Guillaume de Machaut

Machaut [Machau, Machault], Guillaume de [Guillelmus de Machaudio]

Was born in Reims or Machault, Champagne, c1300 and died in Reims, April 1377. Was a French composer and poet.

WULF ARLT

1. Introduction.
Machaut is the most important poet and composer of the 14th century, with a lasting history of influence. His unique oeuvre, contained, thanks to the composer’s own efforts, in manuscripts that include only his works, stands in many respects for itself: in terms of its volume, its poetic and compositional formulation and quality, but also in the number of genres in whose development Machaut played a crucial role. In the compilation and ordering of his works as well as in the testimony of the texts themselves there is a wealth of information about Machaut’s self-awareness and about the production of his works and manuscripts. This ranges from general remarks about poetics and other aesthetic concepts to details about the composition of particular pieces, questions about their fixing and transmission in writing and their realization in sound. Biographical details also allow the works to be placed in a social context.

The greater part of the manuscripts containing his works is taken up by poetry that is not set to music. This comprises over 15 lengthy narrative dits (each with up to 9000 lines) and a collection of lyric poetry known as Loange des dames. Most of the dits are concerned with those members of the high nobility with whom Machaut was in close contact. They bring together allegorical representation, in the tradition of the Roman de la rose, and additional exempla related to historical events and individuals (for example, from the Ovide moralisé), in an instructive framework, to which the author’s repeated designation of the works as ‘traité’ corresponds. Thus the Remede de Fortune (written before 1342) contains nine compositions presented as paradigms of lyric genres. The collection of lyrics ‘ou il n’a point de chant’ (‘where there is no music’) – its title of Loange des dames comes from a rubric given in one of the posthumously copied complete-works manuscripts – contains about 280 poems from the tradition of amours courtois, its content occasionally overlapping with the collection of musical works and dits. It is made up principally of approximately 200 ballades and exactly 60 rondeaux.

In the history of polyphonic music, Machaut is the first artistically important composer of polyphonic music to be known by name. His output holds a key position in the transition between the new ideas that took hold in the decade around 1300 and the music of the late Middle Ages; as a poet-musician he brought together the traditions of secular monophony and the new techniques of the Ars Nova. His 19 extensive lais are a high point in the – by then – long history of this form; the 23 motets take up the achievements of Philippe de Vitry; his Mass is the first cyclic, through-composed setting of the Ordinary. As with the Hoquetus David, the Complainte and Chanson royale (the latter two set to music only in the Remede de Fortune) represent a paradigmatic involvement with older forms. It is critical for the assessment of Machaut’s historical position that for the first time French texts are set in subtly-composed works of distinctive and individual character and that functional and structural differentiation between the three so-called formes fixes is now evident: the new polyphonic ballade, of which Machaut wrote 41, making up the bulk of his lyrics set to music, the 22 polyphonic rondeaux and the virelai, called ‘chanson baladee’ and, in the case of the monophonic works, linked with dance-song. How much these new departures had been instigated by Vitry is unclear, owing to the small portion of his works that is now extant. In any case, however, Machaut must have played a decisive role in shaping these genres of the later Middle Ages.

2. Life.
The details of Machaut's life and social position as well as the themes, form and purpose of Machaut’s works clearly define his position as a ‘clerc-écrivain’ (Cerquiglini, 1985) in the courtly-aristocratic structure of the late Middle Ages. The two parts of his biography that are backed up by documentary evidence as well as illustrated in numerous statements in the dits support this: the first, that from about 1323 he was in the service of Jean de Luxembourg, King of Bohemia, and the second, that from April 1340 he was a canon of Reims Cathedral. Both encourage hypotheses about the undocumented details of his early life: the date of his birth, which must have been between 1300 and 1302; his bourgeois background, his education (probably in Reims), and possibly study for the magister artium. However, the title of magister is not mentioned either in Machaut’s texts or in official ecclesiastical documents. That Machaut was named in a Reims document of 1452 along with other ‘magistri’ and by Deschamps in unofficial sources as ‘maistre’ is evidence of the position and renown that he had by that time won.

For about 17 years Machaut’s life was shaped by his position in the service of Jean de Luxembourg; this in its turn is critical for the understanding of his poetry. As a clerc in the narrow circle of ‘domestici familiares’ he first of all took the post of aumonier, then of notaire, and lastly secretaire. The dits make it clear that for lengthy periods during this time he shared the restless life of his master: this involved visits to the French court (which in 1323–4 could have led to Machaut meeting Philippe de Vitry), and often swift movement between the home lands of the Luxembourgs in the West and Jean’s Bohemian domain in the East, and journeys through much of central and eastern Europe (in particular to Lithuania in 1327–9); but also spending more peaceful periods in Durbuy, Jean’s favoured western residence south of Liège, on the bank of the Ourthe. ‘Li bons roi de Behaigne’ is presented as the ideal of a ruler-knight in Machaut’s texts, and thereby as a representative of the courtly world around which Machaut’s poems are based. His earliest dits, Le dit dou vergier (1330s) and in particular Le jugement dou roy de Behaigne (before 1346), document the role of the poet at court. The chronological order of musical compositions of this time is not at all clear, but the composition of motets and possibly the first lais belong to this period.

As a royal servant, Machaut benefited from the economic security ensured for royal ‘familiares’ through prebends. Machaut is shown to have been in possession of such income, granted to him without the need for his presence in the parishes, in papal documents from 1330 onwards (starting with bulls of John XXII). Before this date he already held a position in Houdain, and the prospect of canonicates in Verdun (1330), Arras (1332), Reims (1333) and a prebend in Saintt Quentin (date unclear). After Benedict XII’s action in 1335 to reduce the large numbers of canonicates ‘in expectatione’, Machaut retained only the canonicate in Reims. He took this up ‘per procurationem’ on 30 January 1337 and then in 1340 by his residence in Reims, where he is recorded for the first time as being present on 13 April of that year.

The office of a canon, who lived in a house ‘extra muros’, was linked to liturgical duties, but at the same time offered a material basis and a new kind of space for literary and musical activities. In the forefront of such activity is the long list of increasingly extensive dits (comprising over 40,000 lines of text in total), also associated with the lives of the high nobility. ‘Moult la servi’, said Machaut of Bonne, Jean de Luxembourg’s daughter, who was already a highly supportive patron before her father’s death in 1346. She is connected with the Remede de Fortune and possibly also with Machaut’s cultivation of the new forms of lyrics set to music, as well as with the first extant collection of Machaut’s works. Other patrons associated with Machaut included Charles II, King of Navarre, Jean, Duke of Berry, Philip the Bold, Duke of Burgundy and Pierre de Lusignan. Documented contacts include the Dauphin’s (later Charles V) stay in Machaut’s house in 1361. The dits also mention more traumatic events, such as the arrival of the plague in 1348–9 and the siege of Reims by the English in 1359–60.

The years 1363–5 saw the writing of Le livre dou voir dit (the Voir dit), with interpolated letters and musical works. Aside from its (at least partly fictitious) setting of the meeting of and love between the elderly poet and his young admirer ‘Toute Belle’ (Peronne), this dit represents a rich documentary source for the events of those years (with details of journeys to different places), for the production and transmission of Machaut's works, his self-awareness and self-depiction, and above all for the process of setting lyric texts to music (chronological overview of the lyrics with musical settings in Leech-Wilkinson, 1993). In Parisian celebrations in early 1368, possibly the scene of a meeting between Machaut and Froissart, Amedee VI of Savoy acquired a ‘roman’, probably a collection of Machaut’s works.

