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How Is Technology Useful in the Study of Ancient Music?

In: Greek and Roman Musical Studies
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Stefan Hagel Austrian Academy of Sciences; University of Vienna Vienna Austria

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Abstract

A variety of possible applications of modern technology for music-archaeological purposes are discussed: from studying and evaluating musical finds and acoustical environments through the presentation of pitch structures down to databases, their statistical evaluation and the necessity and promises of dedicated coding.

Abstract

A variety of possible applications of modern technology for music-archaeological purposes are discussed: from studying and evaluating musical finds and acoustical environments through the presentation of pitch structures down to databases, their statistical evaluation and the necessity and promises of dedicated coding.

Technology and music have gone hand in hand since the Palaeolithic. Among the most amazing feats of Europe’s early human craftsmanship, the famous mammoth ivory flute from Geißenklösterle features highly, while the East boasts the precision of the Neolithic flutes from Jiǎhú 贾湖. The Metal Ages saw huge bronze horns most delicately cast to exacting standards in the West and enormous sets of tuned bells in the East. Classical Antiquity equipped its modulating wind instruments with seamless metal tubes revolving airtight within each other. The Middle Ages built impressive organs, audible across whole cities, and the history of technical advancements in modern instrument production up to the electronic era is well known. Stone and wood, bone and clay, hides and stalks, all sorts of materials have been turned into sound tools serving at all societal levels. Quite obviously, important aspects of ancient music would remain incomprehensible without a grasp of its technical basis – and the technical limitations that might have translated to musical limitations. Unfortunately, this most obvious aspect of ‘technology’ might currently also be one of the least fruitful, simply because ancient craftsmen were often so incredibly skilled that we may struggle to replicate their feats even with modern means. Here, therefore, it is rather the music of antiquity that informs our understanding of ancient technology than the other way round. The present contribution will therefore concentrate on different aspects, mainly the application of exclusively modern technologies to music-archaeological questions.

Which kind of possible approaches to the music of antiquity are there? Firstly, the part scholarly, part scientific background of music archaeology suggests using technology to obtain a better understanding of ancient musical culture, or at least its material and auditory components. Besides, technology may also help re-translate the intellectual results into auditory reality. In practice, both approaches go hand in hand, optimally fertilising each other, and sometimes producing welcome side effects which I will address at the end of this contribution.

1 Realising Pitches and Scales

When first purchasing a computer with a sound chip a quarter of a century ago, one of my first projects concerned the realisation of ‘ancient scales’ as well as playing ancient melodies in those scales. I have not been alone in this endeavour1 (though there were hardly any means of finding out in a world before the internet), and realising the purportedly precise pitch relations worked out by ancient writers has remained a worthwhile application of computer technology ever since. Around the turn of the millennium I published the known fragments of ancient melodies on the internet as sound files, using roughly contemporary ancient tunings.2 Because the technology of that time is now outdated and we have reached new insights regarding the relation of tunings and keys especially in citharodic music,3 Chrēstos Terzēs and I are currently preparing a new internet edition, which will not only supplement the scholarly editions with an audible aspect, but provide a critical apparatus, too, and allow visitors to experiment with various tunings and tempi.

On the downside, the very lack of effort in setting up various tunings by electronic means may easily lead to inadvertently misconstruing their ancient conceptual background. Only concerning the scales derived and reported by Claudius Ptolemy are we on reasonably safe ground. The experimental instruments he developed to exacting standards and described in some detail inspire confidence that the intervals he heard on them were indistinguishable from those our computers produce; and the explicit association he makes between some of his divisions (but not others) and professional lyre tunings, resting his ultimate proof on the musical ear of the contemporary reader, firmly associates his mathematical constructions with the concert halls of his time. This is not similarly the case with any other author. Up to the late Classical period, no monochords appear to have been used; later real monochords before Ptolemy were too clumsy for playing melodies at precise tunings rather than merely demonstrating the basic concords in the classroom.4 Pipes of various length ratios do not produce accurate results either and fingerholes even less so. Likewise, the seeming exactness of harmonicist-Aristoxenian terminology, which replaced integer ratios with notions such as quartertones and thirds of tones, could not possibly be verified with any pre-modern tool. The same goes, very probably, for Roman-period constructions of more extensive systems in huge numbers, which it was not possible to apply to the ruler on the monochord without some kind of approximate conversion (of which there is no hint in the sources). It follows that, in antiquity, the bulk of quasi-precise ancient data on interval sizes was either never realised as an auditory experience at all, or if so, did not necessarily reflect musical reality. In all these cases, modern precise technical realisations may have some intrinsic interest but must obscure rather than further the understanding of ancient music. After careful sieving, computer-aided renditions of the rest – basically the old scales realised ‘by consonance’, i.e. exclusively by fifths and fourths and Ptolemy’s cithara tunings – may be of invaluable help in appreciating the pitch structures of ancient music, both to the scholar and the broader public.

