Commentary from Kevin Rooney on the Correct Rendition of the Quilisma:

The mystery of the quilisma is solved.  The quilisma is a rising portamento, Schleifer, or slide, or alternatively a light passing note.  This is more or less the interpretation that Solesmes has always called for.

Performance: The note before the quilisma is always long, always a quarter note, as Mocquereau observed.  The note after the quilisma can be short or long, eighth or quarter, depending on context.  If you're singing metrically the early medieval way, the quilisma itself in theory takes no time out of the beat.  In reality it steals a sliver of time from the long note before it.  If you sing plainsong, the late medieval way, this translates to Mocquereau's retroactive lengthening of the note before it.

Under the original meter, the three notes together can be performed then as any of the following:

1. Dotted eighth + sixteenth + quarter

2. Quarter + grace + quarter

3. Quarter + 2 graces + quarter

4. Quarter + portamento slide + quarter

Under the modern free-rhythm interpretation, the same thing, except with the beats relaxed.

Manuscript evidence:

1. The quilisma is almost always preceded by a long, exceedingly rarely by a short.

2. The quilisma is never replaced by a long note.

3. The quilisma is replaced by a sub-short passing note in some cases.

4. The quilisma drops out in some cases.

5. The quilisma is parallel to a portamento grace note on a new syllable.

6. The three-note rising sequence containing a quilisma (a quilismatic scandicus) is parallel to a two-note rising sequence without a quilisma (a long pes).

7. The quilismas depicted in Laon-Metz notation and St. Gall notation are alternative medieval symbols for a question mark, as Cardine said.  This is irrefutable historical fact, in that the symbols of early Gregorian neums evolved from punctuation marks used in ecphonetic tone chants.  You can see pictures of the medieval question marks online.  According to the book Eats, Shoots & Leaves: The Zero Tolerance Approach to Punctuation, another symbol was a lightning bolt shape, which I have seen in some notations, Chartres I think, though I can't recall for sure.

8. The quilisma depicted in St. Gall notation looks like the same symbol as the German Baroque Schleifer.  I have an open talk on the Wikipedia page for the Slide, awaiting comment from others.  I have not seen this similarity noticed anywhere else on the internet.

9. The quilisma is called tremula by Aurelian of Réôme in the 850s.  It means literally ‘trembling', and its meaning is to be understood as ‘timid', not as ‘vibrating'.

Too many scholars have contended that the quilisma has a vibrato or trill.  This is wrong because:

1. There is no practical way to execute a vibrato or trill on a light passing note.  It cannot be done without giving the quilisma a long beat, and there is no evidence of that in the paleography.

2. The misunderstanding of ‘tremula' as meaning ‘shaking', as in shaking the voice up and down, is tied to the St. Gall quilisma wherein the pen undulates upward and downward two or three times.  But other notations do not depict the quilisma in this way.  The Laon-Metz notation uses an upside-down question mark, and a question ends with a rising sliding voice, not with a vibration, as Cardine noted.

3. The misunderstanding of ‘tremula' as meaning ‘shaking' may also be due to a confusion in the High Middle Ages between the quilisma (a rising slide) and the salicus (interpreted by Van Biezen as a composite containing a rising mordent).  The first two notes of the three-note salicus are sometimes on the same pitch or one pitch apart, and the voice naturally puts a mordent between them to keep them distinct.  The symbol for the second note is in fact the oriscus, which in Laon-Metz notation is the same symbol as the modern turn, and as the modern day's symbol for the turn.  This is indeed a ‘trembling', i.e. a shaking, of the voice.  [PW: Whether that is the correct interpretation of the figure is doubtful.  I am inclined to understand the oriscus as merely a melodic indication initiating upward or down motion.]  The confusion between trembling = timid and trembling = shaking is a result of the rising quilisma figure and rising oriscus/salicus figure being interchangeable in many circumstances do their rhythmic time equivalence (at least when sung metrically) and their status as ornaments.

The reason the first note is lengthened (usually) is because it too falls on a downbeat, and because the quilisma is too ‘light' to consume much if any of that beat's time.  Likewise, the whole idea that the third note is ‘important' is because in the original metrical rhythm called for by the medieval theorists, including Guido of Arezzo and the Enchiriadis authorities, the third note falls on a downbeat.

Conclusion:

- If you sing Gregorian chant with meter, per the first-millennium authorities, the quilisma is either a rising passing note or a slide, between two beats.