In the last decade of his life the redaction and completion of his oeuvre was Machaut’s primary concern, and the two-part Prologue (comprising four ballades and a verse passage in dit form), dating from about 1372, was written in connection with this. In the same year Machaut’s brother Jean – who had also served Jean de Luxembourg, had been a canon of Reims since 1355 and had lived in the same house as Guillaume – died. In April 1377 Guillaume de Machaut died. The two brothers had established a richly endowed anniversarium, with which the Messe de Nostre Dame is thought to be linked, and were buried in the same grave.

3. Transmission, chronology and stylistic development.
The transmission of Machaut’s works documents in a unique way the central role of the book as a planned collection of the complete oeuvre, for the self-awareness of the poet-composer as well as the diffusion of his compositions. The first signs of such ‘collecting tendencies’ can be found in French poetry from the late 13th century onwards (Huot, 1987), for example with the works of Adam de la Halle (F-Pn fr.25566). Machaut’s concern with his ‘livre ou je met toutes mes choses’ is in evidence from about 1350, and he clearly involved himself in all aspects, including the programme of miniatures for the richly illuminated presentation manuscripts, prepared mostly for aristocratic patrons. The most important sources for Machaut’s music are six large books from the 14th century, which all relate to collections made by the author and must have been copied in part under his supervision. They show different redactions. F-Pn fr.1586 (C) offers the earliest accessible state of his work, possibly representing the first complete-works collection, dating from shortly after 1350. The redaction in US-NYw (Vg) and its copy, F-Pn fr.1585 (B), dates from about 1370. F-Pn fr.1584 (A) contains the only slightly later, last authoritative ordering of the works, with the indication ‘Vesci l’ordenance que G. de Machaut wet qu’il ait en son livre’. Two further collections were clearly copied after his death: F-Pn fr.22545–6 (F–G) offers a slight accretion in the number of works, while F-Pn fr.9221 (E), copied for Jean, Duke of Berry, contains additional voice-parts, at least some of which are probably not by Machaut. These sources preserve the basic order of narrative dits, followed by unnotated lyric poetry in the Loange des dames and then music, the latter itself ordered by genre: in manuscript A the lais come first, then motets, Mass and Hocket, followed by ballades, rondeaux and virelais. Just as isolated examples of lyrics not set to music appear in the music section, so musical compositions used as examples are integrated among the poems in the Remede de Fortune. Transmission of musical pieces in ‘repertoire manuscripts’ stretches into the 15th century but is limited to about 25 pieces.

Because of this specific transmission situation, it is likely that Machaut’s literary and musical works have been preserved practically complete. Beyond that, most of the works can be placed at least roughly into specific creative phases. In this respect the critical factor is the internal order of several groups of works, in principle determined by the order in which they were written. Exceptions to this pattern include the first work in a series and the arrangement of works related to each other. Indications of such groups come from dits that have internal dates or to which dates can be assigned. The basis for the chronological layering of the musical works is the increase in the number of works between C and G. More detailed chronological indications are provided in the Voir dit (c1362–5) for the compositions associated with it. For the earliest period of musical creativity, further layers are revealed by the only partial ordering by genre of the musical works in C: this allows the refrain form compositions (ballade, rondeau and virelai) from the period before 1349 (CI) to be distinguished from those dating from the beginning of the 1350s (CII).

Only the 19 lais are spread more or less evenly over Machaut’s entire composing career. The motets belong in a first phase, with 19 compositions definitely written before 1356 and only four more included in Vg and subsequent manuscripts. The most varied picture is offered by the refrain forms: Table 1 (following the work of Ludwig, Günther and Earp) shows the content of CI and the growth in the number of works from CII onwards (not including the compositions in the Remede de Fortune).

As with the dits, of which only the Dit dou vergier dates from before the Reims years, there is some evidence that the new polyphonic ballades were only written from 1340 onwards. 19 of the 20 virelais in CI are monophonic; thereafter polyphony predominates in this genre as well. Thus the ballade is not only numerically in the foreground of Machaut’s oeuvre, but also with regard to the beginning of his composition of polyphonic songs. And it is precisely in the ballades that the chronological layering is linked with a change in compositional style. This is immediately obvious in the number and function of voices, in the tendency to extend the two-voice cantus and tenor framework and, later, the change in emphasis from triplum to contratenor. (See Table 2, showing ballades added from CII onwards; without the later added voice-parts; not including the Remede de Fortune). The development from the two-voice (cantus-tenor) framework, through its extension to include a triplum, to the three-voice works with contratenor, corresponds to developments in rhythm and other aspects of composition. Such changes often support external grounds for dating and would in many cases, even without the external information, allow a work to be assigned a chronological position. Through analysis, it is thus possible to assess stylistic change in the tangibly personal idiom of Machaut's songs over a period of 35 years.

4. Evidence of self-awareness and about production.
Machaut is the first and, for a long time, the only composer to comment in differentiated fashion on the making, transmission, reception and evaluation of individual works, as well as on music in the wider context of poetics; such remarks afford a specific notion of the approach to music of the ‘faiseur’, the poet and composer of material in French. The two-part Prologue, which Machaut added to the beginning of his complete works about 1372, is typical of his self-reflection – a fundamental aspect of the literary work – as well as of self-portrayal and self-awareness: it is presented in four ballades with a supplementary prose text as well as the long section of narrative verse. In the dialogue of the ballades Machaut accepts the task given to him by Nature personified to portray ‘les biens et honneurs qui sont en Amours’ more than had been done before. ‘Scens’, ‘Retorique’ and ‘Musique’ serve both as a requirement and as a means for realizing the aim (see fig.1). The ensuing appearance of ‘Amours’ delimits the subject matter (‘matere’) to courtly love. In the second part of the Prologue the music is clearly in the foreground: from a catalogue of forms to an all-encompassing classification that, following the typical pattern of the Latin tradition of music theory, begins: ‘Et musique est une science’. Interpretation of this retrospectively formulated central text should take account of numerous similar passages from other dits, from as early as the Remede de Fortune to the Dit de la harpe (probably written in the late 1360s).

Comments on individual works are mostly to be found in the Voir dit. Here it is clear that the normal compositional procedure was to formulate the text first and then its musical setting; but there is also evidence of the quasi-simultaneous conception of text and music based on the ‘sentement’ of a specific situation – from that constantly repeated aspect of the creative process, ‘experience’. Information about notating, dictating and copying, about the transmission of single works as well as about the process of copying larger parts of his oeuvre is combined with detailed observations about working conditions and the external circumstances of production.

The remarks on R17 are typical of the terms by which Machaut rated his compositions: he stated that for seven years he had completed ‘ni si bonne chose ni si doulces a oir’ (‘nothing so good or so sweet to listen to’). Recurring allusions to novelty and specific quality are occasionally varied: so, for example, B33 is characterized as ‘moult estranges’, but with the general comment that it is made in the style (‘a la guise’) of a ‘res d’Alemaigne’ (a term whose meaning is not altogether clear). The lower voice-parts (‘tenures’) are described as ‘aussi douces comme papins dessalés’ (‘as sweet as unsalted gruel’), and Machaut advised Peronne to listen to the melody ‘de bien longue mesure’, without changes (‘sanz mettre ne oster’), as could happen in an instrumental adaptation (Voir dit, letter 10). Evidence of deliberate working out of specific polyphonic solutions corresponds to the role of listening as a basis for aesthetic perception (‘plaire’), but also as a final control over the result. Thus Machaut stated that he never let anything out of his hands until he had heard it; referring to B34 (conceived as a four-voice work), he said that on repeated listening it had pleased him very much. But also in the Voir dit we find an interesting case of the later addition of two lower voices to a rondeau melody (in R18).