As an example of computer-based dissemination, I have developed a Virtual Lyre for the touring Archaeomusica exhibition of the European Music Archaeology Project (EMAP), using sounds sampled from the gut strings of a reconstruction I built together with Scott Wallace in 2003.5 It allows the user to select any of the six cithara tunings detailed by Ptolemy and play these on a nine-stringed instrument on a large multitouch screen, plucking, strumming and stopping the strings much as on a real instrument (with the obvious disadvantage that both hands need to access the strings from the same side instead of both sides of the window of a real lyre). On the more scientific side, I have written a program that recreates Ptolemy’s monochord tables, both in Greek hexagesimal notation and modern fractions, and can also play the resulting pitches.6 Apart from proving the concept of our understanding of the mathematical background of the tables and providing a convenient means for checking the accuracy of modern editions, it can also serve as a tuning tool for musicians interested in historical instruments or in training their ears and voices to second-century CE music.

Ptolemy’s proofs are set out in two complementary ways: first, he encourages his readers to set up the proposed mathematical structures on the experimental instrument and ascertain the identity of the resulting scales with those familiar from musical performances. Then, he inversely asks the reader to establish scale fragments from familiar lyre tunings by ear, from whose mutual relationships further conclusions are drawn. While the full capacity of these tests would have been accessible only to Ptolemy’s contemporary readership – or maybe only to those few who had access to the required devices, perhaps in Ptolemy’s own study – the assessment of his work nonetheless depends on the feasibility of the proposed procedures. Few will have the time and skills (or funding) to build a Ptolemaean eight-string canon, let alone his more sophisticated devices. A digital version, though not able to enlighten us about the technical difficulties the ancient theorist might have faced, at least enables us to experience the combination of auditory and visual clues that was typical of such instruments.7

2 Studying Instruments

When it comes to the remains of sound tools, it goes without saying that the usual suspects of archaeological technology are indispensable. These include, perhaps most prominently, methods of dating such as radiocarbon dating and dendrochronology.8 The determination of the materials used may involve spectroscopy, most importantly using energy dispersive X-ray fluorescence9 and scanning electron microscopy, but also archaeozoology and archaeobotany. These tools may shed light on important questions about workmanship – for instance, whether or not different copper alloys were used for different purposes, and if so, what were the benefits and disadvantages of different materials, both in terms of manufacture (such as enabling the casting or hammering of delicate parts) and functionality (such as controlling friction and corrosion, especially where galvanic corrosion at contact surfaces may have come into play)10; these studies are still in their infancy. Imaging techniques also gain importance, above all in those kinds of sound tools where small differences may have comparatively large effects on the produced sound. All these however come with their limitations and caveats. While X-radiography and computer tomography are indispensable when dealing with the cavities of aerophones,11 the resolution of the latter is normally not sufficient for assessing small mechanical details, while the former produces distortions that need to be carefully eliminated when taking measurements.12 More precise dimensions may be obtained from imaging external surfaces, which, whenever they exhibit a suitable texture, are accessible to photogrammetry and/or laser scanning. For internal surfaces, endoscopy may likewise have its say; a photogrammetric approach to endoscopy would be a highly welcome development, providing measurements that are sometimes excruciatingly hard to obtain. Microscopy, including scanning electron microscopy, may reveal traces of ancient production processes such as scraping, hammering, annealing, filing, or turning on the lathe, but also use-wear marks that can provide important information about how the sound tools were used.

But can modern technology also inform us about the original or intended sounds of broken, corroded, fragmentary remains? That will depend on how much one expects. For more than one reason, I do not think current computing can generate a realistic impression of what ancient instruments (or their modern reconstructions) would have sounded like. On the one hand, we are rarely in the position to assess all relevant parameters. This is even true in the comparatively simple case of woodwind instruments, which may be approximated as consisting of a vibration source (‘exciter’) and the system of cavities that determine which kinds of vibrations are enforced and which are oppressed (‘filter’). While the latter may be well enough preserved and lends itself to computation, the former may consist of air blown across a sharp edge (flutes), thin flexible materials opening and (nearly) closing a narrow pathway (reed instruments) or the lips of the player (brass), all of which are lost and/or could be manipulated, within certain ranges, by the player. This is probably most salient in the case of reed pipes, where the sound may vary greatly with the design of the reed regarding the size and thickness of its blades, the position of the lips and the exerted air pressure. Such parameters would need to be more or less randomly defined. But not even then do synthetic sounds come anywhere close to the richness of an actual instrument.13 Apparently the available algorithms do no justice to the complexities of the physical reality of setting a wind instrument in vibration, let alone to the additional filter effects from the cavities of the player’s mouth and pharynx. Much the same is true for string instruments, especially for the presumably all-wooden types that we only know from the iconography. In all these cases, computed sounds must currently fall short of those elicited from material reconstructions; consequently, any installations in museums or interactive websites are better advised to use wavetable synthesis based on recordings.

