(from Gk. isos: ‘equal’ and rhythmos: ‘rhythm’).
A modern term applied with varying degrees of strictness to the periodic repetition or recurrence of rhythmic configurations, often with changing melodic content, in tenors and other parts of 14th- and early 15th-century compositions, especially motets. Since its introduction, however, the term has been more widely applied than is warranted, often with conflicting meanings. It belongs to a family of descriptive terms including ‘isomel(od)ic’ (see Isomelism), ‘isochronous’, ‘isosyllabic’ and ‘isometric’; for ‘isoperiodic’ and ‘panisorhythm’ (where all voice-parts of a composition participate in rhythmic repeats) see below.
4. England, Italy: isorhythm outside motets.
5. Generic status; limits of the term.
MARGARET BENT
No equivalent term was used or needed in medieval theory, which instead used the words ‘color’ and ‘talea’; these now designate tenor melodic and rhythmic units respectively, and are more supple analytical instruments than any single concept of ‘isorhythm’, although then they were less clearly distinguished (see Color, (1) and Talea). Johannes de Muris (Libellus cantus mensurabilis, ed. in CoussemakerS, iii, 58, with corrections by U. Michels: Die Musiktraktate des Johannes de Muris, Wiesbaden, 1970, p.49), among others, applied the term ‘color’ to the repetition of a rhythmic pattern to different pitches, but added that musicians commonly distinguished ‘color’ as the repetition of the same pitches to different rhythms and ‘talea’ as the repetition of the same rhythms to different pitches. This accords both with modern usage and with instructions for tenor repetition in several musical sources, including ‘color’ for melody in Du Fay's O gemma, lux and Billart's Salve virgo virginum, and ‘talea’ for rhythm in Alpha vibrans/Cetus (ed. in PMFC, v, 1969, no.25 and CMM, xxxix, 1965), Ciconia's Petrum Marcello and Sarto's Romanorum rex. A similar distinction is made by the anonymous vernacular Florentine treatise (ed. in CSM, v, 1957, p.56) and the Berkeley treatise of 1375 (ed. and trans. O.B. Ellsworth, Lincoln, NE, 1984, pp.180–81). Most other Italian theorists follow de Muris's near equation of color and talea (Prosdocimus de Beldomandis: Tractatus practice … ad modum Ytalicorum, ed. in CoussemakerS, iii, pp.228–48; Ugolino of Orvieto: Declaratio musicae disciplinae, ii, ed. in CSM, vii, 1960).
Johannes Boen (Ars, c.1355; ed. in CSM, xix, 1972), perhaps followed by the late 14th-century author of the Tractatus figurarum (see Egidius de Murino), used ‘color’ (‘colorare’) for the division of the tenor melody chosen to be ordered (‘ordinare’, as in the 13th-century ‘ordo’, ‘ordines’) into the rhythmically identical groups now called ‘taleae’. Boen cited specific examples: in Vitry's Impudenter circuivi/Virtutibus, to what we would call the second color (melody) statement ‘the composer applied the same color [rhythmic disposition, what would now be called talea] as before’. (This 30-note tenor is disposed in five six-note ‘parts’ – we should say ‘taleae’ – then the whole melody is repeated in halved values.) Boen also cited Apta caro/Flos virginum, likewise with a 30-note color, stated twice: ‘but then he split [the whole 60-note tenor] into three [rhythmic] parts, 20 notes each, and by an identical arrangement preserved beautiful color in the succeeding two parts’. A similar overlapping of color and talea is seen in Machaut's motet Fons tocius O livoris/Fera pessima (ex.1); another is exemplified by the late 14th-century Anonymous V (Ars cantus mensurabilis, ed. C.M. Balensuela, Lincoln, NE, 1994, p.258), also from a surviving motet, Rex Karole/Leticie pacis (ed. in PMFC, v, 1986, no.26), whose tenor overlaps color and talea with five 24-note rhythmic statements imposed on two 60-note melodic statements. The same theorist gives Ida capillorum/Portio nature as an example of color: the same sounds are repeated but ‘under different figures’ (p.256); the beginnings of these four statements are shown in ex.2. The same tenor is ‘isorhythmic’ in notation but not in result; it is read successively in perfect and imperfect time (i.e. mensural transformation), then again in diminution at the next note-level down, also with mensural transformation. While theorists discussed color and talea mainly with reference to the tenor, contemporary compositions cultivated isorhythmic repetitions (without diminution) in other voices, most clearly in hockets and where the taleae join, and in some cases consistently in all parts, for which Apel used the term ‘panisorhythm[ic]’ (1955, pp.139–40). None of the theorists' examples, of which this is a virtually complete list, is panisorhythmic; their tenor plans differ, and there was no single isorhythmic paradigm. Theorists and musical repertory alike show more interest in cultivating variety than identity.
