Friday, January 23, 2015

BOOK: Florentius de Faxolis, "Book on Music"

Florentius de Faxolis: Book on Music. Edited and translated by Bonnie J. Blackburn and Leofranc Holford-Strevens. The I Tatti Renaissance Library, Vol. 43. Harvard University Press, 2010. 9780674049437. xxiv + 340 pp.

This book contains a treatise on music written in the late 15th century for cardinal Ascanio Sforza (brother of the better-known Ludovico, duke of Milan). Apparently, it was until now preserved only in one manuscript (a very fancy one, judging by the plate showing two richly illuminated pages, included in this book before p. iii — which, incidentally, is the first time we got a colored plate in the ITRL series), and has now been printed for the first time.

Reading this book was an odd experience for me. I know more or less nothing at all about music, and it would normally never even occur to me to pick up a book like this one; I only read it due to my self-imposed programme of reading all the books from the I Tatti Renaissance Library. I don't remember when was the last time that I felt so completely out of my depth while reading a book; perhaps never. I often write in my blog posts that I'm clearly not part of the intended target audience for this or that book that I'd read, but rarely is this true to such an extent as this time.

Introductory part

From the perspective of someone like me, Florentius's treatise may be divided roughly into three parts (which don't correspond exactly to the formal division of the treatise into three books). First there are a couple of introductory chapters about the value and importance of music, as well as about its origins. A lot of this stuff consists of citations from various earlier authors, both ancient and medieval. In fact that practice continues throughout the book — either Florentius thought the book would appear more scholarly and authoritative that way, or he was a bit unsure about his own mastery of the subject and so thought it would be better to focus on providing a digest of what earlier authors had written on it.

Anyway, this early part of the book at least had the good feature of being readable and understandable even by someone like me. Of course, the theories he cites about the origins of music etc. are the typical nonsensical just-so mythological stories that ancients used to cite about origins of things (this reminds me a little of Polydore Vergil's On Discovery; see my old post about it from a few years ago). In a way it was interesting to see what these early authors thought about music and its origins, but at the same time I don't think that having read this has made me understand music any better. There are lots of effusive, airy assertions in praise of music, without any explanations or justifications; rather, the authors cited seem to regard these things as self-evident.

Ancient authors apparently claimed that “an aulete, skillfully brought in and in good measure, cures adders' bites [. . .] very many human diseases were treated by playing auloi” (1.1.17; Florentius cites Aulus Gelius, who cites Theophrastus and Democritus).

Florentius also cites an interesting tale from Macrobius on how Pythagoras discovered the principles of harmony by listening to sounds made by blacksmiths' hammers of various weights; see 1.1.37–42 (p. 33).

I often had the impression that music(ology) is only a small step away from mysticism, and Florentius and his sources often cross it :) He cites Isidore of Seville in 1.1.9: “Without music no discipline can be complete, for nothing is without it. For the very universe itself is said to have been put together with a kind of musical harmony, and the sky itself ot rotate to the sound of harmony.” In 1.3, he divides music into three parts: vocal, instrumental, and music of the universe; on the latter, he cites Boethius: it “is above all to be sought in those things that are observed in the sky itself, or in the assemblage of the elements, or in the variation of the seasons.” (1.3.4)

Down the rabbit hole of etymology!

There's another dubious quotation, this time from one William Brito: music is “so called from moys, which is ‘water,’ because of old it was first discovered by Pythagoras in hydrauli, that is, water organs, and in blacksmiths' hammers. Alternatively, it is derived from moys because it deals with sounds and the proportions of sounds, and without the benefit of moisture there is no pleasure in singing or sounds.” (1.2.5)

This etymology seems to have been popular in the middle ages; some googling finds another mention of it attributed to one Remigius (Johannes Ciconia, “ ‘Nova Musica’ and ‘De Proportionibus’ ”, ed. by Oliver B. Ellsworth, U. of Nebraska Press, 1993, p. 63). A note on the same page says that the derivation “is from the ancient Egyptian mw, which means ‘water.’ In hieroglyphics, this is a single, biliteral sign, represented by three wavy lines that are themselves a pictograph of water”. I guess that explains why I had no luck trying to find moys in the Greek dictionaries on the Perseus project.

Anyway, I don't doubt that, like so many ancient and medieval etymologies, this one is also pure crackpottery. As far as I can tell after some googling, ‘music’ is derived from the Muses, which don't seem to have much to do with water. (Nor does moys seem to have anything with the English word moist; according to, the latter is from Latin mucidus, meaning moldy or musty.)

Musical theory

After the introductory part of the book, Florentius plunges into musical theory proper, and from that moment onwards I understood pretty much nothing. He writes a lot about harmonies, consonances, notes, counterpoints and other technical terms from musicology, and even though he tries to provide definitions of many such terms when he first uses them, the definitions themselves use other terms which I also didn't understand — and this is not surprising, for all these things refer to concepts that I know pretty much nothing whatsoever about.