Nonetheless, physical modelling can have huge merits, as long as we do not expect it to take us all the way. Its greatest merit is doubtless the ability to predict the expected pitches of an instrument with considerable accuracy. Of course this does not apply to instruments with exclusively open strings, each of which could be freely tuned within a substantial range, as is the case with harps and lyres, but it is true for instruments with a vibrating air column of sufficiently regular shape, and for all those where the length of the vibrating medium is manipulated, be it by shortening an air column by means of opening side holes, or strings by stopping them against a fingerboard. Instruments of the horn family are particularly susceptible to physically modelling their oscillatory regimes and determining their fundamental frequency as well as the precise pitches of their various harmonics.14 However, this requires an instrument whose entire length is preserved well enough to take or at least infer the required measurements with reasonable confidence.

In contrast, even fragmentary finds of instruments with fingerholes and a basically uniform bore may allow at least a partial evaluation of their original musical capabilities, if carefully interpreted within the context of comparable finds and our general knowledge of ancient music. This applies first of all to the remnants of doublepipes (auloi/tibiae), which dominate the music-archaeological record of sound tools with melodic capabilities from Classical Antiquity. Since the mathematics of cylindrical resonators with a row of open and closed fingerholes (as well as corrections for wider and narrower sections of the main bore) are well known,15 these instruments lend themselves to a comparatively straightforward calculation of their available pitches.16 This is all the more important because none of them could ever be studied as a complete instrument. Even the best preserved objects lack at least their reed mouthpieces, which not only do influence the quality of the sound but whose extent also determines all the producible pitches and intervals. In such cases, a reconstruction of an instrument’s musical capabilities therefore involves not just a single set of calculations, but requires experimenting with one or several parameters which are varied within plausible ranges. Reeds, for instance, may have extended from their seats from as little as 2.5 cm to more than 7 cm. Wherever the especially fragile upper ends of the pipes are lost as well, the uncertainties become even larger – almost exponentially so, where some parts are incomplete or their correct arrangement is unknown.17 In such cases meaningful results are hardly attainable without software specifically designed for the purpose, which allows experimenting with various options and parameters while re-calculating the resulting pitches, intervals and scales in real time, interpreting these in terms of ancient and modern musical notes, comparing them with known musical structures and, wherever feasible, automatically searching for optimal configurations.18 I have recently adopted a similar approach for the evaluation of late-antique fretted lutes, where the original or optimal placement of the bridge needs to be estimated; here, however, the computational method has, all in all, merely confirmed the results of earlier manually conducted interpretations from one of the most important music-archaeological research projects before computer technology became more widely available.19

3 Material Reconstruction

One of the most important ends of music archaeology has always been the reproduction of sound tools. The most complete approach would aim at employing exclusively ancient technology; when focusing on music-making rather than manufacture, however, it normally suffices to produce objects whose physical characteristics match those of the originals closely enough. This latter approach is typical for the music archaeology of Classical Antiquity, if only for the simple reason that we do not know nearly enough about ancient technological processes to recreate them. Instead, we often struggle to obtain similar results with contemporary means. These may include not only modern machinery, but also tools operated by the computer (CDC). In this way, a digitally controlled lathe or a casting process starting from a printed wax model may reproduce the original shapes with greater precision than a human craftsperson. If these shapes were initially obtained by digital imaging, the scope for human error basically shrinks to feeding and using the software as well as the machines in a sensible way.

Sometimes original materials are of smaller concern than quickly fabricating experimental working models which incorporate a well-defined set of musically critical characteristics while merely approximating others that influence sound or pitch only slightly or not at all. This would be the characteristic scenario for adopting 3D-printing technology (‘additive manufacturing’). Wind instruments provide a typical example, where the crucial factor, a large difference between the impedances of air and the instrument’s wall, is satisfied by any reasonably stiff material. Short to medium-sized printed doublepipes, for instance, can work just as well as reproductions in wood and bone.20 With due caution and sometimes slight manual adjustments using sanding paper – even when printing the same parts twice, the resulting minute variations in diameter may be larger than admissible in the context of controlling the friction between concentric tubes – it has since also proved possible to produce working models of the famous mechanism of rotating sleeves found on Roman-period doublepipes like those from Pompeii, Poetovio or Meroë,21 using selective laser sintering (SLS) technology with Polyamide 12 powder.

