N.B. Those familiar with old journals realize that opposing points of view were often included. Based on messages we have received lately, it would be important for me to emphasize that articles we publish are not necessarily supported (or endorsed) by each of our contributors. If somebody is bothered by the disagreements over e.g. plainsong rhythm, it might be best to skip those articles. Our volunteers have produced something like 40,000 rehearsal videos and PDF scores, so we believe we have plenty of variety for everyone. —Jeff Ostrowski
HE STRUCTURE OF MATERIAL CREATION ACCORDS WITH MATHEMATICAL PRINCIPLES. This has been taken as a fact of life for millennia and certainly by no less than Plato.
[…] when all things were in disorder God created in each thing in relation to itself, and in all things in relation to each other, all the measures [ἀνάλογα] and harmonies [σύμμετρα] which they could possibly receive. For in those days nothing had any proportion except by accident; […] All these the creator first set in order, and out of them he constructed the universe […]
Timaeus On Physis, 69, Plato (translated by Benjamin Jowett)
Plato saw the creation of temporal order as a reflection of eternal laws.
χρόνου ταῦτα αἰῶνα μιμουμένου καὶ κατ΄ ἀριθμὸν κυκλουμένου γέγονεν εἴδη
These are the forms of time, which imitates eternity and revolves according to a law of number.
Timaeus On Physis, 38, Plato (translated by Benjamin Jowett)
The world view of the Doctors of the Church was in line with this conception.
For the death of the sinner springing from the necessity of condemnation is deservedly abolished by the death of the Righteous One springing from the free choice of His compassion, while His single [death and resurrection] answers to our double [death and resurrection]. For this congruity, or suitableness, or concord, or consonance, or whatever more appropriate word there may be, whereby one is [united] to two, is of great weight in all compacting, or better, perhaps, co-adaptation, of the creature. For (as it just occurs to me) what I mean is precisely that co-adaptation which the Greeks call αρμονία [harmony]. However this is not the place to set forth the power of that consonance of single to double which is found especially in us, and which is naturally so implanted in us (and by whom, except by Him who created us?), that not even the ignorant can fail to perceive it, whether when singing themselves or hearing others.
De Trinitate, Book 4, St Augustine (translated by Arthur West Hadden)
This understanding did not merely apply to the frequencies of pitch intervals but to the durations of pitch, and the nature of the durational values involved was very circumscribed, so that even a ratio of 3:10 was relegated to the ‘incommensurable’ class whereas a ratio such as 2:10 was of the preferred ‘commensurable’ class. In book 1, chapter 13 of his De musica, St Augustine is absolutely clear on the undesirability of amensurality.
Duo igitur motus qui ad sese […] habent aliquam numerosam dimensionem, iis qui eam non habent anteponendi sunt.
Therefore two movements [of time] which […] have some numerical measure to them are to be preferred to those which do not have that.
One hand clapping? • St Augustine depicts the student in De musica as taking pains to indicate that the beat that he produces is regular. He has the student say the following in book 2, chapter 13.
[…] admoto plausu ista percurram, ut de hoc quoque diiudicare possis utrum aliquid, an nihil claudicet […]
[…] I shall run through these [metres] to an applied clap so that you can judge from this too whether something or nothing is limping […]
[…] videri opus est […] animadverti acriter quanta temporis mora in levatione quanta in positione sit […]
[…] it is necessary that […] the mind be directed to how much there be of a duration [lit. delay] of time in raising, how much in putting down […]
Sentio quidem nequaquam plausum istum claudicare, et tantum levare quantum ponere […]
Indeed I sense this clap not to limp at all, and to raise by as much [time] as to put down […]
The word plausus indicates an action sufficiently violent to create a noise, so this is not a Buddhist talking. Augustine’s text provides convincing proof of the obvious: that ancient teachers would have taught the concept of beating metrical time to their students in a steady and even fashion so that the proportions in speech would be clearly detected visually by the accurately matching speed of the simple rise and fall of the hand. Complex hand movements waving to this side and that would not achieve that match so effectively.
St Augustine actually mentions water clocks in book 1, chapter 13 of his De musica. By his time, water clocks could have rotating gears and cylinders, dials and pointers and even chime the hour so there is no huge conceptual gap between us and St Augustine with regard to how we think of time. Augustine is only from Africa, not Mars. We perfectly understand his idea of “drops of time” even if we have never seen a water clock because we perceive the interval of time between each drop. The reference is not essential and its absence does not incur a paradigm shift in understanding.
