@OMagnumMysterium ,

So if the "O Filii et Filiae" Alleluia had a Fa, then it would be an issue, you are saying?

@CantorCole

Well, it would still be possible to notate "O Filii et Filiae" in Fa clef even if it had a Fa originally, but every Fa would have to become a Te, and would need a flat sign (following the usual conventions). It could be a bit messy but not necessarily an issue.

The Fa of the Do-Do scale is the equivalent note of the Ti in the Fa-Fa scale. But if you overlay the Fa-Fa and Do-Do scales, making the two scales start and end on the same notes, Ti is half a step higher than Fa. Fa has its half step with the note below (Mi), but Ti with the note above (Do). Flattening the Ti to Te would make the two scales line up perfectly, just like how the C major scale with B flat is the F major scale.

@FSSPmusic

Out of curiosity, what would mode IX be then?

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@FSSPmusic What is the source that says mode 9 should have B-flat? I haven't seen that much. My understanding was that mode 9 was the authentic mode ending on A. Are you referring to the fact that mode-1 chants that use B-flat exclusively are essentially in a transposed A mode?

To go back to the question (hinted at above) of what modes 9 to 12 are, Glarean's big idea was that it would be way more rational to have modes that end on all seven diatonic notes, rather than just the four (D, E, F, and G) that are used in the traditional 8-mode system. So he added two modes for each of the other notes, A, B, and C. B modes are rejected as not having a perfect fifth above the final (B to F is a diminished fifth). So he ends up rejecting those and settling on a twelve-mode system, with two modes each on D, E, F, G, A, and C. Zarlino also adopted this, and it became widespread in theory, existing side-by-side with the old 8-mode system that was retained for chanting, especially because of the connection with the psalm tones. Confusingly enough, Zarlino in a later book kept the twelve modes but renumbered them to start on C. At the same time, the psalm tones each get sort of associated with a particular key, often called the church keys or church tones, so the eight of those are what we might now call D minor, G minor, A minor, E minor, C major, F major, G major, D major. If you've ever accompanied vespers those eight church keys might make sense to you!

The upshot is that when you are reading what anyone says about mode from the sixteenth to eighteenth centuries, you have to bear in mind which system the writer is using, 8 traditional modes, 12 modes (in two different numberings), 8 church keys. It can get confusing!

The broader question, which relates to your original post, is "what does the 8-mode system make of chants that end on A?" It turns out that these irregular finals are always related to one of the normal ones, because these finals have an affinity with the normal ones because of where they are in relation to the half steps and whole steps. So all those mode-2 graduals end on A but are considered mode 2. This actually does happen in other modes too. For instance, the Gloria, Sanctus, and Agnus of Mass 1 are all in mode 4, even though they end on B. The simple Salve Regina is mode 5, even though it ends on C. Notice that it is basically the same scale as Credo 3, which ends on F, because there is an affinity there; because of the B-flat you wouldn't really be wrong to say that those two chants are in the major mode.

@OMM, in your last examples, I'm reminded of the recent hexachordal-solmization thread. In all your comparative examples, the two versions would have the same solmization in that older system.

One of the best pieces of advice I've ever been given, which has helped me progress in chant tremendously, was when a member of our schola told me "always keep track of where the half steps are".

I couldn't agree more. In a way, this sums up the point of the hexachord thing, and it relates to your clef stuff above as well. Another way you might phrase the principle is: "Always know where Fa is." Since Fa sits on top of a half step, this is really the same thing, if you are thinking that every half step is Mi-Fa of some kind. You might even say, "Fa is the key to the scale." And from there it's just a bit of French translation "key=clef" to see that the point of the clefs is that they show you where Fa is, that is, where the half steps are. That's why the F and the C lines were singled out in the first place when the staff was invented, and it's why they get the clefs in Gregorian chant.

This is why, incidentally, I find the Guidonian hand helpful; there are chants where you can’t simply change the clef and therefore must resort to other things (not just the flat sign, but accounting for a flat below the staff that doesn’t exist for Guido). Nevertheless, quite a few common chants can be written with either clef — I don’t see a reason why Solesmes couldn’t have assigned a Fa clef to the monastic version of the hymn Conditor alme siderum. (This is in mode IV, untransposed, so something slightly different is at work, but the general idea is the same.)

So if you change the clef, you get a new idea of the relations, even if you use the modern set of seven syllables instead of Guido’s, and you get yet a different insight if you use Guido’s syllables with the clef found in the modern book (probably a Do clef!)

We have seen above that this isn’t always desirable; the flat in Dextera Domini with a clef change is a little ugly to me.

I keep recommending Early Music Sources here, but his videos on modes in the Renaissance and on chant are very well-done, so I’ll repeat my recommendation for those who like to learn from Youtube videos.

OK so why can descending fourths be an issue (in chant)? This is also an issue for my schola.

OK so why can descending fourths be an issue (in chant)? This is also an issue for my schola.

I struggle with descending fourths too.

There's probably a better explanation for this being a general issue, but for myself, my best guess if the following:

All the other intervals, up and down, I have some theme I remember them by, whether it's from a well known chant or a movie soundtrack.

Half step, up and down - Jaws theme
Whole step - sometimes happy birthday, but usually it's just the small step which is bigger than the half step, just kind of the normal step.
Minor third up - Emperor's theme (Star Wars), or Pueri Hebreorum (Palm Sunday)
Minor third down - Flexus from mode 8 psalm tone (Sunday and Tuesday Compline)
I don't really have anything for major thirds, which kind of messes up my theory.
Fourth up, tone 8 Magnificat (solemn psalm tone)
Fifth up, Puer Natus Est (Christmas Introit)
Fifth down, Solemn Salve

My thinking is that the fourth down is hard because it is not an interval I am as used to hearing often or one that I associate with anything memorable. Perhaps the fourth is the most dissonant of the "chant intervals". Or maybe the half step is the most dissonant, but larger intervals are harder to memorize?

Fourth down - eine kleine Nachtmusik
Fourth up - Taps

But in the moment, in the chant, not sure if these help...

Sure I can use all the tricks, and I do. But it’s a tad unsatisfying if it happens a lot.

Upper Do-Sol and Sol-Do both occurred in the propers of Passion Sunday, in the gradual and in the tract…