- If you sing Gregorian chant with the modern free-rhythm interpretation, per Solesmes, the quilisma is again either a rising passing note or a slide, between two ‘important' notes. 

***

Rigidity is exactly what makes science reliable.  If Solesmes admitted their interpretations were novel, we'd have no problem, since their music can still be lovely.  But, since they claim to have a (mostly) historically accurate interpretation, per Cardine, when in fact nothing could be farther from the truth, it behooves us, in my opinion, to correct that mistake in our understanding.

***

The notion that chant was actually ‘measured' is demonstrable, and has been demonstrated before.  The reason so many honest God-fearing people doubt it is their trust in Solesmes' repeated denial thereof ever since the Vatican edition.  The reasons for their denial are sundry but nonetheless unjustified.  I really don't know if people still get offended about measured chant the way they did in the 60s.

***

I am delighted you gentlemen have the same healthy skepticism I do!  I also have to verify things for myself.

If Ralph consistently has his schola hold the note after the quilisma while I consistently have my schola hold the note before the quilisma... and perhaps James consistently has his schola do a tremolo on the quilisma itself with no holds - will the world stop revolving?

No, but between the three of you, you would be the only one doing it according to its intended interpretation by the people who invented the sign.  I agree with you on the point of science and art.  What I don't get is your wariness about adhering to an objective interpretation.  Are you concerned past tradition isn't as organic as what we do today, or what?

take the note and double the value every time you see this mark

That's exactly what the episema means, according to both the Enchiriadis writings and Guido of Arezzo.  Micrologus (c. 1022), chapter 15, paraphrased, says the duration of a note may be long or short or ‘tremula' (which refers to the quilisma), and whenever it's long it is marked by a horizontal line that doubles the note.

Now, granted, the notes marked by episema aren't always doubled, but not for the reasons you suspect.  The sign isn't always used consistently in the Carolingian manuscripts.  But its intrinsic meaning is still ‘double the note.'  The torculus with three episemas is exactly what you say it is not: three doubled notes.  Comparative analysis with similar four-note figures further supports this.

Chant from its infancy up through the Carolingian era was not measured.

This is not correct.  By measure I mean exactly what you expect: note value.  The term measure is inherent in the medieval word for chant modulatio.  The theory for proportional concord between rhythmic units in cantus melodies reaches all the way back to Greco-Roman antiquity and is consistently held down to the Carolingian era and does not vanish till the second millennium.  The a priori supposition that chant should be free of rhythm is due to (1) the chant's loss of rhythm in the 1000s, (2) Solesmes' historical bias against fixed rhythm, and (3) the a priori assumption that all chant melody evolved from oratorical prosaic rhythm-free psalmody.

It's a big topic, and I recommend another thread with a better title.  Still, to start somewhere, John Rayburn's Gregorian Chant: A History of the Controversy Concerning Its Rhythm, 1964, is required reading.

***

In Early Medieval performance practice, which Solesmes claims is its gold standard:

- quilisma's first note is always lengthened, if it is present.  Paleography proves this.

- quilisma's second note is never lengthened.  Paleography and theory both prove this.

- quilisma's third note is sometimes lengthened.  Depends on the neum.

It seems to me that few, very few, want their chant to sound too much (if any) differently from what their congregations (have been conditioned to) imagine and expect ‘Gregorian' chant to sound like.

Again, impeccable summary!  I would add that, in my opinion, the reason people are against one interpretation or another is nowadays more due to unawareness than anything.  We can blame the previous generation for that.

I sympathize with your reservations—I had the same sentiments a few years back.  My comments in reply:

1) Tempo, according to the medieval theorists, is constant in Early Medieval performance practice, except at the last few notes.

2) Episema isn't always doubled; that's just the default meaning.  Most of the time it is.  But, if you follow the theory of Van Biezen, Gregorian chant also has a bit of notes inegales.  For example, the figure [short, short, Long, short, Long, Long] is then [8th, 8th, dotted 8th, 16th, 4th, 4th].  This makes sense only if you keep the plausus [pulse] encoded by St. Augustine and enjoined by the Enchiriadis writings.  It's a relatively new discovery that removes the chief obstacle that Cardine rejected mensuralism over in 1964, namely that mensural fixity is incompatible with the ‘looseness' (what does that even mean?) of the neums.  Fluidity and aesthetics are not compromised; quite the opposite rather.  In absence of a recording, I recommend Ensemble Organum's Knights Templar album for a loose idea of how it sounds rhythmically.

