far more beneficial for understanding the way notes operate within a tonal system.
Functions much stronger when it comes to the more operational side: as C is always and absolutely Do etc.…
In essence you are trying to compare two different tools, which excel at two different but equally important tasks.
A musician needs to know where C is on their instrument, but also should know how it functions in a set piece of music.
So the question becomes…both, one? Oh what shall I choose?
Once the fact has been established that a musician needs both of these systems the choice between which type solfeggio becomes a matter of opinion.
My opinion is to use moveable Do as your solfeggio system.
In English speaking music theory, we also label notes as C, C#, D etc… This can be used as you reference for an absolute system.
Having solfeggio operating in both systems is confusing. And letter names are easy enough to sing.
In the end you can do whatever you heart chooses; just make sure to have a system for both. ☺
A quick note
There are two really popular arguments against moveable Do that need to be addressed.
It is difficult if a piece modulates
Having to realize the point in which a piece modulates further serves the reason to use moveable Do to strengthen understanding of relationships in a tonal system.
It doesn’t work in atonal music
It doesn’t seem overly complicated to use C as Do, just as in fixed Do in those circumstances.