Two Auloi from Megara

Greek and Roman Musical Studies 10 (2022) 15–77 brill.com/grms Two Auloi from Megara Chrḗstos Terzḗs | ORCID: 0000-0001-7988-1389 Austrian Archaeological Institute, Vienna, Austria christos.terzis@oeaw.ac.at Stefan Hagel | ORCID: 0000-0001-5654-4013 Austrian Academy of Sciences, Vienna, Austria; University of Vienna, Vienna, Austria stefan.hagel@oeaw.ac.at; stefan.hagel@univie.ac.at Abstract Two aulos pairs (Δ1965 and Δ1964), unearthed in 1980 and 2005 respectively at Megara (Attica), are exhibited in the city’s Archaeological Museum. Both are associated with metal sliding keys (resembling the keys on the well-known Pergamon aulos model), either mounted on the pipes (Δ1964) or displayed next to them (Δ1965). The present paper describes the parts, proposes a meaningful re-assemblage of the bone sections, and gives a detailed account of the sliding mechanism, which is here for the first time attested on finds of actual musical instruments, including an entirely new technology of speaker hole keys. A musical analysis, based on determining plausible reed configurations using software modelling, suggests that the finds represent a partially standardised design of professional modulating auloi, playing attested harmoníai while hovering between the enharmonic and chromatic. Keywords ancient musical instruments – Greek aulos – aulos syrinx – sliding keys – Pergamon model – ancient musical notation – Aristoxenus © Chrḗstos Terzḗs and Stefan Hagel, 2022 | doi:10.1163/22129758-bja10040 This is an open access article distributed under the terms of the CC BY 4.0 license. 16 1 Terzḗs and Hagel Introduction After a salvage excavation carried out in 1980 at the private property located at 6 Cheimáras Street (Megara, Attica), the archaeologist on duty, Pantelḗs Zorídēs, proclaimed the discovery of a certain number of burial gifts found in Grave xxxvii, which held a sarcophagus sealed with three covering plaques.1 Besides the skeleton of the deceased, the components of an aulos made out of bone and its set of keys were found, safely preserved in the stone-made coffin. The burial finds also comprise three female clay figurines and an unspecified number of broken pieces formed from molten alabaster. Zorídēs dated the burial to the earlier Hellenistic period and announced a complete publication. Subsequently, the fate of the Megara aulos remained obscure for more than three decades. In November 2015, Chrḗstos Terzḗs visited the Archaeological Museum of Megara for an autopsy of the exhibited instrument, and then applied for access to the relevant entries of the excavation inventory, hoping to be granted permission to examine and publish this important find. The aulos pair was displayed in a suitably tailored showcase under the inventory number Δ1965αβ, accompanied by nine bronze keys lying next to the bone sections, in four pairs of roughly similar items plus one. Surprisingly, another aulos pair, in many respects a sibling, was also exhibited there, under the inventory number Δ1964αβ, but with its bronze keys situated in what was presumed to be their original positions along the sidewalls of the pipes. In the following, we will refer to the older find, Δ1965, as ‘Meg1’, and to the younger find, Δ1964, as ‘Meg2’. The Museum’s sigla α and β refer to the original reassemblage of supposed pipes, even though we will need to modify it in the course of our study. The second pair had been unearthed in 2005 in the course of a salvage excavation of fifteen graves in the northern part of the ancient city cemetery, located along today’s Thēvṓn street. The segments were recovered and re-assembled, together with the bronze keys, in 2012–13 by Geōrgίa Theodṓrou, conservator of the ephorate. On July 13th 2016, at the 9th international MOISA conference, held in Athens, the archaeological context of the Megara Museum auloi was presented by Panagiṓta Avgerinoú, while Geōrgía Theodṓrou described the restoration of Meg2; moreover, a provisional re-assemblage and acoustical demonstration of the pair were presented by the present authors. Avgerinoú (forthcoming) dated both burials by the typology of the other grave goods, inferring that the individuals would probably have flourished in the first quarter of the 3rd century BC. She accepted the results of an osteological study carried out by Ylva Bäckström, suggesting that Meg1 had 1 Zorides 1980, 45. Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 17 accompanied a young female adult aged 20–25 years, whilst Meg2 belonged to an older man, probably aged 50–55 years. Regarding the excavation conditions of the latter, she admits that unconventional methods had to be adopted, given the inclination of the field and the narrowness of the grave, which forced workers to crawl within and pull out clay deposits using their arms as shovels, thus revealing ancient material. Of the other pair, apart from a b/w image of the offerings in situ, the archaeological registry, diaries and restoration data are officially lost. Hence, unravelling the riddle of the Megara auloi amounts to a risky venture, not only because of the absence of crucial metadata but, more importantly, due to the undocumented modern intervention on the archaeological material in the course of restoration and assemblage, which, although carried out with diligence and ingenuity, lacked indispensable archaeomusicological support. However, as we appear to be dealing with sophisticated instruments built for professional musicians, these have hardly exposed even small errors of design or construction. Consequently, by construing and disentangling the intricate design of the Megara musical finds – intricate, that is, in comparison with the known earlier instruments which comprised merely four sections with no mechanism – valuable archaeomusicological insights may emerge from these so far unique instruments, especially if a feasible reconstruction can be proposed. 2 Other Evidence for Slider Keys The evolution of ancient Greek music, particularly towards the end of the Classical period, doubtless brought about organological innovations. The invention of a modulating aulos, ascribed to the renowned Theban aulete Pronomus (late 5th century BC), was said to have enabled him to play Dorian, Phrygian and Lydian tunes on a single doublepipe.2 Unquestionably, such an expansion of the instrument’s potential implies technical modifications regarding the production of alternative pitch sets. The archaeological record attests to two distinct kinds of mechanisms.3 One consists of rotating sleeves, which are mostly known from Roman-period examples,4 where two or three metal layers covered the core of the pipe. Rotating against each other, these sleeves enabled 2 Cf. Ath. 14.631e, Paus. 9.12.5. 3 On auloi with sleeves, see Howard 1893, 7f.; for an extensive list of the published finds carrying sleeves and sliders, Hagel (2009, 337 n. 28) and Sutkowska (2015), who also offers a brief description of both types of aulos mechanisms. 4 For a detailed account of the rotating mechanisms of some auloi from Pompeii, dating from the Roman Imperial Period, see Hagel 2008, 53–5. Greek and Roman Musical Studies 10 (2022) 15–77 18 Terzḗs and Hagel selective covering and uncovering of one or more side holes, making different sets of holes accessible to the fingers at one time. Thus, aulos players became able to adjust both the register and the key (tónos) during their performances. A less sophisticated and probably older type of mechanism served an altogether different task: operating holes that were out of the reach of the player’s hands. Sliders, attached to the surface of the instruments, were designed for motion along their longitudinal axis, extending from the bass region up to the playing position of the hand. In the case of the Megara auloi, each pipe was equipped with three of them, accessing three distinct bass notes. Each ended in a plate, skillfully forged in a curved shape so that it fitted perfectly over the cylindrical bone surface. Rods of various lengths connected these plates to knobs that were evidently situated near the lowest two fingerholes of the pipe. By pulling down or drawing back a knob, the respective sliding plate was remotely set into functional motion. This kind of slider mechanism was originally discovered and described in the early twentieth century, on the basis of the cast of an aulos, or rather the lower half of one of its pipes, most probably once part of a votive statue. The fragment was found near the northwest gates of the Eumenic walls of Pergamon and seems to have been lost during the Second World War. According to Alexander Conze, who offered a comprehensive description, a detailed drawing and convincing functional interpretation of the sliders, the artefact must have been produced before the end of the Attalid Kingdom of Pergamon in 133 BC.5 The relative positions of the pipe’s metal keys can be specified as follows: while the two longer keys (numbered 1 and 3 in Conze) are mounted at opposite sides, the shortest key (2) sits right in between them, at their left side, if viewed from the blowing end. The long slider close to the upper side of the instrument, in turn, sits about 45 degrees left to the extant real fingerholes at the upper end of the fragment. This suggests that it formed part of the righthand pipe of the pair, assuming that the mechanism was operated by the playing hand. Conze correctly states that 1 and 3 shared the same fixing band (x); these bands, which appear wrapped around the pipe sidewalls, would have prevented any deviation from the slider’s predefined path along the pipe surface. The plates of the long sliders 1 and 3 operated the two downmost side holes; slider 3, the longest, is captured at its upper position, whereas the plate of slider 1 is shown covering its respective hole. Towards their upstream end, both pass over the fixing band (y) of key 2. The knobs at the upper ends of the 5 Conze 1903, 7f. Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 19 keys are placed in such a way as to allow one or the other of the player’s fingers to switch their states from closed to open and back. Conze also pointed out that the plate which we would expect at the downstream end of key 2 is missing, though there is also no trace of the respective hole that it would have covered. Note also the (incomplete) representation of a wrapping (z) beneath the sliders, which doubtless depicts the typical reinforcement of the socket-spigot junction that we frequently find on bone auloi. Conze did not comment on the utility of the oblong slots close to the upstream end of the metal keys, right beneath the knobs. These obviously formed the primary means of restraining the longitudinal motion of the sliders. However, such a slot would have been useless without a pin or nail that went through it and was fastened in the sidewalls, thus at the same time keeping the key movement parallel to the longitudinal axis of the pipe and establishing its boundaries. Without such a limiter, the forces exerted from the player’s finger would inescapably increase torque levels at the upper end of the band below, which might easily cause the rod to block, and in consequence bend or even damage its trail. Assuming the original pipe had been equipped with pins, those would have been fastened in the pipe sidewalls through the lower end of the slot of key 3, thus allowing remote covering of the respective side hole. On the other hand, the pins interacting with keys 1 and 2 should have passed through the upper ends of the respective slots, so that the holes would be uncovered by pulling the knobs back. However, while the presence of such limiters in the original pipe appears beyond doubt, the precise technical implementation of the two bands (x, y) remains to be explained: had they been made as a single bronze piece, it would have been next to impossible to assemble them around the rods; on the other hand, simple wrappings of leather or thread would necessarily be too tight to allow for unrestrained movement of the rod beneath them. Conze knew very well that efforts at a musical interpretation of the artefact are hampered by the incomplete evidence in combination with our limited knowledge about ancient music in general. While unmistakably describing the Pergamon artefact as a physical model of an actual instrument, part of a votive offering, he implicitly allowed for inadvertent deviation from the unknown original on the part of the artist when disregarding inconsistencies arising from the operation of the sliders, notwithstanding the seductive precision of the elaborate artefact. Virtually a century later Maurice Byrne glossed over the fact that the object is solid (i.e. it does not have the internal cavity that defines any wind instrument) as well as the missing plate of slider 2 together with its corresponding side hole, and wanted to promote Conze’s model to a Greek and Roman Musical Studies 10 (2022) 15–77 20 Terzḗs and Hagel part of an actual instrument.6 He calculated the presumed length of its missing part, accommodated further tone-holes, suggested a playing technique and thus interpreted it as an actual representative of a newly-introduced type of instrument, the “extended drone aulos”. Certainly, a unique surviving piece of evidence for pipes with sliding keys justified the publication of novel hypotheses concerning its living past; however, the Pergamon find was definitely no instrument, and a perfect level of faithfulness regarding its proportions cannot be presumed without further argument.7 In any case, few finds of actual slider mechanisms have so far come to light. Byrnes’ list comprised the aulos fragments from Meroë at the Boston Museum of Fine Arts,8 those from the Oxus Temple exhibited at two Archaeological Museums in Dushanbe,9 an isolated slider at the Berlin Pergamon Museum (Inv. nr. 30259) and the aulos Meg1. Apart from the second Megara aulos pair (Meg2), two separate sets of bronze sliders, each comprising three pairs of similar length (long/middle/short), are exhibited in the Archaeological Museum of Lefkada. Both were unearthed from graves in the southern cemetery of the ancient town, located at the northern end of the modern village Karyṓtes. The better-preserved group, originally misidentified as a set of “goldsmiths’ tools”,10 was dated approximately to the end of the 4th century BC, whilst an excessively corroded and still unpublished set (Inv. nr. 1758α-στ) was retrieved from a sarcophagus dated to the late classical era. Although the grave comprised disturbed remains of consecutive burials, the first quarter of the 3rd century BC, after which the cemetery was no longer used, constitutes the terminus ante quem for both groups of Lefkadas’ sliders. On balance, the technology of remote-controlled wind-instrument side holes outside the reach of the player’s hand is already attested from the second half of the 4th century BC at the latest. Interestingly, the available evidence comes from a broad cultural environment, extending from (Late classical) Western Greece and the Meroitic Empire (in the early Roman Imperial age) to the easternmost borders of the (Hellenistic) Middle East, though, while the various instances are almost certainly connected by a common technological history, the associated musical practices need not always have been similar. 6 7 8 9 10 Byrne 2002, 367–9. For a positive assessment, cf. Hagel 2009, 347–9. Bodley 1946. For a detailed account of the conservation and technical examination of the Meroë fragments, see Gänsicke and Hagel 2017. Litvinsky 1999; Litvinsky 2010. Kostoglou 1970, 331. Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 3 21 Technical Description and Reconstruction 3.1 Original Restoration by the Museum As is universal among published bone auloi, the instruments from Megara are assembled from multiple bone sections using socket-spigot junctions (Plate 1). The Museum currently presents them on either side of a bronze sistrum (1st BC–1st AD) devoted to the Egyptian deity Isis, whose image appears on the handle. The pair of Meg1 is situated to the left, while on the other side, Meg2, with its slider keys mounted along its sidewalls, is easily identified. Below the sistrum, a bronze ring and nine sliding keys purportedly associated with the left aulos pair are arranged as follows: three lengthwise sorted pairs (i.e. of long, middle and short length) are accompanied by a single key sibling to the middle-sized pair, while a slightly different group of two keys each consisting of two parts connected by a ring complete the series. At the bottom corners of the case, two clusters of six and three broken bone fragments have respectively been placed. Conservators were unable to join them either among themselves or to the assembled pipes. Apparently they belonged to aulos pipes that did not survive.11 Auloi and keys are lying on a slanted surface, facilitating inspection by visitors. The fact that the pipes are all aligned at their bottom ends betrays an intended symmetrical presentation of the finds on behalf of the designer of the exhibit. This, however, precludes perceiving the musically important arrangement of corresponding tone holes that would yield (near-) identical pitches, which would require an alignment at the upper ends. At the left side of the showcase, aulos Meg1 stands with its higher pipe comprising the typical bulbous uppermost section ending in a socket for the reed, an extension part followed by two sections with five fingerholes in total, and, finally, the bottom section with the three side holes that were controlled by slider-keys. Next to it, the lower pipe of the pair is presented. Here the bulb and the cone with the reed socket are made as two separate parts; the long extension part is supplemented by a short extra section, followed by the long middle part with four fingerholes, a notably shorter one with only a single side hole, and finally the bottommost segment of the pipe with two side holes that were equipped with slider keys. The ends of both pipes appear slightly flared, retaining the physical expansion of bones towards the junctions. Hammered bronze 11 The external diameter of some of these fragments matches the internal of others, suggesting layers of bone that could rotate within each other. Metal handles show that for two of them it must have been the external part that moved, allowing the closing and opening of tone holes in a perfectly adjusted inner tube. They resemble fragments from Taranto and are better discussed together with these in a separate paper. Greek and Roman Musical Studies 10 (2022) 15–77 22 Terzḗs and Hagel rings, about 6.5 mm in width, are nailed around the exits, while slightly narrower rings embrace the main tubes close to their upper ends. Surprisingly, what we would regard as the ‘low’ pipe, based on a comparison of treble notes – the pipe whose highest fingerhole is further removed from the mouthpiece – appears to represent the overall shorter pipe in the pair. In fact, the designation of ‘low pipe’ here appears to lose its sense, since its overall ambitus would have been encompassed within the pitch range of the allegedly ‘higher’ pipe. Though not a priori an impossible design,12 this apparent inconsistency alerts us to a potential problem. At the right side of the showcase, the higher component of aulos Meg2 appears to the left, comprising six bone sections ordered similarly: bulb with reed socket, extension, one part with four fingerholes, and finally a second extension followed by two separate bone parts sporting one and two slider holes respectively. In the lower pipe next to it, the arrangement of its five bone sections and the distribution of its tone-holes attest to a component of similar sort, with four plus one fingerholes accommodated across two adjacent parts and three further tone holes controlled by sliders located on a singular longer downmost section. Both pipes are resting backwards, with their thumb-hole in direct sight, highlighting the sets of slider keys that are mounted on the tubes, whose function can thus be easily gleaned by visitors. Unexpectedly, the side hole that is supposed to be covered by the little finger is situated at the underside of the pipe between two adjacent slider keys, in a position where the player cannot possibly cover it. Despite the confusing assemblage of both auloi, a striking resemblance of the lengthwise sorted key pairs either exhibited separately (Meg1) or mounted on the instrument (Meg2) with the orphans unearthed in Lefkada and those observed on the Pergamon model leaps to the eye in respect to their relative sizes and the nature and distribution of their constituting components (knobs, slots, rods and plates). Moreover, the distribution of the keys on Meg2 corroborates the design of the Pergamon model: in both cases, sliders were responsible for remotely operating the three bass tone-holes of the instrument. 3.2 Detailed Description of the Bone Segments Both pairs include the typical bulbous mouth-end pieces (M; cf. Figure 1), the uppermost parts, which, however, did not actually touch the mouth of the player (Plate 2; Plate 3; Plate 6; Plate 7). These typically display an external shape of a truncated cone followed by a bulb, which tapers down to a neck, about as long as the bulb, ending in a spigot, which goes into the next component of the pipe. 12 It is found on the wooden Berlin aulos, which, however, belongs to a later date and a different type; cf. Hagel 2010. Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara figure 1 23 Abbreviations for bone sections and finger holes Internally, its cylindrical longitudinal bore widens slightly but conspicuously at its upper end, forming a concentric socket which would hold the reed. Material loss of limited (Meg2αM, βM, Meg1αM) or more considerable (Meg1βM) extent, observed at the transition point from bulb to the neck, hardly reflects traces of intentional drilling; this kind of damage may be expected given the sensitivity of the thin-shelled narrow neck. Meg1βM comprises two distinct parts joined by spigot and socket: the conical reed socket and its bulb + neck complement. An oblong region of the bulbous sidewalls extending from its upper end towards the point of its maximal diameter is missing. Similarly, a little semi-circular part is missing from the tip of the spigot of the conical reed socket, too. By conjoining both parts and rotating the cone around its axis until material losses are getting aligned, an elliptic hole (8.5 × 6 mm) emerges, but its shape does not in any way suggest an original hole. None of the upper rims of the three M parts have survived; however, the overall length of their upper conical part can satisfactorily be inferred from the preserved dimensions of Meg1βM. The mouth-end pieces connect to cylindrical extensions of varying dimensions, without any side holes (X). Their relative length would typically make a pipe either the high or the low component of the pair. Here these extensions preserve their rims at both ends, providing their overall as well as their effective dimensions (without the spigots). The external surface of their upper end exhibits a very slight recess, 8–9 mm wide and only 0.15 mm deep. Such recesses evidently held some kind of enforcement; sometimes rings of copper alloy are still found in place. However, since the present items show no signs of the green coloration that is so typical for bone parts that were in contact with copper, we must rather reckon with windings of thread as would easily serve the same purpose of keeping the thin bone socket from exploding. Both X sections of Meg1, however, are equipped with a bronze ring in an unexpected position, about 5 mm below the shallow recess. This ring is 5.8 mm wide and nailed to the bone surface.13 Notably, Meg1βX comprises two sections: the upper long one displays extensive damage, resulting in an irregular oblong gap. 13 At the time of the second visit to the Museum in May 2017, in order to inspect Meg1, the ring, which had formerly been placed around the upper end of αFi, had been moved to its correct position, indicated by conspicuous traces on the tube surface. Greek and Roman Musical Studies 10 (2022) 15–77 24 Terzḗs and Hagel The following shorter part holds a small hole (3 × 4 mm) in the upper end of its spigot, reflecting an even smaller, perhaps deliberately drilled original hole, which has probably expanded in the course of ongoing material disintegration. Two adjacent sections of conspicuously different length (Fi, Fii), with side holes controlled by the player’s hands, follow segment X at Meg2αβ and Meg1α. The little-finger hole lies on the lower, shorter part (Fii), while the upper, longer part (Fi) hosts the index, thumb, middle and ring finger holes. Shallow recesses 8 mm in width around their upper ends resemble those found on the X sections and suggest that some sort of bands also reinforced the X-Fi and Fi-Fii joins. On Meg1β, section Fii, which held the little-finger hole, is missing. The external rims of all fingerholes are rounded, ensuring a smooth fit of the player’s fingers. The upper side holes are not perfectly aligned, but lie at slightly different azimuths in the range of about ±30 degrees in Meg1, and ±35 degrees in Meg2; with the thumb hole having been placed opposite to the middle-finger hole, effective handling is ensured and the assignment of each pipe to its proper hand is straightforward. A feature of utmost importance for questions of reconstruction is the presence of two pin-holes close to the downstream end of Fi, though at different distances from it. The one closer to the lower rim of the bone section is aligned with the centre point of the thumbhole, relative to which the other is rotated by about 90 degrees towards the side that faces the other pipe of the pair when played. A similar pin-hole lies on the spigot of each surviving Fii bone sections, lined up with the centre of its side hole. Interestingly, the pipes of Meg2 preserve five out of originally six elegant solid bone pins with semi-spherical heads within their respective pin-holes. A single similar small side hole is located close to the upper end of Meg1αFi, aligned with the thumb-hole centre, preserving a headless pin body within it. A corresponding hole may have existed on the other pipe of the pair, but here, at the upper part of Meg1fiB, we encounter a substantial loss of material; during conservation the extensive gaps were filled with plaster. However, the undersides of both Meg2Fi sections are preserved intact towards their upper ends, showing that no pin was located in this position. The sections Fi and Fii have lost different amounts of material, including parts of their spigots, due to disintegration and subsequent crumbling of the bone. However, thanks to at least partially preserved upper and lower rims, we are able to restore their effective dimensions. Perhaps even the action of the sliding keys during performance, in combination with the presence of corroding metal, had already caused some fatigue of the bone surface beneath the rods and knobs. The unfriendly environment of the grave may have transformed such initial lesions into larger and smaller gaps, none of which necessarily Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 25 reflects original deliberate structural modifications of the tube surface. Extensive material loss has now been filled in with plaster, including the expected positions of the ring-finger and small-finger holes on Meg2βFi and Meg2αFii respectively, holes whose presence was not anticipated during conservation. Below the F sections, the end of each pipe, with its three slider side holes, is formed either by a single long section (Meg1αS, Meg2βS) or a couple of two successive shorter parts (Meg1βSi + ii, Meg2αSi + ii). We cannot detect recesses at their upper ends. Surprisingly, Meg2αSi does not feature a spigot at its downstream end like all other parts, but bears two sockets of dissimilar depth at both ends, into which the spigots of the preceding and subsequent segments fit perfectly. Unlike the fingerholes, all slider holes maintain a sharp edge. They are allocated to the side walls of the single long sections Meg1αS and Meg2βS as follows: in respect to the upper hole, the intermediate one is located 90 degrees clockwise, while the lowest hole, close to the exit, stands opposite to the latter, and therefore 90 degrees counterclockwise from the former. Within the two shorter corresponding sections on the other pipes, the lower one (Sii), which terminates the pipe, features two side holes at different distances from the pipe exit, lying at opposite sides of the tube, while the preceding section (Si) features a single hole. Both Meg2αSi and βS preserve a pin-hole close to their upper rims, which fit perfectly with those on the Fii spigots, thereby determining the rotational alignment between sections Fii and S. Only Meg2βS features another small hole close to its end, at the rim of the bronze collar that encloses all pipe ends.14 Meg2αSi + ii are preserved in excellent condition. Overall, all sections with slider-operated holes maintain their upper and lower rims, so we are able to obtain their effective lengths, which are so crucial for our research. However, significant loss of material, now substituted with plaster, occurs especially in regions over which a slider key must once have moved. Interestingly, thorough inspection reveals a few pairs of deliberately engraved spots or short and shallow transversal niches. Sporadically these are accompanied by barely detectable lines, presumably defining certain distances or points of particular 14 The purpose of this hole is doubtful. It might have held a pin, but not of any discernable purpose. It is too small to serve as a tuning hole, as it would raise the bass note only by 3 cents while not effecting any other pitches. Had it been drilled to regulate the sound of the bass note, we would expect similar holes on all pipes. Lying at the outermost usable part of the bone, which was usually discarded except when becoming an exit section, it might have been drilled for pinning the piece to the lathe at an early stage of production. The hole would then have been filled, for instance with a mixture of glue and bone meal, like the grooves in the bone under the lowest slider plates needed to be filled in order to make these functional. Greek and Roman Musical Studies 10 (2022) 15–77 26 Terzḗs and Hagel interest for the aulos makers. Their significance will be revealed in the course of the following detailed account of the construction and function of the slider keys. 3.3 Slider Keys: A Descriptive Analysis A typical slider key of the Megara type comprises four distinct structural parts in the following order: knob, slot, long rod, and plate. A knob consists of two concentric, closely spaced, half-lenticular compact shapes of different diameter, standing in upright position, with the larger one forming the upper end of the key and both ending in flat bottoms. Its shape enabled the aulētḗs (or aulētrís, as regards Meg1) to control the slider-key with the fingertips. The slots provide a linear path within which the key is allowed to travel, ensuring its moving direction along the longitudinal axis of the pipe. The pin-holes that are found drilled on all the tubes and the surviving pins on both pipes of Meg2 suggest that the latter were firmly secured in their holes through the key slots. Consequently, the slot function was twofold: to direct the slider movement along the right path and to confine the motion of the plate within a limited range. The knobs are attached to the slots by means of a short rod of rectangular cross-section. The longer intermediate part of the key is formed by a flat-based rod of initially rectangular cross section which gradually transforms into a triangular cross-section. Interestingly, at some point within its lower half, the rod, in a sharp step, narrows down markedly, to a mere 1 mm in both height and width, until it either joins the plate or returns to its primary dimensions before reaching the plate. Thus, a precisely confined region is generated, bounded by the two points that define the transition from the initial rod cross-section dimensions to the smaller ones and the back. These points are further marked by a bump at either side on top of the rods, terminating their wider parts towards the constriction. Within the narrow region, a separate roof-shaped guide is accommodated, which terminates in sharp protruding edges at its four corners, calling to mind the pairs of engraved spots or short and shallow transversal niches that we have observed on the S sections. Apparently the roof-shaped guides were firmly pressed onto the tube, so that their sharp edges created those niches, which fit their dimensions accurately. Within the roof-shaped guide, the triangular portion of the rod can travel freely. At the same time, its movement is once more restricted within precise limits defined by the respective widths of the guide and the narrow section of the rod. The finds do not tell us how the guides were so firmly attached to the tubes. However, with the roofshaped guides the Megara finds provide the evidence to substantiate Conze’s bands covering both rods and tubes on the Pergamon artefact. Whether these Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 27 were made of leather, hide or tight windings of thread, the ‘band’ would likely obscure the guide underneath from view to such an extent that the maker of the Pergamon item would have been content to show only the former. At any rate, the material must have been very thin, because it could pass below other rods, as can also be observed on Conze’s object. At such places, slight recesses are worked into the underside of the rods or slot parts, obviously in order to prevent any friction between the band material and the metal. The plate, finally, is carefully adjusted to the cylindrical curvature of the