Such comments on individual works correspond to the key words ‘divers et deduisans’, mentioned with respect to music in the part of the Prologue that deals with the three aspects of formal creation: Scens, Retorique and Musique. As can already be seen at the beginning of the second section of the Prologue, these key words can be interpreted in the light of further texts: rather than forming a mere succession, these aspects interact in a hierarchy in which Scens is dominant (see Cerquiglini, 1985). One indication of this is the centrality of the Orpheus figure in Machaut’s works, both as poet (‘le poete divin’ in the Dit de la harpe) and as musician, who with a tuned instrument, the harp (also a reference to harmony) and as a singer demonstrates the wondrous effect of music; the interconnection of such aspects is evident even in the choice of words, as in the dit section of the Prologue: ‘Cils poete dont je vous chant / harpoit si tres joliment / et si chantoit si doucement’.

In the wider sphere of Machaut’s theoretical reflections on art, the key word ‘soutil’, the emphasis on ‘maniere’ and the aspect of ‘aourner’ are all significant in relation to music. Such differentiation allows the use of categories through which interpretations can be made of individuality, innovation and poetic and compositional techniques as characteristic elements of the oeuvre, and which further provide the conditions for a proper understanding of the links between aesthetics and analysis.

5. Motets and lais.
The motets and the lais are the only large groups of works in which Machaut directly followed older forms; he had a specific impact on both. In the case of the motet this encompasses a phase of the development of this genre between the new methods of formal structuring present in the Roman de Fauvel and especially in the works of Philippe de Vitry, and the fully isorhythmic compositions of the last third of the century.

The motets constitute the oldest extant part of Machaut’s musical oeuvre. Only the last three (M21–23), which are datable from references to political events of the years 1358–60, can be shown to have been composed after the middle of the century. 19 were already written by the time of the first available redaction of his works (in C); M4, first transmitted in Vg, may have been erroneously omitted from C. Early involvement with this genre is confirmed by M18, written for the appointment of Guillaume de Trie as Archbishop of Reims in 1324. The beginning of the motet series with the triplum ‘Quant en moy vint premierement Amour’ must, as in other work groups, be seen as programmatic. Following this – without indications of chronological layering, but often organized according to structural or thematic relationships – there come first of all those works with French upper-voice texts and then works with Latin texts (the latter from M18 on), with the exceptions of M9 (Latin) and M20 (French). Two motets (12 and 17) combine a Latin motetus with a French triplum.

Those characteristics of Machaut’s motets which correspond to aspects of the genre as he found it include three-part texture, only rarely expanded to four parts (only four of Machaut’s motets have a contratenor); the intertextual relationship of the two text-carrying upper parts and the semantic connotations of the liturgical tenor melody; also the basically strophic disposition resulting from the interaction between text structure, text-setting and melodic-rhythmic organization of the tenor into color and talea. The same is true of the integration of refrains and other quotations, and the use of specific techniques – such as articulation through the use of short passages of hocket – and also of the three works with non-isorhythmic song melody tenors (M11, 16 and 20), of which one (M16) is fully texted. The melody of M13, ‘Ruina’, is identical to a corresponding tenor in the Roman de Fauvel (Super cathedram/Presidentes). An intensive engagement with the achievements of Philippe de Vitry has been shown for the four four-voice motets (M5, M21–23; Leech-Wilkinson, 1989).

The importance of Machaut’s motets in the history of the genre lies in their rhythmic and tonal formulation on the basis of the ‘quatre prolacions’ and systematic formulation of harmonic progressions according to the rules of contrapunctus on the one hand, and on the other the structural interconnection of all voices through rhythmic and partly also melodic correspondences. The isorhythmic organization of the tenor shows a tendency towards longer rhythmic segments and increasingly complex intersections between color and talea. In ten motets the last section is in diminution (mostly in half-values). Even in works without an isorhythmic tenor, rhythmic and melodic relationships between the upper voices created by hocket and other significant features represent deliberately applied organizational devices. In passages of diminution such correspondences extend in many cases over large sections. In M13 almost the entire composition is thus structured; M15 is one of the earliest examples of a ‘pan-isorhythmic’ motet.

Semantic interpretation of individual compositions as specific text-settings is still some way off, however; recent research has exposed a broad spectrum of ways in which Machaut, as a poet-musician, used the specific compositional possibilities of this genre.

Machaut’s 19 lais mark the final phase of a longstanding tradition. As in the motets there are further indications of his engagement with the Roman de Fauvel, yet although the composition of these works stretches into Machaut’s late years. That the lais in manuscript C are transmitted with miniatures emphasizes their importance in Machaut’s oeuvre (see Huot, 1987; also on the order of pieces). In their integration of the new rhythmic procedures of the Ars Nova into a defined musical structure (generally in 12 sections, of which the last refers to the first, often by way of transposition), Machaut’s lais elevate a now old genre, offering unique solutions for large-scale text-setting in monophony. The expansion of the form into polyphony is a further part of this process: polyphony is indicated in two cases by rubrics (L16 and L17; 11 and 12 in Schrade) and in two more (L23 and L24; or 17 and 18 in Schrade) is implicit in the traditional method of successively notating sections of melody that are to be performed simultaneously.

6. Mass and Hocket.
Both of these compositions are unique in the 14th century and among Machaut’s works. The three-voice Hoquetus David is the last example of its kind. Like the Mass it is transmitted for the first time in Vg (it actually appears immediately following the Mass) and must have been composed in the 1360s. It may well have close connections with Reims; it was possibly associated with the coronation of Charles V there in 1364. It is based on an isorhythmically worked setting of the passage ‘David’ from the Alleluia verse Nativitas gloriose virginis.

The four-part Mass represents the earliest instance of a Mass Ordinary setting (including the Ite Missa est) that is stylistically coherent and was also conceived as a unit. Research on the Ordinary melodies used and the mass foundation has confirmed that this composition can be linked to a Saturday Lady Mass instituted in Reims Cathedral in 1341; this corresponds to a rubric in its oldest source: ‘Ci commence la Messe de Nostre Dame’. Machaut’s Mass, probably written in the early 1360s, was connected with the Reims celebration and on the death of his brother it was transformed into a memorial mass. It continued to be performed after Machaut’s death, perhaps continuing into the 15th century (see Robertson, 1992). In the Mass, isorhythm and diverse other compositional techniques of Machaut’s late period are brought together in one work that is outstanding in terms of artistic merit and belongs among the most impressive works of the Middle Ages.

7. Ballades and rondeaux.
Machaut’s ballades are the first available evidence of a genuinely new genre of French song, one that remained of central importance in text-setting until the middle of the 15th century. The beginnings of this new kind of ballade cannot be traced before about 1340 (even through indirect witnesses). And its specific combination of features in the context of the newly differentiated formes fixes suggests that Machaut, even if he was not the instigator of the new form, played a crucial role in its development.

