Jump to ContentJump to Main Navigation
Latin in Medieval Britain$

Richard Ashdowne and Carolinne White

Print publication date: 2017

Print ISBN-13: 9780197266083

Published to British Academy Scholarship Online: September 2017

DOI: 10.5871/bacad/9780197266083.001.0001

Show Summary Details
Page of

PRINTED FROM BRITISH ACADEMY SCHOLARSHIP ONLINE (www.britishacademy.universitypressscholarship.com). (c) Copyright British Academy, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in BASO for personal use.date: 01 June 2020

English Music Theory in Medieval Latin

English Music Theory in Medieval Latin

(p.147) 7 English Music Theory in Medieval Latin
Latin in Medieval Britain

Leofranc Holford-strevens

British Academy

Abstract and Keywords

Medieval English music theory, almost always expressed in Latin, though not isolated from Continental—in particular French—developments, has a strong tendency to resist them and go its own way in both language and content; moreover, despite the early establishment of the name proprius cantus (‘properchant’) for the natural hexachord, it is more characteristically marked by divergence from one writer to another, so that even when doctrines are compatible the same thing may be called by different names and the same name may be applied to different things. This chapter studies the variations in conception, notation, and terminology exhibited in the works of numerous English authors from the 13th to the 16th centuries, noting differences from the far more standardised French Ars nova associated with the names of Philippe de Vitry and Jean des Murs.

Keywords:   Ars nova, Jean des Murs, music theory, notation, Philippe de Vitry, Proprius cantus

UNTIL THE 15TH CENTURY, WRITING ON MUSICAL theory in Western Europe, on the Continent as well as in England, was almost exclusively in Latin, by clerics (often monks) for their peers or their future peers in school. Since classical Greek music theory, as made available to readers of Latin above all by Boethius, had become divorced even from Greek musical practice and bore virtually no relation to the music of the medieval West, in order to describe this music new terminology had to be invented either by pressing special meanings onto ordinary words or by inventing new ones. It is no surprise that there was considerable diversity, to which English writers made their contribution. In this chapter I examine words and usages peculiar to English authors, whether writing in England or abroad, and whether or not their doctrines were home-grown rather than imported.1 Many of these concern notation, which over the period developed from forms we cannot fully interpret to forms that, though not yet our own nor used in our own way, nevertheless bear a superficial resemblance to those employed today; however, that was merely one part of music theory, in England and elsewhere, beside the study of the fundamentals that it recorded (Herlinger 2001: 246).2

1. Theinred of Dover

Theinred of Dover (mid-12th century), convincingly identified with John of Salisbury’s contemporary Tenredus,3 and therefore the first known English (p.148) music theorist with a surviving and securely attributed treatise to his name, wrote De legitimis ordinibus pentachordorum et tetrachordorum in three books, attacking Guido of Arezzo, an early example of unavailing English protest against Continental achievement. As might be expected of one attempting to describe specialised concepts in ordinary language before a technical language has been agreed, Theinred is inconsistent in his terminology, which admits both synonymy, the use of different words for the same thing, and homonymy, the use of the same word for different things: thus the Guidonian system is in successive sentences distinctio Guidonica and ordo Guidonicus, but both distinctio and ordo are used in other senses elsewhere.4 On the other hand he also coins new words (Snyder 2006: 146–8):

diuersisonorum autem alii sunt equisoni alii iniquisoni. equisoni sunt qui cum sint diuersisoni eque tamen sonant, ut qui diapason semel vel sepius terminant. iniquisoni sunt qui non eque sonant, ut qui diapente vel tonum terminant

Of the differently sounding (notes) some are equal-sounding, others unequal-sounding. Equal-sounding are those that although they are differently sounding yet sound equally, like those that once or oftener bound the octave [i.e. are the lowest and highest notes of the octave or its multiples]. Unequal-sounding are those that do not sound equally, like those that bound the fifth or the tone.5

Aequisonus (‘equal-sounding’) already existed in Late Imperial Latin, being used indeed in a similar context by Boethius (De institutione musica 5. 11), and was employed with characteristic vagueness of sense by Frithegod; but diuersisonus (‘differently sounding’) and iniquisonus (‘unequal-sounding’) are new.

2. Properchant

A little later, at about the turn of the century, a brief Latin treatise on solmisation (the organisation of pitches into hexachords or rows of six notes) and mutations (changes from one hexachord to another by way of pitches common to both) added to a calendar of Wherwell Abbey in Hampshire included explanatory diagrams with Anglo-Norman text (meant for nuns, which explains why a vernacular language should be used rather than Latin), one of which used the term ‘propre chaunt’ for the natural hexachord (the series of (p.149) six notes beginning on C). This reappears as proprius cantus in Latin treatises by English authors from the second half of the 13th century onwards (and later in English as ‘properchant’).6 One such treatise is the Musica manualis formerly ascribed to its 15th-century copyist John Wylde, in which the term glosses, and is glossed with, its standard synonym, naturam vel proprium cantum (Sweeney 1982: 53, ‘nature [i.e. the natural hexachord] or properchant’), proprio cantu, quam naturam dicunt (ibid. 68, ‘by properchant, which they call nature’). It is discussed at length in the Practica artis musice written in 1271 by an English priest called Amerus (or Aimerus) also known as Aluredus (i.e. Alvredus, Alfred), who in the same passage uses cuna (‘cradle’) for ‘hexachord’, or, as the normal term was then, deductio, and radix (‘root’) for its lowest note (Ruini 1977: 91). Cuna is unique; so is radix in this sense, but it is also found, in the exposition of rhythmic modes, for the chant melisma on which the initial statement of the mode is based in the English author known as Anonymous IV and in De musica mensurabili positio, a late-13th-century revision of the mid-13th-century De musica mensurabili traditionally ascribed to Johannes de Garlandia (also called Johannes Gallicus), who until 1969 was commonly identified with the English author of the Parisiana poetria.7 More recently, it has been proposed that the French Garlandia was not the original author but the reviser, both of this work and of a treatise on plainchant;8 in any case Anonymous IV knows the French treatise and the reviser, whatever his nationality, shows awareness of an English practice.9

Another usage shared with Anonymous IV by the reviser, but not attested generally, is of remotus used in classifying intervals greater than others, although the details differ.10 Anonymous IV states, not with perfect consistency (Reckow 1967: i. 75, 86):

notandum, quod triplex est modus faciendi discantum secundum veros discantatores. primus modus est ex propinquis proportionibus, hoc est infra diatesseron vel diapente; alius modus est ex remotioribus quae continentur sub diapason cum praedictis; tertius modus est ex remotissimis infra diapente cum diapason vel duplex diapason vel ultra etc.

It must be noted that there are three ways of making a discant according to real discantors. The first way is from near intervals, that is below the fourth or fifth; another way is from remoter ones confined under the octave with the aforesaid; (p.150) the third way is from the remotest ones below the twelfth or the double octave or beyond, etc.

iterato tertiae sive remotae dicuntur semiditonus cum bis diapason et ditonus cum bis diapason, diatesseron cum bis diapason, diapente cum bis diapason, quod quidem in humana voce potest reduci ad effectum quoad plures homines, non quoad omnes

Again, ‘third-class’ or ‘remote’ [consonances] is the term for the double octave and minor and major third, the double octave and fourth, and the double octave and fifth, which in respect of the human voice can be realised by many people, not by all.