The German word Isorhythmie was coined by Friedrich Ludwig in 1904 (SIMG, v, p.223) to describe exact rhythmic repeats, to different melodies, in the 13th-century motetus part of On parole/A Paris/Frese nouvele (F-MOf H196, no.302, 368v–369v; ed. Y. Rokseth: Polyphonies du XIIIe siècle, Paris, 1935–9, and in RRMMA, ii-viii, 1979). He next applied it in 1910 (pp.444–5), still for the 13th century, to successive phrases of equal length but not necessarily the same rhythm, a phenomenon whose 14th-century use Besseler (AMw, 1926, p.201, n.1) called ‘isoperiodic’ (the German noun is Isoperiodik), meaning that ‘the upper voices only follow the plan of the lower voices in a general way or have merely a few bars rhythmically identical in each Tenor period’ (Günther, MD, 1958). Isoperiodicity, unlike isorhythm, cannot survive diminution of the overall length of a phrase. Sanders developed the idea of modular numbers to represent the periodic construction of motet upper voices bounded by rests (Grove6; 1973), sometimes non-coincident, or offset (see also Harrison, PMFC, xv, 1980/R). Ludwig (AdlerHM) extended the term ‘isorhythm’ to 14th-century repertory on the basis of his work on Machaut and the manuscript I-IVc, and it was this sense that Besseler adopted, listing the isorhythmic motet repertory as then known (AMw, 1926, pp.222–4), though including many motets with a very weak claim on the definition. Sanders favours defining ‘“isorhythm” in the sense of such rhythmic occurrences in all voices’ (Grove6).
The more closely panisorhythm was approached, the higher the generic status became: ‘the Tenor (color) is frequently repeated several times and usually made up of a number of rhythmically identical periods (taleae). If the upper voices also follow this scheme, the composition is an isorhythmic motet’ (Günther, MD, 1958, p.29). Thus the term ‘isorhythmic motet’ came to denote a distinct and more exalted genre cultivated from the 1310s to the 1440s, irrespective of scale, text or occasion.
Modern analytic formula notations have been devised to summarize isorhythmic motet structures. The systems of Besseler (1926), Reaney (CMM, xi, 1955–76, xviii), de Van (CMM, i/1, 1947) and Günther (CMM, xxxix, 1965) do not indicate color, color-talea relationships or the extent and nature of diminution. Apel (1955) adopted a simpler system to indicate color-talea relationships in the tenor only, which is likewise incomplete (see Turner, MAn, 1991). Such systems can convey overall proportions but not, or not so readily, the mensural transformations that cause them or new rhythmicization of the second color, let alone the extent of isorhythm in the upper parts. Varying combinations of letters and numerals, sometimes illogical or inconsistent, are used by editors to mark these events in the scores. Principal parallel events can be aligned, as Ludwig did in his Machaut edition; and although such layout still cannot represent overlaps and displacements, it can help the modern reader more effectively than most formulae. The analyst must consult not only editions (with their pitfalls for the unwary) but often also manuscripts. The repertory's resistance to standard formulations belies the widespread modern notion of a strict and uniform ‘isorhythmic’ principle.
From the start, motets were shaped by tenor repetition. Short repeating rhythmic-modal units (ordines; see Rhythmic modes) in 13th-century pieces are occasionally superimposed on non-coincident melodic units. Despite such repetitions, the status of ‘isorhythmic’ is now usually reserved not for the 13th-century repertory that prompted it (see the exclusions by Sanders, Grove6) but for later motets where such repetition extends to parts other than the tenor (Günther, MD, 1958), or to more ambitious schemes of a kind of ‘developing variation’. Besseler cited Se je chante/Bien dois/Et sperabit (F-MOf H196, no.294) as the earliest instance involving all voices in rhythmic recurrence in the hocket passages, but without regular tenor patterning (see Sanders, Grove6, esp. ex.2). Upper-voice correspondences were hardly present in the 13th century, but rapidly increased in the 14th, first in hocket sections and around talea joins (see ex.1). In the 14th century tenor units often became longer, and repetitions more systematic and more adventurous. The rhythmic innovations of the French Ars Nova enabled upper-voice micro-relationships to mirror the more sustained tenor durations that undergirded the structure, but no single new principle emerged that was neither anticipated in the 13th century nor extended in the 15th.