Its newness lies in the bringing together of features of different origins. The texts take on a formal, fixed structure that was already evident in the 1330s in the works of Jehan Acart de Hesdin and Jehan de le Mote. In language the ballade adopts the high style of grand chant. The interaction of the new types of voice-parts, conceived in relation to each other, is founded rhythmically on the ‘quatre prolacions’ and tonally on the deliberate exploitation of the qualitative differences between perfect and imperfect intervals, as they would be described in the teaching of contrapunctus and here used in such a context for the first time. Until the late 14th century Machaut was alone in his use of these means for ‘subtle’ text-setting in which every aspect of the text is expressed, from form to semantics, and in the latter case even as far as the meaning of individual words. In this regard only the monophonic songs of Jehannot de Lescurel offer any comparable examples of text-setting.

As with the number of voices and the expansion of a two-voice texture through the addition of triplum and/or contratenor (see §2 above), so also rhythmic procedures and the introduction of different compositional techniques can be used to demonstrate a clear change between the earlier and later compositions. Nonetheless, even the earliest ballades exhibit a specific compositional quality; in the 14th century this is distinctive, and contributes considerably to the impression that, in the sense of a personal style, the works of Machaut can be separated from those of others (of which many composed within his lifetime remain extant). His extreme control of material suggests a high level of reflection. Analytical findings allow the examination of aesthetic criteria, through key concepts such as richness of association, varietas, multi-layered structures, balance on all levels and in particular the interaction of parameters already discussed: from melodic to harmonic to formal (see for example the discussion of B7 by Fuller, 1987). Different solutions to the text-music relationship correspond to the individualization of each composition in terms of an emphatic understanding of ‘the work’. This individuality determines the boundaries of the examination of isolated aspects and the findings of such investigations. But it offers, at the same time, an essential basis for text-critical studies (most of which have yet to be undertaken).

The status of the new genre is underlined by its position at the beginning of the songs in the complete-works manuscripts. Its breadth and importance is emphasized by the evidently programmatic opening of the series: B1 is the only ballade with an ‘isorhythmic’ structure, and the works that follow it also have specific points of compositional interest; B2 offers an equally singular construction created from the tension between two sonorities; B3 has an intertextual reference as homage to Jehan de le Mote; B4 demonstrates a striking grasp of compositional art in the use of different mensurations (notated in coloration) and a complex pattern of suspensions.

The beginning of B14 is typical of the regular declamatory rhythm of the early ballades. Rests on the caesura and at the end of a phrase correspond to the formal characteristics of the text-line. The structural sonorities lead after the caesura in the first text-line to an open sonority (bars 4–5), but then move (with the syntax) at the end of the line (bar 7) through the 3rd on f–a (an interval described in contemporary theory as ‘tendere’, i.e. ‘striving’ or needing resolution) towards the emphasized central word ‘Amour’. Dissonances are integrated in short melodic motifs, which themselves provide consonant series of structural sonarities, even where the consonant notes do not sound together, as for example in bar 10. At the same time, bar 10 marks off a repetition of the sonorities of the opening bars (1–5) after the mid-point of this part of the song (bars 11–13). This balances the asymmetrical relationship in the length of the text-lines and also in the altered repetition of the progressions of bars 7–9 in bars 14–16, itself underlined by the same progression in minims (quavers in transcription) in bar 13. The articulation and emphasis of particular words by the musical structure corresponds in further strophes to a rhetorical stress on key words in the discourse of the poem as a whole.

The degree to which semantics can be understood to operate in each individual setting is shown at the beginning of B6: in the significant melodic descent of the cantus firstly through an octave (bars 1–4) and then through a minor 6th (bars 5–6), in the underlying declamatory rhythm in long note values and above all in the use of the ‘tendere’ imperfect consonances. They are employed to emphasize the word ‘oy’ (‘hear’) with the written accidental g (bar 2) and the surprising opening of the second text-line ‘A toy’ with b–g (after the previous e–g sonority).

One of the key features of text and music of this new genre is the role of the refrain which can be understood in traditional fashion on the one hand as a highlighted résumé at the end of a strophe and on the other hand as a starting-point for the poem and the composition – regardless of whether it is formed from pre-existing material (e.g. in B12 for text and music and in B13, at least for the text) or is completely new. The beginning of B13 clarifies the relationship between refrain and strophe in text and music (‘Esperance’ represents a concretization of the refrain; the music also corresponds). The ‘indirect preparation’ by the opening of the 4th in bar 2, the deliberate placing of rests (bars 5 and 7) and the emphasis of the words ‘sans per’ by the use of a high tessitura and inserted syncopated hemiola demonstrate Machaut’s subtle use of different musical devices. In this way the text-setting opens the way to readings of the text, showing for instance that Machaut uses the verb ‘asseurer’ transitively and not intransitively, as the punctuation of the editions would suggest (for further discussion see Arlt, 1982).

The expansion of the musical texture by the addition of a triplum and, later, of a contratenor voice-part resulted in greater complexity, in particular in the higher proportion of dissonances arising from interval progressions (to what extent the triplum and contratenor in works transmitted in four parts should be seen as alternative extensions of a two-voice work can only be clarified through analysis, and is a matter for debate). However, greater diversity results from the use of multiple levels of mensuration (for instance perfect tempus, major prolatio or perfect modus, imperfect tempus, minor prolatio), syncopation or more varied declamation. The re-use of material in different sections (and not just in similar endings of the musical rhyme in a long ‘recapitulation’) points to a concern with questions of form. For example, in the series of ballades 26 to 28, issues about the use of specific melodic patterns can be studied. But here again the particular demands of the individual text form the starting-point for the composition. The fact that, for B26, Donnez signeurs, both an older and a revised version of the work are preserved, allows glimpses into the compositional process. A comparison of the two versions shows how the systematic reworking of all three voices achieved subtlety on many levels of the definitive version, and therefore allows conclusions to be reached about Machaut’s musical and poetic compositional art (see Arlt, 1993, and Bullock). A series of songs from the period of the Voir dit show that Machaut’s working-out of specific compositional problems was significant even beyond the ballade genre (Leech-Wilkinson, 1993). Rhythmic and harmonic interaction between the voices is typical of the complexity of the compositions of this period, demonstrable through, for example, the way in which the contratenor supports the 4th between cantus and tenor at the beginning of B32; in the same piece the interwoven lower voices provide both rhythmic foundation and cross-rhythmic activity against the cantus; and in B36 the changing relationships between voices as a result of the treatment of dissonance. In contrast, the later ballades (38 to 40) exhibit the traits of a late compositional style.

In the rondeaux (which, like the ballades, are mostly polyphonic) Machaut took up an already established compositional form that had been associated since the 13th century with three-voice settings. Yet here also, the first piece in the series, with its structural use of imperfect consonances, points clearly to a new kind of composition. The fact that the basically syllabic declamation of R1 is untypical of Machaut’s treatment of the song-form also emphasizes its special position. In general, the greater use of melisma and concentration on compositional innovations along with many-layered correspondences between the two musical parts can be directly associated with the shorter texts and bipartite musical layout (with refrain repeated at the end). The late R19, in which the use of different mensurations in the cantus and lower voices is combined with a long ‘isorhythmic’ recapitulation structure (see Günther, 1962–3, with partial reproduction of the original notation), shows the greater compositional freedom afforded by the form. In an extreme and unique way, the specific formal qualities of the rondeau form are exploited in R14, first transmitted in B (missing from Vg). Here the text Ma fin est mon commencement provides the clue to a realization in which the triplum is created by reading the cantus line in reverse and the second half of the lower voice consists of its first half read in reverse.