The remotest have become simply remote, since the remoter are now called secondary (p. 85). Different again is the classification of the reviser (Reimer 1972: i. 94):

proprium est diapason et infra, remotum est duplex diapason et infra usque ad diapason, remotissimum est triplex diapason et infra usque ad duplex diapason

Proper are the octave and below, remote are the double octave and below down to the octave, remotest are the triple octave and below down to the double octave.

3. Neumes

When musical notation, which had ceased in late antiquity, was brought back into use, it was not based on the Greek system preserved in Boethius, but on symbols that for the most part could remind a singer already acquainted with a melody of its contours but not enable one not so acquainted to sing it from sight. These neumes, as they are nowadays called in preference to the unspecific contemporary term notae, varied from place to place in name, shape, and value; but in the early 14th century, long after staff notation had become universal, Walter of Evesham, often called by moderns Odington through confusion with a contemporary polymath,11 presents a long table of plainchant symbols (Hammond 1970: 93–4), based on the notes and ligatures in common use but given names based on those used for neumes: for instance, the virga prediatessaries et subdiapentis, in which a long is preceded by four currentes (for which see §4.1 below) ascending through a fourth and followed by five more descending through a fifth. His table was taken over in mid-century by one William (Willelmus), as it appears prior of Dover, in his Breviarium regulare musicae (Reaney 1966: 22); it is he who first calls its author Odington.

(p.151) 4. Durations

4.1 The 13th century

Even when staff notation was introduced, specifying pitches as most systems of neumes had never done, the notes did not at first indicate precise duration; when in the 13th century they began to do so, the earliest division of note lengths was into long and short (longa English Music Theory in Medieval Latin and brevis ■). Alternative conceptions make the long (as in quantitative Latin metrics) properly worth two breves, being called recta (‘right’), but extensible ultra mensuram (‘beyond measure’) to three, and equivalent by default to three breves, being then called ‘perfect’, but reducible to two (‘imperfect’) by a preceding or following breve; it was the latter conception that would prevail. On the other hand, when two breves preceded a long, one of them would be doubled in length in order to achieve perfection; this was normally the second (altera, whence the doubling came to be known as alteration), the first being recta, but an alternative practice that made it the first survived in England long enough to be condemned by Walter of Evesham. However, musicians ceased to be satisfied with these durations, but sought values longer than the long and shorter than the breve.

Although the term ars antiqua, used in the early 14th century by a writer commonly called Jacques de Liège but henceforth to be known as Jacobus de Ispania (Bent 2015) to denote the good old music he had grown up with in contrast to the narrow range of genres and hyper-subtle notation practised by the likes of Philippe de Vitry, has been extended to describe the music of the 13th century as a whole, the music of the time was far from being static. Much of the theoretical development lies outside our purview; nevertheless, English authors are not to be neglected. It is in this period that we find the duplex longa and the semibrevis, which might be either major (worth two-thirds of a breve) or minor (worth one-third); however, the lozenge shape in which the semibreve was written (◆) might also be used in runs of short notes indicating rapid stepwise motion, called currentes (‘running’) by Amerus (Ruini 1977: 99), Anonymous IV (Reckow 1967: i. 37–9, 43–5, 87), and in the next century Walter of Evesham (Hammond 1970: 138). In attempting to describe various ways of writing the symbol, Anonymous IV uses the Arabic names for the rhombus, the rhomboid, and the trapezium he found, already corrupted, in a translation of Euclid (Reckow 1967: i. 41):12

(p.152) elmuahim vero oblique saepe protrahitur; et quidam protrahunt ipsam simile elmuahim.13 Item est quaedam elmuarifa, quae potest dici irregularis, quae habet tractum in sinistra parte descendendo, sicut Anglici depingunt vel notant, quod idem sonat etc.

But the rhombus is often drawn obliquely, and some draw it as a rhomboid (lit. a like-the-rhombus). There is also a trapezium, which may be called irregular, which has a stem on the left side going downwards, as the English depict or write it, which sounds the same etc.

Later on, Anonymous IV attempts to describe the rubato with which melismas were sung. These were notated in accordance with certain rhythmic patterns known as modi, in English ‘modes’, consisting of longs and breves, subject to the usual rules of imperfection and alteration; but in performance these notes might be stretched or compressed at a singer’s whim, or inspiration, producing irregular modes qui modi dicuntur voluntarii et sunt multiplices (Reckow 1967: i. 84, ‘which modes are called arbitrary and manifold’). Naturally such renditions could not be codified; our author does his best, qualifying notes by such epithets as nimia (‘excessive’), festinans (‘hastening’), mediocris (‘middling’),14 but certainly does not make his meaning clearer when he writes that the third mode (which in principle consists of a long followed by two breves, of which in France the second is altered, making a rhythm of 3 1 2 (cf. Sanders 1962), as it were dotted minim, crotchet, minim, in English practice the first, making 3 2 1), in the first of three irregular varieties, est una longa nimia15 cum duabus longis tardis (irrespective breves dicuntur) et tertia mediocris, prout melius competit coniunctim, iterato similes tres coniunctim, et sic procedendo etc. (ibid., ‘is an excessive long and with two slow longs (which are called breves regardless) and a middling third, taken together as well as may be, again three similar notes taken together, and proceeding thus etc.’)

Evidently the initial long is extended and the following notes regrouped so that the long shall be last instead of first; the slow longs are presumably called breves because they take the place of breves, but it hard to see what a slow long can be if not a note longer than the normal long, let alone how such a note can take the place of a right breve. I suspect we have to do with a polar error, longis being put by mistake for brevibus: the slow breves are nevertheless (p.153) still called breves. Such errors, in which a word is substituted for its antonym, are far from unknown, and are as likely to be authorial as scribal;16 here it would be the easier both because longa precedes and because the following parenthesis might seem to point away from breves. But of particular interest is the word minima, which as the DMLBS notes, is used in the description of the first and second irregular modes. Whereas in their regular form these modes consisted respectively of a long followed by a breve and a breve followed by a long, the long being imperfected in both modes, the irregular modes, that is to say the modes as actually sung, were more complex. Of the first such mode Anonymous IV writes that it procedit per unam longam duplicem et17 per semibrevem vel minimam et longam debitam, et sic per talem brevem et longam continuando etc. (ibid., ‘proceeds by a double long and by a semibreve vel minimam and a due long, and continuing thus by such breve and long, etc.’)

The words vel minimam may be understood in any of three ways: ‘or else a minim’, ‘also called a minim’, ‘even a tiny one’; but this last is hard to reconcile with the following brevem. Passing over an example from the chant Alleluia Posui adiutorium, we move on to the second irregular mode:

secundus modus irregularis est brevis parva vel minima cum longa duplici vel nimis longa coniunctim, iterato eadem brevis et eadem longa, et sic continuando etc.