tube, so that, in the closed position, it can form an air-tight seal. One might surmise that this was additionally ensured by some soft, organic material fixed to the underside of the plate, as is generally the case on modern woodwind; at any rate, inspection by the naked eye could not corroborate any such traces. The width of the plates approximately equals a quarter of the tube circumference, while their length varies between 13–17 mm. We have thus gained a comprehensive picture of the functional design of the sliders: the motion of the keys was not only efficiently restrained to a linear path along the pipe but was also confined between precisely determined limits that were defined by the length of the slot, on the one hand, and the extent of the narrow part beneath the guide, on the other. Clearly, both these means of limitation would optimally prescribe precisely the same motion range with identical extreme positions. Such a simultaneous constraint of key movement at two different places, one near the upper, one close to the lower end of the rod, creates two significant technical advantages. Firstly, being fixed in its longitudinal position at two places, the rod cannot act as a lever when undesired lateral forces are applied during operation, preventing wear and damage that would be associated with the high torques exerted on a single guide. Secondly, the pushing and pulling forces exerted by the finger are split between the pin in the slot on the one hand and the ends of the guide on the other, preventing damage of the more delicate of these components. The minimal distance by which a slider would need to move in order to cover and uncover its side hole completely, is obviously equal to the diameter of the latter; the maximal distance is determined by the length of the plate. On the reasonable assumption that optimal sealing is achieved when the centre of the plate is aligned with the centre of the hole, the optimal movement range, given a mean slider hole diameter of 9 mm, varies between 12 and 14 mm, depending on the size of the respective plate. As a consequence, the length of the slot as well as the size of the plate form a solid basis for assessing the original length of the guide, where it has perished, or the length of the narrow rod part below it, where corrosion has agglomerated guide and rod in a way that obscures one of the ends of the narrow section. Greek and Roman Musical Studies 10 (2022) 15–77 28 Terzḗs and Hagel As has become clear, each pipe of the instrument Meg2 is equipped with three slider-keys, which, despite variation in detail, come in three general sizes, which we will address as long, intermediate, and short (Plate 8; Plate 9). Since no more than three pin holes per pipe are detected on this particular instrument, we have good reason to assume that three similar pairs of sliders, one in each length category, constitute a complete set of keys. This assumption is corroborated by the similarly arranged three sliders found on the Pergamon model, and the two identical sets of keys at the Museum of Lefkada, which were doubtless retrieved from independent burials. On the other hand, Meg1 was not only found together with such a set of six, but with an additional key of the intermediate kind, and, moreover, with the specially shaped pair of keys that include a middle ring, which end in a significantly smaller plate than all the others, suggesting that these were dedicated to plugging a sýrinx (speaker) hole, located above the highest fingerhole (Plate 4; Plate 5). Whether a similar key would also have been present on the Pergamon model, whose upper part is missing, remains obscure. At any rate, it is highly improbable that the aulos Meg2 was equipped with sýrinx keys, though we cannot exclude the possibility of simple sýrinx holes as observed on other fragments that must normally have been plugged by other means. Knob, slot, rod and plate are all found on the sýrinx keys, too. However, the rod, following the cluster of knob and slot, at about half its length splits in two strands, which bend outwards and upwards to form a ring that stands perpendicular to the original part of the rod. Where the two strands meet again, they bend once more, uniting again to a single rod that extends further in the same direction, running parallel to the first part, though on the other side of the tube, and terminates in the small curved plate. However, neither sýrinx key has survived intact. Apart from various flaws along their body, one part of the rod was apparently detached from the ring in both cases, affecting the connection between the knob-side rod part and the ring on the shorter of the two keys, and that between the plate-side rod part on the longer. Both were re-attached during restoration. Surprisingly, on a first glance, the key with the longer knobside rod part ends in a somewhat shorter plate-side part. Although there is no trace of roof-shaped guides, sharply set-off sections of reduced diameter close to the plate suggest that such parts once existed; their length can be retrieved by subtracting the effective range of the slot (i.e. the slot length minus the pin diameter) from the length of the narrow region. A pin body surviving in its hole, aligned with the thumb-hole towards the upper end of section Meg1αFi, must have run in the slot of one of the sýrinx keys and thus furnishes the position of one of them. With the slot and the knob at the underside of the instrument, and the ring, which obviously went around the tube, switching the pathway Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 29 of the rod to the opposite side, the sýrinx hole was therefore situated at the upper side. The question of the apparent sýrinx keys is further complicated by an older drawing by our late colleague Maurice Byrne, a copy of which Olga Sutkowska kindly provided. This drawing presents the slider keys in their natural size, and it may reflect an earlier restoration phase. Here the longer of the two keys is sketched with its plate-side segment flipped around: instead of continuing its way towards the top of the instrument, the rod thus doubles back, so that the plate is ultimately not very far removed from the knob, albeit on the opposite side of the tube. In addition, the knob-side part of the shorter sýrinx key does not appear on the drawing at all. Similarly, one of the two short keys is not represented, whereas one of the keys of the intermediate size appears both in top and side view. Otherwise, only small discrepancies can be observed between the shape and size of the rest of the slider-keys as displayed in the drawing and in their present condition. On the other hand, the in-situ photograph flatly contradicts the drawing, since it clearly shows the plate-side part of the longer slider key pointing towards the upper end of the pipe, while still being attached to (parts of) the ring that engulfs the tubing. We shall return to this matter after dealing with the arrangement of the bone segments in an effort to reconstruct both auloi pairs with reasonable certainty. 3.4 Towards a Meaningful Assemblage of the Megara Pipes Despite our limited understanding of the technical intricacies associated with ancient music culture, some ubiquitous observations on the surviving aulos finds of various types ranging from the Classical up to the Roman Imperial eras allow us to state two specific rules that are borne out by all the evidence that has surfaced so far. Firstly, an aulos consists of a ‘low’ and a ‘high’ pipe, in the sense that their highest fingerholes do not coincide, even though the ranges covered by each hand always overlap; within this overlap, the respective fingerholes on both pipes are seemingly intended to produce identical pitches. The shift between the pipes varies between one and three fingerholes, though the evidence so far favours offsets of merely a single hole. Secondly, a ‘rule of the 4L’ has been established,15 postulating that the lower-pitched pipe is simultaneously the longer, played by the left hand, with its thumb-hole lying slightly leftwards from the position opposite to the other fingerholes. 15 The “4L rule” was introduced by Stélios Psaroudákēs (2008, 202) on the basis of his measurements of surviving aulos sections of the early type. The 4L rule is still applicable to those parts of the Megara finds that reflect the design of such instruments, but cannot be applied to the lengths of their downmost slider sections. Greek and Roman Musical Studies 10 (2022) 15–77 30 Terzḗs and Hagel On Meg2, the little-finger hole of the left-hand pipe as well as the ring-finger side hole of the right-hand pipe are lost due to substantial damage of the tube wall at their expected positions (now indiscriminately filled in with plaster). The centre of the little-finger hole on Meg2αFii, as far as can be determined, may have sat at any distance up to about 26 mm from the upper rim of the section, likely close to the lower end of that range, where the downmost part of its round edge may just be discernible. But then, any effort to align corresponding tone holes among the pipes is doomed to fail, because the wider-spaced upper three tone holes (1–3) on βFi cannot possibly be aligned with the more closely packed (2–4) on αFi that ought to correspond with them. Moreover, the Museum’s original assemblage of Meg2 violates the 4L rule by assigning the longer low-pitched pipe to the player’s right hand. However, conservator Theodṓrou has convincingly put together the appropriate segments with tone holes, i.e. the F and S sections of both pipes, on the basis of the only possible solution that aligns slider pins with slider holes while at the same time accounting for the lengths of the existing slider keys. Given the problematic distribution of tone-holes between the alleged pipes and notably, the already mentioned unconventional methods applied in the excavation, an alternative distribution of bone sections between the pipes suggests itself. The only possible re-arrangement merely involves exchanging their extensions or the entire upper parts, for instance resulting in a high pipe of the scheme α(MX)β(FS), and a low pipe of β(MX) α(FS). In this way, the 4L rule is preserved, and the corresponding side holes align themselves within the customary offset of one hole. Moreover, the centre of the lost ring-finger hole on the higher pipe can now be placed in a natural position, 6 mm above the lower rim of βFi (without spigot), corresponding to the middle-finger hole on the lower pipe’s αFi. These suggestions have now also been accepted by the conservator, and the exhibits have been readjusted accordingly, without any violation of the basic archaeological criteria for potential joins, such as surface texture and coloration. A closer inspection of the remains of Meg1, in turn, leads to a discomforting though inescapable realisation. Taken as it is, its longer pipe would generate the higher treble note, again in violation of the 4L rule. A comparison with the longer pipe of Meg2 suggests that Meg1β is missing one of its segments; this is corroborated by the extant sliders, as we shall see. Pipe Meg1α, however, resembles the higher member of Meg2, comprising a similar number of bone sections, equivalent in form and size, with their tone and pin holes at similar positions and almost identical azimuths. Only one major deviation leaps to the eye: the presence of the aforementioned pin body in Meg1α, aligned with the thumb hole, but positioned at some distance from it towards the upper end of the pipe. As we have seen, this pin probably constrained the movement of the sýrinx hole key. Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 31 The single surviving photograph of the find in situ, which Panagiṓta Avgerinoú generously provided, not only enables us to trace the missing section, but also to determine its relation to the adjacent parts, and finally to estimate its length. The instrument was found resting between the leg bones of the deceased, with the right-hand pipe placed to the right, resembling the playing position. The disintegration of the junction between Xii and Fi seems to have resulted in a slight displacement of the part of the pipe below it, whose finger holes were facing the ground, probably as the result of a counterclockwise rotation (from the viewpoint of the deceased) by approximately 180 degrees. The parts of the higher pipe of the pair at the right side displayed a similar shift of the MX complex, presumably also resulting from its collapsing in the course of the body’s decay. Although βFi and βSi have consecutively been arranged during conservation, close observation of the series of bone fragments in the excavation image reveals an extensive gap between βFi and βSi, reflecting severe damage of the find at this particular point. The image clearly suggests that this gap was occupied by an additional bone section, then highly fragmented, equipped with a small hole. How this part became lost remains a mystery – after all, a significant number of other little fragments were successfully recovered. At any rate, precise measurements of the preserved pipe components enable us to determine the total effective length of the missing βFii section as 71.1 mm. The rest of the available lengths can be verified on the image, with one exception. Meg1αS exhibits an almost transparent short cut at its otherwise entirely broken upper end, giving the impression of a surviving rim. However, close inspection of the in-situ image suggests that the upper end had actually been longer by about 3.5 mm (resulting in an unusually deep socket of no less than 21 mm), so that it accommodates the extant slider keys nicely. 3.5 Assigning Slider Keys to Their Original Positions Since conservator Theodṓrou has assigned the three sizes of keys to their proper positions – the long one (L) to hole S3, the intermediate (M) to S1, and the short (S) to S2 – one may wonder why the sliders were not accordingly placed on the tubes of Meg1. Of course, devoid of its Fii part, Meg1β could not have accommodated any of the available triads of keys. On the other hand, given the striking structural similarities between the F-S complexes of Meg1α and Meg2β, the restoration of its keys to the former would have been straightforward. Also, by matching the remnants of Meg1α with the available keys, the absence of an Fii part as found in its counterpart Meg1β would have promptly emerged. Greek and Roman Musical Studies 10 (2022) 15–77 32 Terzḗs and Hagel However, detailed measurements of the keys reveal mismatches, at least at first glance: some of them do not seem to fit in their proper positions perfectly. Disconcertingly, this does not only concern Meg1, but also Meg2. However, since we can hardly doubt the functionality of the mechanism, unless we misunderstand something very basic about its function, we must assume that the mismatches are the result of small dimensional distortions (possibly accumulative) caused by the required restoration work. We would therefore like to conclude this preliminary study of the Megara instruments by suggesting probable corrections, while at the same time providing the raw data that will allow a critical assessment of our suggestions (Table 1–Table 4). Our search for a feasible solution can be based on some robust parameters, most of all the fixed lengths of the bone segments of Meg2, which are safeguarded by surviving rims, as well as those joints whose rotational alignment is precisely determined by a pin hole through socket and spigot. Furthermore, the sliders of Meg1 appear to be in excellent condition, so that we can exclude any modification of their lengths in the conservation process. No solution ought to be proposed that tampers with these data. Interestingly, all twelve slider holes on the two instruments can be assigned well-fitting sliders, as long as only the lower part of these, consisting of guide and plate, is considered, establishing matches between the guide niches, the movement range and the edges of the side holes. The niches thus match the lengths of the roof-shaped guides, and this leads to configurations where the holes are nicely covered and uncovered. Thus it emerges that six out of the seven surviving sliders associated with the find of Meg1, and doubtless the entire set assigned to Meg2 indeed belonged to the instruments under investigation. The discrepancy concerning Meg1α is apparently systematic: compared with the distance from pin to hole, all of its sliders appear too long by 3.5 mm. This is easily accounted for by increasing the length of its S section by the same amount: the preserved end of this fragment does not present its original upper rim, after all. The case is different with Meg2, whose section lengths are undisputed, while the poorly preserved sliders also appear slightly too long, but by different amounts. This can probably be explained by the nature of the conservation process, in the course of which the rod lengths became misrepresented