8. Virelais.
As a result of the creation of the new ballade and Machaut’s differentiation between the three formes fixes, the old dance-song function associated with the term ‘ballade’ became concentrated in the virelai or ‘chanson ballade’. Statements such as ‘Ainssi doit elle estre clamee’ in conjunction with the latter term (‘thus should it be named’; Remede de Fortune, line 3450) point to a delimitation that is by no means self-evident. Nevertheless, the simple musical form of the early monophonic virelais and the fact that in the Remede de Fortune only this form is explicitly connected with dancing (see fig.2), correspond to the delimitation. This narrow concept of the form is unique in the 14th century, and was later abandoned by Machaut in favour of more complex musical formulations, including polyphonic settings.

With their formulaic rhythm and the use of a higher tessitura in the second section, the early virelais show restricted scope for manipulation of form. The formulaic rhythmic patterns are varied for the first time in V5, which – characteristically – is melodically based on an earlier chanson de toile. From Vg onwards polyphonic settings are also found. The beginning of V36 (V30 in Schrade) exposes aspects of virelai construction which differ from those of ballades and rondeaux: for example, the use of an upbeat, the equal pitch-range of the voice-parts, and also the secondary role of the ‘tendere’ imperfect intervals in comparison to the melodic direction of each voice. The case of V29 (V26 in Schrade), in which the second voice was a later addition to the monophonic work transmitted in C, is also helpful for the determination of such differences (see Fuller, 1991).

9. Reception.
In 1350 the chronicler Gilles Li Muisis, in his Méditations, named Machaut with Vitry and Jehan de le Mote as poets of his day (‘Or sont vivant bieaus dis faisant …’). References to Machaut as poet continue into the second half of the 15th century (see Earp, 1995). In the anonymous Regles de la seconde rhetorique, dating from the beginning of the 15th century, ‘maistre Guillaume de Machault’ is named as ‘le grant retthorique de nouvelle fourme, qui commencha toutes tailles nouvelles et les parfais lays d’amour’. This statement should be understood in association with what precedes on the subject of Vitry (‘qui trouva la maniere des motés, et des balades, et des lais, et des simples rondeaus’). Machaut and Vitry are seen here in retrospect and from a historical perspective as formative figures of new groundrules of poetric and musical composition, with typical overlapping of characterization. In any case, Machaut’s poetry offered an corpus of exemplars that was widely used as a point of reference (with the lyric forms also used as models) into the early 15th century; explicit citations are found in the works of Eustache Deschamps and Oton de Granson, but his direct influence can also be seen in those of Jean Froissart, Geoffrey Chaucer and Christine de Pizan.

Also in the mid-14th century, the Libellus cantus mensurabilis (sometimes attributed to Johannes de Muris) referred to the distinctive notational practices of Machaut, and this continued in musical writings until the Practica musice (1496) of Gaffurius. But the number of his works transmitted in the so-called ‘repertory manuscripts’ is strikingly small (see Table 3, after Earp, 1985 and 1993). In the extensive Cambrai fragments (F-CA 1328) there are only three works by Machaut (M8, B18 and R7); and only four (M8, M15, M19, R17) are included in the Ivrea Manuscript (I-IVc 115). The largest number of his pieces in such a collection is indicated in the index (dated 1376) of the lost Trémoïlle Manuscript (F-Pn n.a.fr.23190), with nine motets, eight ballades (including two from the Remede de Fortune) and one rondeau. Correct ascriptions in the notated repertory manuscripts are restricted to the Chantilly Manuscript (F-CH 564) for two out of three ballades. For the motets, the above-named sources contain nearly all the pieces transmitted outside the Machaut manuscripts. Some of the chansons (B18, B23, B25, B31 and R7) were remarkably widely distributed, and they continued to be copied in the 15th century; but for the majority transmission was rather more sporadic. To what extent the comparatively small number of 12 ballades and three rondeaux transmitted outside the complete-works manuscripts is explicable by the very existence of those manuscripts is open to question. The serious lack of sources from the first three quarters of the 14th century must also be taken into account here; however, the general picture of a narrow transmission pattern tends to be confirmed each time manuscript fragments are rediscovered.

From the last quarter of the 14th century – in citations and also in a large number of intertextual references – there is evidence not only of an adoption of texts but also of musical engagement with Machaut’s work. Here, with the exception of B15, all those pieces evolved are transmitted in the repertory manuscripts.

A more exact picture of Machaut’s influence demands comparative stylistic study of the numerous other songs of the 14th century, usually anonymously transmitted. These are clearly different in form as well as in style: for instance, the virelai, of which there are many examples, appears almost invariably (with one exception) in its polyphonic form; other songs use pre-existing melodies in the tenor. The fact that the polyphonic ballade appears for the first time in larger numbers in the Trémoïlle Manuscript source that might point to reception of Machaut's work, especially since in this eight of the 12 ballades transmitted outside the Machaut's manuscripts are present.

In any case, in the artistic level and specific quality of his works, Machaut stands on his own late into the 14th century. That Deschamps described him with the term ‘poëte’, referring in a new sense to the poetry of his own time (Brownlee, 1978), corresponds to the importance of his literary oeuvre. Here begins a new kind of reception in which poet and composer are separated. The older unity is continued in music-related poetry, as represented in the late 14th century by Senleches.

Johannes Ockeghem - Requiem & Missa "Mi-Mi"

Most fifteenth-century composers were singers by trade in the way that most eighteenth-century and nineteenth-century composers were pianists. This means that their music is profoundly vocal in idiom and is imbued with the memory and pattern of plainchant which formed the aural background to their working life. Johannes Ockeghem seems to have been an outstanding example of the singer-composer, to judge by the reports of his contemporaries, who praised his voice, character and music with the complementary attributes of virtue, sweetness and discernment.

Ockeghem was born c. 1410, possibly in eastern Flanders, but spent most of his professional life (from 1453 or earlier) in the service of the French Royal Chapel, where he served under three kings, Charles VII, Louis XI and Charles VIII. He was honoured by Charles VII in 1459 with the gift of a benefice as treasurer of the important Abbey of St Martin-de-Tours; and under Louis XI further material rewards came his way, including a canonry at Notre Dame in Paris, 1463-70. During subsequent years he is known to have travelled to Spain (1470) and Flanders (1484). His death in 1497 occasioned poems of tribute and Lamentation from Crétin, Erasmus and Molinet.

The Missa Mi-Mi survives in three separate manuscripts in the Vatican library. In one it is described as the Missa Quarti Toni by Okeguam, in another it has no name, but in the third, the Chigi Codex, an important source of Ockeghem's music, it is called 'My-My'. This title is assumed to derive from the short motif that appears in the bass voice at the beginning of each main section, and consists of a falling fifth e to a; in the technical parlance of the period, these two notes are both called 'mi' in the natural and soft hexachords (six-note medieval scales) respectively.

This manuscript, which is also the sole source for Ockeghem's Requiem, is abundantly decorated with illuminated letters, miniatures and grotesqueries, and the style and content of these drawings confirm its Flemish origin: probably (according to H. Kellman, Joumal of the American Musicological Society XI, 1958) it originated in Ghent during the last years of the fifteenth century and seems to have been intended for use in the chapel of Philip the Fair of Burgundy.