3) Ambrosian Gloria IV Ad Libitum, Graduale Romanum/Triplex p. 794, I haven't studied, so I can't say.  Consequently, I'd sing it oratorically in absence of knowledge.  Neums and/or mensural notation, if they exist, would benefit.  Without those, one must rely on comparative analysis, which is highly sophisticated to say the least.  However, I can say, if neums exist, and Solesmes' markings are precise, then here is a case where the copyist is saying to slow down for the final cadence.  It happens in other neum manuscripts too, especially Laon, in melismatic chants.  So there's another exception to the rule. 

***

Direct observation.  All of that evidence is available on the internet. I wish I could say “See for yourself," but I concede most people lack time and patience to sit down and study it.  So here's a lengthy synopsis.

Fact #1: The note before and below the quilisma is always lengthened, never short.

Mocquereau gives three pages of demonstration. Pp. 415-417 of his Le Nombre, English translation.  If that's not enough, you can peruse the Triplex editions just to be sure.  I've perused both the Proper and the Antiphonary, and I have yet to see a quilisma preceded by a note that isn't long, either explicitly or by comparative analysis.

Fact #2: The quilisma itself never lands on a downbeat.

Mocquereau, p. 415: The rhythmic pulse always falls on the note before the quilisma, never on the quilisma itself.  Cardine, p. 201: The melody always “tends toward” the note that follows the quilisma, in that the paleography consistently places a rhythmic accent upon the upper note that follows the quilisma, but again never on the quilisma itself.

Fact #3: The quilisma itself is never long.

There is not a single instance in the repertory of first-class Gregorian chant manuscripts of a quilisma lengthened by a horizontal episema or by a Romanus letter t for ‘tenete’ = ‘hold’.  This suggests that the quilisma is never a long note.

Fact #4: The quilisma is interchangeable with a light passing note.

We see it sometimes replaced in Laon and Chartres by a breve (short) depicted as a dot.  It happens more often when the ascending interval is larger than a minor third.  In Old Roman notation, which doesn't depict rhythm but does like to add Italianate decorations, the quilisma is never depicted as any fancy figure, but just an ordinary note on the semitone.  (The oriscus, on the other hand, is often replaced by a turn in Old Roman.)

Fact #5: The quilisma is interchangeable with an ascending grace note.

The rising initial auxiliary note of an initio debilis sign found on the second of two syllables is interchangeable with a quilisma bridging the same interval over a single syllable.  Because the first note of an initio debilis sign is functionally a grace note or appoggiatura (per Cardine, Murray, and Van Biezen), it follows that the quilisma is performed similarly, if not the same.

Fact #6: The quilisma is omittable.

It often disappears in parallel places of some Gregorian chant figures (Cardine p. 205), as seen when the quilismatic long pes is replaced by an ordinary long pes and vice versa (Cardine, p. 204; Van Biezen 2016, p. 16).  This can also be seen in parallel passages throughout Old Roman Bodmer C74.  The quilisma is therefore an ornamental note not necessary to the structure of the melody.  Mocquereau, p. 417:

The history of the quilisma during the period of greatest decadence fully confirms this deduction.  One of the most significant and most common characteristics of this epoch was the total omission of the quilisma.  The loss would be inexplicable if a fundamental or lengthened note had been in question.  There are many instances of such omissions.  Where however the quilisma note itself has been retained, it appears as the middle note of the neum of which it formed part, though this again does not imply that it had been originally strong or long.

Thence we can determine from the paleographical evidence alone that the quilisma is never long, never structural, never on a downbeat, and never important; but rather always light, always ornamental, always functioning like a passing note, and perhaps always optional.  Vollaerts 1958/1960, p. 110, gives a list of chants for comparative analysis to confirm the above points.  I'd be glad to give my own as well.

Still, that's not enough, and so here's some more evidence, philological and testimonial:

Fact #7: The quilisma symbols of at least three medieval notations are medieval question marks customary in their respective regions.

Cardine's first page on the quilisma chapter mentions this.  The medieval punctus interrogativus calls implicitly for a rising intonation of the voice.  Well, likewise, a rising portamento or slide is musically equivalent to, even acoustically the same vocal effect as, the rising of the voice at the end of a spoken question.

Fact #8: The German Baroque Schleifer is identical to the St. Gall quilisma.

