We use the solfege associated with the clef, so for Angelis suis we would use SOL as the starting pitch. Similarly, if we are using solfege with polyphony, we would use the key signature as the DO (so a key of a minor and C major would both have a DO of C). We do a fair amount of chant alternated against polyphony, so over time the expectation is for choir members to use solfege to connect through the transitions.

There may be an occasion where a transposition occurs between Gradual and Alleluia / Tract... where we read the DO clef as a FA clef or vice versa. An example might be if our ending pitch of the Gradual (DO clef) is SOL and we are transitioning to an Alleluia (in mode 2 FA clef, say) with a starting pitch of DO... in which case the DO of the new key might be the SOL of the old key. In that case, we may demonstrate the correspondence of the old modal scale to the new modal scale... but typically that is only long enough to demonstrate the transposition.

We would simply call that flatted-ti "te."

Is this modified if there is actually a B-flat key signature, e.g. the solemn tone Alma Redemptoris and Regina caeli? Does B-flat become fa and F do?

I think not. Alma Redemptoris (Mode V) begins on fa, the first few notes being fa la te do do re fa fa. I think you are trying to force the modern concept of key (signature) into chant notation here.

I understand, but in movable do with modern notation, a key signature of one flat means that B-flat is called fa instead of te.

I don’t follow this logic. (Isn’t the 7th scale degree the only one that is ever altered in chant? “Fa” might become home base in a chant depending on the mode, but it doesn’t stop being “fa” and “te” doesn’t stop being “te” either. It’s tempting to want to pretend that it is in “fa major” perhaps, but then you are confusing the two systems. [and it’s not actually Fa major.])

Movable do is my system of choice for all tonal music because it more accurately represents the function of the tonal system; however, for modal music such as chant I find the "fixed do" system far more intuitive.

"Fixed do" in Gregorian chant - do always refers to the note indicated by the C clef/fa always refers to the note indicated by the F clef, regardless of the mode of the chant or key signature.
"Movable do" in Gregorian chant - do refers to the finalis of whatever mode is currently in use.

I use whatever is easiest, and usually both systems within the same chant. Often times a different modality is established for short sections, so I change "do" to whatever scale degree makes singing the intervals easier.

For instance, in Mass I, I would start on "mi", and then at the "Pleni sunt" I would do "do-sol-le-sol-fa-me" and then at "-ria tua" I would sing "re-re-mi-la-sol-sol."

I would do the same for modern keys and switch up solfege if it makes it easier to sing phases with alternate tonality, secondary dominance, etc.

I don't think "movable do" is a term that quite encapsulates solfege for chant, since tonal harmony has only the named key or its relative minor, whereas in chant there are usually more than these 2 tonal scales that roughly approximate the mode. For instance, in the Lydian mode, usually the easiest thing for me is to call scale degree 5 "do", since Lydian approximates G major.

Yes, in a fixed do system "do" refers to the pitch of C, no matter the key; whereas in a moveable do system "do" refers to the tonic pitch.

Restating the question as clearly as possible:
With a key signature of one flat, if we call F fa, B-flat te, and C do, is that an example of fixed do or movable do?

This misses the forest for the trees, though. The modes denote scales and their inherent pitch relationships. For me, the most valuable tool of solfege is the aural recall of intervallic relationships between scale degrees. The problem is that the majority of my training and the vast preponderance of my aural exposure has been to tonal harmony and mode I, the tonal scale. Thus it is far easier for me, and I would expect for many, to relate the intervallic relationships between the other modes to mode I, with tonic as "do."

When there is clear aural recall of these intervallic relationships, it becomes easier to apply a mode 1 mental frame of reference to short sections of music, and to call any pitch class of convenience "do" where its tonicity has been established

I try to chant Vespers (in the middle of the week) and keep a fixed do when I do that, across all the chants of the particular hour.

I’ve found this thread quite helpful as I’ve been wrestling with this question for some time. Please understand that I am trying to understand. What I write below is merely an illustration of my confusion. I am seeking assistance to understand the long term consequences (positive or negative) of what I suggest.