4 Soundscape Studies

Sound production is always embedded in an environment, whose geometry and surface texture shape the way it will be perceived by listeners in various positions, and without the study of which a science of ancient sound must be incomplete. Hardly any ancient site, however, has survived unaltered, and complete on-site restorations are generally as unrealistic as would be a reconstruction in a different place. Only virtual reconstructions might therefore promise access to a fuller appreciation of past auditory events. Respective projects are normally spawned by an interest in dissemination by means of ‘immersive’ experiences, such as in exhibitions22 or, as virtual reality equipment becomes more accessible, through websites or computer-game-like software.23

Simulating a complex environment may require significant computing resources in addition to highly specialised IT skills. Few individuals will possess both the archaeological expertise to evaluate the validity of reconstructed ancient spaces and the technical knowledge required to assess the effect of changes in unknown variables on their reconstructed sonic characteristics, not to mention the music-archaeological experience required for discriminating between the various levels of historical informedness in the ‘reconstructed’ sonic events one might virtually place in a space, or their respective appropriateness for that space. Projects of such a kind must therefore not only be collaborative, but ensure ways of communication in which contributors coming from different fields are made aware not only of the potential, but more importantly of the various shortcomings associated with the available data as well as the applicable algorithms.24

5 Databases

The computer age, with its ever increasing storage capacities, has put the tasks of collecting and organising information on a totally new footing. Like all classicists, scholars of ancient music extract relevant material from common tools such as the Thesaurus Linguae Graecae,25 the Perseus Digital Library26 or the Beazley Archive,27 and like all musicologists, they may avail themselves of the rich material provided for instance by the Répertoire International d’Iconographie Musicale.28

Such collections will instantly produce valuable results, but these will likely represent arbitrary subsets of the catalogued evidence, especially when the material was not indexed specifically for musicological purposes. So it may be a good idea to look for ‘flutes’ when one is actually interested in auloi/tibiae/doublepipes, and in extreme cases, for ‘harps’ when searching for lyres. Anybody interested in finer details or contexts will need to sift through endless lists, which are nevertheless a blessing.

Images in particular are not always free to share. Legal issues may thus prevent especially databases assembled in more specific and therefore smaller projects from going online, barring most researchers most of the time from accessing precisely what might prove the most useful and best-indexed resources, compiled with a musicological focus from the outset.29

Copyright questions are of smaller concern when ancient texts are provided with various sorts of machine-readable annotation.30 For musical studies, metrical data are of primary interest here. These may be made accessible only through an interface, limiting the capabilities of automated exploration,31 or in the form of files,32 typically containing text tagged in XML.33

6 Counting and Testing

Databases, however ambitious and extensive, do not add to our knowledge. With suitable interfaces, they will allow a human mind to explore some aspects of evidence about past musics, proving or disproving hypotheses or establishing new meaningful connections. In this way, modern technology merely continues approaches developed long before the digital age, though taking them to new levels regarding the comprehensiveness of the available material and the ease in accessing it. The full potential of electronic resources, on the other hand, can only be exploited by electronic means.

The recourse to statistical methods, above all, if applied with insight and due caution, can augment traditional areas of research with methodologies that allow the scholar to assign levels of certainty to various results, in a way that has long been indispensable in most research fields but has only rarely been applied to the study of ancient texts or musical documents. The reasons for this neglect are difficult to surmise. On the one hand, it is certainly true that a majority of minds that are drawn to Classical Philology, at least, are little at home with scientific methods. Add to this the inevitable inferiority complex of an increasingly struggling discipline desperately asserting its value within a society that no longer takes its inherited conceit for granted, and one might think to understand why anything smelling of STEM often seems to elicit more frowns than welcomes. But that is hardly the whole story, and some suspicion must be regarded as justified. As long as mathematical methods do not form part of the average Classicist’s training, assessing the merit of their application for particular research questions is difficult. All too easily methodological blunders might hide behind sufficiently technical jargon, especially whenever the data and/or algorithms are not sufficiently specified.

This is a veritable conundrum. Without a respective tradition, including established means of sharing the data on which publications are based, the burden of quality control in digital ancient music studies currently lies mostly on the shoulders of peer reviewers, practically none of whom can be expected to possess the blend of very diverse expertise required for assessing approaches to complex research questions. Similar concerns of course apply to other novel methodologies as well, such as computer modelling of acoustical processes as discussed above. Only where these employ a limited set of techniques that have become established in other disciplines as well, can we expect a more solid fundament of scientific quality control in the near future. However, such considerations must not discourage researchers from exploiting the potential of deeply computer-based approaches. On contrary, only by adopting these much more broadly might a new generation of scholars be able to find more definitive answers to old questions that have proven impermeable to the circularities of traditional reasoning. On balance, however, the neglect of the latest technical potential probably presents a much smaller danger to ancient musical studies than does their naïve adoption at the expense of the traditional tools of philologists, historians, ethnomusicologists, music theorists and so on. Hardly anything can do more damage than claims produced with the help of awe-inspiring technology that no one can assess by people who have insufficiently engaged with generations of scholarship and therefore failed to grasp some fundamental conceptions.

