We are currently living in a time when colourisation and photogrammetry are all the rage; sparkling words for dazzling effects intended to make the experience of the past more vivid, immediate and, even, meaningful. Thus Peter Jackson injected colour into old footage of WW1 soldiers in his documentary film They Shall Not Grow Old (2018), bringing faces and people back to life in a way which renders Jeremy Deller's re-enactment project in British train stations We're Here Because We're Here (2016) ploddingly cosmetic in comparison. Meanwhile, high-tech equipment is used to create 3D architectural models in stunning detail of places which have been hidden, invisible or damaged; from old IS tunnel systems to the grand ruins of the Acropolis. Through photography and computer design emanating very much from virtual reality and computer games, viewers gain a real sensation of moving within and inhabiting these historical spaces.

Angela Mariani's new book on medieval music is, in many ways, a similar venture. It is an eminently practical handbook, providing a summa of improvisatory practices developed over the last five decades by professional practitioners of medieval music. Clearly organised and presented – undoubtedly arising from Mariani's own profound experience in performance and university teaching – it is intended not only for performers but also for music historians and theorists seeking to understand a range of medieval repertories, both monophonic and polyphonic. The book brings medieval music, or the putative processes which underpinned the production and dissemination of medieval music, alive.

In terms of structure, the book opens with a number of chapters devoted to a broader methodological outlook around inventio and memory before moving on to a series of practical, chapter-length case studies on mode, dance, organum and poetry. At the very outset, Mariani is keen to emphasise the otherness of medieval music, thereby expecting minimal previous knowledge. More specifically, she seeks to create bridges between the diverse musical experiences of her contemporary readers and centuries-old medieval repertories. Thus references are made throughout the book to rock and roll, Celtic folk, Bach, Mozart, Duke Ellington or John Lennon. In other words, this is not a book which seeks to return to first principles and lay out exhaustive information on performance practice gleaned from Latin treatises and other writings from medieval Europe. Rather, it works pragmatically and, one could argue, honestly with the fact that musicians today will bring a range of skills, experiences and expectations to their encounter with these challenging repertories which date from the ninth to thirteenth centuries. As Mariani writes, ‘any performance we create – of any music – will also unavoidably contain ourselves’ (p. 7).

The two opening chapters are designed to address the twin concepts featured prominently in the book's title: improvisation and inventio. Mariani builds on the work of Mary Carruthers in Chapter 1, ‘The Process of Inventio’, by applying the concept of an active use of information stored in the memory for rhetorical purposes on to musical parameters. In effect, this entails a thoroughgoing socialisation in a specific musical idiom which includes internalising models to facilitate performances not bound to written materials. This intensive work with musical building blocks also informs Mariani's understanding of improvisation. She carefully breaks down various dichotomies that still ghost around some approaches to medieval music and music studies in general – improvisation versus composition, written versus oral or unwritten, primitive versus complex – and prefers to explore the ways in which orality and writing can mutually influence each other. In fact, this back-and-forth between the written and the memorised is an essential aspect of the book and forms the basis of the boxed exercises contained within the chapters which readers are encouraged to practise for themselves. Indeed, this subtle manipulation of learnt models, formulas and gestures according to context is given the special term ‘fluid composition’ by Mariani (p. 7). Having established the scope of these concepts, Mariani broaches in Chapter 2, ‘Living and “Imagined” Models: A New Oral Tradition’, the more vexed issue of using vernacular or world music models in the process of recovering medieval repertories. Again, she places this issue within a more dynamic nexus of concerns. First, she points out, as others have, that the collaborative work between Thomas Binkley (1931–95) and North African ensembles was more focused on processes and procedures, rather than a direct adoption – or appropriation – of Arabic intonations, scales or rhythms. This particularly concerned the ways in which unwritten traditions work in performance, but also embraced practices such as preluding. Second, she adjudges contemporary vernacular traditions as only one part of a ‘new syncretic model’ (p. 22) of performance practice which brings together a range of elements, such as textual documents, pedagogical influence, individual musical experience across different repertories, and interpretations from other medieval ensembles and vernacular traditions. By means of conclusion, these two more methodological chapters end with a series of exercises allowing the reader to hone critical skills with respect to medieval performance practice. Again, the approach is practical: it begins with an exercise which confronts readers with questions about their own musical ‘lineage’ (p. 25). Following this individual orientation, a further exercise is given which is based on parsing a medieval recording along the lines of different musical parameters and reflecting on the inspiration behind such interpretational decisions. As befits a pedagogical book, it is fundamentally shrewd to confront students first aurally with a recording as a means of deepening critical engagement with medieval music. Focusing primarily on a practical approach obviates the need, in the first instance, for a broader bibliography which – on the subject of ‘improvisation’ and medieval music – could have included recent articles by Leo Treitler in Archiv für Musikwissenschaft 72 (2015) and Andreas Haug in the Basler Jahrbuch für historische Musikpraxis 31 (2009).