by the frequent necessity to apply larger portions of glue between the corroded edges of the broken and distorted parts. Unquestionably, the conservator has wisely refrained from jeopardising the physical preservation of fragmented rods for the sake of an ultimately unrealistic functional restoration. Therefore the nature of the evidence suggests estimating the lengths of the poorly preserved Meg2 sliders from the intact bone parts; conversely, in the case of Meg1 we needed to assess the dimensions of a missing and a broken bone secGreek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 33 tion from the well-preserved sliders. The proposed reconstruction therefore includes the lost section Meg1βFii of 71.1 mm length, adding 3.5 mm to the upper end of Meg1αS, as well as reducing the rod lengths of the Meg2 keys, by up to 5 mm in one extreme case. In this way, we obtain twelve perfectly functional slider keys (Table 5). Of the three preserved slider keys of intermediate size, it emerges that I2 does not fit on either pipe.16 It must have been part of another instrument, perhaps the one otherwise represented only by the aforementioned small bone fragments that cannot have belonged to any of the pipes discussed here. Finally we need to assess the original shape and mechanism of the supposed sýrinx keys. Their function appears to include the otherwise mysterious nailed bronze rings on the tube, which occupy corresponding positions on both pipes. When adjusting a model of the short key (Sy1) to the surviving pinhole (p.s.) on Meg1αFi, the ring of the key comes to lie above the nailed ring and consequently moves between it and the first few millimetres of the recess around the upper rim of αX, situated about 5 mm above. The same seems to be true on the other pipe: when the slot of the longer key (Sy2) is aligned with the probable pinhole position (p.s.) on the spigot of Meg1βXii, its ring similarly moves from above the corresponding nailed ring towards the recessed area near the upper rim of Meg1βXi. By butting up against these fixed rings, the moving rings on the sliders thus restricted the downward movement of the key, assisting the corresponding functionality of pin and (probably) guide. In addition, they would be forced into a precise position regarding all three spatial dimensions, which guaranteed the accurate placement of the plate, irrespective of otherwise possible wobbling of the construction. This detail suggests that the plates covered their holes when the sýrinx keys were in the downward position. Notably, such a construction, however, conflicts with the notion of ‘pulling downward’ (κατασπᾶν) for activating the sýrinx, which is found in Aristoxenus as well as the Peripatetic De audibilibus.17 As described above, an early drawing appears to suggest that the part of the sliders, or at least of the long one, that connected ring and plate did not extend further towards the upper end of the instrument, but turned back towards the knob, though on the other side of the tube. When we implement such a design, 16 17 One of our reviewers wondered whether a slider hole may have been lost. This is impossible on the higher pipes because the bone at the respective position is undamaged, as is the surface where the corresponding slider pinhole would be expected. On the lower pipe, the absence of a pinhole similarly precludes a fourth slider key. Aristox. Harm. 1.21 (27.1 Da Rios), [Arist.] Aud. 804a. Greek and Roman Musical Studies 10 (2022) 15–77 34 Terzḗs and Hagel reversing the direction of the plate parts in regard to their present state, the slider plate of the short key (Sy1) settles on the upper-left side of the indexfinger hole of Meg1α, in a region where the original tube wall has not survived. On Meg1β, in turn, the key plate of the longer key (Sy2) would extend to the lower end of a large gap on the top surface of the bone section, corresponding with the assumption that extensive damage may be correlated with the corrosion of a bronze rod on the bone surface. The resulting distances of the sýrinx holes from the upper ends of the pipes would thus differ by less than 6 mm. Interestingly, this difference would disappear by exchanging the rod parts containing the plates among both keys; but this would presume that the rings themselves are assembled wrongly from fragmentary portions – an assumption that cannot be explored at present, but appears a priori not all too likely. This kind of design has one obvious advantage: consisting of facing parts on opposite sides of the tube, the keys would easily maintain an even grip on it and consequently guarantee the sealing of their holes exceptionally well. Also, if the key did not run along the bulb, it would impact less on the aesthetic appearance of the instrument. However, it is hard to see why such a large and complex mechanism would have been implemented for bridging such a small distance between operating finger and sýrinx hole, and why it would have been designed to go around the tube. After all, there was no reason to place those holes on the upper side of the instrument. More importantly, such a design would have compromised the functionality of the instrument. On the one hand, on a respective model of the high pipe, the plate of the sýrinx key sits so close to the index finger hole that it encumbers its operation significantly, since the finger can hardly seal the hole without touching the plate. On the other, a small hole so close to the finger holes is ill placed for producing the intended effect of serving as a speaker hole, which is meant to switch the pitch produced on the instrument to a higher partial by weakening the oscillatory regime of the fundamental, at least, or even of several of the lowest partials.18 For this purpose, a speaker hole needs optimally to be placed at about one third of the distance between mouthpiece tip and the highest open finger hole. In practice, a single speaker hole may work well for several or all finger holes, but it still needs to be situated high up the pipe. At the position effected by the hypothesis of downward-reaching sýrinx key plates, it might work only for the lowest tone holes, if at all. Indeed such a position is not paralleled on any of the known eleven certain or possible extant sýrinx holes.19 Especially the earliest examples are generally situated on the uppermost parts, 18 19 Cf. Hagel 2012a, 498f., with 515 fig. 1. Hagel 2012a, 517 fig. 5. Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 35 either in the narrow section between reed socket and bulb (Delos, B5168; Taranto, National Museum 12528/7 and s.n. 2; apparently also the Reading aulos in the Ure Museum), on the bulb (Athens, Agora BI 593) or on the neck below it (Paestum Archaeological Museum 23068, both pipes); on later instruments they may also be found on the bulb (Berlin, Egyptian Museum 12462), or on the tube immediately below it (Berlin, Egyptian Museum 12461; Naples National Museum 76892; one of the Meroë fragments, Bodley (1946) pl. 3.2). Would the sýrinx keys in the shape suggested by their present state work out better? When the slot of the longer of them is aligned with the pin in Meg1αFi, it turns out that the plate of the longer would extend beyond the expected upper end of the pipe, which is impossible. The shorter, in contrast, would reach up between bulb and cone, ending about in the region of the socket where the reed stem is inserted. The longer sýrinx key would thus need to be assigned to the lower pipe, just as one might expect, where it would terminate in about the same region, when its slot is aligned with the possible pin location at the spigot of Meg1βXii. It is difficult to establish the positions of the expected sýrinx holes with precision, due to small uncertainties regarding the repairs of the rods as well as the placement of the nailed rings. Figure 2 displays the results of three different approaches, one working from scaled photographs of the individual parts, starting at the fixed rings, another calculating the measured distances from the placement of the fixed rings, and the third one starting from the pin holes. Each of them predicts a specific range within which the slider plate would move; in both cases, these are somewhat higher when the last method is used. Judging from the placement of the fixed rings, therefore, the measurements for the lower rod lengths appear slightly too long: when the sliders are drawn downwards until stopped by the pin, the moving rings would still not touch the fixed. The discrepancy is in the range of less than 2.5 mm, however, and larger on the higher pipe, where the slider is badly bent and corroded and the correct alignment of the rings difficult to establish (Table 6). Each moving plate establishes two possible regions for the hole, one on either side of it. Above we have concluded from general consideration concerning the alignment of the rings that the sýrinx hole was more probably closed by moving the slider key downwards. This appears corroborated by the ranges. As can be gleaned from Figure 2, the sýrinx plate on the higher pipe came to lie above the reed socket when pushed upwards. Here a hole would be useless, because it would only extend down to the wall of the reed, once one was inserted. One might of course drill a matching hole into each reed; but that would be extremely impractical for several reasons. Apart from the troubles involved in aligning the holes, such an approach is hardly compatible Greek and Roman Musical Studies 10 (2022) 15–77 36 figure 2 Terzḗs and Hagel Possible sýrinx hole positions on Meg1 for straight sýrinx keys with the practice of ensuring an airtight connection by a winding of (waxed) thread around the foot of the reed. Even if the thread would initially be placed so as not to cover the hole, it would likely move when the reed is pushed into its socket. Secondly, one would lose the paramount possibility of fine-tuning the instrument by changing the position of the reed in its socket. On the lower pipe, the plate, when pushed upwards, would come to lie below the reed socket, where it might cover a functional speaker hole. However, as far as we see, the wall of the cone is intact throughout the respective region without showing a trace of a hole. Consequently, both sýrinx holes must have been situated at the downward-side of the slider plate. Indeed the higher pipe preserves a tiny opening about 64.5 mm above the lower effective end of the bulb section (Meg1βM), resembling other extant sýrinx holes, in the range predicted by the ring-based approaches. Its position on the slope of the bulb close to the narrowest point resembles that on one of the mouth-end pieces in Taranto. Given the nature of the slope, the plate would need to be inclined; consequently, a hole at this position can only be closed when the slider is pulled downwards. Being situated within the predicted areas of two out of three methods and no more than 3 mm removed from the lowest usable position of the third, this small opening therefore plausibly formed the sýrinx hole of its pipe. On the low pipe, no similar hole is preserved. The bulb has lost substantial material around where we would expect it, and once more this is likely related to the proximity of the copper alloy. However, the calculated ranges fall within that length of the bulb where the spigot of the cone part was inserted, which has survived largely intact, with only one larger part missing from the rim. If we have not overlooked traces of restoration elsewhere, it is apparently here that we have to search for the original hole position. The innermost edge of the gap seems consistent with the assumption of a small drilled hole and lies just within the calculated boundaries, about 2 mm from their centre, at Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 37 about 59.2 mm above the effective lower end of the bulb section (Meg1αMii). For optimal functionality, the upper part of the rod ought to be at least 1.3 mm shorter than our data suggest; this small mismatch may once more result from uncertainties associated with the restoration and measurement of the bent slider rod. Interestingly, at 58 mm from the effective lower end of the bulb piece, a transversal line can be observed that might be related to the placement of the slider, perhaps indicating the position of the slider’s roof-shaped guide. On balance, the sýrinx keys in their present state seem to make much more sense than they would in the way they appear on the early drawing: for the shorter key, an existing hole strongly suggests that it extended beyond the bulb; the longer, in turn, would appear dysfunctional in the reverted form. On top of this, the precise curvature of its longest intact fragment appears to reflect the shape of the bulb and the neck below it (cf. Figure 2); aligned backwards onto the cylindrical surface of the tube, its shape would be incomprehensible. The stretched-out version of the keys also explains other details. First of all, the sýrinx hole of the higher pipe is also situated a bit higher – about 5.5 mm – just as has been observed on the Paestum and the Berlin auloi, the only extant pairs with such holes on both pipes. Since the rings sit at similar heights on both pipes, doubtless for aesthetic reasons, it is consequently required that the plate-side rod of the higher pipe and therefore of the overall shorter key is longer: what appeared a curiosity, thus becomes a necessity. The additional enforcement of this particular type of key with a system of two rings was likely prompted by the reduced stability of the part of rod that needed to move in the air above the curved surface, in contrast to the tone-hole keys that could rest safely on a straight underground. Finally, the precise positioning of the holes at asymmetric distances from the respective pipe tops shows that their location was carefully chosen. The higher one, on the higher pipe, appears precisely at the highest possible position. As we have seen, it could not be placed within the range of the reed socket in the cone. Consequently it needed to be drilled on the slope of the bulb, just far enough from the cone so that the latter would not obstruct the upwards movement of the key plate when the sýrinx was opened. This is no coincidence. As the comparison with Meg2 shows, the two instruments differ almost exclusively in two respects: Meg1 features sýrinx keys, and its upper part is longer. The latter now emerges as a corollary of the former: in order to put the sýrinx holes at the desired positions, the tubes had to be extended, shifting the bulbs closer to the player’s mouth. However, it appears that this prolongation involved hardly a millimetre more than was absolutely necessary – perhaps an indication that suitable bone was not an unlimited resource, after all, or that long reeds were still favoured for aesthetic reasons. Greek and Roman Musical Studies 10 (2022) 15–77 38 Terzḗs and Hagel Sealing a hole on a three-dimensionally curved surface by means of a metal ‘plate’ posed a significantly greater technical challenge in comparison with the cylinder segments that covered the lower holes. Possibly the plates were cast from a wax form that had been moulded right onto the pre-fabricated bulbs. Or the lower surface of the plates was simply padded with some softer material such as leather. How the slider guides, whose existence is suggested by the narrower lengths of rod close to the plates, may have been shaped and fitted on the bulbs needs to be explored by further experimental research. Have they disappeared because they were made from a different material? It has been proposed that aulos makers of the Roman period may have placed the sýrinx holes at one third of the distance between the upper pipe end and the highest finger hole.20 This rule of thumb would have disregarded the reed cavity; but Roman-period reeds were much shorter than those of early instruments. Clearly, at least on those which had their sýrinx holes at the mouth side of the bulb, a very different strategy must have been followed. For instruments with holes throughout down to the end, obvious points of reference might have been the upper and lower end of the pipes as well as the centre or the upper edge of the highest finger hole. Of all possible combinations of these, the design of Meg1 gives a meaningful result only for that of upper pipe ends and index hole centres, analogously to the later examples.21 However, instead of using a factor of three, the sýrinx holes appear to have been drilled at only a seventh of the distance to the highest finger hole. At least, this model predicts the positions we have suggested above by error margins of 0.4 and 0.6 mm. Unlike the later rule of thumb, this practice would not have been optimal for producing the first available harmonics, (approximately) a twelfth above the fundamental scale, throughout. Was the sýrinx of these early instruments meant to destabilise this oscillatory mode as well, in order to produce even higher notes, even more suitable for depicting a dying dragon’s hisses? After all, on the later instruments, the second mode would have extended the available scale upwards, which, it has been argued, was an important function of the sýrinx at least on the Berlin aulos.22 On the instrument from Megara, in contrast, the different vibration modes inevitably create well-separated scales, in accord with Aristoxenus’ take on the matter, which appears to presuppose at least the second available harmonic, two octaves and a major third above the 20 21 22 Hagel 2012a, 505–9. For this purpose, the length of the mouth-end part of the higher pipe was extrapolated by scaling its lost cone section by the same tiny ratio by which its bulb section is smaller, shrinking the extant cone of the lower pipe by 1.16% or a quarter of a millimetre. Hagel 2010. Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 39 fundamentals.23 With the mitigating effect of the comparatively long reeds, at any rate, the effective ratios would amount to 3.28 and 3.55 for the index holes, so that overblowing to a twelfth may have been possible from the highest fingerholes, while lower tone holes would likely have produced higher harmonics. The effects cannot be predicted, though – too much depends on the softness of the reed blades, on lip control and playing pressure. 3.6 Conclusions A close study of the Megara pairs thus corroborates the first impression that they belong to an otherwise unattested aulos type. Each pipe had five fingerholes plus three holes towards its downstream exit that were operated remotely by bronze sliders. While the arrangement of these holes follows the same general principles on both pairs, their precise positions nevertheless differ so markedly as to suggest intentionally different musical designs. Most conspicuous is the divergence between the upper two key holes on the higher pipes, as well as the wider spacing of the fingerholes on the higher pipe of Meg2, leading to an enormous distance between the centres of index and small finger of 13.5 cm, compared with the already straining 13.2 cm on the higher pipe of Meg1. Generally, the comparatively even spacing of the fingerholes resembles the design of earlier auloi, which have been interpreted in terms of tones and ¾-tone intervals or equally divided tetrachords.24 The small steps between adjacent slider holes at the lower end, however, suggest smaller intervals. Regarding the function of the sliders, it is paramount to appreciate that the finger that operated any of them could not do so without releasing its own fingerhole. As a consequence, it would never have been possible to play two bass notes in immediate succession. Between these, the player would either have had to pause, or some higher note would have sounded, the one associated with the fingerhole of the operating finger or any higher fingerhole note by lifting another finger as well. In this way, the sliders appear more suitable for changing the available bass note, and thus effecting some kind of modulation, than for melodic use. Nonetheless, the considerable technical effort associated with the production of remote keys, as opposed to other means of changing the available pitches, such as plugging of holes, certifies that they must have been used for swift action right within a performance, not merely between different pieces. 23 24 Aristox. Harm. 1.20–1 (26.8–27.3 Da Rios); cf. Hagel 2012a, 497; 511–13; 518 fig. 8. For a detailed discussion of potential tetrachord divisions of surviving auloi of the early type, see Hagel 2021a, 436–47. Greek and Roman Musical Studies 10 (2022) 15–77 40 Terzḗs and Hagel The astounding parallels in the arrangements of the bone sections and the placement of the keys might suggest that the two instruments originated in the same workshop. On the other hand, the two similar sets of slider-keys unearthed in Lefkada, in combination with the fragment from Pergamon, testify to standardised features far beyond the region of Megara. Common characteristics would have included the number of finger and slider holes, the latter constrained by the available space around a tube, and the arrangement of the sliders, guided by practical necessities – most importantly, the rods must not encumber the fingers. Within these general parameters, individual designs seem to have differed widely; the much larger spacing of the Pergamon slider holes does not resemble the small intervals found on the Megara instruments. These differences set aside, we may well be dealing with the most important general type of professional modulating aulos of the Hellenistic period, flourishing across a large geographic region. 4 Musical Evaluation 4.1 General Considerations The music-archaeological evaluation of an aulos cannot be considered complete without embedding its design within our wider knowledge of Greek music in terms of scales, pitches, notation, ‘modes’ and their evolution. This endeavour can hardly become more exciting than in the case of the instruments from Megara, the lifetimes of whose owners likely overlapped with those of Aristoxenus, to whom we owe most of our knowledge of ancient musical structures, and Theophrastus, our primary literary source for the construction of aulos reeds. As we have seen, the Megara auloi were almost certainly modulating instruments, and in spite of all their structural similarities, also different enough not to be addressed as two different specimens of precisely the same design. Their modulating nature emerges from the number of consecutive small intervals at their ends, operated by sliders (though hardly available in immediate melodic succession). Such a row of microtones does not fit any single-scale system of ancient theory, from its earliest attestation in Aristoxenus up to late antiquity. On the other hand, similarly small intervals are not, and for obvious reasons cannot, be implemented between the five finger holes per pipe. Nevertheless, if the instruments modulated between scales where the small intervals in the bass region played a role, similar intervallic shifts are also to be expected in the higher pitches. Without a mechanism for changing the position or size of the fingerholes, or switching between different sets of them, and without the option to use cross-fingering (which is useless on instruments where the Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 41 fingerhole diameters approach that of the bore), such modifications of pitch would have to be effected by partially covering fingerholes and/or perhaps modifying the effective lengths of the double reeds by moving their respective positions relative to the player’s lips. As a consequence, we must anticipate the possibility that the physical positions of many, if not most fingerholes result from a compromise. Moreover, the nature of this compromise is difficult to determine a priori. On the one hand, it would be straightforward to drill each hole so that it emits the highest pitch that may be required from it. On the other hand, the nature of Greek music ascribes the status of ‘fixed’ notes to the lowest of a triplet separated by small intervals (called a pyknón), and these lowest notes were evidently of higher modal importance than the ‘moving’ notes inside the tetrachord. An instrument where many of these ‘fixed’ notes would need to be played by the unstable means of partial covering or reed manipulation, making them in practice more mobile than their ‘moving’ peers, would appear particularly awkward. We ought therefore to reckon with instrument designs that tried to achieve modulating capabilities while maintaining stable ‘fixed’ notes as far as possible – and as far as anything is stable on a double-reed instrument. However, the probable nature of the expected compromises deprives us of one of the mightiest tools of aulos research. Since vital consonances may have been played between open and partially covered holes, the automated search for an optimal reed configuration in terms of maximised harmonicity may yield misleading results. Nevertheless the technique of modelling the pitches expected for various reed lengths by means of dedicated software must form the basis of the following considerations, in the hope that the physical design of the instrument reflects at least a sufficient amount of structurally primary notes – and that consistent results will eventually justify the method. After all, the uneven distribution of fingerholes betrays that they were carefully placed precisely for determining their pitch relations;25 any musical interpretation of the instruments must therefore account for all these positions. Since, as we have seen, the key lengths and bone sections of our instruments control each other sufficiently to establish most of the musically decisive data – though the precise position of three fingerholes is unfortunately lost – the paramount question, as usual, concerns the effective length of the required reeds. On early auloi, these may have extended up to a palm from their socket, while they typically measured only a few centimetres on later instruments. At 25 Note the existence of at least one treatise ‘On the drilling of auloi’, in more than one book (Aristox. ap. Ath. 14.634e). Such an approach stands in contrast to instruments with evenly spaced fingerholes (or fingerholes with evenly increasing distances in either direction) in many musical cultures, which require pitch adjustment throughout. Greek and Roman Musical Studies 10 (2022) 15–77 42 Terzḗs and Hagel any rate, the reed sockets from Megara preserve the characteristic step which ensures that the internal diameter of the reeds continues that of the main bore as smoothly as possible. This is important, because it allows us to work from the assumption that the effective length of the reed can, in very good approximation, be treated as a constant for all notes on a pipe. With the given wide diameter of the bore and consequently the reed, the blades of the latter, which resulted from flattening one end of a length of cane,26 must have been quite substantial: starting from a tube of 13 mm diameter (i.e. that of the reed socket), the resulting blades would be 20 mm wide and proportionately longer than those of narrower auloi. Their tips must have extended beyond the pipe end by more than 35 mm. On the other hand, their maximal extension cannot have exceeded 70 mm by much.27 Notably, three of the four fragile reed sockets were destroyed beyond repair, so we only know the total dimensions of the uppermost sections of Meg1β; for Meg2 we need to estimate the length of the missing reed socket from its extant termination. If the depths of the reed sockets were similar, and identical on both pipes, Meg2αM would have been 9.1 mm longer, and Meg2βM, 11.6 mm. On a typical aulos pair, the effective reed lengths for the two pipes differ only marginally. It may, however, be expected that the reed of the right-hand (higher) pipe, even if cut to the same physical length, would be effectively shorter by a slight amount, up to a few millimetres, if the pair of reeds was retrieved from the same internodium of a single plant, as described by Theophrastus.28 4.2 Bass Notes While the actual pitches of each side hole note as well as the actual intervals between these notes depend on the absolute effective reed lengths, this is not similarly true when we confine ourselves to the question of the identity between respective notes on the two pipes of a pair, as long as it is assumed that the pipes were equipped with identical reeds (of any reasonable length). By computing the expected pitch relations, we may thus be able to determine, 26 27 28 Cf. Hagel 2021a, 430–5. Cf. Hagel 2021a, 428f. Hist. Plant. 4.11.7 συμφωνεῖν δὲ τὰς γλώττας τὰς ἐκ τοῦ αὐτοῦ μεσογονατίου, τὰς δὲ ἄλλας οὐ συμφωνεῖν· καὶ τὴν μὲν πρὸς τῇ ῥίζῃ ἀριστερὰν εἶναι, τὴν δὲ πρὸς τοὺς βλαστοὺς δεξιάν. τμηθέντος δὲ δίχα τοῦ μεσογονατίου τὸ στόμα τῆς γλώττης ἑκατέρας γίνεσθαι κατὰ τὴν τοῦ καλάμου τομήν· ἐὰν δὲ ἄλλον τρόπον ἐργασθῶσιν αἱ γλῶτται, ταύτας οὐ πάνυ συμφωνεῖν. ‘The tongues from one and the same internodium, they say, are in concord, but not the others; and the one closer to the root is the left-hand, the one closer to the blossom the right-hand [tongue]. When the internodium is cut in two, the mouth of each tongue is fabricated at the cut of the cane. If the tongues are manufactured in another way, they are not in good concord, it is said’. Cf. the 3–4 mm predicted difference in effective length for the Pydna and Paestum auloi in Hagel 2021a, 429. Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 43 tentatively at first, whether it is likely that two fingerholes at roughly the same distance from the upper end of each pipe were intended to play in unison or not. Or, alternatively, assuming that a certain pair of notes between two pipes sounded the same pitch, we would become able to establish for which of the other potential note pairs this would have been true as well and for which not. When the upper ends of the pipes of Meg1 are aligned in this way, the pitch of the second-lowest slider hole of the lower pipe is only slightly higher (within less than 20 cents) than that from the exit of the higher pipe. The pitches become identical when we make the reed of the lower pipe effectively longer by 5 mm, in the way Theophrastus leads us to expect, but perhaps by just a bit too much. Meg2 is slightly different. With the proposed reconstruction that switched the entire complexes of mouth-end plus extension sections between the pipes, a similar 4 mm difference between the reeds yields 20 cents difference between the respective pitches, but in the opposite direction; similar effective reeds therefore give an even larger difference of 32 cents, and in order to get the respective pitches from the higher pipe exit and the lower pipe secondlowest slider hole identical, the effective reed lengths would need to differ by an unrealistic 10 mm. However, the mouth-end parts of higher and lower pipe are not completely identical; between the termination of the reed socket and the effective end they measure 70.85 mm and 69.5 mm respectively. Since their spigots, however, appear identical, it should be possible to exchange them between the reconstructed pipes, so that the slightly shorter item becomes part of the shorter pipe. In this way, the required effective length differences between the reeds drop by 2.7 mm. Correspondingly, the pitch difference with equal reeds is diminished to 25 cents, and with a more realistic assumption of 4 mm effective difference between the reeds, to 13 cents. Therefore we propose revising the original Museum restoration of Meg2 only by exchanging the extension sections (X), leaving the uppermost sections (M) in place. 4.3 Coincidence of Pitches: Higher Tone Holes When the discussed pair of pitches is aligned, those of the highest slider hole (s1) of the lower and the middle slider hole (s2) of the higher pipe also become very close – though apparently not identical; once more with reeds differing by 4 mm, these holes are predicted to differ by 20 cents on Meg2, and by 16 cents on Meg1, though in opposite directions: the hole on the lower pipe is lower on Meg1, but higher on Meg2. But what about the fingerholes? On the known early auloi, four of them generally coincide: with an offset of a single interval, index to ring finger on the lower pipe can play the same notes as do thumb to small finger on the higher. Greek and Roman Musical Studies 10 (2022) 15–77 44 Terzḗs and Hagel On the Megara instruments, in contrast, the respective hole positions coincide only very roughly, and the distances are incompatible. As a result, even though the pitches of these holes, which form the higher range of the pipe, are much more sensitive to changes in reed length, no plausible configuration can make them coincide. On Meg1, the central two of the four hole pairs in question may play identical notes, when the reed of the shorter pipe is effectively longer by 7 mm, contrary to expectation and Theophrastus’ statement. But even in this way, the outer notes differ significantly, by almost a sixth of a tone. Since those of the higher pipe span a larger distance, its lower note in question is lower than its counterpart, and the higher note is higher. On Meg2, a much better accord can be achieved, but here also the reed on the shorter pipe would need to be longer, by 7 mm. Nonetheless, had we only this instrument, we would almost certainly try to enforce a musical interpretation on that basis. The obvious structural parallels with Meg1 encourage us, however, to take into account the possibility that non-matching fingerholes might form a structural feature, after all. 4.4 Intervals: Bass Notes Independently from the precise reed lengths, the two lowest intervals on the long pipes as well as the consecutive lowest on the short pipes must have been very close to actual quartertones. We can specify the boundaries with some precision on Meg1β, where the depth of the reed socket is known. For the shortest possible reeds, the intervals in question would measure 47, 63, and 61 cents respectively; for reeds extending rather extreme 80 mm from the instrument, they would instead amount to 43, 58, and 56 cents. Such differences are barely noticeable; all the values are close to the true quartertone (50–51 cents29) or lying between a quartertone and a third of a tone (67–68 cents). Assuming similar reed socket depths, the respective ranges on Meg2 are 55–60, 53–58, and 60–64 cents. These figures, it must be noted, refer to plausible reed-length ranges on the two instruments individually. However, although the upper ends of Meg2 are not preserved, it is clear that the distances between the highest fingerholes and the top of the instrument without reed were obviously smaller on Meg2. Normally this would indicate that the instrument was higher pitched overall. 