Statistics is notoriously prone to mistaken application – not because it is an unreliable science but because doing it right may involve counterintuitive procedures. Most people will be aware that counting and comparing instances is wrong in most situations, while percentages are better: the note MM is found about 113 times in the Hellenistic period and 186 times in the Roman era, but this does not indicate that it became more fashionable, for the simple reason that we have so much more material from the latter period. Actually, when comparing percentages, the use of the note has dropped (from 9.4% to 8.6%).34 But even the percentages are devoid of musical meaning. An unsuspecting reader would likely conclude that the difference is hardly worth mentioning. A more detailed investigation of the musical documents in contrast reveals that the musical conventions were completely overturned during the transition between the two periods. In fact, MM mostly serves as Phrygian mésē in the early documents, where 93.8% of its instances come from pieces in the ancient ‘flat keys’ from Hypophrygian to Dorian, which later all but vanish from the evidence. The Roman-Imperial pieces, in contrast, employ MM only as Lydian diátonos, a note that the Hellenistic preference for the chromatic had previously marginalised in favour of khrōmatikḗPP.35 Two basically independent revolutions, one abandoning the ‘flat’ for the ‘sharp’ keys, the other re-establishing the dominance of the diatonic by phasing out the chromatic and enharmonic genera, together brought about the accidental result of hardly affecting the frequency of a particular pitch, whose musical meaning had however transformed completely. Curiously, instead of the typical case of side effects being mistaken for having explanatory value, we have here an instance of two side effects almost cancelling each other out, so that potent causes become all but invisible in a particular statistic.

If such complications can be found in a simple example, one can imagine what more complex research questions might entail – most of all, those where musical issues are entwined with linguistic considerations. This concerns not only the fragments of ancient vocal melodies but especially the study of ancient ‘lyrical’ metres and what it may reveal about the rhythm of their original musical setting. There are important linguistic aspects that merit consideration: the placement of accents, which may have been expressed in the musical setting or not; submetric characteristics of individual syllables that may become meaningful when the text is understood as song; details of responsion between strophes that basically follow the same metrical scheme.

The greatest advantage of a valid statistical approach is its robustness. The evaluation of individual passages or fragments is often fraught with difficulties related to uncertain readings and doubtful transmission. When a larger corpus is evaluated, in contrast, significant tendencies are expected to stand out in spite of such problems: for many research questions, these merely create some random noise, against which the non-random signal of all the correctly transmitted instances will still stand out. Caution is only due wherever the editors of the analysed texts may have considered precisely the questions under scrutiny – for instance, by emending particular metrical abnormalities in poetry, or melodies for better conformity with pitch accents.36 The detection of significant tendencies furthermore requires engaging with the concepts of ‘tendency’ and ‘significance’. The latter is more straightforward, since mathematics provides ready-made formulas for many situations, many of which have become part of the standard equipment of spreadsheet software. Tendencies, on the other hand, are tricky. In order to know whether some characteristic occurs more or less often in certain circumstances than would be expected, it is necessary to know what would be expected. At any rate, in our field this is hardly ever some average value, as becomes obvious by briefly inspecting any example from metrical/rhythmical/accentual studies. For instance, it is long known that many ancient melodies follow the word accent to some degree. But where only some agreements are observed, in contrast with more or less blatant disagreements in other places, how can we tell a composer’s intention from purely random agreement? In other words, how many agreements and disagreements (of various kinds) would be expected for a random melody that still exhibits all stylistic features of the actual melody? Since a clear-cut definition of melodic style is impossible, an answer to this question can only be approximated, for instance by shifting the words of the text randomly around to various positions in the melody and observing the agreements and disagreements these configurations create, or by comparing the actual melody with random computer melodies created by adherence to certain characteristics found in the actual melody. Charles H. Cosgrove and Mary C. Meyer have developed such methods and applied them to the more substantial fragments, with interesting results.37 Most surprisingly, one melody, the so-called Ajax fragment (P.Berlin 6870, 16–19), appears to have been composed specifically against the word accents. This finding is so important that inspecting its credentials in more detail may form a worthwhile example for assessing statistical arguments. The piece in question contains 9 words, in none of which the accentuated syllable happens to incorporate its highest melodic pitch – indeed an eye-leaping clash. The authors do not specify the expectation values their three alternative algorithms created for the specific piece, but since they say that overall these ranged between 44% and 80%, it is clear that an observed 0% must be significant. Accordingly, the p-values lie around 0.5%, indicating that the chance of finding such a melody fragment would only be one in two hundred if the composer did not write the melody against the accents by design. Does this settle the case? Not necessarily, because the original scope of the study did not include only the Ajax fragment but all known fragments of ancient vocal music. From that pool, the Ajax fragment was singled out for being tested for intentional mismatch just because it seemed to show it. Such a process of preselection invalidates a simple test: a sufficiently large data pool will normally contain some weird instances as well. This is precisely the nature of chance. On average, a set of a hundred samples will contain one that, evaluated on its own, produces a p-value of one hundredth. Now the authors have not evaluated 200 pieces, within which we would indeed expect to find on average one outlier like the Ajax fragment, but only 27 (if I count correctly).38 Even so, the chance of finding at least one item with a p-value of 0.5% in a pool of 27 is almost 12%. Consequently, as long as there is no a priori reason to assume that of all extant documents it is precisely the Ajax lament that should have been composed against the accents, it appears that the conclusion that it was is not statistically warranted: we cannot reject the hypothesis of its forming a random outlier with reasonable certainty. At the same time, this does not imply that we would be entitled to assume that it was not composed against the accents. We simply do not possess enough material to be sure. Only a couple of words more might have sufficed.39 As things stand, a prudent interpretation needs to leave room for doubt: the Ajax fragment was probably composed deliberately against the word accents.40