About moveable do. When I teach beginning Lydian mode chants (Ave Regina caelorum, Regina caeli) with a consistently flattened ti to te, to beginning readers of both chant and tonal music, I pretend that the clef is moveable and that do is on the second line of the staff with the flattened ti being an accidental rather than the the tonal key signature. (Is it possible that when we say “moveable do” we actually mean “moveable clef”?) I do this because my choristers sing both tonal music and chant, and I have found it easier for them to sing Lydian with a flattened ti, as if a major scale, since the tetrachords line up.

I justify the above by prioritizing the chant over the method. Whatever system or method I use to teach sight singing in either chant or tonal music, it is merely a tool to teach the music as efficiently as possible for the choristers to worship God.

But is it in fact efficient? In the long term, does it do harm to singing more advanced chants in the future? What am I not understanding? Can anyone point to a resource where I could read on the matter? What authority would you appeal to?

Grateful.

Singing F-mode pieces with B-flat where you treat F as do makes a lot of sense. It's a little different from the issue of Guido's system, where the scale F G a b-flat c d e f is actually ut re mi fa sol re mi fa.

I have advocated for this old six-note system and teach it often. That said, a lot of what it accomplishes can also be done in other systems. I don't think it is necessarily superior. But it was in use for centuries. As Matthew says, it continued to be taught in Italy into the nineteenth century, and the boundaries between six-note and seven-note systems were roughly along confessional lines, with Catholic Italy and Spain remaining with the old system while the Protestant north favored either letter names or seven-note solfège. I say "roughly" because France adopted the seven-note system early. England actually favored a four-note system that also took root in Appalachia.

That said, there are advantages to the six-note system that I think make it worthwhile. And it serves well for any chant, since it was indeed designed for chant. The chief advantage is that any position in the scale is defined by how far it is from a particular half step. Do always has a mi-fa pair two steps above. Re always has such a pair one step above, and so forth. This is nice because it means you are sort of in the gravitational field of that half step and it ought to be something you are attuned to and oriented toward. If you go far enough away from it, you enter instead the orbit of a different half step. I have often thought that if we were coming up with the system now we might speak of mutations as being like rocket thrusts that give us enough delta v to carry us into a different orbit. This is whimsical but worth learning about. The rules are themselves simple but get you into some pretty deep awareness of how scales work, I think.

Attached is a recent example from a talk I gave on the subject. There is a certain nice logic to the resulting orientation to the half steps.

Edited to add: Clefs are always fa this way, which I why I include both here!

Early on, Laus in Ecclesia regards a flat at the beginning of each line as a key signature, but says "that it affects all the instances of Ti in the piece," not that ti becomes fa according to the key signature; even so, that gives us only two possible key signatures for chant, and, without a solfege example, it doesn't answer the question about movable versus fixed do. According to the first page of the Rules for Interpretation in the Liber Usualis, "For the fluent reading of Plainsong and the transposition of the melody at sight, the Tonic Sol-fa system is invaluable — almost indispensable — for the ordinary reader." Tonic sol-fa is a type of movable do solfege, where the tonic of whichever key used is called do. As for the "four-note system that also took root in Appalachia," Sacred Harp (and Shenandoah Harmony, etc.) singing uses movable fa. The pitch itself is also relative, and the printed notes don't necessarily correspond to the same tuning standard from one song to another. It has been noted that people who learned music with fixed do often have great difficulty switching to movable fa. I had limited exposure to solfege as a child and used numerical sight-singing in both high school and college, and I've never needed to use fixed do, unless we consider Gregorian solfege as fixed rather than movable.

"Movable do" in Gregorian chant - do refers to the finalis of whatever mode is currently in use.