In his Confessions, Augustine tells us that you could make a shorter poem last longer than a longer poem just by reading the shorter poem more slowly and the longer poem more quickly. With this, he is stating something that is quite obvious to us all. He later on makes the obvious assertion that you can’t tell how long a note is while it is still being sung: you have to wait until it is finished and then you know. This is neither rocket science nor alien. All modern musicians can measure time in their heads in the same way as Augustine (i.e. without clocks) and agree with St Augustine when he writes, “in te, anime meus, tempora metior” (in you, my mind, I measure times).
Beauty in equity • The ninth-century Musica et scolica enchiriadis reinforces this tradition of assigning the greater value to musical metre built on simple ratios.
This, therefore, is to sing numerically—to measure the calculated morulas [little time units] by long and short soni [sounds], not by arranging to protract or contract more than one should, but to constrain the vocem [utterance] under law of scansion, so that the melum [melody] can finish with that mora [time unit, lit. delay, here meaning ‘pace’ or ‘tempo’] with which it began.
The source presents the antiphon Ego sum via as an example of the 2:1 ratio in operation, a ratio regarded by the tradition as commensural and thus preferred.
The first iteration of the antiphon Ego sum via in BSB Clm 18914
With regard to the notation of Ego sum via in the 11th/12th manuscript Clm 18914 in the Bayerische Staatsbibliothek, Munich, the breve (short) and macron (long) signs can be seen to match not the number of Daseian notes but the number of syllables.
Ego sum uia 4 breves, 1 macron = 5 syllables
ueritas et uita 5 breves, 1 macron = 6 syllables
alleluia alleluia 7 breves, 1 macron = 8 syllables
However, the text actually assigns the shorts and longs not to syllables but to pitches.
Ego sum uia 5 breves, 1 macron = 6 pitches
ueritas et uita 6 breves, 1 macron = 7 pitches
alleluia alleluia 9 breves, 1 macron = 10 pitches
By making the wrong match, and by doing it badly, the diacritic notation is not reliable. This source is recognised for advocating numerositas ratio (calculation of rhythm by number) and enjoins aequitas and aequalitas as a general principle on the ensemble of singers.
Caution should be observed above all that the chant is performed with diligent equality; otherwise, if this be absent, it is deprived of its essential character and defrauded of its legitimate perfection. Without this (equality) the choir [chorus] is set in confusion by the discordant ensemble; neither can anyone join in harmoniously with others nor sing artistically by himself. In equity manifestly has God the creator appointed all beauty to consist, nor less that which the ear than that which the eye perceives; for he has ordered all things in measure, weight and number.
Musica et scolica enchiriadis (translated by Dom Gregory Murray)
The treatise is quite clear on the matter of changing the tempo.
… if at any time you wish, for the sake of variation, to change the mora [basic unit of time], i.e. to adopt a protensiorem [more drawn out] or incitatiorem [more sped up] cursum [flow] either near the beginning or towards the end, you must do it in double proportion, i.e. you must change the mora either into duplo correptiore [twice as short] or duplo longiore [twice as long].
The laws of metre • This is not the sole mention of singing an antiphon at two different speeds, with one twice as fast. The tenth-century Commemoratio brevis de tonis et psalmis modulandis adds to the Enchiriadis testimony of singing antiphons at half and full speed.
Repetitio antiphonarum quae in fine uersuum inter cantandum fit eadem qua psalmus celeritate percurrat, porro finito psalmo legitima productione protendatur duplo dumtaxat longius, excepto dum cantica euangelica sic morose psalluntur, ut non longiori, sed eadem morositate antiphonam subsequi oporteat.
The repetition of the antiphons (which, at the end of the verses to be sung in between, is made at the same speed that the psalm runs along at)—when, in turn, the psalm is finished—by [metrically] lawful lengthening, extends exactly twice as long, except when the Gospel canticles are played so slowly that the antiphon should follow, not longer but with the same slowness.
Rhythmic unevenness is firmly rejected.
Masters of schools should studiously impress this on those learning and, from the start, they should instruct in the same discipline of equity [aequalitas] or rhythm [numerositas] and, during the singing, teach about number through the beating [percussione] of feet or hands or something else as you wish, so that, from practice in youth, they will understand the difference between evenness [aequalium] and unevenness [inaequalium] and not get used to worse habits [peiore usu].
A measured silence • In the early eleventh-century Micrologus, Guido shows himself a mensuralist.