29 The double values are necessitated by the unclear relationship between Aristoxenus’ definitions and the modern notion of an equally tempered tone. The smaller value follows from an equation of Aristoxenus’ tónos with the latter, according to his stance that the circle of fifths can be closed for practical purposes, the larger from his definition of a tone as the difference between perfect fifth and fourth, intervals that the master would not have experimentally ‘tempered’ in real-life music-making. Greek and Roman Musical Studies 10 (2022) 15–77 45 Two Auloi from Megara But in the present case such an interpretation is hardly possible. The general hole disposition is very similar on both pairs, pointing to very similar ranges or even standardised pitch. Moreover, where we observe significant variation at all, in the finger spans required for the two higher pipes, Meg2 has the larger distance, demolishing the hypothesis of its representing a higher-pitched variant of the same design. Consequently we must assume that the difference in upper lengths was compensated by a difference in reed length. As we have seen, the longer tubing of Meg1 was almost certainly adopted in order to accommodate the sýrinx slider keys, which inevitably shifted the boundary between bone instrument and cane reed upwards. Taking the preserved lower ends of the reed sockets as points of reference, we would therefore expect that reeds suitable for Meg2 were about 14–18 mm longer than those for Meg1. This in turn narrows down the plausible ranges for the effective reed lengths, because the shortest possible overall length on Meg2 would produce reeds which are too short on Meg1, while the longest plausible reeds on the latter would demand improbably long ones on the former. Set aside the differences between the pairs for the moment, and the plausible ranges thus emerge as 50 mm to about 80 mm maximum for Meg2, and 35–65 mm for Meg1. This affects the ranges for the lowest intervals only marginally. Their sizes in cents are now predicted as follows: low E – S3 Meg1: Meg2: low S3 – S2 44–47 59–63 103–109 55–59 53–56 109–115 high E – S3 58–61 60–63 Irrespective of the originally intended reed sizes and ensuing absolute pitches, we may thus state, as a first certain result, that on the Megara instruments a crucial structural function was attributed to intervals that ancient theory clearly assigned to the enharmonic genus. Still, the presence of any sort of ‘quartertones’ in the slider notes as such does not a priori prove the melodic use of these intervals; after all, we have seen that slider-operated notes could hardly be played in immediate succession. At any rate, the lowest couple of tone holes on the longer pipes together with its exit form a veritable enharmonic pyknón. Greek and Roman Musical Studies 10 (2022) 15–77 46 Terzḗs and Hagel On Meg1 the quartertones of this pyknón add up to a very precise semitone, which, as we have seen above, is practically identical with the difference between the exits of the pipes. If the pipes were in fact intended to differ by a semitone (either the abstract ‘tempered’ semitone of Aristoxenus and his predecessor harmonicists of 100–102 cents, or the slightly smaller one of 92 cents obtained by tuning or modulating in perfect fifths and fourths), the coincidence of this semitone with the size of the enharmonic pyknón would be reduced to a corollary of the strictly Aristoxenian nature of the latter. In this case, we should not expect a similarly precise coincidence on Meg2 with its slightly wider pyknón. 4.5 Intervals: Higher Tone Holes In spite of the closely-packed pyknón-like structures at the bottom of the instruments, the distances between the fingerholes on the upper parts by no means reflect the distinction between smaller semitone-like and wider intervals of which the respective enharmonic scales or their related semitonic diatonic and chromatic counterparts would consist. Instead, the wide and comparatively regular – though not equidistant – spacing appears to proliferate the raw tonality of older auloi with neutral thirds and near-equally divided tetrachords,30 where the smaller intervals which appear in all regular scales would mostly have been realised by partial covering. On the one hand, such a design may certainly be explained by purely physical demands: with the required extreme finger span, a distinctly unequal spacing of fingerholes becomes impossible to manage. On the other hand, a wider spacing also opened up richer choices of playable microtonal shades, given a sufficiently expert performer. 4.6 Octave Harmoníai On balance, we must therefore expect that the makers of the Megara auloi were inspired by a musical system that worked with quartertones, perhaps aligning its scales along an ideal grid of quartertones, while at the same time encouraging playing techniques which reflected the microtonal variability that plays such an important role in Aristoxenus’ theory of tetrachord divisions. Aristoxenus mentions two models that endeavoured to incorporate existing scales within a comprehensive system of potentially modulating musical keys (tónoi or trópoi).31 He explicitly associates one of them, which places some scales at distances of three quartertones, with the making of auloi. 30 31 Cf. Hagel 2021a, 436–43. Aristox. Harm. 2.37–8 (47.1–16 Da Rios). For the reconstruction of these scales see Hagel 2000, 165–89; Hagel 2009, 371–90. Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 47 The other one is entirely ‘commensurable’ on a quartertone grid. Although it appears more modern, Aristoxenus mentions it first, so that we do not know whether the author’s final criticism of an approach to which he refers by the term katapýknōsis “condensing [the scheme]”32 as unsuitable and violating the harmonic rules would apply to both or only the one described second. At any rate, it is difficult to find any principal fault with the first-mentioned system on the grounds of Aristoxenus’ own tenets, so his presentation may have inverted the historical sequence precisely in order to obfuscate the fact that the more modern system did not actually merit his condemnation. As is well known, the interval of the octave had always featured prominently in ancient music theory. Apart from systematic endeavours to describe all modal scales as ‘species of the octave’,33 it is telling that the dignified term harmonía itself had acquired the sense of ‘harmonically structured octave’ as early as Philolaus.34 Even the overall pitch range of early auloi, in spite of their dearth of tone holes, was evidently defined by an octave between the exit of the lower pipe and the highest fingerhole on the higher.35 Later the lower pipe alone on an instrument such as the Louvre aulos would form an octave scale.36 It does not therefore come as a great surprise that the lower pipes of the Megara auloi also appear to comprise an octave when equipped with reeds whose lengths realise the mean of the discussed plausible ranges, approximately 65 mm for Meg2 and 50 mm for Meg1 (resulting in intervals of 1219 cents and 1186 cents, respectively; precise octaves are predicted for 71 and 45 mm). Moreover, on Meg1, this octave is structured into a low fifth and a high fourth by the ringfinger hole (with a perfect octave, these are predicted to measure 705 cents and 495 cents, respectively, indistinguishable from perfect consonance). The same is, however, not true on Meg2, where the hole in question sits a quartertone lower – so far the strongest indication that the instruments are not intended to be identical. A reed of corresponding length on the higher pipes also creates acceptable octaves between their respective bass notes and thumb holes. Fascinatingly, when the reeds are chosen so that the respective octaves on each pipe of Meg1 are perfect (45.5 and 40 mm), the coincidence between the lower pipe middle slider hole and the higher pipe bass note also becomes exact. 32 33 34 35 36 Cf. Aristox. Harm. 1.7 (12.15 Da Rios) καταπυκνῶσαι βουλομένοις τὸ διάγραμμα. Associated with the name of Eratocles, cf. West 1992, 126–8. Cf. Hagel 2018, 447–50. Hagel 2021a, 424–7. Hagel 2014. Greek and Roman Musical Studies 10 (2022) 15–77 48 Terzḗs and Hagel 4.7 Absolute Pitch Starting from these plausible octaves, we may finally assess possible absolute pitches. Based on a perfect octave between the bass and treble notes of the lower pipe of Meg1, a frequency of 294Hz is calculated for the latter. According to the established absolute pitch of ancient notation (I I ≈ 245Hz),37 this corresponds to the note written E E in diatonic/chromatic Lydian and Hypolydian, but G G in the Phrygian and Dorian tónoi. This is precisely the note that, according to the reconstructions of the pre-Aristoxenian systems, typically formed their higher boundary, representing the characteristic highest melodic pitch of a modulating aulos – apart from the Mixolydian key in what has been called the ‘commensurable’ system, which reached a semitone higher – and a typical treble note of melodies from the Hellenistic period.38 That reconstruction of an ancient paradigm, on the one hand, and the present reconstruction and preliminary evaluation of the Megara finds, on the other, thus corroborate each other. 4.8 Dorian and Mixolydian In the said ancient mappings of tonal space, the octave down from G G was universally shared between Dorian, Phrygian, Lydian and possibly other scales whose structure eludes us (only those happen to have been transmitted in the extant literature whose names associated them with the modes famously mentioned in Plato’s Republic). The pyknón that we find on the lower end of the Megara auloi would, however, only appear as part of the Dorian, but not the Phrygian or the Lydian scale (and hardly the Hypodorian or Hypophrygian). We have already established that the bass notes of the higher pipes stood a semitone above those of the lower pipes. The octave extending upwards from this note thus coincides with the Mixolydian scale of the ‘commensurable’ system. Like the Dorian octave, the Mixolydian also featured a pyknón at its lower end. However, although the higher pipes also start with a sequence of small intervallic steps, only the lower of these can be addressed as a quartertone, while the second one, between the two lowest slider-key holes, is larger, equating three eighths of a tone (78 cents) on Meg2, and a full semitone (about 106 cents) on Meg1. The sum of the two lowest intervals thus amounts to 139 cents on Meg2, and 166 cents on Meg1. The former is practically identical with what Aristoxenus defines as the boundary between enharmonic 37 38 For the ancient pitch standard, cf. West 1992, 273–6; Hagel 2009, 68–95; Hagel 2012b; Hagel 2014; Hagel 2019, 185; Hagel 2020, 302. Precise data are only retrieved from Roman-period sources, but all available earlier evidence is consistent with it. Hagel 2009, 343–51. Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 49 and chromatic (133–136 cents), while the same author would have accepted the latter only as some narrow variant of the chromatic. When discussing the practical demise of the narrow quartertone enharmonic in contemporary music, Aristoxenus interestingly associates the ‘chromaticising’ enharmonic with the notion of greater ‘sweetness’, obviously transferred from a culturally agreed evaluation of the chromatic as sweet and mournful, which later musical writings still echo.39 The notion of mournfulness in turn fits the Mixolydian exceedingly well, which was also consistently associated with such an ethos during the period from which the Megara instruments date.40 The enharmonic, in contrast, was said to reflect typically male qualities,41 as was the Dorian.42 It appears, therefore, that the literary sources can explain the different sizes of the pykná on the higher and lower pipes of the Megara pairs as the reflex of a twofold harmonic dichotomy. While the austere ‘real’ enharmonic quartertones on the lower pipes emphasised the manly character of its Dorian scale, the near-chromatic or chromatic on the higher Mixolydian pipes underlined the sweet sorrow of a scale that Aristoxenus traced back to none other than Sappho. The respective passage is of the highest relevance for our subject: Ἀριστόξενος δέ φησι Σαπφὼ πρώτην εὕρασθαι τὴν Μιξολυδιστί, παρ᾿ ἧς τοὺς τραγῳδοποιοὺς μαθεῖν· λαβόντας γοῦν αὐτὴν συζεῦξαι τῇ Δωριστί, ἐπεὶ ἡ μὲν τὸ μεγαλοπρεπὲς καὶ ἀξιωματικὸν ἀποδίδωσιν, ἡ δὲ τὸ παθητικόν, μέμικται δὲ 39 40 41 42 Aristox. Harm. 1.23 (29.14–30.8 Da Rios) γλυκαίνειν ‘to sweeten’; Anon. Bell. § 26 ἥδιστόν τε καὶ γοερώτατον, ‘the sweetest and most mournful’; gloss to Aristid. Quint. 2.18 (92.25f. Winnington-Ingram) ἥδιστόν τε καὶ γοερόν, ‘sweetest and mournful’; Theon 55.6f. Hiller γοερώτερόν τε καὶ παθητικώτερον ἦθος, ‘most mournful and emotional character’. For the combination of emotions cf. already Od. 22.500f. τὸν δὲ γλυκὺς ἵμερος ᾔρει / κλαυθμοῦ καὶ στοναχῆς, ‘but he was overcome by sweet longing for weeping and groaning’. Plat. Resp. 398e τίνες οὖν θρηνώδεις ἁρμονίαι; … Μειξολυδιστί, ἔφη, καὶ συντονολυδιστὶ καὶ τοιαῦταί τινες, ‘So what are the mournful harmoniai? […] Mixolydian, he said, and Taut Lydian and similar ones’, Arist. Pol. 1340b ἀλλὰ πρὸς μὲν ἐνίας ὀδυρτικωτέρως καὶ συνεστηκότως μᾶλλον, οἷον πρὸς τὴν μιξολυδιστὶ καλουμένην, ‘but to some [harmoníai the listeners would become] more tearful and constrained, as for example to the so-called Mixolydian’; Aristox. ap. [Plut.] Mus. 1136d καὶ ἡ Μιξολύδιος δὲ παθητική τίς ἐστι, τραγῳδίαις ἁρμόζουσα, ‘And the Mixolydian is emotional, fitting for tragedies’; Plut. Recta rat. aud. 46b “εἰ μή τις ἦς ἀναίσθητος” εἶπε “καὶ ἀμαθής, οὐκ ἂν ἐγέλασας ἐμοῦ μιξολυδιστὶ ᾄδοντος, ‘If you wouldn’t lack taste and education’”, [Euripides] said, ‘you wouldn’t have laughed when I sang in Mixolydian’. PHibeh 13.15–22 κακῶς εἰδότες ὅτι οὔτε χρῶμα δειλοὺς οὔτε ἁρμονία ἀνδρείους ποιήσειεν τοὺς αὐτῇ χρωμένους, ‘without realising that it is not true that the chromatic would make those who use it cowards or the enharmonic, manly’. Plat. Resp. 399b, Arist. Pol. 1342a: ἠθικοῖς, ‘moral’. Greek and Roman Musical Studies 10 (2022) 15–77 50 Terzḗs and Hagel διὰ τούτων τραγῳδία. ἐν δὲ τοῖς ῾Ιστορικοῖς τοῖς Ἁρμονικοῖς Πυθοκλείδην φησὶ τὸν αὐλητὴν εὑρετὴν αὐτῆς γεγονέναι. [Plut.] Mus. 1136d Aristoxenus says Sappho has invented the Mixolydian and the tragic composers learned it from her. At any rate, they took it and coupled it with the Dorian, since the latter produces magnificence and dignity, but the former emotions, while tragedy constitutes a blend of all that. However, in the History of Harmonics he says that the aulete Pythocleides was its inventor. Not only do we find the Mixolydian associated with the aulos, which is no surprise given that this was the typical instrument to accompany laments, we also learn explicitly of its being paired with the Dorian in tragic music. The term συζεῦξαι, normally used for the physical, for example sexual, pairing of two objects, conveys a curiously technical flavour. Since the aulos was the instrument of drama, it is tempting to read the remark as a reference to the creation of an instrument that played precisely these two harmoníai. If each of its two pipes was mainly associated with one of them, as appears to have been the case with the Megara instruments, the idea of coupling two modes gains a much more physical notion.43 It is therefore not implausible that the quotation in ps.-Plutarch preserves an echo of Aristoxenus’ familiarity with auloi that may have looked and functioned very much like those under scrutiny, which, after all, may well have been produced during the author’s lifetime, and which ended up only a good day’s march from the Lyceum. 