Schönbergian seems to refer something like movable do with minor do instead of minor la—or perhaps fixed do with minor la, depending on how you look at it. I suppose we could call it modal do, but I doubt that that's accepted nomenclature or that anyone uses it for chant. A new singer recently asked me whether the fa clef indicated F2 or F3. I must have looked like a deer in the headlights, because the question represented, to me, a total misunderstanding of what we were doing and how I approach pitching the chants. Upon reading this thread, it seems that some think "movable" means that the clef moves on the staff, others that the pitches move relative to the keyboard or tuning standard, and others that the solfege syllables move relative to the notated key, where applicable; this last seems like the only reasonable way to understand movable do. A whole series of questions comes to mind:
--Is the printed note meant to correspond to a specific pitch standard, such as A=440?
--Does the syllable or note name correspond to a specific pitch standard?
--Is it related to the key signature?
--Is it related to the mode?
--Can the music be transposed without altering the syllables or note names?
--Is the clef movable on the staff? (This seems almost irrelevant, but I include it since it was brought up already.)
--Is the syllable or note name chromatically altered in the case of accidentals?
--Are the same alterations used for sharps and flats notated in the key signature?
--Can the tonic note be reset in the course of a piece?
--If yes, is doing so a frequent or rare occurrence?
--Are the syllables or note names arranged in octaves, hexachords, tetrachords, or something else?

Using the movable tonic sol-fa recommended in the Liber, we would have to answer as follows:
--No, the printed note is not meant to correspond to a specific pitch standard.
--No, the syllable or note name does not correspond to a specific pitch standard.
--Yes, the syllable or note name is related to the key signature.*
--No, the syllable or note name is not related to the mode.
--Yes, the music can be transposed without altering the syllables or note names.
--Yes, the clef is movable on the staff.
--Yes, the syllable or note name is chromatically altered in the case of accidentals.
--No, the same alteration is not used for a flat notated in the key signature.*
--No, the tonic note cannot be reset in the course of a piece.
--The syllables or note names are arranged in octaves.

*Others would answer that the syllable or note name is not related to the key signature and that the chromatic alteration is indeed used for a flat in the key signature.

Ahah. I had seen the first two but not the third. (Sigh. Must we wait a year or more between entries?)

Anyway the rules in action are interesting: the first mutation occurs when perhaps we are inclined to still sing La. Which is not that big of a deal, but it’s helpful to be consistent, so you sing Sol-Re-Ut.

Also, we need a good computer diagram of the Guidonian hand. The one on Wikipedia is low resolution. But the rest are photos of beautiful medieval manuscripts which don’t print well either and which can be hard to read.

@francis Early Music Sources has this pdf which is fairly clear and might be of use. They also have a full video on solmization which I remember was quite good.

I'm glad the subject of Guido's method is getting some interest. As Patrick points out, it's a separate issue from whether to reinterpret F as do in chant with B-flat in the signature. I also have found a lot of interest in the subject among my academic colleagues. The future of six-note solfeggio in practice is bright. I think it's cool that the hand physicalizes the singing of scale degrees in much the same way as the Kodaly signs or the Ward gestures. It's even better because of how modal it is; notice the middle finger is all Ds and As, which is really great for centering the hand.

Patrick also notes that it's tricky for those trained with heptachordal solfège to make the switch, but this is precisely why it's useful in a graduate-level conservatory program aimed at fostering historical methods! My students are usually evenly split between fixed-do and movable-do backgrounds, so I just make them all learn hexachords as many illustrious composers learned to solfège.

Here is the first half of a talk I recently gave that was a source for that chant I attached above. The second half was all about applying this to tonal music from the eighteenth century; fascinating but a little off topic from our purposes.

https://youtu.be/mjzcnriarKM

I will also be doing some colloquium sessions on the putting this into practice; and I'm also offering a class at the CISM in July. I'm on fire to spread this method to those who are interested in learning about it, as a supplement to all the other kinds of solfège that are out there.

I had to pull my copy of Grout's A History of Western Music and I will start looking at the theory again. Its been decades since I looked at the Guido.

Wow, I learned about some of this material in undergrad school...Grout was our music history text. It's been a long time for me too.