Of over 100 surviving 14th-century motets, only 15 are panisorhythmic. Many others (including some by Machaut and in I-IVc) have at least tenor isorhythm; many have extensive upper-part isoperiodicity and some exact isorhythmic repetition, especially in hockets, around talea-joins and in diminution sections (see ex.1). Before about 1350, panisorhythm occurs only in Machaut's Amours qui ha le povoir Faus Samblant/Vidi Dominum (no.15) and in four motets in I-IVc. Early datings in the 1310s have recently been suggested for some motets with upper-voice isorhythm and precocious features of notation (Leech-Wilkinson, 1995; Kügle, 1997, chap.3; see Vitry, Philippe de). Günther argued from statistics of survival and characteristics that ‘the [isorhythmic] motet with its long tradition as an art-form of the first rank has had to give way [around 1400] before the more modern polyphonic song’ (MD, 1958, p.47). This view of a declining genre is superseded by Allsen's listing (1992) of 134 mostly panisorhythmic motets (including fragments) from the first half of the 15th century. Among the better-known composers of altogether nearly 250 ‘isorhythmic’ motets are Vitry, Machaut, Ciconia, Dunstaple and Du Fay; many motets are anonymous, including 40 in I-Tn 9 (from Cyprus). Other principal manuscript repositories include the Roman de Fauvel (F-Pn fr.146; 34 motets), I-IVc (37), the Machaut manuscripts (23), F-CH 564, the Old Hall Manuscript (GB-Lbl Add.57950), I-Bc 15 and I-MOe X.I.11. (see Sources, ms, §§V, VII and IX, 1–3). These approximate figures for the repertory need adjustment to take into account different modern understandings of isorhythm; in addition, isorhythmic mass movements and many anomalous or non-isorhythmic motet forms should be considered. It was in the first half of the 15th century, and not in the 14th, as is generally believed, or in the 13th, for which Ludwig first coined the word, that the cultivation of rhythmic identity had its brief and major flowering.
Color and talea can be manipulated in many combinations. Usually there are several taleae within a color. Sometimes melodic and rhythmic units are overlapped (as in Rex Karole and several of Machaut's motets; see ex.1). Some motets present subsequent statements of the color in the same rhythm; others challenge an isorhythmic classification by presenting the repeats in mensural transformation and/or diminution. In ex.2, taleas I and III are read in perfect modus; II and IV interpret the same notation in imperfect modus and therefore do not have the same rhythmic results; the first two statements inex.3 are likewise distinguished from the third; ex.5 achieves the ‘same’ results but counted out in different, accelerating mensurations. In ex.2 taleas III and IV are read in diminution; ex.4 has a written-out diminution to which mensural transformation is also applied. In ex.3, the first statement is in augmentation in relation to the last (notated). The second color is sometimes not even a diminution of the first but independently rhythmicized and with its own separate set of internal repeats (though such distinctions are now rarely made). Occasionally, tenors are presented in retrograde. Machaut's motets with irregularly repeating song tenors have not normally been counted as isorhythmic; nor have extreme cases of mensural transformation (such as Inter densas/Imbribus, see Bent, 1992), though slight deviations due to the same principle have often been overlooked in motets commonly classified as isorhythmic.
Although the isorhythmic motet has usually been considered mainly a French phenomenon, Sanders draws attention to numerous early English instances, unknown to Ludwig and Besseler, that form an important background to the wide variety of motet styles in 14th-century England (ed. in PMFC, xv, 1980/R); about 25 have some form of tenor isorhythm (Sanders, Grove6; 1973). The Old Hall Manuscript applies French techniques to diversely ‘isorhythmic’ works; its later motets settle to a panisorhythmic English tripartite design (Allsen, 1992, chap.4), best known from Dunstaple (Bent, 1981, chap.4; see ex.3).