Further objections might be raised against the particular algorithms for producing alternative melodic settings. For instance, the melodic sequence of pitches or intervals might not unfold independently from but interact with the rhythm, which in turn is entwined with the prosody of the words, which again determines possible locations of the accent. If, for instance, certain notes were associated with rhythmically strong and others with weak positions,41 this would not be reflected in the computer simulations and, as a result, the estimated expectations of accent-melody correlation might be too low.

In other circumstances, it may be possible to calculate expectations directly from the data pool. In metrical studies, for instance, one typically needs to compare some characteristics of the texts with those that would arise from a purely metrical arrangement of the poetic word material without concern for the feature under scrutiny. What this means may be differently assessed in different genera. Stichic versification, such as the epic hexameter or iambic trimeters with their typical caesuras and bridges, imposes restrictions upon possible locations of particular metrical word shapes and generates favoured configurations of such shapes.42 If one is interested in the characteristics of a certain position in the verse, one might calculate plausible expectation values by first creating a table of metrical word shapes that appear in that position, all with their relative frequencies, then evaluate how each of these would define the characteristic under scrutiny, and finally add up the products of these characteristics with the respective relative frequencies. For greater accuracy, it may be advisable to start out not from words but appositive groups, since these are much more relevant as metrical units.43 In order to resolve any doubts whether observed tendencies might be side effects of grammatical conventions in versification in spite of the liberal word order of the Classical languages, it may also be worthwhile to perform separate evaluations for different word types such as nouns or verbs.

In non-stichic poetry, the concept of localisation of metrical shapes has at most a very limited application and cannot serve for generalised statistical analyses. Expectation values can still be generated in analogous ways. Any metre-based evaluation of the free forms of choral poetry, for instance, will need to define the metrical patterns it examines. These can then be treated much like the verses of stichic poetry, by cataloguing the word shapes or appositive-group shapes attested within the patterns and comparing their characteristics with those of similar word or appositive-group shapes found elsewhere in the investigated corpus.44

We needed to go into some detail here to illuminate a crucial point. Processing the texts and evaluating what often become multi-dimensional tables with thousands or even millions of possible entries not only requires the help of a computer, but also of a programmer. No ready-made software will be able to deal with the specialised procedures required to scan ancient verse and extract specific metrical or linguistic information. On the one hand, modern technology thus explodes conventional methodological limits. On the other, it also stretches the required expertise beyond conventional comfort zones. This is often aggravated by typical sources of frustration when classicists and programmers need to cooperate while talking at cross purposes in different languages. Moreover, at the start of an innovative project it is hardly possible to know the precise requirements for its software, since every step may raise new questions which can be answered only by implementing additional algorithms. This calls for the closest possible collaboration throughout most of a project’s lifecycle, which may be comparatively costly. On balance, programming classicists are probably best equipped for implementing their scholarly conceptions, seamlessly fusing research and software development.

Tailored non-standard software, while necessary for many tasks of ancient music studies, exacerbates the issues related to our field’s underdeveloped culture of data sharing. Scientific results ought to be reproducible, but if this requires re-creating complex software even where the data are available, who should take on the thankless task of checking published results? Publishing relevant code together with the data addresses the problem only at first glance, because figuring out and evaluating somebody else’s computer program may be even more difficult than rewriting the whole thing. Anyway, in the case of sophisticated integrated tools, researchers cannot be expected to release much more of their work than would be required for assessing one publication, thereby giving away the basis of future ones.