Critical awareness is further sharpened in Chapter 3, which bears the somewhat provocative title ‘Notation and Memoria: What's Not on the Page’. Standard introductions to medieval performance practice might launch, at this point, into an involved taxonomy of notational forms in medieval Europe, beginning with the various neume families. Mariani takes the opposing approach by asking the simple question of what is not immediately apparent musically when analysing a folio of a medieval manuscript. One of the benefits of this approach is that it provides a ready-made toolkit for engaging with the plethora of medieval music manuscripts now available online. Similarly, it starkly distinguishes the scrupulous description of a source from its interpretation. Finally, it shines a spotlight on inventio and the possibilities for individual initiative. Of course, the amount of musical information in medieval manuscripts varies according to time and place as well as to the performing or other conventions underlying the copying process: Mariani thus presents two very different examples of notation with Hildegard of Bingen (1098–1179) and Martin Codax (fl. mid-13th century). These are analysed for what musical information can or cannot be directly extracted. This exercise lays the groundwork for introducing the practice of the ‘mnemonic score’. This comprises personalised performing materials – crib-sheets, as it were – which individual performers can prepare for their own needs. In some cases, this might comprise text, neumes (copied out judiciously from the medieval source), and a pitched transcription. At other times, this information might be reduced to text and neumes or even, with familiarity and confidence, to text alone. The process of making one's own working edition aids memorisation. Indeed, the chapter ends with Mariani drawing on architectural models of memory taken from the Rhetorica ad Herennium and Cicero's De inventione, superimposing the image of a columned temple on to the strophic text of the Martin Codax song presented earlier. Undoubtedly, such techniques could be of use for performers nowadays internalising medieval repertories. It is, nevertheless, difficult to avoid the slight unease in reading this chapter that performers will, ultimately, require a deeper understanding of nuance in medieval notation – especially neumes – in order to be able to mine the affective depths of any one chant. Indeed, in Mariani's own transcription on page 46 of the beginning of the Gradual, Viderunt omnes, from St Gall Stiftsbibliothek codex 359, page 40, the significative letters ‘s’ and ‘c’ above the neumes are missing. This may simply have been a casualty of layout but, of course, such signs were performing indications and very much set out ‘what's on the page’.