So I can't really say anything sensible about this part of the book. I'm sure it is interesting to people with the right sort of background knowledge, who might use it to learn about the state of musical theory in Florentius's time. As for me, it would be better if I had picked up a book of the ‘music for dummies’ type, if one exists — although there's a good chance that I'd turn out to be too big a dummy to understand even that.

From 1.4.15: “The species of voices, on Isidore's showing, are these: sweet, perspicuous, subtle, fat, hard, rough, blind, curly, and perfect.” :S Florentius proceeds to quote Isidore's definitions of all eight, which unsurprisingly didn't really clear anything up for me (“Sweet voices are slender, dense, clear, and high-pitched” etc.).

I had heard of the solmization syllables before, which are basically one-syllable names for different notes (do-re-mi and so on), and was interested to see what appears to be an earlier form of this system here in Florentius's book. He uses ut instead of do (1.5.10), and often uses curious combinations of three or more syllables and even an extra letter at the start (e.g. we find “Csolfaut, Dlasolre, Elami” in 1.6.1). I wasn't able to understand what he means by that, but found it fairly fascinating anyway.

Occasionally, there are examples of short passages of musical notation, and I was interested to see how the Latin text on the left-hand pages shows the notation of Florentius's day, while the translation on the right-hand pages also ‘translates’ the music into modern-day notation. The two seem to be fairly closely related, but nevertheless different. For example, the bodies of Florentius's notes are little rectangles and parallelograms rather than little ellipses like the modern-day ones.

It seems that musical notation could be srs bsns: “Some persons, too, have perverted the notes in their own way, which ligatures we not only reprehend but utterly reprove and cast out” (3.8.5). You can practically see him reaching for the thesaurus in an outburst of righteous rage :) Florentius goes on to show an example of these abominations, and you won't be surprised to hear that to my uneducated eye they look hardly any different from all the other notes in his book :))

Classification of proportions

The last few chapters of the treatise (3.15–20) became a little bit more intelligible to me again, because they wander into mathematics more than musical theory, and I know at least a little about mathematics. Florentius says that he is discussing proportions, and although this was presumably relevant to his discussion of music (though I couldn't quite see how), what he's really doing here from a mathematical point of view is classifying fractions according to a very peculiar and impressively abstruse system. (At the end of the book, there are some bits of musical notation that are apparently intended to illustrate various kinds of fractions, though I don't pretend that I understood how exactly they do so; pp. 227–35.)

I imagine that this classification of fractions probably must have been largely a long-established system rather than Florentius's inovation. In fact I wouldn't be surprised if this sort of things went back all the way to ancient Greek mathematics. I remember reading years ago in Thomas Heath's History of Greek Mathematics various similarly pointless efforts to categorize integers, where they came up with groups such as triangular numbers and their various generalizations (figured numbers, polygonal numbers).

So I'm not surprised that fractions inspired similar and even more complicated efforts. Just like in the case of integers, I didn't quite see the point of such classifications; they introduce a lot of new terminology and definitions but don't really lead us to understand the numbers any better. They strike me as the sort of thing that people would do if they are more interested in mysticism and numerology than in mathematics. I guess it's natural enough that such ideas emerged when mathematics was in an early stage of development, but I for my part consider myself lucky to live in an age when we can say more interesting things about numbers than to pointlessly categorize them like this.

Introducing new definitions and terminology is all well and good, but it's only valuable if some of the things you have thus defined have interesting new properties, if you can prove some theorems about them, etc. For example, the concept of prime numbers is valuable because so many interesting properties and theorems involving them have been found; but not many such findings exist about e.g. triangular numbers. Florentius's classification of fractions strikes me as similarly unproductive.

Florentius's description of the classification of proportions (i.e. fractions) is at times very confusing, but as far as I understood it, he divides them into five genera, each of which is then divided further into species (one for each value of a in the formulas below), and each species consists of infinitely many proportions (which you can get by multiplying the numerator and the denominator by any constant positive integer, thus e.g. you have a species that consists of 3 : 2, 6 : 4, 9 : 6, etc.). Thus the proportions that constitute a species are really all equal to each other in a mathematical sense, but he seems to think it's important to list them separately.

  • (1) multiples: a : 1;
  • (2) superparticular: (a + 1) : a;
  • (3) superpartient: this is further subdivided into three modes:
    • (3.1) super(b)partient: (a + b) : a, where 2 ≤ b < a and b does not divide a;
    • (3.2) superpartiens (b)as: this seems to be intended to mean (a + a/b) : a, where b does divide a, although Florentius's explanation is completely confusing (see the editors' commentary, pp. 316–17);
    • (3.3) super(b − 1)partiens (b)as: (a + (b − 1)/b · a) : a.
  • (4) multiple superparticular: (c · a + 1) : a for c ≥ 2;
  • (5) multiple superpartient: (c · a + b) : a for c ≥ 2 and b that does not divide a.