The second irregular mode is a small breve vel minima with a double long or an excessive long taken together, again the same breve and the same long, and continuing thus etc.

Here too, in view of parva before it, vel minima cannot well mean ‘even a tiny one’; it might mean ‘(a small) or very small (breve)’, which would require the phrase to mean two different things in the two places, or still be either an alternative note or an alternative name (as indeed ‘excessive long’ may be for ‘double long’). Unfortunately we are not told what difference if any there is between a small breve and a semibreve, but if there is a difference, since one must be longer than the other, the minima (or indeed the very small breve, if the distinction be real and not merely conceptual) does not seem a plausible alternative to the longer note; even if there is none, then in taking for granted a note smaller than a semibreve, the author would have been in advance of his time. The alternative must remain more probable, that minima was as yet (p.154) simply a synonym for semibrevis; even in the 14th century, as we shall see, its place in the hierarchy of note-values was not, in England, fixed.

4.2 The 14th century

Experiments with shorter note values, at first marked by visually undifferentiated semibreves, led to codification as the ‘four prolations’ in the theory known as the ars nova18—a term now extended, like ars antiqua, to cover a whole period—and associated with the names of the poet-composer Philippe de Vitry and the mathematician Jean des Murs (Johannes de Muris). In it each of the five notes maxima, longa, brevis, semibrevis, and minima except the last contained either three (though the maxima took a while to supplant the duplex longa)19 or two of the next note down,20 being respectively perfect or imperfect except in the case of the semibreve, which was said to be in major or minor prolation; the minima was definitively established as a notevalue in its own right, rather than as a species of semibreve (semibrevis minima), by being given an upward stem English Music Theory in Medieval Latin The relation of the maxima English Music Theory in Medieval Latin to the long was known as major mode (modus maior), that of long to breve as minor mode, that of breve to semibreve as tempus (‘time’, a term already used for the length of a breve in the 13th century); the value of a perfect breve was known as a perfection, the nearest approach that music of the time had to our concept of the bar. All notes could be imperfected (except of course for the shortest) or altered on the same principle as the breve; imperfection could now take place at long distance, not merely from an adjacent note. There was, however, some fluidity in the system below the breve, especially when it was extended to incorporate a semiminima English Music Theory in Medieval Latindespite the philosophical objection that nothing could be smaller than the note that by definition was smallest;21 in time the latter would be further subdivided into the fusa or even the semifusa.

Despite this fluidity, the French ars nova was a coherent system that contrasted with the English experimental interpretations of existing principles (p.155) (Bent 1978). Minims were still written without stems, semibreves were not susceptible to imperfection, and both in paired breves and in paired semibreves it was generally the first that was altered. In other respects, however, English writers, especially in the second quarter of the century (Lefferts 1986: 154), innovated both in notation (for instance, dotted rests and the swallow-tail, cauda hirundinis, used with the breve as a mark of alteration, neither without controversy; Bent 1978: 71–2) and in terminology; the bewildering variations yield the impression that every writer was inventing his own wheel. These developments in English theory can be matched in English music, even though it survived in far less abundance than French (Lefferts 1986: 93–154), from which it maintained its independence (Bent 1978: 65).

4.2.1 Long notes

Despite similarities that lead Lefferts (2001: 218) to speak of ‘early 14th-century Anglo-French notational and mensural theory’,22 England, still going its own way, resisted full adoption of French terminology without developing a standard system of its own. What in France was the maxima was in England generally called the larga, Anglicised since Morley as ‘large’ but properly ‘wide’, from the extended rectangular shape of the written note-head;23 so for instance the writer whom Lefferts (2001: 218) calls ‘Anonymous II of London [British Library Add. MS] 21455’ (see his Example 1, p. 222).24 However, in two works of apparently the mid-14th century we also find a higher note-value, the largissima (‘widest’). In Willelmus’ Breviarium regulare musicae the list of simple notes begins (Reaney 1966: 26, corrected from MS Bodley 842 f. 70r):

prima regula: largissima perfecta est figura quadrangularis cuius latitudo transit longitudinem, et habet tractum a parte dextra de superius et inferius, et valet 3 perfectas largas25secunda regula: larga perfecta est figura quadrangularis cuius latitudo transit longitudinem, tractum gerit a parte dextra tantum,26 et valet tres longas perfectas vel longam rectam et alteratam

(p.156) First rule: the perfect largissima is a rectangular note-shape whose breadth exceeds its length,27 and it has a vertical stroke to the right upwards and downwards, and is worth three perfect larges. … Second rule: the perfect large is a rectangular note-shape whose breadth exceeds its length, and it has [lit. ‘wears’] a vertical stroke to the right only, and is worth three perfect longs or a right [i.e. unaltered] and an altered long …

The anonymous Tractatus de figuris sive de notis also uses the terms, but proposes the alternative names longior and longissima, which were already in use on the Continent for the double and triple long, or imperfect and perfect large (Reaney 1966: 44):

et illa nota quae vocatur larga bene et evidentius posset appellari longior in comparatione ad longam, eo quod longiori tempore quam longa mensuratur. Et per consequens illa quae largissima vocatur in comparatione ad longam et longiorem, longissima posset appellari proprie, ita quod istae tres notae sic vocantur: longa, longior, longissima

And that note which is called larga could well and more clearly be called the longer in comparison with the long, because it is measured with a longer time than the long. And in consequence that which is called largissima in comparison with the long and the longer, could properly be called the longest, so that these three notes are called thus: long, longer, longest.

These notes are nowhere defined, but the music examples on pp. 43 and 51, in which values are given both as notes and as rests, represent larges and largissimae by only two and four long rests respectively. That distinguishes this system from that attributed to ‘Phillipotus’—be he an otherwise unknown Philippe in the diminutive or a falsely invoked Vitry—by Pierre de Saint-Denis (Petrus de Sancto Dionysio; after 1321), which equated the longior with three longs and the longissima with nine, their imperfect counterparts being the semilongior and the semilongissima (Michels 1972: 154–5); but these authors too show English affinities (Lefferts 2001: 135–6).

By contrast, Robert de Handlo, of Hadlow in Kent, whose Regulae were completed on 9 May 1326, extends the term longa to all values higher than the breve, from the longa simplex of three breves, to which and not to the breve he attaches the term perfectio, to the ninefold longa novem perfectionum, each ‘perfection’ being marked by a discrete rectangle, void and not like other note-heads black, to the left of the note-stem (Lefferts 1991: 116):

  1. (p.157) (Rubrica V, Regula I)A. Figura siquidem habens in se tres quadrangulos longa triplex, id est trium perfectionum nota, vocatur.

  2. B. Si quatuor habeat, quadruplex, id est quatuor perfectionum nota, dicetur.

  3. C. Si quinque, quinque; si sex, sex; si septem, septem; si octo, octo; si novem, novem.

  4. D. Nec ultra debet maiorari.

  5. E. Quia sic longa simplex habet in valore novem semibreves minores, sic longa novem perfectionum novem longas in valore debet habere et non plures.

