Yes, Se.

The Ut, Re, ..., Si, Ut nomenclature wasn't rigged to handle accidentals, except for Si-flat (Se). Instead, when one uses Do, Re, Me, Fa, Sol, La, Ti, Do, one can put in the sharps and flats readily.

Flats: Re-flat is Ra, Mi-flat is Me, Sol-flat is Se, La-flat is Le, Ti-flat is Te.

Sharps: Do-sharp is Di, Re-sharp is Ri, Fa-sharp if Fi, Sol-sharp is Si, La-sharp is Li.

Note Do-flat, Fa-flat, Mi-sharp, and Ti-sharp are not permissible.

The college I attended abandoned those terms and used numbers, instead. Consequently, I am more comfortable with numbers. For accidentals we used, for example, 3-flat.

For accidentals we used, for example, 3-flat.

I know everyone just prefers whatever they learned, and all systems are equally good, and all that other stuff. But this strikes me as stupid.

Or, do the proponents of this system never use it at-tempo in a quick piece with a seven-flat in an eighth note run?

I first learned using a movable "do" for major scales and then beginning on movable "do" for the minor scales. I later worked with a Kodaly teacher who insisted that minor begin on "la". Suddenly it all made much more sense. This has also worked teaching scales on violin to my children. How does one sing using numbers?

It could be 3-sharp. Sometimes I use sharp-5 in hymn harmonies when I improvise a bit. It could also be Recto Tono, but that gets into copyright issues. ;-)

I haven't had any problems using syllables or numbers. Both work.

So, according to Mancini, the syllable for Si(b) would be...

I'm most familiar with the solfege that Chuck Giffen mentioned. It's very easy to sing the accidentals, without extra thought.
I was taught to start minor keys on "la," as it makes the most sense, harmonically.

I teach fixed DO, as that is what the old masters taught

I teach fixed DO, as that is what the old masters taught

Oh dear, if we are now referring to Hindemith and Nadia Boulanger as the "old masters," that makes me feel ancient. But Guido, Zarlino, and even Fux certainly did not teach fixed Do. In some languages, pitches were named Ut Re Mi instead of C D E, but not scale degrees. If you wanted to refer to the first note of a D major scale, for example, you would have to say Re-Ut, i.e. the Ut (Do) that is found on Re (D). I don't know of a source that presents fixed Do as we now know it before the 20th century (although I imagine there could be some from the 19th).

Edit: After reading the above cited treatise by Mancini, I am now aware of a source (thank you!) from as far back as the 18th century that presents a system of naming the notes according to an absolute pitch (that of the cembalo). However, this is a singing method and not a theoretical treatise, which Mancini himself is quick to point out. (It's unfortunate that a printing error on p. 81 obscures the point the author is trying to make about the facility of his system). Unlike the 20th century idea of fixed-Do commonly taught in conservatories today, Mancini has a different name for each of the 12 chromatic tones so that F-double-sharp would be sung as sol (whereas in modern fixed-Do it is often sung as Fa). Mancini's systems makes more sense to me, and it does work if one is only singing music of his time. However, it remains that chant and polyphony from before 1600 (which is the foundational repertoire of sacred Catholic music), does not lend itself to this "modern" (i.e. 18th century) system imho.

Edit: The excellent Wikipedia article on Solfège is also quite exhaustive.

If by "exhaustive" you mean exhausting, I agree. I gave up trying to edit things that were absolutely untrue, since there would always be 10 times as many second year music students who would revise anything I wrote to match their limited understanding of music theory.

G'day,

Ah this takes me back. I don't really have a pozzy on this but...

Things I discovered at uni:
I like both, find both useful for different things.
Fixed can help give you pitch memory.
Moveable can give you relative pitch.
Moveable works best for different pitch systems especially werkmeister II.
Fixed works really well for tuning pianos.

Weird other ways of obtaining aural skills:
As someone who underwent some training as an organ tuner/builder I can say I even had to sing using frequency names for a little while just so I could memorise the difference and pick the temperament of the organ. If you do that course you'll never need to use solfege again for aural training, though reading might be another story.
I have pitch memory but I also am able to ignore it for the purpose of varying the temperament of instruments.
I do recommend learning the frequency of common starting notes, using motet first notes as an example. How many tenors sing the first note of Sicut cervus without really thinking about it? Or think about the start of lion king, nobody knows the words (well most don't) but how many can sing the first note?
Sometimes rather than singing scale degrees you can sing the position in the chord such as fifth, sus4-res3, this is great for thinking about the notes vertically and helps create ripper reading skills for keyboardists trying out figured bass.

Education:
Orff school is fixed (and based on letter names not solfege syllables.
Kodaly I believe is moveable? Someone please correct me if I'm wrong.
French conservatoire only like fixed. (I do wonder if they hand out pieces in C# major in their auditions)
Dalcroze, no idea but they definitely use hand signs and ladders so I'm guessing moveable.
Hand of guido is probably the best place to start if you want to use it the way it was originally intended which I believe would have been moveable UT. This is also one you can take on public transport without people looking at you like you're off your tree.

Importance:
People are all different and will respond to different stimuli, so learn and teach it all and too right you'll work out their strengths. Deadset, people can learn using any or all of these methods but when it comes to singing fast I fail to believe that any of these really work, after that it all becomes muscle memory of the ENT.