Speaking of the third genus, for some reason he doesn't generalize mode (3.3) to allow an arbitrary c/b instead of (b − 1)/b, although his naming convention could easily support that. In fact this generalization would also cover mode (3.2) if you allow c = 1. (Speaking of the naming conventions, the translators at this point give up trying to translate Florentius's abstruse naming of fractions into English and just leave them in the original Latin, with an note: “These terms have been left in Latin for want of English equivalents”; p. 295, n. 86. Earlier they say of the terminology of mode (3.1): “These are scarcely English words, but no equivalents exist”; p. 295, n. 82.)

Besides, I don't quite see the point of dividing genus (3) into the three modes, since modes (3.2) and (3.3) are really just alternative ways to reach some (but not all) fractions from mode (3.1).

The requirement that b must not divide a in (3.1) and (5) makes sense; in fact you could go a step further and require that a and b must be coprime. This is because if they shared a common divisor, e.g. d, so that b = B · d and a = A · d (where A and B are now coprime), a fraction from the (3.1) mode becomes (a + b) / a = (A d + B d) / (A d) = (A + B) / A (with A and B coprime), so you don't miss any fractions by limiting yourself to the case where a and b are coprime. The same argument applies to fractions of the genus (5).

In fact, if b was a divisor of a, so that e.g. a = A · b, a fraction of the (3.1) mode would actually fall into the genus (2): (a + b) / a = (A b + b) / (A b) = (A + 1) / A. Similarly, a fraction from genus (5) would actually end up in genus (4).

I also couldn't help feeling that some of the divisions between the genera are unnecessary complications. If you allow b = 1 in the definition of (3.1), it will thereby also absorb genus (2); similarly, if you allow c = 1 in the definition of genera (4) and (5), they will absorb the genera (2) and (3), respectively. But then, all these unifications would be just a long-winded way of saying that if you have a fraction n / a where the numerator n is greater than the denominator a, you can of course express the numerator as n = c · a + b for some quotient c and remainder b (such that 0 ≤ b < a). The distinctions between genera (2), (3), (4) and (5) are obtained simply by distinguishing between c = 1 and c > 1, and between b = 1 and b > 1. And by allowing a = 1, you also cover genus (1), i.e. the fractions which are really integers.

Anyway, whatever we think of its perhaps unnecessary complications, Florentius's scheme does neatly cover all the fractions greater than 1. He doesn't specifically discuss fractions between 0 and 1 (though he mentions them briefly in 1.15, p. 195), but obviously they could be classified in an analogous manner, just by reversing the roles of the numerator and denominator. Florentius cites Boethius's terminology for the five genera of the fractions between 0 and 1: submultiple, subsuperpatricular, subsuperpartient, multiple subsuperparticular, multiple subsuperpartient (3.15.11).


I wonder if the cardinal got his money's worth. Apparently, Florentius's text is often a bit unclear, confused, or just plain wrong, and the editors point out such many places in the notes at the end of the book. I was often delighted and amused by these notes, as they led me to feel that perhaps my inability to understand this or that passage was not 100% my fault, just 99% or so :)

“We have tried to make Florentius's thought as clear as possible (sometimes it is not possible)” (p. 243).

“The intended sense appears to be as given, but the original syntax is beyond repair.” (P. 274, n. 177.)

“Florentius appears to have developed a sudden and inappropriate scruple against predicating a singular complement of a plural subject.” (P. 296, n. 95.)

The editors conclude their discussion of Florentius's confused treatment of proportions: “as in musical matters Florentius is an amateur attempting to punch above his weight” (p. 318).

“Florentius's Latin is a strange brew of classical and unclassical, elegant and incoherent” (p. 321); “at times Florentius's Latin is incoherent to the point of incomprehensibility” (p. 324).

After so many mentions of Florentius's mistakes, I couldn't help thinking that, if I had been in Florentius's place, I'd prefer to see my book languish in manuscript than to have it published by such editors :)) Even the scribe is not safe from their eagle eyes and sharp tongues: “so far was Verrazzano from understanding the text that he often began a new paragraph in mid-sentence” (p. 242).

The editors' introduction mentions that Florentius's “vernacular name, not attested, will have been Fiorenzo Fasoli” (p. viii); they add in an interesting note: “Fasoli, stressed on the second syllable (Fasòli), is a dialect form of fagioli, ‘beans’” (note 7, p. xx). I guess that this Italian word must also be the source of our fižol.

The editors' notes occasionally mention interesting points of difference between Latin and English style. Thus, when Florentius ends the dedication of his book to the cardinal with the words “fare well and love me” (p. 5), they add in a note: “We assure the recipient of our love (in the broadest sense); Latin letter-writers more honestly ask to be loved.” (P. 257, n. 5.)


What to say at the end? I can't say that I understood anything much of this book, but in the end I had more fun reading it than I had expected to. In this no small thanks goes to the editors for their interesting notes and their witty comments on the many missteps and blunders of poor Florentius. Nevertheless I hope that highly technical books such as this one will not show up often in the ITRL series.

Labels: , ,


Post a Comment

<< Home