I have yet to find whether there is a continuity here over five centuries, but, even if there wasn't, it's a striking coincidence, given the equivalence between the Schleifer's performance and the quilisma's performance, as supported by all the evidence I just gave.

Fact #9: Aurelian of Reome, circa 850, calls the quilisma ‘tremula', or “tremulous inflection".

He points to the word “canticum" in the verse of Gradual “Exultabunt sancti", which has a quilisma.  See also Treitler, p. 191.  Or, for Aurelian's actual text, see the online Thesaurus Musicarum Latinarum.  He uses the Latin word “tremula" (“trembling") more than twice in his writing, and that suggests the meaning was clear through the word itself.

Robert Fowells, Cardine's translator, says the following (“Gregorian Semiology: The New Chant.  Part II,” in Sacred Music, vol. 114, no. 3 (1987), p. 9):

Because its appearance looks somewhat like a mordent and early manuscripts say it should be sung with a “tremulous” sound, many musicologists feel that it is a sign for a mordent or a shake, somewhat in the baroque sense.  However, “tremulous” not only means “shaking” but “timid”.  The Solesmes school has always held that the latter interpretation should prevail and that the note should be passed through lightly.

Fact #10: Guido of Arezzo, circa 1022, enumerates ‘tremula' with long and short as a separate category of duration.

Micrologus, chapter 15:

... and some notes compared to others have a duration twice as long, or twice as short, or trembling, i.e. a varying duration which, whenever long, is signified by a virgula plana assigned to the letters.

The virgula plana, which means a horizontal line, is the episema.  But the ‘trembling' or ‘tremula' note, i.e. the quilisma, is never long, because it is never furnished with an episema.  So it is obvious in Guido's grammar here that he means the ‘trembling' note is a third category of note duration that is not long and not exactly short either.

Fact #11: The ‘tremula' is defined in the medieval theory as two or three small notes.

From the Quid Est Cantus and other medieval treatises, a ‘tremula' note is:

ex tribus gradibus componitur, id est, ex duabus brevibus et acuto

composed of three pitches, i.e., of two short notes and a high note

The high note is the third note we talked about.  The “duabus brevibus" here are together the single note that we call the quilisma itself.  Elsewhere in the testimony, it is described as “two or three" short notes.  When you're singing two or three short (enharmonic) notes compressed into the timespan of a single swift note, as the paleographical facts above require, the result is a slide.

Fact #12: Nonantola notation depicts the quilisma not as a question mark but as two rising dots.

So two rising dots in Nonantola are equivalent to the swift note implied by the paleographical facts.  The only resulting interpretation then is exactly what the medieval theorists' definition calls for.

Conclusion:

First note = long.  Second note = slide or swift passing note.  Third note = not restricted by the above evidence; its length depends on the melody.

***

I gave the data to settle the matter, because the interpretation of the quilisma itself as a sliding transition requires the length of the note before it, and since the quilisma cannot be interpreted any other way according to the evidence, it follows that the note before it is required to be long.  If the note before it were short, it would merge into the quilisma and become part of the slide.  This is a more musicologically accurate way to say what Mocquereau always said: that the quilisma retroactively lengthens the note before it.

I don't have Cardine with me, but I don't recall him really disagreeing substantially with Mocquereau.  I think his observation that the first note is long on account of its sign is easier to reckon with than Mocquereau's retroactivity, but that's splitting hairs.  Mocquereau might have made mistakes in interpreting the data, but in my opinion when it came to data observation he was a fantastic paleographer.  Same with Cardine.

On the other hand, I admit showing the first note is long in and of itself would require good examples.  And showing it is never short is harder, since it would require all examples!  To ease things, might you be willing to flip the burden and explain why Fr. Columba (if I read you right) advocates the first note being short?  I'm not too acquainted with his teachings.

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His logic, at least the way you worded it, makes sense.  A fast rising quilisma puts much melodic ‘energy' into that high note.  The energy stops, emphasizing note 3.  I don't see the awkwardness that you see, but then I haven't heard his recordings.

However, it's not the only option.  If note 3 is not the end of the neum, say in Introit Gaudeamus's cadence, then you can justify its shortness by imagining that energy moving past it, through note 4, to note 5, which then is lengthened.

D [E] F E F

long + quilisma + porrectus

quarter + slide + eighth + eighth + quarter

or

dotted eight + sixteenth + eighth + eighth + quarter

or, in Cardine's terms,

heavy + lightest + light + light + heavy