7 Understanding by Coding

I will finish with what I think is a mostly overlooked advantage of software engineering in the humanities: the procedure of developing computer code for various tasks may put our comprehension of the underlying facts to the test. The failures of a program when dealing with ancient material, be it instruments, texts or melodies, mercilessly alert us to the gaps in our understanding. Writing software for metrically scanning ancient poetry, for instance, forces us to define ‘rules’ and ‘exceptions’ with absolute precision. Conversely, in many contexts, the specifics of software design may expose the underlying assumptions of an approach and consequently its potential weaknesses much more clearly than do customary publications, which may omit discussion of or gloss over similar logical flaws with skilful rhetoric.

The attempt to encapsulate what we think we know within the rigid framework of computer code may be especially rewarding in fields where our understanding is still incomplete, because it may help us to locate and define inherent problems. For me, it was particularly fascinating to work on automating the transcription of ancient musical documents to modern stave notation. Previous editors had to make many ad hoc decisions in the process of interpreting and manually transcribing the sources, regarding the value of a few note signs in unusual contexts and, above all, the interpretation of rhythmical notation. Is it possible to simulate their decision-making process? If so, what kind of information would the computer need? If not, is this just a sign of bad software design or does the failure contrarily expose human inconsistencies and biases? Of course we should not assume that the extant musical documents would necessarily ascribe to the same notational conventions, which is a priori unlikely given their very diverse dates, places of origin and cultural context (and some developments are obvious). Nonetheless it is essential that we spell out all major and minor auxiliary hypotheses that have, consciously and unconsciously, been informing modern transcriptions. It is difficult to imagine anything more apt to expose these than an endeavour to crystallise the essence of our reasoning in the structure of program code.

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1

Cf. Franklin 2005.

2

Currently available as Hagel 2012d.

3

Cf. Hagel 2012d, 219–326.

4

Creese 2010; Hagel 2012a.

5

Anon. 2015.

6

Freely available online: Hagel 2021d.

7

A virtual canon is included in Hagel 2021d. For visuality on the canon, cf. Hagel 2009, 210–16.

8

Cf. the spectacular results in Quiles et al. 2021.

9

E.g. Pelosi et al. 2016; Pelosi et al. 2018.

10

Cf. the not further substantiated claim that metal tubes rotating within each other in Roman-period auloi were self-lubricating in Byrne 2000, 282.

11

E.g. Bellia and Pavone 2021.

12

Cf. Hagel 2012b.

13

Cf. Sun et al. (2020) as well as Rodà et al. (2021), who also briefly discuss methods of synthesis. Note especially p. 368, with the sound sample referenced in n.6, based on a waveguide model (cf. e.g. Smith 1992): although clearly imparting the impression of a brass onset (as doubtless defined by the exciter model and in no way specific to the Roman instrument under investigation), the timbre of the notes then becomes much less distinct. Contrast Sun, Rodà et al.’s sober approach with the sweeping claims in Kouroupetroglou et al. (2021) – e.g. “will be able to hear how it sounds” (433), which seem not to be borne out by the dull and indistinct sound samples I have heard presented.

14

Cf. e.g. Caussé et al. 2020.

15

Cf. Benade 1960; Fletcher and Rossing 1998.

16

First described in Hagel 2004a. Note that a waveguide approach may easily omit important factors such as the presence of closed sideholes further up and open sideholes further down the pipe, as is apparently the case in Andreopoulou and Roginska (2012) – a study that in any case investigates not the remnants of an instrument, but an amalgamation of unrelated instrument parts of various diameters, jumbled together in undocumented ways. A more complete implementation is described in S. Polychronopoulos et al. 2021.

17

Cf. e.g. Hagel 2019.

18

Cf. Hagel 2021a.

19

Compare Hagel (2021c) – a publication compromised by an error in the second equation on p. 166, as Chrēstos Terzēs kindly informs me – with Eichmann 1994; Eichmann 2002.

20

The production of printed copies of the Louvre aulos (and also the Berlin aulos) at Middlesex University starting in 2014, undertaken by Neil Melton, Peter Holmes and colleagues in collaboration with the present author in the course of EMAP, considerably helped launch what is now regarded as an international revival of ancient doublepipes. Similarly, I have since printed and played models of the finds from Pydna, Paestum and Megara; cf. Psaroudakes 2008; Psaroudakes 2014; Avgerinou forthcoming; Hagel 2021b; Terzēs, Hagel 2022; cf. also Bellia 2019.