And above all, such care should be taken in the distribution of neumes so that […] neumes are related to each other, always however either in the number of notes [vocum (of sounds)] or in ratios of durations [tenorum (of holds)], and answer now equal to equal then double or triple to simple or else three to two, or four to three.
Aribo writes in the late eleventh century in order to expound Guido, not to contradict him. In his De musica, Aribo goes so far as to clarify that even the silence between two notes is to be mensural and accord with the basic unit of time, the morula.
A duration is twice as long or short if the silence between two notes [voces] is double in relation to another silence between two notes. In the same way, a duration [morula (little delay)] is twice as short if the silence between two notes is simple in relation to a silence between two notes.
Even if Aribo’s version of the first line of Dixit Dominus mulieri Chananeae was more or less identical in rhythm to Hartker’s version, Aribo would surely have advised applying a mensural ‘hold’ or ‘delay’ to subdivide the distinctions, as per Guido.
The new rhythm order • All the evidence, from the composition of St Ambrose’s metrical hymns right up to the emergence of the rhythmic modes and cantus fractus, indicates that the singers of the Church inherited the age-old classical approach to rhythm. Following Augustine and Guido, their teachers would have advocated strict measure, and discouraged and even deplored the alternative.
The implications of this may already have occurred to the reader: that, during the Romantic era (when musicians were casting off the strictures of classical forms in exchange for the indefinable and unattainable), there opened up a breach with the ancient musical tradition of the Church; an anti-mensuralist spirit arose in the Roman rite which wiped out almost every trace of metrical rhythm in the communal singing of Mass and Office. That would be the familiar story of innovation destroying tradition on the back of biased and unsound liturgical archaeology and claims that the liturgy was being restored to its true form.
Only a remnant of mensuralists were therefore left to attempt a true restoration in line with its centuries-old mensural tradition. Despite being instructed for a master’s degree by advocates of Cardine’s interpretation, I became a part of that mensural tradition during my studies in Ireland that year. I found that statistical studies of the ancient manuscript notations showed that the mensural approach was more likely to be the correct way to interpret the Latin chant repertoire. Bamberg lit. 5 (with its binary patterns in sequences) and Hartker’s antiphonary (with its metrical compensation in stock melodies) are two chief sources of evidence in support of the mensuralist view of tradition, but the strongest evidence comes from statistical patterns repeated across multiple sources.
O-Mocq-See • To try and justify the continued existence of their historically new liturgical fashion, then, the amensuralists of today would, according to this thesis, need to cast doubt on what is beyond reasonable doubt in the sources and to punt what is uncertain, all the while hinting at the alleged intolerance, lack of openness and even lack of spirituality among mensuralists who, like Eastern-rite Catholics, would prefer to sing metrical hymns to that awfully unmusical thing called a beat, rather than hirple around Mocquereau or Cardine’s arrhythmic obstacle course.
If all this is true, then it should come as no surprise that, in his two recent submissions, “Weaver Responds to Williams” (July 14) and “Stomping Feet, Clattering Hooves, and Other Chant-Related Matters” (July 20), Charles Weaver refers to Guido’s metaphor of a racing horse; after all, Dr. Weaver himself is trying to sell us a lame one, and the purported holiness of that non-binary beast is more important to him than its health, so he deems a historically inaccurate edition of chant potentially more holy than a historically accurate one.
If Guido had wanted to describe a simple deceleration, he could have used the simple example of a man running for that: as he comes to a halt, the duration between his steps gradually increases and there is no change in gait, because a man only has two legs.
Guido instead chose the example of a horse because, unlike a man, a horse does not merely slow down: it changes gait from a four beat gallop to a two beat trot. This is the perfect metaphor for a binary change from four short notes (four beats) changing to two long notes (two beats) within the same duration, just as the writer of the Scolica enchiriadis proposes.
The characteristic four-legged switch from one rhythm to another would have been as well-recognised in Guido’s time as now, and that is most likely why that metaphor was considered most apt. It would be a very unsound horse that would slow down bit by bit without adjusting its beat rate. Dr Weaver’s notion of chant therefore seems all too pedestrian.
Disathairne 5 Lùnasdal 2023
(Glasgow, Saturday 5 August 2023)
Alasdair Codona is a singer, composer, arranger, translator, teacher, and specialist in Gaelic and medieval music living in Glasgow, Scotland. In addition to his musical activities, he is famous for undergoing a hunger strike outside of the Scottish Parliament, which resulted in the overturn of legislation depriving homeless people of basic public services.