Apart from the opening motif, the Missa Mi-Mi is not known to be based upon any prior material, whereas most Masses of that time were either 'parodies' of other compositions, sacred or secular, or were built around a cantus-firmus. Ockeghem foregoes this method of construction and, in effect, extemporises an intricate, compelling web of sound out of thin air. Having so started, he even avoids any but the most passing instances of imitation. The voices are forever sefting one another off, but each voice has something very different to say about any melodic or rhythmic idea proposed by another. There is a supple, always varied and often very complex use of rhythm, sometimes climactic (at the end of the Gloria or Credo), or pictorial as when (in the middle of the Credo) a sudden fluttering of notes depicts the heavens as the upper voices sing 'descendit de caelis': the descent being depicted by the final curve of the lines and the reiterated notes of the bass. Ockeghem had equal mastery of the fluid melodic style that had characterised the Generation of Dufay (d. 1474), and to his manifestation of this Tradition he adds a new dimension of harmonic colouring, particularly where he wishes to emphasise an emotional direction in the music (especially at the beginning and towards the end of the third repetition of the words 'Agnus Dei').

In the Requiem (the earliest extant polyphonic Requiem unless Dufay's lost setting is discovered), we encounter an even wider diversity of techniques and vocal scorings that range from duets for high voice in strict imitation to the full, rich style that makes its first resplendent appearance at 'Rex tremendae'. The whole shape of the work is suggestive of a gradual descent from the predominance at first of generally high ranges to the closing repose of lower pitches provided by divided basses. Similarly the compositional techniques move from the opening ritualistic style of parallel chords to the complexities of the Offertorium. Before the Council of Trent (1545-63) the form of the Requiem set by composers varied. We have included the four further sections , that Ockeghem did not set, sung to plainchant; not to propose an 'authentic' ceremony, but to complete the musical logic by fully unwinding the thread of chant that begins the Introitus and continues, though often greatly embellished, throughout the polyphony as a cantus-firmus.

Ockeghem did not compose huge quantities of music (some ten masses, various individual mass movements, a handful of motets and twenty-two chansons), and it is not unreasonable to assert that two of his finest works are those to be heard on this record.

Paul Hillier

(1985)

Giovanni P. da Palestrina's Missa Brevis

Despite its title Palestrina's famous Missa Brevis is one of the most substantial and sonorous of all his mass-settings to be written in four parts. The reason for its title (meaning 'short mass') is a mystery, though the use of it may be connected with the lack of any obvious model for the setting. Palestrina, early in his career, liked to use other composers' motets or plainsong chant to rework in 'parody' fashion, an old and respectable technique. Many people have looked for such a model in this case but without success. Plainsong was the most likely starting-point, but if so the melodies are not consistently applied. The mass was first published in 1570 and was a success from the start, being reprinted several times before 1620.

The most likely explanation for this general descriptive title 'Brevis' is that no other came readily to hand. In other cases of a 'free' setting Sine Nomine was common; but some of these, like the one which has recently been proved to be based on Josquin's motet Benedicta es, are bigger pieces in terms of the number of voices employed, and perhaps a distinction between the titles Sine Nomine and Brevis is implied. Not that anyone ever proposed the title Missa Longa. The idea that the word 'Brevis' comes from the fact that every movement starts with a breve in the original notation is discounted since literally hundreds of works start with that note and it is hard to imagine anyone fixing on this detail as being worthy of comment.

The music has a strong character, confidently written, with the motif of the falling minor third, usually followed by upward movement by step, appearing very regularly. This happens not only at the beginning of most movements, but frequently during them, for instance in the remarkable sequence in all the parts to the word 'Amen' in the Credo. This interval alone goes some way to explain the unusually subtle cohesion which the Missa Brevis displays on close acquaintance, where a casual glance might judge it to be disparate. The music is for SATB, increasing to SSATB for the beautiful second Agnus Dei. The phrase at the beginning of the first Agnus - an ascending scale - is inverted at the beginning of the second, which rounds off the music in the most satisfying way.

Peter Philips

(1986)

Musica Enchiriadis

Anonymous 9th-century Latin music treatises of signal importance for the early history of modal theory and of polyphony. They are generally transmitted together in the manuscript tradition, frequently with other contemporary tracts (ed. in Schmid, 1981) but most of all with Boethius’s De institutione musica. Though best known for containing the earliest extant discussions of (improvised) polyphonic singing (organum), they are equally notable for transmitting the first chant melodies preserved in a precise pitch notation and for drawing upon a wide range of late Latin literary and philosophical sources; they thus document the intellectual environment as well as the state of musical theory and practice of the Carolingian Renaissance. Although the origins of the treatises are still wrapped in mystery, major advances in the understanding of Musica enchiriadis and Scolica enchiriadis have been possible following the completion of Schmid’s critical edition (1981), the dissertation by Phillips (1985) and the first complete published translation of both treatises (Erickson, 1995) since Schlect’s German translation (1874–6) based on Gerbert’s edition of 1784. (Unless otherwise stated, the edition and translation of Musica enchiriadis and Scolica enchiriadis referred to in this article are those by Schmid, 1981, and Erickson, 1995.)

Content

Musica enchiriadis [ME], which has no title in the earliest sources, is a succinct, well-argued account of the theory and practice of ecclesiastical music of the time. The first nine of its 19 chapters are concerned with monophonic chant, a notational system for representing melodies (dasian notation), a description of the modes based on both final and ambitus (but not of modal octave species), vocal exercises for practising different modal characteristics (determined by the placement of the semitone), and basic musical and mathematical terminology. Chapters 10–18 take up the ‘symphonies’ (consonances of octave, 5th and 4th) and their use in simultaneous (in unum) singing, whether in octave doublings or in improvised polyphony (diaphonia, organum) in which the chant is generally replicated at the 4th or consistently replicated throughout at the 5th, with octave doublings possible in both cases. Chapter 18 closes with philosophical musings concerning the mysterious fact that some tones when combined produce harmony and others do not, that ‘the same principle that controls the concord of pitches regulates the natures of mortals’ and that the harmony of the world is due to the mathematical relationships that regulate and unite all things in it. Chapter 19, which addresses essentially the same issues in different terms, notably by an interpretation of the Orpheus myth in a unique version largely based on Fulgentius, could therefore be considered as superfluous and may well be the misplaced prologue to Scolica enchiriadis [SE], to which it apparently refers in a concluding reference to ‘the little work following’ (Phillips, 1985).

SE, on the other hand, is a dialogue in three unequal parts, the total being three times as long as ME. Its title, probably original, may have been modelled on the rhetorical treatise in dialogue form of Fortunatianus (see Spitta, 1889; Phillips, 1985) entitled Scolica (i.e. ‘excerpts’) enchiriadis (possibly a corruption of the Greek encheiridios, ‘handbook’). Part i defines music in Augustinian terms as ‘bene modulandi scientia’ and states that the skilled or learned singer (cantor peritus) must know the properties of the individual pitches, the rhythmical aspects of chant performance, and other things beyond these (extrinsecus occurrentibus) that are never clearly defined but might refer to polyphony or possibly (as one 11th-century gloss suggests) even singing ability (bona vox). In addition to describing piecemeal the dasian pitch set of 18 notes and their correlative symbols and tetrachords, SE discusses at length common errors in singing chants, caused by misplacing the semitone in a melody, all of which are represented graphically as well as in words. These examples also emphasize the pentachordal structure characteristic of the dasian system (which also produces modal identity at that interval). Part i closes with a discussion of how chants may be adorned by varying the lengths of notes; the description is not precise but does indicate that the ratio of long to short notes is 2:1, that lengthening of notes would be especially appropriate at the ends of phrases and verses, and that entire text units (such as a psalm verse) could be doubled or halved in tempo. Nonetheless, the oldest manuscripts are lacking clearly legible examples, so any reconstruction of the illustrations is speculative.