21

Cf. Hagel 2012c; Sutkowska 2015; Hagel 2019.

22

Cf. e.g. Anon. (2019), describing a virtual realisation of the theatre of Orange, including aulos music ‘played’ by a “double virtuel” of a modern performer.

23

Cf. Till (2018), an application combining the visual and auditory reconstruction of sites such as Stonehenge and the ancient Theatre at Paphos with the sound of period instruments. Originally developed for EMAP’s Archæomusica exhibition, it was subsequently adapted for all common operating systems.

24

Cf. Hagel 2021a, 403–5.

29

E.g. the MITOS database of the Archive of Musical Iconography and Literary Sources at the Aristotle University of Thessaloniki; cf. Goulaki-Voutira 2013. The world of Classical music archaeology is currently looking forward to the Repertorium Instrumentorum Musicorum Antiquorum (RIMAnt), prepared in a cooperation of Italian and French institutions.

30

On the problem of missing open-access versions of many texts, cf. Henriksson 2016.

31

Cf. e.g. Moore n.d.

32

Cf. e.g. Chamberlain (n.d.), who also provides an interface for displaying the metrical data, or Colombi et al. 2021 with an interface for searching metrical patterns (currently) in hexameters and pentameters.

33

On the shortcomings of XML and possible alternatives cf. Efer 2017.

34

The numbers are based on the notes not marked as doubtful in Pöhlmann and West 2001.

35

By the way, the difference between the periods can of course be established beyond doubt, in the case of MM boiling down to a 2×2 contingency table (‘flat’ keys vs Lydian and BC vs AD) with χ²=270.3 (266.2 with Yate’s correction) and p < 10–59.

36

E.g. West 1992, 10f.

37

Cosgrove and Meyer (2006), an outstanding study also to be recommended for its lucid discussion of the methodological problems in determining expectation. It is nonetheless worth drawing attention to one minor problem as an example of why painstaking philology is prerequisite to statistical analyses: the authors shed doubt on the accent-governed design of the famous Seikilos song (75), based on two ‘violations’ against eight ‘observances’ of the single accentual rule they evaluate: whether the accentuated syllable of a word includes its highest pitch. An overall assessment would need also to take the observance of other rules into account (81), notably the fact that three out of four circumflexes in the piece are set to falling pitch. More importantly, one of the ‘violations’ is illusory because ΕΣΤΙ should be accentuated στι, not ἐστ (Danek 1989). Finally, the authors duly provide alternative figures under the assumption that the initial ‘clash’ of a rising σον is melodically necessitated, as is commonly assumed. Indeed it may even be regarded as phonologically warranted by proclitic subordination of the pronoun, whose individual accent consequently becomes suppressed. Such details would be negligible in larger data sets; for a song with only ten evaluated words they become crucial.

38

Note that the items for which no simulation was run because the result was clear enough from the outset need to be included in this count.

39

In order to be significant at a level of 5% when taking the preselection process into account, the raw p-value for the piece would need to drop below 0.2%. From the given p-values, we can infer a simulated expectation value of about 44.5% (with n = 9; p(x) = 44.5% and x = 0 we obtain p = 0.5%, the average of the reported p values); consequently, with 11 preserved non-monosyllables the raw p-value would amount to about 0.15%, which would push the overall significance beyond the 5% level (p = 4.1%).

40

A note of caution is also due regarding mistaking p-values for expressions of the strength of a tendency instead of the certainty with which we observe it. The conclusions in Cosgrove, Meyer 2006 appear to be slightly flawed in that respect: “These comparisons illustrate how differences in the character of the pieces – word types, intervalic [sic] movement and repetition – affect chance accord. P-values go down as the average syllable count per multisyllabic word goes up; p-values go down as the average size of intervalic movement goes up; p-values go down as the frequency of repeated notes goes down” (80). This would be the case only if the sample sizes were all identical, since, as we have seen, even small changes in the sample size affect the p-value greatly. Instead, an adequate expression of the tendency to respect the word accents in the musical setting would need to give both the deviation from the expected value, x/E(x), and the p-level, as respective representations of the strength of the tendency and the certainty that it is not random. Even more useful would it be to combine both types of information within a confidence interval, such as: “with a certainty of 95%, the melody respects the word accents 1.5 to 1.8 times more often than would be expected in a random distribution”. This would also permit a straightforward graphical comparison of individual pieces: one nice chart may profitably replace pages of clumsy language and tedious figures.

41

Cf. Hagel 2022, 163f. with Fig. 13.

42

On approaches to ‘localisation’, cf. O’Neill 1942; Dik 1998; Hagel 2004b.

43

Cf. Hagel 1994.

44

For expectation values derived in such a way, cf. Hagel 2018.

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