  6. (Rubric 5, rule 1)A. For a note-shape containing three rectangles is called a triple long, that is a note of three perfections.

  7. B. If it has four, it will be called quadruple, that is a note of four perfections.

  8. C. If five, five [i.e. fivefold]; if six, six; if seven, seven; if eight, eight; if nine, nine.

  9. D. And it ought not to be expanded any further.

  10. E. Since thus the simple long has the value of [lit. in its value] nine minor semibreves, thus the long of nine perfections ought to have the value of nine longs and not more.

Earlier in the treatise, however, he renames the imperfect long the semilonga (Lefferts 1991: 88), not ‘half-long’ but ‘less than long’ (in fact two-thirds of a long), just as the semibreve was not a half-breve save in minor prolation but a third of a breve, the semitone not exactly half a tone, and the semiditonus or minor third not half a ditone or major third, which would be a single tone, but a tone and a semitone.

Although French ars nova theory was well established in England by the time John of Tewkesbury finished his Quatuor principalia on 4 August 1351,28 it was very far from silencing the native woodnotes wild. John Hauboys, by entrenched error called Hanboys,29 from Great or Little Hautboys in Norfolk, although writing his Summa c.1370, largely based himself on Handlo but still gave the note beyond the long the old name of double long, duplex longa, even when it contained three longs, and applied larga to its multiple, equivalent to nine longs if it contained three perfect double longs, or a lower number (even as low as four) if it was imperfected (Lefferts 1991: 198):

larga aliquando valet novem longas, aliquando octo, aliquando septem, aliquando sex, aliquando quinque, aliquando quatuor.

(p.158) The large is sometimes worth nine longs, sometimes eight, sometimes seven, sometimes six, sometimes five, sometimes four.30

4.2.2 Short notes

Even in France there was at first variation below the breve; in England it abounds, the constant feature till late in the century being refusal to accept imperfection of the breve by a semibreve, let alone of a semibreve by a minim. Whereas the Tractatus author refuses to go beneath the minim on philosophical grounds (Reaney 1966: 40):

cum nulla vox sit minor minima, quia minus minimo non est dandum in rerum natura

since no note is less than the minim, because a thing less than the least is not to be admitted in nature,31

Walter of Evesham observes (Hammond 1970: 128):

sed quia continuum est divisibile in infinitum, et tempus continuorum est, voces quidem sunt mensuratae temporibus quare divisibiles erunt in infinitum

But since a continuum is infinitely divisible, and time is one of the continua, notes are measured in units of time and will therefore be infinitely divisible.

He states (ibid.) that former musicians (priores) divided the breve into a minor and major semibreve, but the moderns divide it into three, although it may also be found divided into six or seven parts improperly still called semibreves. The semibreve in its turn may be divided into three parts ‘quas minutas voco’ (‘which I call minutae’).

John Torkesey, thought to have died in 1340, devised a very popular diagrammatic presentation of note-values with a brief introductory exposition, in which the breve is divided, on the same ternary principle, into semibrevis, minima, and simpla (Gilles & Reaney 1966: 58); the latter term is cited from other sources by the DMLBS. Willelmus follows suit, but renames the last two minuta and minima, thus making the minima the smallest note as its name implies, but with the alternative name crocheta, in modern English ‘crotchet’ (p.159) (Reaney 1966: 26). Handlo recognises not only the major and the minor semibreve of the ars antiqua distinction, marking the former with a down-ward stem, and the minima as used in the ars nova yet still written without its stem, but also a minorata or ‘lessened’ semibreve equivalent to two minims; Hauboys, taking over these divisions in his turn, investigates various ways of distinguishing their values in notation (Lefferts 1991: 262–4).

Here and elsewhere Handlo claims, with quotations, to be following ‘Johannes de Garlandia’ (Lefferts 1991: 110–12). There is no trace of the quotations or the doctrines in either the original or the revised treatises associated with that name, but since de Garlandia in any given case might be the French surname ‘de Garlande’, the English surname ‘Garland’, or a badge of participation in the Paris faculty of arts (Rasch 1969: 130–4; Reimer 1972: i. 16), there must have been numerous Johns ‘de Garlandia’ at any one time.32 From the character of this man’s teachings Rasch (1969: 55) concludes that he must have been an Englishman; we presumably meet him again in the 14th-century English theorist Roger Caperon, who undertakes to take further the writings ‘magistri mei reverendi Johannis de Garlandia’ (Bevilacqua 2008: 5), ‘of my to-be-revered master [i.e. teacher]33 Johannes de Garlandia’.

Handlo’s Garlandia occasionally uses minor by itself in such a way that it appears to be rather a noun by itself than an adjective with semibrevis understood (Lefferts 1991: 110):

minimas et minoratas agnoscere oportet. nam minor semibrevis tres minimas valet, brevis valet tres minores, ergo brevis novem minimas valebit.

It is necessary to recognise minims and minoratae. Now the minor semibreve is worth three minims, the breve is worth three minores, therefore the breve will be worth nine minims.

Just as minorata has here become a noun even though Garlandia speaks of minoratae semibreves in the next rule, so has minores even though he goes on to say that minims should be written like semibreves minores;34 in the absence from the context of major semibreves it is impossible to understand a contrastive ‘minor ones’. The noun minor also appears in Lefferts’s Anonymous II (2001: 222), who also divides the minim into two semiminims sneaked in as it were through the servants’ entrance, with no name and no corresponding rest; (p.160) in the latter respect, as we learn from Hauboys (Lefferts 1991: 338–42), he differs from Brother Robert ‘de Brunham’, whose notation of rests otherwise resembles his but who allows the semiminim a rest of its own.35

Although Hauboys purports to be quoting Brother Robert’s own words (sic dicendo, ‘saying thus’), the account of rests below the breve merely states that they are ut supra (‘as above’), which must refer to the preceding exposition (Lefferts 1991: 336–8). It is therefore not certain whether or not he anticipated Hauboys’s terminology, used in this citation and elsewhere, in which what are usually called semibreve, minim, and semiminim are minor, semiminor, and minima (Lefferts 1991: 192):

et sicut sunt octo toni sive modi, sic sunt octo species figurarum, scilicet larga, duplex longa, longa, brevis, semibrevis, minor, semiminor, minima.

And as there are eight (psalm-)tones or modes, so there are eight kinds of note-shapes, namely the large, duplex longa,36 long, breve, semibreve, minor, semiminor, minim.