Part ii of SE is itself subdivided into (1) a discussion of the symphonies and organal singing, and (2) an introduction to quadrivial thinking which asserts the importance of number and mathematics for music and which adduces an extended passage from Augustine’s De ordine (ii.4f) to underscore how number is the foundation of all the disciplines of the quadrivium. This discussion prepares the way for part iii, which is almost as large as the previous two parts combined and consists primarily of a systematic but selective account of number theory drawn mainly from Boethius and Cassiodorus. Topics include definitions of numerical and spatial (continuous) quantity (multitude and magnitude, respectively) and how ‘in likeness to both kinds of quantity, arithmetic brings forth out of itself music’ so that ‘when the differences of pitches are based on quantity in this way, the pitches sound together in a sweet mixture according to the contrary natures of the two types of quantity’ (Schmid, 116.12f; Erickson, 70). Moreover, because music treats non-movable quantities not in terms of themselves (per se) but in relation to other such quantities (ad alium), an investigation of inequalities is necessary. There thus follows a detailed exposition of types of inequality (multiple, superparticular, superpartient, multiple superparticular, multiple superpartient) and why only two types of inequality – multiple and superparticular – are suitable for music. The intervals of music are matched with multiple (i.e. duple – 2:1, triple – 3:1, quadruple – 4:1) or superparticular (sesquialter – 3:2, sesquitertian – 4:3, sesquioctaval – 9:8) ratios. Then, beginning from the integer 192 and using these ratios as multipliers, an octave scale is constructed with the resulting numbers 192 216 243 256 288 324 364½ 384 representing the pitches (Schmid, 142.477–144.510, 145.descr.4; Erickson, 86f, fig.43). Although uncommented upon, this series is not congruent with any pair of tetrachords in the dasian system but matches rather the modern C major scale, which is the basis for most of the diagrams in part iii, and is possibly connected with the scale given by Hucbald that he associates with the organ (GerbertS, i, 110b–111a). There then follows a monochord division to produce the same scale. Finally, in the treatise’s closing paragraphs, the discussion reverts to the different intervallic arrangements of tetrachords and their relationship to the modes by the placement of the semitone, reasserting that, in the dasian scale, modal identity is to be found at the 5th degree but not at the 8th. This means that when an octave consonance is desired with a given tone in the scale, the octave must be made perfect, even if this means going outside the pitches of the dasian scale. The treatise closes non-climactically with the statement that such application of the duple proportion ‘both preserves the symphony [of the octave] and retains the category of trope [i.e. mode]’ in the two voices.

Sources, dating, authorship, dissemination

If the number of extant sources (46 listed in Schmid, 1981; plus one more described by Lochner, 1988) is any indication, the Enchiriadis treatises must be considered among the most widely read musico-theoretic texts of the Middle Ages. Only Boethius’s De institutione musica, the dialogue attributed to Odo, and Guido of Arezzo’s Micrologus survive in more sources than ME and SE. Moreover, other medieval treatises much valued today, such as Hucbald’s De harmonica institutione, had very little currency in the Middle Ages, whereas Guido of Arezzo, Berno of Reichenau, Hermannus Contractus, and the author of the Quaestiones in musica all draw on (or criticize) the terminology and teachings of ME and SE.

Regarding the origins of ME and SE, recent research suggests that the oldest extant source, D-DÜl H 3, may have been copied from the non-extant original of SE. Surviving only as a fragment, D-DÜl H 3 was most likely written at the Benedictine abbey of Werden (near Essen) in the last years of the 9th century, possibly during the rule of Abbot Hoger (d 906), to whom authorship is ascribed in some of the earliest sources (see Torkewitz, 1997, and 1999). The oldest more or less complete source of both treatises, from 10th-century St Amand, is F-VAL 337. There are also five later sources that transmit the so-called Inchiriadon (ed. in Schmid, 1981), a compilation of an apparently earlier version of part of ME mixed with aspects more advanced than ME. More primitive in this work is the less technical and less sophisticated use of Boethius’s De institutione musica than that found in ME (see Duchez, 1980); more advanced is the incorporation into its modal theory of the notion of modal octave species and, associated with them, the Greek tribal names Dorian, Phrygian, Lydian and Mixolydian (Schmid, 204.462–4), although the last name occurs only in the associated diagram and not the text (204.descr.14). In any event, the complete texts of ME and SE as they are found in the early sources are probably not in their original form: as mentioned above (§1) chapter 19 of ME would serve more appropriately as an introduction to SE; nothing prepares the reader in the opening passages of SE for the enormous emphasis on number theory that dominates more than half of the treatise; and as a practical handbook, part i and the first half of part ii can be seen as roughly equivalent to ME and satisfy quite adequately the practical information needed by the ‘skilled singer’. These and other features suggest that both ME and SE have complicated histories involving several stages of evolution – of addition, replacement and of shuffling of materials – ultimately resulting in the texts that have been transmitted. It is therefore possible that at least parts of the texts date from the first half of the 9th century; but it also seems likely that the standard versions of ME and SE known today are from much later in the century.

Specific similarities in content (dasian notation, discussion of organum etc.), as well as dissimilarities to other treatises of roughly the same period (Aurelian of Réôme, Hucbald of St Amand), clearly suggest that ME and SE came from the same intellectual and musical environment. However, there are also indications that ME and SE did not have the same authors. (It is also possible that both had more than one author, and that, especially in the case of SE, a compiler rather than an author might have played some role.) Sometimes this is revealed in small differences in locution: ME refers to ‘the tetrachord of the graves [notes]’ but SE to ‘the grave tetrachord’; similarly, neuma regularis in SE is simply neuma in ME. Sometimes there are more substantial differences: a change of locus for the organal voice when the chant melody has a wide range is discussed in ME (chap.18) but not in SE. Moreover, the term ‘organum’ is not used identically in both: whereas both use it to designate the organal voice, only ME equates it with the two-voice musical texture also called diaphonia. Finally, ME’s author (chap.16) is very aware of the necessity of justifying the 11th as a consonance (as does Ptolemy, Harmonics, i.6, translated by Boethius, De institutione musica, v.9) to rationalize octave doublings of organum at the 4th, but SE presents the 11th (in different places) variously as a consonance and as a dissonance and lays great stress on the principle of commensurality or connumerality (Schmid, 109.198f, pp.125–8, passim; Erickson, 67, 76–8), which does not apply to the ratio 8:3 (the 11th). Thus the theoretical justification for octave doubling of organum at the 4th illustrated elsewhere in SE is undermined (Schmid, 96.descr. and 100.descr.36; Erickson, 59, figs.32 and 62, fig.36). This inconsistency contrasts markedly with ME, which strongly argues that the 11th is a consonance.

The dasian scale and notation.

One of the most characteristic features of ME and SE is the use of a notation that is found only in a small number of theoretical writings (a rare, partial use in a practical source occurs in F-Pn 9488; see Santosuosso, 1989, p.35); it is one of the few precise pitch notations used before the development of the staff in the second half of the 11th century. Therefore, the melodies represented by this notation – mostly from the Office Hours and none from the Mass – in the Enchiriadis treatises are among the oldest examples of melodies whose precise pitch content is known. Dasian notation is so called because it is based on the use of the Greek grammatical accent for rough breathing known as the daseia: ‘. By combining it with the letters ‘C’ and ‘S’ and rotating the symbols (notae, figurae, karacteres) in various ways, the symbols for the 1st, 2nd and 4th pitches (protus, deuterus, tetrardus) of each tetrachord are generated; the 3rd pitch (tritus), which marks the semitone – ‘the very heart and soul of music’ (Schmid, 151.590f; Erickson, 90) – has an anomalous set of signs to signal its distinctiveness. The entire scale of 18 pitches, made up of four named tetrachords and two additional pitches added at the top. Although the authors of ME and SE both refer to the ‘dasia’ in connection with the notation, presumably because of the familiarity with the grammatical sign, the same graphic form is also a note form of Greek vocal notation transmitted by Boethius in his De institutione musica (iv.3).