Chapters 4 to 7 each take one repertory in turn and culminate in a creative exercise at the end to produce an improvisation or fluid composition based on the practices, models and formulas outlined. The focus of Chapter 4, ‘Mode: The Vocabulary of Melody’, concerns effective ways of internalising modal behaviour or, more specifically, the modal behaviour of so-called Gregorian chant repertories of the Middle Ages. Recourse is made to modal formulas, neuma, intonation gestures and pedagogical exercises (‘Primum quaerite’) from the ninth century onwards as well as to tonaries. A modern systematisation is provided in the form of oblong boxes of heptatonic length, one per mode, which lay out the series of intervallic patterning alongside the letter-names of pitches, giving thereby a clear overview of the different species of the fourth and fifth in each mode which Mariani considers significant. These modal exercises are well known – Mariani also points to the work of Terence Bailey – but it is useful to be reminded that they can (and should) be internalised, not least as an analytical tool. As for the systematisation of the eight modes, there is never an uncontroversial manner of presenting them visually in class. Questions will always arise concerning the designation of the individual modes – Greek, Latin or numerical – or the apparent inconsistences in the use of individual pitches (mainly B-molle and B-fa). Nevertheless, this section on mode could have benefited in my opinion from placing simple modal materials at the start (e.g, psalm formulas) before moving on to more involved modal models (Alleluias, responsory verses) before arriving at a systematisation. Moreover, such a presentation may have underlined the flexibility within modal behaviour rather than its hegemonic status within medieval chant which, according to Mariani, also extends to secular song. This is a not uncontroversial statement and could have been further developed, including by reference to Benjamin Bagby's work on the possible role of instruments in furnishing modal materials for the voice. Instruments, however, take centre stage in Chapter 5, ‘Inventing Melody: Old Instruments, New Voices’, which ends with the composition of an entirely new estampie, based on melodic material taken from Hildegard's Ordo Virtutum. This is a wide-ranging chapter which takes in a number of vital issues: an idiomatic style of instrumental playing arising from a specific instrument; the improvisation of preludes, interludes and postludes; the place of the drone in accompaniment; the mouvance of a musical text; and the identification and use of ornamental figures in performance. Each of these topics would be worthy of a separate article in itself so the following complementary thoughts are kept brief. While Binkley's injunction of playing what the instrument wants to play makes sense, it does not on the surface expose the dialectical relationship between instrumentalist and an idiomatic playing style defined by the specific instrument (let alone the practical frustration of learning a medieval instrument). His championing of preludes and postludes marks out his performances of medieval music, but analytical work by Mark Everist and the present reviewer on the medieval cauda would provide further insights from historical models. As for mouvance, it can often be useful to bear in mind the social environment in which the music was performed as a key to variability: Dominican chant was quite strictly controlled but contemporaneous Parisian organa are found in myriad forms. Thus, the picture can, of course, be differentiated. This does not, however, detract from the ingeniousness of the Ordo Virtutum estampie, presented in full at the end of the chapter by Mariani.

Chapter 6, ‘Inventing Organum: Memoria and Formula’, is perhaps the most straightforward of the practical chapters as it steers close to the Vatican Organum Treatise, working through examples and creating convincing fresh improvisations of organum purum and discantus based on Viderunt omnes and thus neatly linking back to Chapter 3. Finally, Mariani delves deeply into the rhetoric of medieval Latin song in Chapter 7, ‘Playing Poetry: The Rhetoric of Invention’, which ends with a new melody for a Boethian metrum that was not supplied with notation in the Middle Ages. The central purpose of this chapter is to reclaim the affective power of monophonic song whose melodies can sound somewhat similar to the uninitiated. Thus Mariani embarks on a close reading of the Planctus cygni, underlining rhetorical devices used throughout the song. She then picks up the idea of the ‘mnemonic score’ from Chapter 3 again in devising a way of making the rhetoric of any one medieval song really speak: here, the reader is invited to work on and develop personalised translations which at first might be free but can then work more towards the line-lengths of the original medieval song. This subtle preliminary work on the text Cum polo Phoebus blossoms in Mariani's hands into a modally coherent, rhetorically shaped song.

In the final chapter of the book, ‘The Long Memory: A Reflection on Teaching Medieval Music’, Mariani turns her attention from the ‘how’ of medieval music to the ‘why’. At one level, the ‘relevance’ (p. 192) of the study of medieval repertories comes from the keen engagement with historical materials; this is the ‘long memory’ of cultural history referred to in the title. This is, undoubtedly, to be applauded but from another perspective Mariani's project could be viewed as the shorter history of a particular path in medieval performance practice of the later twentieth and early twenty-first centuries; namely, the remarkable, global impact of Thomas Binkley and the Studio der frühen Musik, his pupils Benjamin Bagby and Barbara Thornton who formed Sequentia and his other pupils from the Early Music Institute at the University of Indiana and the Schola Cantorum Basiliensis in Switzerland. As a summation of this work, the book is hugely successful and highly timely. However, Mariani is not only interested in looking backwards, but also forwards. She notes in her conclusion how curricula in conservatories and universities have changed over the last few decades and how the practice of medieval music can tessellate with current interests in musical vernaculars. This, she avers, will presumably cause challenges in terms of teaching and assessment as the back-and-forth of inventio and improvisation have to be delivered in the classroom in a different form to traditional teaching and examinations would need to take account of this fluidity. Yet as a prospectus for deepening knowledge and appreciation of the rhetorical refinement and affective power of medieval music – and providing the practical tools to achieve this – Mariani's book is a colourful, three-dimensional and, above all, inventive text.