Both these passages are recorded by the DMLBS. Other English writers use minor or simplex minor for the minim and minima or duplex minor for the semiminim (Lefferts 2001: 240).37

4.2.3 Erect notes

Handlo (Lefferts 1991: 82–6) states that if the stem on the right-hand side of a long goes up instead of down, it is called an erect long (erecta longa) and indicates that the pitch is raised by a semitone; if the upward stem is on the left instead, the note is an erect breve (erecta brevis), and likewise indicates the raising by a semitone.38 Outside the expected echo in Hauboys (pp. 220, 236) these erect notes reappear only in another English source, the London Anonymous II (Lefferts 2001: 222–4, 227), though as note-shapes they are reproduced, without explanation of their use, as ‘appropriated upwards’ (the author regularly uses appropriare for ‘provide with a stem’) in the Englishinfluenced Omnis ars sive doctrina (Sweeney 1971: 32–3, cf. Lefferts 2001: 242).39

(p.161) 5. The 15th Century

About the turn of the century, Thomas Walsingham, best known as a chronicler,40 produced his Regulae de musica mensurabili, brief yet long enough to be inconsistent in its terminology (Reaney 1983: 74–98) by reason of interpolation (Lefferts 2001: 243–4): having begun by listing six levels of note-length, larga, long, breve, semibreve, minim, and crocheta, it switches in chapter 3 to longissima, longior (‘which some call a perfect large’), long, breve, brevior, brevissima or minima; the first six have imperfect counterparts imperficiens [sic]41 longissima, semilongior (‘which some call an imperfect large or semilarga’),42 semilonga, semibrevis, semibrevior, but the minim is indivisible and therefore unimperfectible (Reaney 1983b: 81):

sed nunc addita est ulterius, id est ultra minimam, scilicet non per artem sed per placitum, quae dicitur crocheta

But now there has been added further, that is beyond the minim, not of course by the rules of the art but arbitrarily, what is called the crotchet.

This chapter, which interrupts the sequence of topics announced at the outset, has clearly come in from elsewhere; but even without it Walsingham is not on top of his material: of the five ways in which he asserts that a long may be imperfected (ibid. 82), three yield not imperfect longs but altered breves (admittedly with the same temporal result), and having in this discussion used tempus correctly, when he comes to his chapters de cantu perfecto et imperfecto (ibid. 84–9) he uses modus when he means tempus and tempus when he means prolation.

The largissima reappears in the anonymous ragbag De origine et effectu musice (or as the explicit has it De effectu musice speculative tractatulus), this time accompanied by a largior equivalent (if perfect) to six perfect longs, like the old duplex longa (Reaney 1983a: 114, 117); evidently the author reasoned that if the positive and the superlative degrees could name a note, so should the comparative. The remaining notes are long, breve, semibreve, minim, ‘crocheta vel simpla’, this last being incapable of alteration (ibid. 114); the largissima is said to contain twelvescore minims (‘xiiXX’, British Library, (p.162) Lansdowne MS 763, f. 58r), which Reaney (ibid. 117) emends to 243, but not 729 of those second-class citizens crotchets.

The same manuscript that contains this work, and also the Musica manualis mentioned above, includes twenty texts of music theory in all, copied by Wylde, three of them in English (Meech 1935). As such these lie outside our purview; but the second, anonymous treatise includes the instruction to begin and end one’s ‘countergemel’ on a unison (Meech 1935: 261). This is the voice added in a specifically English form of counterpoint known as gymel—a term derived from gemellus, ‘twin’—in which a voice-part was divided, one voice proceeding mainly in thirds and sixths against the other; the word, known in musical manuscripts as a voice-label and used by the Scottish poets Robert Henryson and Gavin Douglas, is also found, describing the English practice, in the De preceptis artis musice et pratice compendiosus libellus of the theorist Guilielmus Monachus, writing in Italy but not necessarily an Italian (Blackburn 2001a: 337 n. 110).

From this time vernacular languages were beginning to encroach on Latin as vehicles of musical teaching, above all in Spain (Blackburn 2001a: 309–16). Both Latin and Italian were used at Lucca by the expatriate English theorist John Hothby (c.1430–87), whose treatises (several still unpublished) survive only in variant versions, often faulty, sometimes incomprehensible, originally taken down by his students (Blackburn 2001a: 319–20; 2001b: 749). He devised a peculiar terminology to express, or to conceal, radical theories (Blackburn 2001a: 324–5; 2001b:750); thus ordo, or in Italian ordine, denotes one of six realisations of a note (natural, flat, sharp, and three others available only on his own special keyboard, with red keys for quartertones), so that B flat, which others called b fa or trite synemmenon, is in Hothby’s Latin or Italian ‘A of the second order’, this order being defined as the black keys on his ‘sounding monochord’ (Tractatus quarundam regularum artis musice, British Library, Add. MS 36986, f. 5r). He calls the solmisation syllables nomina offitialia, ‘official names’ (ibid.), extends the Greek-derived terms for the fourth, fifth, and octave to the other intervals to form the series diadion, diatrion, diatessaron, diapente, diaex, diaepta, diapason (ibid. f. 5v), and styles the hexachords acies, ‘lines of battle’ (f. 15v). Nevertheless, in the normal way of radicals he was conservative, even reactionary, in other matters: though of a later generation and compelled by usage to allow notes below the minim, namely the semiminima, croma, and semicroma (the latter two still the Italian names for the quaver and semiquaver), he still, in his Regulae cantus mensurati as reported in a Florentine manuscript, objected to the term semiminima, admitting that it was in use (Reaney 1983b: 20):

(p.163) ultra minimam non datur minimum, licet habeamus in usu abusive hoc vocabulum semiminima quae dicitur quasi minimae medietas; sed proprie non dicitur semiminima sed minima bis vel ter prolata eodem tempore in quo minima debet pronuntiari.

beyond the minim there is no minimum [sic], although we have in use, catachrestically, this word ‘semiminim’, which is so called as being the half of a minim. But properly it is not called a semiminim but a minim performed twice or thrice in the same time in which a minim ought to be sung.

No wonder the battle was lost.

A little further on, needing to state that a semicircle without a dot inside it marked the (imperfect) semibreve as containing two minims (i.e. being in minor prolation), he spoke of the semicircle’s vacuitudo (Reaney 1983: 21), a grandiose coinage that might be translated ‘emptihood’ and may have been inspired by the normal word plenitudo, ‘fullness’;43 just afterwards he discusses mensuration signs in which a circle or semicircle indicated major mode (minor mode and tempus being indicated by the figures 2 and 3), irrespective of its ‘fullness or emptihood’, plenitudo sive vacuitudo (since the presence or absence of the dot still indicates prolation).

This text is thought to report Hothby’s lectures more faithfully than most; in an exposition De cantu figurato secundum Hothbi —‘according to Hothby’, an expression that arouses doubt in the wary44—a manuscript in Faenza makes him speak like other theorists of the semicircle’s vacuitas (‘emptiness’), but another, in Venice, calls it vacuum (Reaney 1983b: 28, 41). The problem of determining what is Hothby’s and what a copyist’s arises again in a text known as Regulae cantus mensurati secundum Ioannem Otteby,45 known only from English manuscripts, one written at the beginning of the 16th century by the theorist John Tucke and the other copied from it, where the term radix, which we have already encountered in two different senses (see §2 above), appears in yet a third, the indication of major mode in the complex signs discussed in the Regulae considered just above indicating major mode, minor mode, tempus, (p.164) and prolation, but here preceded by another sequence with the same meaning. These are the signs for ‘mixed numbers’ in which both perfect and imperfect occur (those mensurations in which all are perfect or all imperfect having already been treated) (Reaney 1983b: 54):

ponitur etiam maxima pro numero mixto cuius radix est perfecta, similiter pro numero mixto cuius radix est imperfecta, ex quibus numeris mixtis generantur mensure quatuordecim.