Although this arrangement has elements in common with ancient Greek theory (tetrachords, 18 pitches etc.), it is different from all other tetrachord-based systems. Generations of scholars have been puzzled by the inconsistency of intervals at the 4th and especially 8th degree, since ME and SE both discuss octave doublings and (essentially) parallel organum at the 4th. It is possible that the pitch series actually corresponds to the melodic content of 9th-century melodies, which were later modified when an octave-based modal theory was imposed on the chant repertory (see Phillips, 1985).

Theory of the modes.

The eight ‘modes’ or ‘tones’ (cf Atkinson, 1987) are described in the Enchiriadis treatises with greater precision than in Aurelian’s (presumably) earlier Musica disciplina (c840), using both final and ambitus as criteria. Each mode has an authentic and plagal form, sharing a final but having different ranges: the lower boundary for both is said to be the 5th below the final, while the upper boundaries are a 9th and a 5th above the final for authentic and plagal modes respectively.

SE also recognizes that transposition at the 5th degree does not change the mode. Tones a 5th apart have the same name, hence the same function; therefore, SE asserts, they are ‘concordant with each other because of a certain natural kinship [socialitas]’ (Schmid, 73.161f; Erickson, 43); however, tones a 4th away (compares, ‘compeers’; Schmid, 82.320; Erickson, 48) are also said to enjoy a similar relationship (although the term compar is also used for a note a 5th away; Schmid, 173.159, Erickson, 42). SE also finds these notes ‘associated with the final’ used as the last notes of phrases (comma, colon; Schmid, 82.321–3, Erickson, 48f).

The modes in ME/SE are named from their finals and qualified by their ranges, e.g. protus authentus, protus plagis, although other terms are used (e.g. minor, subiugalis and lateralis for plagal). The tribal names Dorian, Phrygian, and Lydian (a trio that frequently appears in Greek music theory as well as in Boethius) also occur (in ME only), but they are not associated with specific modes until the Alia musica and, as mentioned above, Inchiriadon.

Theory and practice of organum.

Although a discussion of singing in parts was new in the theoretical literature, the practice was apparently not a novelty when the Enchiriadis treatises were written: ME refers to it as ‘diaphony, that is, two-voiced song, or, customarily, organum’; SE does not, in fact, give this practice a name. (However, in both treatises organum is a term for the organal voice.) Organum properly refers to singing in 4ths and 5ths. In the Enchiriadis treatises, the organal voice (vox organalis) is below the principal voice (vox principalis) in a basic two-voice texture.

Within the dasian system complete parallelism is possible in organum at the 5th , but not at the 4th , because the interval between a deuterus pitch and the tritus below it is a tritone, not a perfect 4th, thus prohibiting the organal voice moving below tetrardus, especially at the beginnings and endings of phrases. In ex.3, therefore, the two voices begin in unison to avoid the tritone E–B that would occur on the third and last syllables. According to SE: ‘at the symphony of the diatessaron an organal voice does not so simply and consistently accompany a principal voice as at the diapente but, by some natural law of its own, it stands still in certain places and is not able to proceed further consonantly’ (Schmid, 102.87–90, Erickson, 61).

In chapter 18 of ME, it is further shown that when the chant melody shifts into different tetrachords it may be necessary for the organal voice to do likewise, the new lower limit being the tetrardus of the new tetrachord.

Octave doubling is not regarded as organum, but rather as a natural phenomenon produced, for example, when men and boys sing the same melody. Although octave, 5th and 4th are all considered ‘symphonies’ (Schmid, 23.6–8; Erickson, 13), the octave is singled out as an equisonus (‘equal-sounding’) interval, ‘for in this symphony a pitch is revealed anew’ (Schmid, 26.27f; Erickson, 15). Nonetheless, octaves may be employed in the performance of plainchant or of organum. In organum, principal and organal voices are subject to octave doubling both above and below such that each voice could sound in three octaves, the highest being sung by boys; SE even gives examples of doublings at one or two octaves above the basic organal voice, which itself, however, is omitted, suggesting that virtually any combination of up to six parts might be employed (Schmid, 96.descr.6 and 101.descr.11; Erickson, 59, figs.32 and 63, fig.37). Moreover, the use of instruments was also apparently sanctioned: ‘For human voices can be mixed with one another and with some musical instruments, not only two and two but also three and three’ (Schmid, 40.10–12; Erickson, 22).

It should be noted that in the manuscript sources examples illustrating organal practice more often than not dispense with dasian notation for voices other than the chant melody; the notation was designed to represent the plainchant melodies only and is therefore generally incapable of representing all the pitches used in an organal performance, especially at the 4th and/or with octave doublings. Nowhere in the treatises is it suggested that the notation was invented to accommodate multi-voice textures.

Literary sources.

One of the most interesting and impressive aspects of the Enchiriadis treatises, distinguishing them from all other medieval writings on music theory, is the wide range of classical, patristic and other late Latin sources that they draw upon. There are terminological borrowings, direct quotations and/or paraphrases of passages from Virgil’s Aeneid, Censorinus’s De die natali, Calcidius’s translation and commentary on Plato’s Timaeus, Augustine’s De musica and De ordine, St Jerome’s Vulgate (Romans), Boethius’s De arithmetica, De institutione musica, and Consolatio philosophiae, and Cassiodorus’s Institutiones. By far the most influential author is Boethius, not only in terms of the number of works utilized but as regards the extent of the borrowings. Boethius’s name is also invoked more than any other author; he is referred to as the ‘doctor magnificus’ (Schmid, 44.11; Erickson, 25) and ‘praestantissimus auctor’ (Schmid, 59.39; Erickson, 32; see also Cohen, ‘Metaphysics’, 1993). Second in importance is Augustine (a direct source for SE only), whose De musica probably provides a model for the dialogue form and opening of SE and also for the brief discussion of rhythm found at the end of part i SE, and whose reflections on the origin of the various arts and disciplines in De ordine is quoted at some length in part ii. Cassiodorus also figures prominently as a source for the introduction to quadrivial studies in SE, part ii, and in the discussion of inequality in part iii, although mixed in with Boethian and other materials.

The name of the 9th-century philosopher Johannes Scottus Eriugena has, since the time of Coussemaker, been associated with ME. Although certain Neoplatonic elements in both ME and SE have been attributed to Scottus (Phillips, 1985), there is really no direct evidence that he influenced or was influenced by the two treatises; in fact the Neoplatonic and neo-Pythagorean aspects can be shown to have a more likely origin in Boethius (Erickson, 1992).

Byzantine elements.

ME and SE contain many features that recall Aurelian’s presumably earlier tract Musica disciplina and which may well reflect Byzantine-Frankish contacts in the 8th and 9th centuries: eight categories of mode (suggestive of but not identical with the Byzantine oktōēchoi) divided into two groups of four, although the modes themselves are different; a basic scale system made up of tetrachords; the Greek-derived terms protus, deuterus, tritus, tetrardus; the noenoeane formulas (used in ME and SE to exemplify different modes) that recall the Byzantine enēchēmata.