The earliest Italian uses of rhythmic repetition are not in motets but in madrigals: Landini's Si dolce non sonò (in praise of Vitry) and Lorenzo da Firenze's Povero zappator, in which short units are immediately followed by their own diminutions and the resulting larger patterns are repeated. Only after 1400 did isorhythm enter the Italian tradition of ceremonial and occasional motets (Bent, 1992; Allsen, 1992, chap.3). In each half of Ciconia's motet Petrum Marcello the tenor follows the undiminished form immediately with its diminution, while in two other motets Ciconia makes the second half an undiminished rhythmic replication, in all voices, of the first. The tenor of his Doctorum principem is read in three different mensurations, and is therefore not isorhythmic in result. In both the Italian and English repertories rhythmic repetition takes its place among a wide range of techniques less well served by the criteria developed largely for French repertory.
Various forms of isorhythm also appear in other French genres, including Machaut's ballade S'Amours ne fait (no.1, before 1350) and in three rondeaux in the late 14th-century Chantilly manuscript (F-CH 564) by Matteo de Sancto Johanne (Je chante ung chan), Haucourt (Se doit il plus) and Vaillant (Pour ce que je ne say), as well as in the 15th-century English goliardic-texted drinking song O potores in GB- Lbl 3307. A few 14th-century mass movements (notably Machaut's) employ some form of isorhythm, and around 1400, especially in England, isorhythmic principles of various kinds and strictness are applied to mass movements, separately or in cyclic combination.
The formal expansion enabled by 14th-century notational advances is paralleled by the 15th-century extension of the principles and spirit of these structuring techniques to the related movements of mass cycles, and to extended motet or antiphon compositions, often in several proportioned sections, articulated by mensural change, vocal scoring and isorhythm. It is hard to establish boundaries for the concept of isorhythm within the evolution of these large forms; there is an ongoing body of music governed by mensurally, proportionally or rhythmically (but not necessarily isorhythmically) structured tenors or sections, representing the evolution rather than the cessation of a tradition (Dammann, AMw, 1953; Brothers, JAMS, 1991). Some of Du Fay's grandest motets of the 1430s have only a single talea per color, which precludes intra-sectional upper-part isorhythm, thus calling their isorhythmic credentials into question.
Indeed, the cyclic mass extends principles of rhythmic unification and proportioned sections defined by mensuration change to Ordinary cycles on a single cantus firmus. The movements of Dunstaple's Jesu Christe Fili Dei are related to each other by tenor isorhythm; in addition, each surviving movement is internally isorhythmic, with two cantus firmus statements, the second in diminution, each with its own proportioned (but not isorhythmic) perfect–imperfect time change. The anonymous ‘Caput’ Mass has tenor identity between all movements, but two differently rhythmicized statements of the cantus firmus in each, respectively in perfect and imperfect time. Dunstaple's Mass Da gaudiorum premia and Power's Alma Redemptoris Mass likewise have tenor identity between but not within movements, with change from perfect to imperfect time; the length of non-tenor duets varies among movements. Rex seculorum presents a differently rhythmicized version of the same chant in each movement, but retains the same chant divisions between perfect and imperfect time sections. The movements of Du Fay's Missa ‘Se la face ay pale’ are unified by single or multiple isorhythmic statements of the cantus-firmus, and by carefully controlled proportions. On the isorhythmic status of such cases, as on the cantus-firmus based sectional motets and antiphons of the later 15th century, opinion remains divided.
The emphasis on identity has fostered a view of the isorhythmic motet as a rule-bound monolith, whence it became the prestigious and defining genre of the French Ars Nova, to the detriment of the varied range of motet strategies both covered by and excluded from it: ‘the grandiose manifestation of the speculative medieval view’ (Dammann, AMw, 1953, p.16). It was precisely during the period (1920s to 50s) when serialism was introduced and evolved to total serialization that medievalists rejoiced in uncovering a validating intellectual construct which, in its purest form, could account for every note of compositions. In the 20th century composers including Birtwistle, Maxwell Davies, Wuorinen, Messiaen and Berg used isorhythm (see Kügle, MGG2).