The maxima is also put for a mixed number whose root is perfect, likewise for a mixed number whose root is imperfect, from which mixed numbers there are generated fourteen mensurations.

As often with Hothby, this is not as clearly expressed as one might wish, but in the list that follows, the signs are grouped according to the major mode, which suggests that that is the value intended by radix. One might wonder whether the word was imported by Tucke, whom Reaney (1983b: 13) suspects of intruding the alternative symbols into the manuscript; however, Tucke’s own writings on the subject offer no support for either notion. We may therefore ascribe radix to Hothby, who may or may not have been instigated to use the term by finding it, albeit otherwise used, in Anonymous IV, but who undoubtedly reached into the latter’s work when in an Italian treatise he designated the semibreve (h)elmuaym (McDonald 1997: 42, 46).

Tucke was, nonetheless, a terminological innovator in his own right: diaphonicos for music composed according to the heraldic colours with which he indicated proportions, concepcio for tenors increasing in duration by arithmetical progression, deductio—falsely ascribed to Boethius—for a note’s location on the monochord (Woodley 1993: 70–2, 96,102); and much else. But by now we are at the end of the Middle Ages, and in Great Britain of Latin music theory: with the possible exception of John Dygon (Dumitrescu 2007: 223), no more native music theory is known until the vernacular treatises written in Scots and English towards the end of the 16th century.

6. Context and Conclusions

Differences in the language of music theory take their place alongside the features that distinguish English music and its notation from Continental, such as in the 13th century the alternative third mode, in the 14th the consonant ‘just’ third and sixth instead of the dissonant Pythagorean, in the early 15th the use of complex colour-coding for proportions and later on the resistance to the simpler style of composition emerging across the Channel (p.165) (Wegman 2005: 105–65). That does not mean that England was cut off from developments elsewhere, which indeed would have been impossible when large tracts of France were subject to the English king, and numerous Englishmen studied in Paris; besides the interactions already noted, there was a time in the first half of the 15th century when English music, its distinctive style recognised, enjoyed Continental fame and influence. The English had their own way of doing things; they also had their own way of talking and sometimes of thinking about them.


Bibliography references:

Aluaş, L. F. (1996), ‘The Quatuor Principalia Musicae: A Critical Edition and Translation, with Introduction and Commentary’, PhD dissertation, Indiana University, UMI no. 9627364.

Baltzer, R. A. (2001), ‘Johannes de Garlandia’, in S. Sadie (ed.), The New Grove Dictionary of Music and Musicians, 2nd edn (London, Macmillan), xiii. 138–42.

Bent, M. (1978), ‘A Preliminary Assessment of the Independence of English Trecento Notation’, in L’Ars nova italiana del Trecento IV (Certaldo, Centro di studi sull’ars nova italiana del Trecento), 65–82.

Bent, M. (2001), ‘Notation, §III, 3: Polyphonic Mensural Notation, c1260–1500’, in S. Sadie (ed.), The New Grove Dictionary of Music and Musicians, 2nd edn (London, Macmillan), xviii. 129–40.

Bent, M. (2015), Magister Jacobus de Ispania, Author of the Speculum musicae, RMA monograph, (Farnham, Ashgate).

Bevilacqua, G. (2008), ‘Il Commento super Cantum di Roger Caperon: Introduzione ed edizione critica’, doctoral dissertation, Bologna.

Blackburn, B. J. (2001a), ‘Music Theory and Musical Thinking after 1450’, in R. Strohm & B. J. Blackburn (eds), Music as Concept and Practice in the Late Middle Ages The New Oxford History of Music, New Edition, iii. 1 (Oxford University Press), 301–45.

Blackburn, B. J. (2001b), ‘Hothby, John’, in S. Sadie (ed.), The New Grove Dictionary of Music and Musicians, 2nd edn (London, Macmillan), xi. 749–52.

Blackburn, B. J. (2008), ‘Properchant: English Theory at Home and Abroad, with an Excursus on Amerus/Aluredus and his Tradition’, in D. B. Cannata, G. Ilnitchi Currie, R. Charnin Mueller & J. L. Nádas (eds), Quomodo cantabimus canticum? Studies in Honor of Edward H. Roesner (Madison, WI, American Institute of Musicology), 81–98.

Burnett, C. (1986), ‘The Use of Geometrical Terms in Medieval Music: Elmuahim and Elmuarifa and the Anonymous IV’, Sudhoffs Archiv: Zeitschrift für Wissenschaftsgeschichte, 70: 198–205.

Cristante, L. (ed.) (1987), Martiani Capellae De nuptiis Philologiae et Mercurii, Liber IX, Medioevo e Umanesimo 65 (Padua, Antenore).

Desmond, K. (n.d.), ‘Omni desideranti notitiam: A Music Theory Treatise from the Fourteenth Century’, http://www.arsmusicae.org/ (accessed 18 March 2016).

(p.166) Desmond, K. (2012), ‘Texts in Play: The Ars Nova and its Hypertexts’, Musica Disciplina, 57: 81–153.

Desmond, K. (2015), ‘Did Vitry Write an Ars vetus et nova?’, Journal of Musicology, 32: 441–93.

Dumitrescu, T. (2006), John Dygon’s Proportiones practicabiles secundum Gaffurium (Practical Proportions according to Gaffurius): New Critical Text, Translation, Annotations, and Indices, Studies in the History of Music Theory and Literature 2 (Urbana and Chicago, IL, University of Illinois Press).

Dumitrescu, T. (2007), The Early Tudor Court and International Musical Relations (Aldershot and Burlington, VT, Ashgate).

Fuller, S. (1985–6), ‘A Phantom Treatise of the Fourteenth Century? The Ars Nova’, Journal of Musicology, 4: 23–50.

Frobenius, W. (2003), ‘Johannes de Garlandia’, Die Musik in Geschichte und Gegenwart: Allgemeine Enzyklopädie der Musik, 2nd edn, Personenteil, ix. 1089–93.

Gilles, A. & Reaney, G. (eds) (1966), Johannes Torkesey, Declaratio trianguli et scuti, in G. Reaney (ed.) MS. Oxford, Bodley 842 (Willelmus): Breviarium regulare musicae; MS. British Muse[u]m Royal 12 C. VI: Tractatus de figuris sive de notis Corpus Scriptorum de Musica 12 (American Institute of Musicology), 53–63.

Hamilton, E. G. (2014), ‘Walter of Evesham Abbey and the Intellectual Milieu of Fourteenth-Century English Music Theory’, PhD dissertation, Bangor University.

Hammond, F. F. (ed.) (1970), Walteri Odington Summa de speculatione musicae, Corpus Scriptorum de Musica 14 (American Institute of Musicology).

Hammond, F. F. (ed.) (1977), Iohannis Vetuli de Anagnia Liber de Musica, Corpus Scriptorum de Musica 27 (American Institute of Musicology).

Herlinger, J. (2001), ‘Music Theory of the Fourteenth and Fifteenth Centuries’, in R. Strohm & B. J. Blackburn (eds), Music as Concept and Practice in the Late Middle Ages The New Oxford History of Music, New Edition, iii. 1 (Oxford University Press), 244–300.

Hiley, D., rev. Payne, T. B. (2001), ‘Notation III, 2: Polyphony and Secular Monophony to c1260’, in S. Sadie (ed.), The New Grove Dictionary of Music and Musicians, 2nd edn (London, Macmillan), xviii. 119–29.

Hiley, D. & Szendrei, J. (2001), ‘Notation III, 1: Plainchant’, in S. Sadie (ed.), The New Grove Dictionary of Music and Musicians, 2nd edn (London, Macmillan), xviii. 84–119.

Lefferts, P. M. (1986), The Motet in England in the Fourteenth Century (Ann Arbor, MI, UMI Research Press).

Lefferts, P. M. (ed.) (1991), Robertus de Handlo, Regule, The Rules, and Johannes Hauboys, Summa, The Summa: A New Critical Text and Translation, Greek and Latin Music Theory (Lincoln, NE, and London, University of Nebraska Press).

Lefferts, P. M. (ed.) (2001), ‘An Anonymous Treatise of the Theory of Frater Robertus de Brunham’, in M. Bernhard (ed.), Quellen und Studien zur Musiktheorie des Mittelalters, iii, Veröffentlichungen der Musikhistorischen Kommission 15 (Munich, C. H. Beck), 217–51.

McDonald, T. L. (ed.) (1997), Johannes Hothby: La Calliopea legale, Corpus Scriptorum de Musica 42 (Neuhausen, Hänssler-Verlag and American Institute of Musicology).

(p.167) Meech, S. B. (1935), ‘Three Musical Treatises in English from a Fifteenth-century Manuscript’, Speculum, 10: 235–69.

Michels, U. (ed.) (1972), Johannis de Muris Notitia artis musicæ et Compendium musicæ practicæ; Petrus de Sancto Dionysio: Tractatus de musica, Corpus Scriptorum de Musica 17 (American Institute of Musicology).

Palisca, C. V. (2001), ‘Theory, Theorists’, §§1–10, in S. Sadie (ed.), The New Grove Dictionary of Music and Musicians, 2nd edn (London, Macmillan), xxv. 360–76.

Pinegar, S. (1991), ‘Textual and Conceptual Relationships among Theoretical Writings on Measurable Music of the Thirteenth and Early Fourteenth Centuries’, Ph.D. dissertation, Columbia University.

Rasch, R. A. (1969), Johannes de Garlandia en de ontwikkeling van de voor-Franconische notatie (Brooklyn, NY, Institute of Mediæval Music).

Reaney, G. (ed.) (1966), MS. Oxford, Bodley 842 (Willelmus): Breviarium regulare musicae; MS. British Muse[u]m Royal 12 C. VI: Tractatus de figuris sive de notis Corpus Scriptorum de Musica 12 (American Institute of Musicology).

Reaney, G. (1983a), ‘The Anonymous Treatise De origine et effectu musicae: An Early 15th Century Commonplace Book of Music Theory’, Musica Disciplina, 37: 101–19.

Reaney, G. (ed.) (1983b), Johannes Hothby, Opera omnia de musica mensurabili; Thomas Walsingham, Regulae de musica mensurabili, Corpus Scriptorum de Musica 31 (Neuhausen, Hänssler-Verlag and American Institute of Musicology).

Reaney, G., Gilles, A. & Maillard, J. (eds) (1964), Philippi de Vitriaco Ars nova, Corpus Scriptorum de Musica 8 (American Institute of Musicology).

Reckow, F. (1967), Der Musiktraktat des Anonymus 4, 2 vols, Beihefte zum Archiv für Musikwissenschaft 4–5 (Wiesbaden, Franz Steiner).

Reimer, E. (ed.) (1972), Johannes de Garlandia: De mensurabili musica. Kritische Edition mit Kommentar und Interpretation der Notationslehre, 2 vols, Beihefte zum Archiv für Musikwissenschaft 10–11 (Wiesbaden, Franz Steiner).

Ruini, C. (ed.) (1977), Ameri Practica artis musice, Corpus Scriptorum de Musica 25, (American Institute of Musicology).

Sanders, E.H. (1962), ‘Duple Rhythm and Alternate Third Mode in the 13th Century’, Journal of the American Musicological Society, 15: 249–91.

Snyder, J. L. (ed.) (2006), Theinred of Dover’s De legitimis ordinibus pentachordorum et tetrachordorum: A Critical Text and Translation with an Introduction, Annotations, and Indices, Musical Theorists in Translation 18 (Ottawa, Institute of Mediaeval Music).

Sweeney, C. (ed.) (1971), Anonymus, De musica mensurabili, Corpus Scriptorum de Musica 13 (American Institute of Musicology).

Sweeney, C. (ed.) (1982), Johannis Wylde Musica manualis cum Tonale [sic], Corpus Scriptorum de Musica 28 (American Institute of Musicology).

Wegman, R. C. (2005), The Crisis of Music in Early Modern Europe 1470–1530 (New York and Abingdon, Routledge).

Wegman. R. C. (2015), ‘The World According to Anonymous IV’, in A. Zayaruznaya, B. J. Blackburn & S. Boorman (eds.), Qui musicam in se habet: Studies in Honor of Alejandro Enrique Planchart (Middleton, WI, American Institute of Musicology), 693–729.

(p.168) Whitcomb, P. (1999), ‘Teachers, Booksellers, and Taxes: Reinvestigating the Life and Activities of Johannes de Garlandia’, Plainsong and Medieval Music, 8: 1–13.

Woodley, R. (1993), John Tucke: A Case Study in Early Tudor Music Theory, Oxford Monographs on Music (Oxford, Clarendon Press).


(1.) I am very grateful to Margaret Bent, Bonnie J. Blackburn, and Peter M. Lefferts for assistance and suggestions.

(2.) For a general overview of theory in the period covered see Palisca (2001: 367–71); for the 14th and 15th centuries see Bent (1978), Herlinger (2001), and Blackburn (2001a). On notation see also Hiley and Szendrei (2001), Hiley (2001), mainly concerned with rhythmic modes, and Bent (2001).

(4.) Snyder (2006: 10–12). This is no new thing: in classical Latin numerus or its plural may mean ‘rhythm’, ‘metre’, or ‘melody’; Martianus Capella, in the treatise on music theory that comprises the last book of De nuptiis Philologiae et Mercurii, uses modus in many different music-related ways (Cristante 1987: 234).

(5.) All translations are my own, a principle that does not imply dissatisfaction with those published.

(6.) See Blackburn (2008) for a full exposition.