Number and proportion have been stressed as guiding principles of motet construction and isorhythmic diminutions (Sanders, 1973; Trowell, PRMA, 1978–9; Bent, 1990; Bent and Howlett, 1990; Brothers, 1991; Turner, 1991; Bent, 1992; see also Du fay). Combinations of numbers, structural features and allusions remain the basis for identifying linked pairs or groups of motets (whether by the same or, as homage or competition, different composers) and numerous instances of allusion and play in which one motet acknowledges another (such as the series of ‘musician’ motets, mostly ed. in PMFC, v and xv, the Marigny motets, in F-Pn fr.146; see also Leech-Wilkinson, PRMA, 1983; Allsen, 1992, chap.6; Kügle, 1997, chap.3). The combination of mensural transformation and proportional diminution mentioned above in Ida capillorum/Portio nature (see ex.2) is also conspicuous in the Credo Omni tempore (Bent, 1990). But further examination shows that most such diminutions, and any irregularities of result, are due to a mensural strategy with proportional consequences, proportions that may indeed be deliberate and reflected in other quantifiable aspects of the motet, such as textual elements. In the 14th century diminution (see Diminution, §2) was defined not (as is now usual) by numerical proportion, but as the substitution of the next lower note value, which may produce an asymmetrical relationship; the resulting proportion, regular or irregular, is a consequence of this, not the cause. For example, Humane lingue/Supplicum voces (PMFC, xv no.36; see ex.4), presents the tenor color first in normal values (in imperfect modus, perfect tempus) then in written-out diminution (in perfect tempus, minor prolation) at the next level down. This produces different results: the perfect-time notes take a third of their former value, the imperfect (coloured) half.
Recent work challenges the continuing appropriateness of the term ‘isorhythmic motet’ in the face of increasingly refined analyses, new repertories and anomalous forms marginalized as motets mainly because they are not ‘isorhythmic’ (Bent, 1992; Kügle, 1997, chap.3). A more neutral general term, or a repertory of specific terms, would suit a fuller range of structuring techniques. Several procedures commonly subsumed under ‘isorhythm’ do not, or do not necessarily, produce rhythmic identity; these include:
(i) newly rhythmicized second color statements (as in Vos/Gratissima, Firmissime/Adesto, Douce/Garison);
(ii) mensural transformation of a color repeat. Such transformation between perfect and imperfect relationships will not always result in the ‘different’ rhythms of exx.2 and 3, depending on the permutations and note-values actually used. The same notation and the same process may produce either the same or different results; it is therefore wrong to classify all such cases as isorhythmic, and artificial to segregate differing outcomes generated by the same procedure. Some such transformations have been loosely classified as diminutions because the tenor notes become progressively shorter; but as in Sub Arturo plebs (ex.5), an imperfect long whose breves successively contain nine, six and four minims is still an undiminished but mensurally transformed long in each statement. The resulting proportions are contrived by mensuration signs and named in the motetus text as ‘twice by hemiola’. This tenor is strictly isorhythmic, not because of its transformative process, but only because it avoids shorter note values that would have been subject to alteration and imperfection thereby producing different rhythms.
(iii) diminution of a color repeat. This involves the substitution of a note of the next level down, a breve for a long, etc.; such diminution can be applied mentally, or it can be written out. When duple and triple relationships are reflected in the diminution process, the resulting rhythms are indeed the same (isorhythmic), and the result is, for example, ‘by half’, as indeed some theorists say. But if those duple and triple relationships shift, or if successive statements invoke different mensurations with different applications of alteration and imperfection, their relationship can no longer be properly described as isorhythmic.
Mensural transformations and diminution can each produce the same or slightly or extremely different internal rhythmic relationships; on the other hand, apparently slight differences may result from new rhythmicizations of the color, while some deceptively extreme mensural essays (such as Inter densas/Imbribus) derive from the same notation, as can retrograde forms and canons. To create an isorhythmic/non-isorhythmic distinction within the conflated categories of mensural and diminutional transformation obscures fundamental differences between these categories, as does modern notation. Only exact repetitions with no change of mensuration and no diminution can reliably, if trivially, meet isorhythmic criteria; other repetitions may only do so by virtue of constraints such as the avoidance of variable note values. In addition, an isorhythmic classification privileges one particular kind of periodic repetition at the expense of melodic and verbal craft, all of which are interrelated in complex and varied ways; it subordinates the artistic cultivation of variety, difference and displacement, such that these are noted negatively, as absence, irregularity or incompleteness of isorhythm. Composers and theorists throughout the period cultivated variety rather than uniformity: almost every motet of the period is a unique essay in difference not identity. As a descriptive term of limited application, isorhythm is unproblematic; but as an overall validating name for a genre, it is ripe for reconsideration.