(7.) The two were distinguished by Rasch (1969: 88–129), Reimer (1972: i. 1–17). See also §4.2.2 below.

(9.) Reimer (1972: i. 13, cf. 91 and n.). On Anonymous IV, see Wegman (2015).

(10.) The passage from Hothby included in the DMLBS entry pertains elsewhere.

(11.) The two are dissociated in Hamilton (2014).

(12.) Burnett (1986). The rhombus is an equilateral but not rectangular figure; in the rhomboid only opposite sides and angles are equal; the trapezium is any four-sided figure that is not a square, rectangle, rhombus, or rhomboid (Euclid, Definitions 1. 22).

(13.) Reckow emends ipsam to ipsum to agree with simile, but ipsam agrees with figuram understood and simile elmuahim is predicative; cf., in the translation quoted by Burnett (1986: 203), alia simile helmuahym (‘Another [figure is] the like-the-rhombus’).

(14.) Margaret Bent compares the threefold division of tempo (more longo, <more> mediocri et more lascivo) advanced by Petrus le Viser ap. Handlo (Lefferts 1991: 104).

(15.) In BL Add. MS 4909, copied by Pepusch from Cotton Tiberius B. IX before it was damaged by the fire of 1731, this reads minima, but ‘the smallest long’ makes no sense.

(16.) Pepusch too reads longis tardis.

(17.) The manuscripts here have vel, which Reckow emends to et; clearly ‘or by a semibreve’ is contradicted by the context, and although Late Imperial and Medieval Latin not infrequently uses vel for ‘and’, the structure of the sentence tells against that reading here.

(18.) There was a similar but not identical development in Italy, which lies outside our scope; gradually, however, the ars Gallica made inroads into the ars Ytalica.

(19.) So Paris, Bibliothèque nationale de France, ms. lat. 7378A, f. 61v (Reaney et al. 1964: 57), and in the treatise Omni desideranti notitiam, §8 in Desmond (n.d.), who against Fuller (1985–6) suggests that both texts are by Vitry: see Desmond (2012: 84–103; 2015).

(20.) Duple mensuration was a new development frowned on by Jacobus.

(21.) On this maxim see Lefferts (1991: 189–93 n. 15); note too Aristotle’s hypothesis of the minimum time for actions at De Caelo 2. 6, 288ƀ31–289a1, invoked in Willelmus’ assertion of a ‘minimus sonus in musica’ (Reaney 1966: 23), ‘least sound [= shortest note] in music’; in the purported Ars nova of Vitry and in Paris lat. 7378A, f. 62r such scruples are overcome by calling the minim semiminor and the semiminim minima (Reaney et al. 1964: 24, 65). Omni desideranti notitiam knows nothing of any note shorter than the minim.

(22.) In both countries some writers understood the new system as an extension of the old, others as a fresh departure based on gradus (‘degrees’) of note-lengths (ibid.).

(23.) The term was known to Jacobus, whom Bent (2015) credits with an English education; when it resurfaces on the Continent it appears to be under English influence (Lefferts 2001: 238–43). See, however, Desmond (2015: 447–8, n. 13).

(24.) This text is one component of the conflation published as Regula de monocordo by Reaney et al. (1964: 71–8).

(25.) Reaney prints longas here and largas in the next sentence; I have restored the manuscript text, as the sense requires.

(26.) This wrongly implies that the largissima has strokes to both right and left; one would expect a parte dextra de inferius tantum, ‘to the right downwards only’, in which de inferius might easily be omitted by scribal error after dextra; however, the same wording recurs in the description of the long, figura quadrata, gerens tractatum a parte dextra tantum (‘a square note-shape with (lit. ‘wearing’) a stroke to the right only’).

(27.) We should say that its length exceeded its height.

(28.) On authorship and date see Aluaş (1996: 5–39).

(29.) Similarly Jan z Olomouce is commonly called Johannes de Olomons instead of Olomous, in both cases because a scribe to whom the name was unfamiliar, faced with a letter that might be either n or u, guessed wrong.

(30.) The next sentence, as transmitted, muddies the waters: novem longarum, quando larga de largis et duplicibus longis perfectis ponitur ante largam vel ante punctum (‘[It is] of nine longs, when a large consisting of perfect larges and double longs is placed before a large or a dot’). A large cannot itself consist of larges: evidently largis is a perseverance error (authorial or scribal) for longis.

(31.) John of Tewkesbury roundly denied that Vitry, the ‘flower of musicians’, had countenanced ‘crochutam vel semiminimam aut dragmam’ (Aluaş 1996: 382); dragma is attested in Continental authors for the half-semibreve.

(32.) A bookseller Jean de Garlande, also called John the Englishman (‘Jehan l’engleis’), has been implicated as the reviser by Whitcomb (1999).

(33.) ‘Master’, in this sentence, is not an academic title but expresses his relation to Caperon his pupil.

(34.) To avoid confusion, a small circle (signum rotundum, ‘round sign’) is to be written after three minims, two minoratae, or a lone minor (Lefferts 1991: 110–12 with 111–12 n. 76). Hauboys (Lefferts 1991: 268–9) discusses an alternative notation devised by one ‘W. de Doncastre’.

(35.) All notes from larga to minor are registered in both their perfect and imperfect varieties, equated in the line above with respectively three or two of the next lower value, and accompanied by the correponding rests; the minima is recorded without a qualifier, with two semiminimae above it. The semiminima itself has no entry.

(36.) See §4.2.1 above.

(37.) On minor in general see Lefferts (2001: 243–4)

(38.) On the visual identity between erect notes and one-stemmed plicae see Bent (1978: 73–4).

(40.) See Childs (this vol., ch. 4).

(41.) Each subsequent perfect note is said to be imperficiens, since it imperfects the value above it; but since there is no value above the longissima, and this note is worth two-thirds, not one-third, of it, here the word required is imperfecta.

(42.) The latter term was used in the mid- or late 14th century, along with larga, by Johannes Vetulus de Anagnia (Giovanni Vecchi of Anagni), whom Walsingham cannot be supposed to have read; see Hammond (1977: 33). It would appear that he is acquainted with English theory, but nothing is known of his life.

(43.) Although in certain abstracts -tudo is the standard suffix, in general the competition between-monia, -tas, and -tudo was won in Golden Age Latinity by -tas; the rival forms had an archaic feel, but for that very reason might, when the taste for Early Latin revived, be accorded greater dignity or weight (see Aulus Gellius, Noctes Atticae 17. 2. 19). The adjectives plena and vacua for white and black notes respectively are standard.

(44.) Ars nova treatises secundum Philippum de Vitriaco or secundum Johannem de Muris cannot be relied upon for the unvarnished teachings of those masters. This is obvious when the master can still speak for himself: John Dygon, in his Proportiones practicabiles secundum Gaffurium from the early 16th century, besides adding or substituting his own music examples, incorporates matter apparently of his own devising but in any case not taken from Gaffurius (Dumitrescu 2006: 38–47).

(45.) On the variations in the surname see Woodley (1993: 52 n. 1) and Blackburn (2001b: 749).