See also Discant; Mass, §II; Motet, §I; and Old Hall Manuscript.
AdlerHM (‘Die geistliche, nichtliturgische, weltliche einstimmige und die mehrstimmige Musik des Mittelalters’)
Grove6 (E.H. Sanders)
MGG2 (K. Kügle)
F. Ludwig: ‘Die 50 Beispiele Coussemaker's aus der Handschrift von Montpellier’, SIMG, v (1903–4), 177–224
F. Ludwig: Repertorium organorum recentioris et motetorum vetustissimi stili (Halle, 1910/R as SMM, vii), 444–5
H. Besseler: ‘Studien zur Musik des Mittelalters’, AMw, vii (1925), 167–252; viii (1926), 137–258
H. Besseler: Die Musik des Mittelalters und der Renaissance (Potsdam, 1931/R)
R. Dammann: ‘Spätformen der isorhythmischen Motette im 16. Jahrhundert’, AMw, x (1953), 16–40
W. Apel: ‘Remarks about the Isorhythmic Motet’, L'Ars Nova: Wégimont II 1955, 139–48
G. Reichert: ‘Das Verhältnis zwischen musikalischer und textlicher Struktur in den Motetten Machauts’, AMw, xiii (1956), 197–216
U. Günther: ‘The 14th-Century Motet and its Development’, MD, xii (1958), 27–58
K. Mixter: ‘Isorhythmic Design in the Motets of Johannes Brassart’, Studies in Musicology: Essays … in Memory of Glen Haydon, ed. J. Pruett (Chapel Hill, NC, 1969), 179–89
W. Dömling: ‘Isorhythmie und Variation’, AMw, xxviii (1971), 24–32
E.H. Sanders: ‘The Medieval Motet’, Gattungen der Musik in Einzeldarstellungen: Gedenkschrift Leo Schrade, ed. W. Arlt and others (Berne, 1973), 497–573
A. Ziino: ‘Isoritmia musicale e tradizione metrica mediolatina nei mottetti di Guillaume de Machaut’, Medioevo Romanzos, v (1978), 438–65
B. Trowell: ‘Proportion in the Music of Dunstable’, PRMA, cv (1978–9), 100–41
M. Bent: Dunstaple (London, 1981)
D. Leech-Wilkinson: Compositional Procedure in the Four-Part Isorhythmic Works of Philippe de Vitry and his Contemporaries (Cambridge, 1983)
D. Leech-Wilkinson: ‘Related Motets from Fourteenth-Century France’, PRMA, cix (1983), 1–22
M. Bent: ‘The Fourteenth-Century Italian Motet’, L'Europa e la musica del Trecento: Congresso IV: Certaldo 1984: L’Ars Nova italiana del Trecento, vi (Certaldo, 1992)], 85–125
P.M. Lefferts: The Motet in England in the Fourteenth Century (Ann Arbor, 1986)
M. Bent: ‘The Yoxford Credo’, Essays in Musicology: a Tribute to Alvin Johnson, ed. L. Lockwood and E. Roesner (1990), 26–51
M. Bent and D. Howlett: ‘Subtiliter alternare: the Yoxford Motet O amicus/Precursoris’, CM, nos.45–7 (1990) [Sanders Fs, issue, ed. P.M. Lefferts and L.L. Perkins], 43–84
T. Brothers: ‘Vestiges of the Isorhythmic Tradition in Mass and Motet, ca. 1450–1475’, JAMS, xliv (1991), 1–56
C. Turner: ‘Proportion and Form in the Continental Isorhythmic Motet c. 1385–1450’, MAn, x (1991), 89–124
J.M. Allsen: Style and Intertextuality in the Isorhythmic Motet 1400–1440 (diss., U. of Wisconsin-Madison, 1992)
M. Bent: ‘The Late-Medieval Motet’, Companion to Medieval and Renaissance Music, ed. T. Knighton and D. Fallows (London, 1992), 114–19
L. Lütteken: Guillaume Dufay und die isorhythmische Motette (Hamburg, 1993)
D. Leech-Wilkinson: ‘The Emergence of Ars nova’, JM, xiii (1995), 285–317
K. Kügle: The Manuscript Ivrea, Biblioteca capitolare 115: Studies in the Transmission and Composition of Ars Nova Polyphony (Ottawa, 1997)