4.9 Pyknón Shapes While the size of the Mixolydian pyknón may be comprehensible from our sources from the fourth century BC, and its division into two roughly equal intervals of about a third of a tone on Meg2 is entirely inconspicuous in terms of Aristoxenian tetrachord divisions, its internal structure on Meg1 calls for further comment. As we have seen, the respective intervals amount to roughly 60 and 106 cents, about a third of a tone and a semitone. This is not a division Aristoxenus acknowledges expressly, though it falls straightforwardly within the boundaries he delineates. Once he even quotes the possible combination of a third of a tone with a larger second interval, but (implicitly) exemplifies 43 For the idea of an aulos forming a harmony of two pipes with qualities that are opposed on a gendered axis, cf. Poll. 4.80 καὶ τὸ μὲν γαμήλιον αὔλημα δύο ἦσαν αὐλοί, μείζων ἅτερος, συμφωνίαν μὲν ὑποδηλοῦντες, μείζω δ’ εἶναι χρῆναι τὸν ἄνδρα, ‘And the nuptial aulos performance consisted of two pipes, one of them larger, indicating concord, but with necessary pre-eminence of the male’. Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 51 the latter with two thirds of a tone.44 Many centuries later, however, we learn from Ptolemy that within his musical horizon any pyknón would need to consist of a smaller and a much larger interval.45 In Ptolemy’s numerical account of their sizes, his music-mathematical axioms forced him to make the larger almost twice as large as the smaller, so it is difficult to assess how well this would have reflected actual musical practice;46 but there can be no doubt that the difference as such was conspicuous at least in the Eastern Mediterranean of the second century AD, and probably in a much wider region, since touring star musicians would doubtless have spread musical fashions quickly. Meg1 might therefore be taken as the hitherto earliest evidence for an unequal pyknón in actual practical use, more than 400 years before Ptolemy. Its structure is practically undistinguishable from Ptolemy’s ‘soft chromatic’, whose mathematical description in terms of the superparticular intervals 28:27 × 15:14 evaluates to 63 + 119 cents. 4.10 Realising Harmoníai So far the proposed interpretation of primarily Dorian and Mixolydian instruments is based on a couple of octaves, a fourth and two groups of microtonal intervals per pair, plus the perfect pitch coincidence with a theoretically reconstructed system. It is therefore time to turn to the remaining tone holes and the instruments as a whole. Figure 3 displays the pitches of Meg1 as predicted by modelling software,47 on the basis of effective reed lengths that are not very different from those lengths that produced the perfect octaves discussed above, but which establish a good compromise between various intervals. Fortunately, this instrument preserves all tone holes except the small-finger hole on the lower pipe, whose position needs to be estimated. This could be done, however, without too much uncertainty on the basis of the slider key that was operated by the same small finger, and for that purpose ran up to the small-finger hole. Even in order only to cover its hole, the player’s finger was already stretched to a span that is only available to trained players. Nonetheless, it needed to reach out even further in order to push the key downwards, and again further to catch the knob and pull it back. Clearly, there was no space to be wasted: every millimetre more or less would have crucially encumbered or facilitated the handling of the instrument. Thus we may safely assume that the knob, in its upwards position, came very close to the small-finger hole, stopping short of its rim only by about a millimetre, so as not to get in the 44 45 46 47 Aristox. Harm. 2.52 (65.4–20 Da Rios). Ptol. Harm. 1.14 (32.23–5) and 1.15 (34.11–35.12 Düring). For discussion of Ptolemy’s more doubtful semitones see Hagel 2009, 217–19. Cf. Hagel 2021b. Greek and Roman Musical Studies 10 (2022) 15–77 52 Terzḗs and Hagel figure 3 Predicted pitches of Meg1, in comparison with the ‘commensurable’ trópoi as reconstructed in Hagel 2000 way of the finger when it uncovered and covered its hole during normal playing. From the position of the key hole, the length of the rod and the length of the intervening sections, which can also be established within very small margins, the probable position of the small-finger hole can thus be retrieved. In the figure, its centre is placed 44 mm above the lower end of the missing section, which in turn must have been about 71.1 mm long. The diameter of the hole is set to 9.5 × 9.8 mm, by extrapolating the minute difference between the middle-finger and ring-finger holes. As can be gleaned from Figure 3, the hole thus plays a pitch about 525 cents above the bass note, an eighth of a tone higher than the fourth we would expect at this place because it would complement the internal structure of the pipe’s octave to the fundamental tetrad that underlay the central octave of theoretical systems no less than all known ancient lyre tunings, and which had been recognised as implementing two mathematical means long before the Megara instruments were interred.48 Conceivably the required lower position for that fingerhole in order for it to play a true fourth would have exceeded the physical capabilities of the player; in this case, one would have needed to correct the pitch during playing. Alternatively, the lost hole might also have been made slightly smaller; with a diameter of 8.5 mm, for instance, the divergence shrinks to 17 cents. At any rate, in the figure the corresponding pitch is distinguished by a fainter line, so that it is not mistaken for part of the evidence. 48 Lyre tunings: Hagel 2009, 133f.; means: cf. Arist. ap. [Plut.] Mus. 1139b. Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 53 On the right hand of the figure, the lines indicating the pitches of all tone holes are overlaid with the reconstruction of the ‘commensurable’ system as it was published more than twenty years ago.49 The black circles there indicate relative pitches that are attested in Aristides Quintilianus, our only source for the structure of some harmoníai of the Classical Period, presumably taken from a lost work of Aristoxenus. The lines without such circles represent mere educated guesses about how the Hypophrygian and Hypodorian might have fitted into the picture, two scales whose positions in the system we learn from Aristoxenus, without ever being told about their structure. We see how the bass notes of the lower pipe coincide nicely with the pyknón at the lower end of the Dorian octave. Below, Aristides’ Dorian expands the ‘Dorian octave’ by another tone, which is absent on the pipes. This may confirm earlier speculation that the extra bass note had its original place as the hyperypátē of lyre music.50 Next would come mésē P P, which would supposedly have been sounded from the problematic lost fingerhole, as we have just discussed. The following paramésē M M can be played on both pipes. It forms the basis of another pyknón, which must be realised by half-covering the next higher fingerhole. Being spaced in the traditional manner at a distance of about three quartertones, this hole supported not only a narrow enharmonic but also wider variants up to a soft chromatic. The index-finger hole, finally, provided the treble note nḗtē. The thumb hole below it could supply a diatonic paranḗtē, if required (Aristides’ harmoníai come only in enharmonic guise, even though the age and the primary role of the diatonic were recognised among ancient theorists).51 In the lower tetrachord, at any rate, only a very soft version of diatonic might have been available, using the upper slider hole. Interestingly, Aristoxenus, if taken at face value, testifies to a universal use of precisely such a soft diatonic variant by the adherents of a modern musical style: χρώμενοι γὰρ αὐτοὶ τοιαύταις τετραχόρδων μάλιστα φαίνονται διαιρέσεσιν, ἐν αἷς τὰ πολλὰ τῶν διαστημάτων ἤτοι περιττά ἐστιν ἢ ἄλογα· μαλάττουσι γὰρ αἰεὶ τάς τε λιχανοὺς καὶ τὰς παρανήτας. [Plut.] Mus. 1145cd They themselves seem to use precisely those types of tetrachordal divisions in which the majority of the intervals is either odd [i.e. comprise 49 50 51 Hagel 2000, 172, Abb. 23. Hagel 2009, 408–11. Cf. e.g. [Plut.] Mus. 1134f–1135c for a pre-Aristoxenian speculative derivation of enharmonic from diatonic; in general, cf. Franklin 2002. Greek and Roman Musical Studies 10 (2022) 15–77 54 Terzḗs and Hagel an odd number of quartertones] or irrational [i.e. do not form a multiple of quartertones at all], since they soften the likhanoí and the paranêtai all the time. The notion of softening the notes in question, which are the higher ‘moving’ notes in the tetrachord, in a way that results in odd multiples of quartertones can only apply to diatonic or chromatic intervals. The ensuing soft chromatic features a pyknón of about 150 cents, like we find on the higher Megara pipes. The higher ‘moving’ note of a respective soft diatonic tetrachord, in turn, would lie about 250 cents above its bottom note, which coincides with the highest slider note on the lower pipe. Is it conceivable that the Megara auloi testify in such detail to the material background of the music that Aristoxenus had perceived as modern? The combination of some of these apparently fashionable traits, on the one hand, with some old-style quartertone enharmonic, on the other, might locate them within a cultural environment that embraced innovation without necessarily abolishing all characteristics of an earlier style wholesale. The higher pipe also starts with a pyknón, albeit of the wider, chromaticising type. The next hole, operated by the highest slider key, plays S S, precisely the irregular ‘diatonic’ note that characterises the lower part of the Mixolydian scale. There, another pyknón would now follow, the lowest note of which is, however, beyond the possible reach of the small finger. As a consequence, this pyknón would only have been playable starting from its highest note, reaching its ‘fixed’ bottom component by the precarious technique of half-covering. Here, more than anywhere else on our instruments, Plato’s remarks would seem perfectly appropriate: οὐκοῦν μεστὴ μέν που μουσικὴ πρῶτον, τὸ σύμφωνον ἁρμόττουσα οὐ μέτρῳ ἀλλὰ μελέτης στοχασμῷ, καὶ σύμπασα αὐτῆς αὐλητική, τὸ μέτρον ἑκάστης χορδῆς τῷ στοχάζεσθαι φερομένης θηρεύουσα, ὥστε πολὺ μεμειγμένον ἔχειν τὸ μὴ σαφές, σμικρὸν δὲ τὸ βέβαιον. Plat. Phlb. 56a Isn’t music, firstly, somehow full of that, as it tunes the consonances not with the help of some measure but by practical aiming, and entirely the art of the aulos, whose hunt for the right measure of each note amounts to aiming at a moving target, so that it has a great deal of uncertainty attached to it, but little that is definite. In Aristides’ version, the top half of the Mixolydian consists merely of an empty interval of a tritone, which leads directly to the thumbhole of our pipe. At the Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 55 period in question, however, theorists had long realised that the structurally decisive note, mésē, from which its relation with other scales would be determined, would sit within that empty interval, one whole tone below the treble note. On our pipe, this Mixolydian mésē Z Z is also available, as the middle-finger hole. As we have seen, both the Dorian and the Mixolydian harmonía appear indeed provided for, as far as this was possible given the physical restriction of the human hand. There is perhaps one shortcoming. Being played downwards from the available fingerhole, the Mixolydian central pyknón would apparently need to remain closer to a quartertone enharmonic than its lower pyknón is. The lower pitch of the two produced by partial hole-covering would belong to the category of ‘fixed’ notes and ought to stand a perfect fifth below the treble note of the scale, at least in theory. The size of the central pyknón between that note and the one produced from the open fingerhole would thus be restricted to about 130 cents. Without any information about how the Mixolydian used to be accompanied on the other pipe, we cannot, however, know whether the possible melodic fifth needed to be ensured harmonically, or whether the apparent restriction might have been less relevant in practice, and a larger pyknón might therefore have been practicable by bending its lowest note below its theoretical position. Above the highest Mixolydian note, the instrument still provides a higher hole, belonging to the index finger of the right hand. When fully opened, it would have sounded a whole tone higher than its lower neighbour, and 290 cents higher than the treble note of the left-hand pipe. This hole must typically have been used for accompanying various notes from the left-hand pipe, presumably by modifying its pitch in various ways by partial closing or manipulation of the reed.52 We will leave further exploration of this point to future experimental players. 4.11 More Harmoníai The modulating capabilities of Meg1 are not exhausted with Dorian and Mixolydian. Using pitches from the two pipes alternately, all notes of the (Syntono-)Lydian harmonía are accessible. The bounding notes of its pyknón reuse the holes for S S and P P; the mesopyknon in between can be produced by partial covering of the latter. Its mésē I I is provided by the right ring finger, and its highest note is identical with the Dorian nḗtē by definition. Using 52 For notes belonging to the accompaniment (kroûsis) lying above the perceived melody (mélos) in a certain style of aulos music, see Aristox. ap. [Plut.] Mus. 1137b–d; cf. Hagel 2009, 407–11. In modern literature it is sometimes asserted that in ancient Greek music the accompaniment was invariably above the melody, which may be an unwarranted generalisation. Greek and Roman Musical Studies 10 (2022) 15–77 56 Terzḗs and Hagel the thumb hole of the left-hand pipe, one could further create another pyknón above I I, which would modulate to Phrygian and presumably Hypophrygian; the Phrygian mésē is in turn supplied by Dorian paramésē M M. The lower Hypophrygian pyknón might have been identical with the Lydian. However, at first glance, no provision seems to be made for the lowest part of the Phrygian scale. Only the middle note of its pyknón can be played from slider key holes; in order to access its lowest note, one would have to shut one of the respective sliders partially, while it cannot easily be seen how the highest might be provided at all. However, if the instrument, as we had reason to speculate, reflected the design of a theatrical aulos suitable for tragedy, we might expect some support for both Hypophrygian, which may have been employed for solo arias, and for Phrygian, which was allegedly used already by Sophocles.53 We have so far ignored a special constructional conundrum related to the ‘intermediate’ slider key of the lower pipe of Meg1 (I3). While its plate is comparatively short, measuring no more than 14 mm, the range within which it was designed to move is unusually large: its slot length and the difference between the length of the guide and the constricted part that moved in it agree on a motion range of 16.8–17 mm. This seems to make no sense; in order to close its hole most efficiently, the plate ought to travel no more than the total length of the hole diameter plus half the difference between this diameter and the length of the plate, which in this case would amount to 11.35 mm. But here, assuming that plate end and hole rim just coincide when the slider key is in the open position, pushing the slider downwards the whole way moves the plate beyond the position where it covers its hole. As a consequence, when the plate has reached the lower end of its path, a 3 mm-wide segment of the hole has re-emerged behind it. On the surface, the problem might be mended by moving the initial position of the plate from the hole edge by about 5 mm. But this has the consequence that the slider needs to travel an extra half centimetre across the closed tube wall without achieving anything, which is not only entirely pointless but positively annoying: bent over the pipe in order to reach the upper part of the key, the player’s middle finger is considerably restricted regarding its lateral movement and will find it rather difficult to switch the key between its extreme states in one swift motion. Since nothing would have impeded the makers from manufacturing this key precisely as all the others, whose proportions appear technically perfected, we must infer that this singular design fulfilled a special function. It is difficult to see what such a function might have been other than precisely the effect described above, pushing the plate beyond the hole. The slider would in this way acquire three possible states: open (knob in highest 53 Hypophrygian: [Arist.] Pr. 19.48; Phrygian: Aristox. ap. Vit. Soph. 23. Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 57 position), closed (knob pushed downwards as far as on a normal slider key), and partially open (knob pushed downwards completely). From the available dimensions it is fortunately possible to predict the effect of the third state with some precision.54 The resulting opening has the shape of an ellipse segment with an area of somewhat less than 17 mm2. Part of this opening is, however, obstructed by the rod that extends across it at a slight elevation, leaving an effective opening that can be estimated to about 11–16 mm2. It functions as a small tone hole, producing a significantly lower pitch than the same hole does in its fully open state. The predicted configuration for an effective opening of 13.5 mm2 is shown in Figure 4; it does not differ much across the possible range. It emerges that the hole fills the gap in what is now a row of five quartertones in the bass region, providing the missing Phrygian hypátē F F (a fourth below its mésē M M), which probably also formed the Hypophrygian mésē. This would complete the Hypophrygian harmonía, as far as we are able to guess its structure. The low part of the Phrygian, however, would not be available in the enharmonic genus without resorting to the much more difficult trick of halfshutting the highest slider hole on the high pipe. Otherwise, only a chromatic pyknón is available on the high pipe, once more of the ‘Ptolemaic’ soft variant (64 + 131 cent), as well as a diatonic with a very small ‘semitone’, if the higher ‘moving’ note is obtained from the low pipe. This ‘semitone’ is identical with that of Ptolemy’s standard diatonic, where it is described as the ratio of 28:27 figure 4 54 Predicted pitches of Meg1 with slider key I3 in partially-shut state over hole βS1 Notably, the strict requirements of this slider key also contribute to determining the length of the lost pipe section within very small margins. Greek and Roman Musical Studies 10 (2022) 15–77 58 Terzḗs and Hagel (63 cents), which he also quotes from the much earlier account of Archytas, and which also resembles the ‘third of a tone’ that Aristoxenus acknowledges as a possible lowest diatonic interval.55 The virtually missing enharmonic Phrygian may in turn be related to another statement of Aristoxenus, where he asserts that the enharmonic is suited for the Dorian harmonía, and the diatonic for the Phrygian.56 Once more, a seemingly impressionistic tenet of ancient music theory might thus assume material cloth. 4.12 Notation The melodic range of the pair (i.e. excluding the highest note, which was very probably used only in the accompaniment) therefore extended from the highest note of the Mixolydian octave harmonía to the lowest of the Dorian. In terms of ancient notation, the Mixolydian of the ‘commensurable’ system was Aristoxenus’ ‘Higher Mixolydian’, being situated a semitone higher than the Mixolydian of the rivalling scheme. Much later, in the revised nomenclature of the fifteen-tónoi system known from the Roman period, it would appear under the name of ‘Hyperiastian’.57 The note signs, however, remained the same. In the older, ‘instrumental’ notation, the common highest note of the Dorian, Phrygian and Lydian harmoníai, as far as they are present on our instrument, was written as G, presumably abbreviating ‘nḗtē’ as the traditional term for the treble pitch. Here the highest Mixolydian note would require a secondary sign, of the form A; apparently the ‘instrumental’ notation was older than the design of an instrument with a higher variant of this scale. In contrast, the younger ‘vocal’ notation appears perfectly suited for such an instrument. Here the Ionian alphabet was distributed precisely across its melodic range. The Mixolydian treble note thus appears as A, and the Dorian bass note as W.58 If the Megara items are indeed the remains of professional instruments 55 56 57 58 Aristox. Harm. 1.27 (35.3–7 Da Rios). Aristox. ap. Clem. Strom. 6.88.1. Cf. e.g. Hagel 2020, 299, Figure 21.1. Regarding a terminus ante quem for this innovation that would predate the Megara finds, a much discussed passage in Aristotle’s Metaphysics (1093b) may be relevant. There he exemplifies numerical pseudo-philosophy by the notions ὅτι ἴσον τὸ διάστημα ἔν τε τοῖς γράμμασιν ἀπὸ τοῦ Α πρὸς τὸ Ω, καὶ ἀπὸ τοῦ βόμβυκος ἐπὶ τὴν ὀξυτάτην νεάτην ἐν αὐλοῖς, ἧς ὁ ἀριθμὸς ἴσος τῇ οὐλομελείᾳ τοῦ οὐρανοῦ, ‘that the distance is the same in the letters between Α and Ω, and from the bómbyx to the highest nḗtē in auloi, the number of which [nḗtē] is equal to the totality of the heavens’. If this refers to the association of ancient notation with an instrument design similar to the Megara auloi, it would reduce the alleged arguments in Hagel (2005) to nothing more than the excessive, though deplorably baseless, speculation for which that author is all too well known. However, two problems remain: firstly, the notes are named in reverse sequence in respect to the letters (perhaps Aristotle Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 59 as were used in prominent civic events, for which the most celebrated poetcomposers would provide the music, it would be no wonder to find crucial innovations regarding the notation of melodies associated with their design.59 The notes emitted from the index-finger hole of the higher pipe, by the way, would not necessarily require corresponding notation, if this hole played only what was perceived as the accompaniment, which was indeed never written down. 4.13 Further Differences What about Meg2, whose predicted pitches are shown in Figure 5? Here, as well, the placement of the left-hand small-finger hole needs to be estimated, and the positions of the hole for the ring finger of the right hand cannot be established with precision either, while the exact diameter of the small-finger hole is also difficult to assess.60 Notably, an optimal configuration requires assuming a comparatively large divergence between the effective lengths of the reeds. In the diagram, it is set to 4 mm (for Meg1, 2 mm proved sufficient). In many respects Meg2 appears to have functioned much like Meg1. Apart from the aforementioned differences in the size of the Mixolydian pyknón, the following divergences must, however, be noted. Most importantly, the ring finger hole of the lower pipe appears too low. The resulting interval of only 166 cents below it is clearly too small for the expected Dorian disjunctive whole tone (even if minor adjustments of fixed notes, as mentioned by Aristoxenus,61 are granted). The hole in question might instead be suited for supporting a Hypodorian pyknón. The Dorian paramésē M M, in turn, would need to be supplied from the right-hand pipe. Secondly, the highest slider-key hole on the higher pipe appears to sit too high for either the Lydian bass note or an irregular Mixolydian note at the ‘expected’ position. At any rate, the difference to Meg1 is so eye-catching that it must be intentional, unless we assume a gross production error. Whether it represented a different flavour of Mixolydian (while disregarding the Lydian option), must for the present remain a matter of speculation. At any rate, the 59 60 61 was not really acquainted with musical notation?); secondly, how does a treble note notated A possibly reflect some number of cosmological significance? On might wonder whether the following facts are somehow related: (a) the Megara instruments implement no strictly enharmonic pyknón in the bass region of the Mixolydian and (b) the same pyknón cannot be written as a sign triplet in the ‘instrumental’ notation. The figure is based on the following assumptions: Meg2αFii, small-finger hole: 39.5 mm above rim, 9.5 mm effective diameter; Meg2βFi, ring-finger hole: 6.5 mm above rim, 10 mm effective diameter; Meg2βFii, small-finger hole: diameter 10.7 × 10 mm. Aristox. ap. [Plut.] Mus. 1145d; cf. Hagel 2009, 140–2. Greek and Roman Musical Studies 10 (2022) 15–77 60 figure 5 Terzḗs and Hagel Predicted pitches of Meg2, in comparison with the ‘commensurable’ trópoi as reconstructed in Hagel 2000 theoretical optimal size of the central Mixolydian pyknón, which follows from the requirement of a perfect fifth between its base note and the highest note of the scale, precisely matches that on Meg1. The treble note of the whole instrument is significantly higher. Fully opened, it produces a good fourth with the thumb hole of the left-hand pipe, and a good fifth with its middle-finger hole, crucially augmenting the harmonic capabilities. The required increased finger span, however, may not have been accessible to the owner of Meg1. Finally, Meg2 has no three-state slider key for the Phrygian F F, but a perfectly normal one. To achieve the same effect, one would need to push it to just the right amount of ‘almost shut’, hitting the correct position within a millimetre or less without any guidance – at least none that has left detectable traces, as far as we see. The advantages of the fancy solution realised on Meg1, which sets the important pitch with precision, stand out all the more clearly. Here the motional guesswork concerned the closed state, which required much less precision: with a slider plate of 14 mm length and a hole of merely 8.7 mm diameter, any position within a range of about 5 mm would have served the purpose. 4.14 Conclusions Our findings, in combination with literary sources going back to the period in question, suggest that the two doublepipe instruments held in the Museum of Megara represented professional instruments of the highest cultural level, Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara 61 probably similar to those accompanying theatrical performances in the late Classical period. They share traits of a standardised design, adhere to a standard pitch, which would remain stable for some centuries, but also exhibit small idiosyncrasies that probably reflect both the musical tastes and the physical capabilities of the artists who had originally commissioned them. Their tonality is informed by theoretical efforts that are reflected in the literature. The reconstruction of the respective scalar systems in recent years has predicted many aspects of their design; as far as we know, these are the first published instruments that confirm those predictions. Unlike the known simpler auloi from earlier periods as well as those from the Roman era with an altogether different kind of metal mechanism, the pairs from Megara are above all characterised by a microtonal mismatch between their rows of fingerholes, which probably called for a stupendous degree of virtuosity, complementing the primary pitches, which were built right into the instrument and can therefore be evaluated, with fitting intervals from the other pipe that almost certainly involved a good deal of pitch-bending.62 Acknowledgements We would like to express our sincere thanks to Panagiṓta Avgerinoú, director of the Archaeological Museum of Megara, to the Ephorate of Antiquities of West Attica for granting permission to examine and publish the finds, and especially to Geōrgίa Theodṓrou, conservator of the Ephorate, for the invaluable information she has so kindly and generously shared on the restoration process of the aulos Meg2. Two expert reviewers invested substantial energy to supply a treasure trove of suggestions; our gratitude to both must not eclipse the fact that we can only hope to satisfy one of them fully. Parts of this publication are based on research funded by the Austrian Science Fund (FWF) through grant P32816-G, and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 787522), respectively. The views presented here, however, reflect only those of the authors; neither the ERCEA nor the FWF are responsible for any use that may be made of the information contained. 62 As one of the reviewers points out, such a procedure is familiar even to players of to modern Western reed instruments, in environments where they need to achieve pure thirds or a dominant seventh that reflects the harmonic series – the latter involving a deviation from the instrument’s designed pitch by about a sixth of a tone. 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Ανασκαφικαὶ Εργασίαι. Καρυῶτες. Αρχαιολογικὸν Δελτίον, 25 (Χρονικά), pp. 329–332. Litvinsky, B.A. (1999) греческие флейты (авлосы) в глубинной азии. Greek Flutes (Auloi) in Central Asia. In: J. Duchesne-Guillemin, ed., Monumentum Marcelle Duchesne-Guillemin, Leuven: Peeters, pp. 517–543. Litvinsky, B.A. (2010) Храм Окса в Бактрии, 3: Искусство, Художественное ремесло, Музыкальньие инструменты (The Temple of Oxus in Bactria. 3: Art, Fine Art, Musical Instruments). Moscow: Vostochnaya Literatura. Psaroudakēs, S. (2008). The Auloi of Pydna. In: A.A. Both, R. Eichmann, E. Hickmann, eds, Challenges and Objectives in Music Archaeology, Rahden, Westf.: Marie Leidorf, pp. 197–216. Sutkowska, O. (2015). Archäologische Auloi/Tibia Funde mit Mechanismen. Tonkunst 9, pp. 412–422. West, M.L. (1992). Ancient Greek Music. Oxford: Clarendon Press. Zorides, P. (1980). Μέγαρα. Αρχαιολογικὸν Δελτίον, 35 (Χρονικά), pp. 41–55. Greek and Roman Musical Studies 10 (2022) 15–77 64 Terzḗs and Hagel table 1 Megara auloi; bone segment dimensions Bone section effective length (mm) Meg1αM 78.2 socket depth / ⌀ (mm) spigot length / ⌀ (mm) ⌀ (int) (mm) (10)/(12) 14/(14.5) 11.7 Meg1αX Meg1αFi Meg1αFii Meg1αS 62.8 141.0 54.15 133.8 + 3.5 14.2/(14.5) 15.5/(14.6) 13.5/(14.5) 18.1 + 3.5/(14.5) 14.8/(14.5) 13.5/(14.5) 17.5/(14.5) – (11.7) (11.7) 11.7 11.7 Meg1βMi Meg1βMii Meg1βXi Meg1βXii Meg1βFi Meg1βFii Meg1βSi Meg1βSii 22.7 68.7 94.5 20.4 126.6 71.1 42.8 68.8 19.6/(13.3) (13)/(14.2) 15.9/(14.8) 12.5/(14.5) 13/(14.5) 14.1/(14.5) 13.2/(14.2) 18.2/(14.2) 13.3/(14.2) 15.8/(14.4) 12.5/(14.5) 12.7/(14.5) 14.1/(14.5) 13.2/(14.2) 16.7/(14.2) – 11.7 11.7 11.7 11.6 11.7 11.7 11.7 11.7 Meg2αM Meg2αX Meg2αFi Meg2αFii Meg2αSi (81.35) (47.5) (153.15) 65.3 52.8 16.85/15.2 18.3/15.3 (17)/(15.5) (18.5)/(15.5) – 11.7 11.7 (11.5) (11.5) (11.5) Meg2αSii 63.0 (10.5)/(13) (>15)/(15) (>17.5)/(15.5) (17)/(15.5) 18.5/(15.5) 14(15.5) – 14/(15.5) Meg2βM Meg2βX Meg2βFi Meg2βFii Meg2βS (77.5) 82.7 149.0 59.2 134.2 (8)/(12.5) (17)/15.5 (18)/(15.5) 17/(15.5) 17.5/(15.5) (17)/15.5 17.8/15.5 17/(15.5) 17.5/(15.5) – (11.5) 13.1 × 12.8 (11.5) (11.5) <(11.7) (11.5) 11.5 12.5 ⌀ (ext) max/min ↔ × ↕ (mm) upper rim lower rim × ✓ (18) × (17) (19) × (17.5) (18.5) × (17.5) (18) × (17.5) (20.5) × (16.5) 18.3/15.8 19.4/14.25 (18) × (17) 17.5 (19) × (17.5) (18.5) × (17.5) 18.2 17.5 (20.1) × (18) 19.25/14.5 18.0 18.3 18.3 18.2 ✓ ✓ ✓ ? × ✓ × ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ × × ✓ ? ✓ ? ✓ × × × ✓ ✓ ✓ ✓ ✓ ✓ ✓ 18.2 21 × 16.7 19.25/14.5 18.2 (18) (18) (18) × (17.5) (19) × (17.5) ✓ ✓ × ✓ ✓ ✓ ✓ ✓ × ✓ ✓ ✓ 18.5/14.0 In brackets: Approximate values; in bold: proposed dimensions Greek and Roman Musical Studies 10 (2022) 15–77 65 Two Auloi from Megara table 2 Aulos Meg1: side hole/pinhole centre distances from segment upper rims ⌀↔×↕ (mm) azimuth (degs) transveral niches, lower pair transveral niches, upper pair <1 2.2 9.8 × 10.2 9.8 × 10.0 9.75 × 10.0 9.65 × 9.8 2.2 2.2 0 180 20 180 0 −5 −105 180 n/a × × × × × × × n/a × × × × × × × 9.75 × 10.0 2.2 25 25 × × × × 2.2 25 × × n/a (60) + 3.5 61.3 + 3.5 n/a × × × × × × × × n/a n/a 49.5 + 3.5 10.7 × × × × × × × × × × n/a n/a n/a × × n/a −2.4 −11.5 Bone section Hole distance from upper end (mm) Meg1αM Meg1αFi » » » » » » s.h. p.s.h. f.1 f.2 f.3 f.4 p.1 p.3 Meg1αFii » f.5 p.2 Meg1αS p.2 » » » Meg1βMi Meg1βXii Meg1βFi » » » » » » s.1 s.2 s.3 s.h. p.s. p.s. f.1 f.2 f.3 f.4 p.1 p.3 Meg1βFii » Meg1βSi Meg1βSii » f.5 p.2 s.1 s.2 s.3 13.7 26.45 32.7 63.6 93.13 129.28 123.4 130.5 < d < 138 130.7 23.23 56.6 < d < 57.5 <57.05> (2.5) < d < (3.4) 2.9 42.8 + 3.5 78.3 + 3.5 110.1 + 3.5 (9.5) 22.9 (2.5) 21.75 51.7 84.95 115.55 112.4 117.7 < d < 123 120.6 27.1 63.0 25.95 30.15 49.75 s.h.: p.: f.: s.: in brackets: sýrinx hole pin hole finger hole slider hole values drawn on indirect measurements; in bold: proposed positions 9.2 9.2 9.2 (<1) 2.2 2.2 9.9 × 9.8 9.8 × 10.0 9.9 × 10.2 9.7 × 10.0 2.2 2.2 −105 25 180 0 180 180 −20 180 0 5 105 180 9.5×9.8 2.2 8.7 × 8.8 9.5 9.5 −25 −25 105 −25 180 Greek and Roman Musical Studies 10 (2022) 15–77 66 table 3 Terzḗs and Hagel Aulos Meg2: side hole/pinhole centre distances from segment upper rims Bone section Hole distance from upper end (mm) ⌀↔×↕ (mm) Meg2αFi » » » » » Meg2αFii » Meg2αSi » Meg2αSii » Meg2βFi » » » » » Meg2βFii » Meg2βS » » » » f.1 f.2 f.3 f.4 p.1 p.3 f.5 p.2 p.2 s.1 s.2 s.3 f.1 f.2 f.3 f.4 p.1 p.3 f.5 p.2 p.2 s.1 s.2 s.3 p.x 41.88 78.15 115.1 145.1 133.15 146.65 26.0 67.5 2.2 28.05 22.8 40.5 37.05 72.25 108.34 142.5 132.0 140 < d < 146 26.05 66.2 7.0 33.9 84.35 110.15 127.2 9.55 × 10.6 10.2 × 10.3 10.2 × 11 9.6 × 10 2 2 9.6 × 10 2 2 9.5 9.0 9.0 10.3 × 10 9.3 × 10.6 10.4 × 9.3 10 × 10 2 2 10.7 × 10 2 2 10.6 9.3 9.5 2 p.: f.: s.: In bold: azimuth (degs) −20 180 0 5 90 180 −10 0 0 90 0 180 20 180 0 −5 −90 180 10 0 0 −90 0 180 −35 transveral niches, lower pair transveral niches, upper pair × × × × × × × × × × × × × × × × × × 7 2 4 × × × × × × × × × 12 66 n/a × −7 −8.5 −10 × × × × × × × × × n/a 54 n/a × pin hole finger hole slider hole proposed hole positions Greek and Roman Musical Studies 10 (2022) 15–77 67 Two Auloi from Megara table 4 Megara slider key dimensions Slider O.L. SlU – E SlL – E CL – E Sl.L C.L. G.L. Pl.L. Meg1L1 Meg1L2 Meg1I1 Meg1I2 Meg1I3 Meg1S1 Meg1S2 Meg1Sy1 Meg1Sy2 Meg2αI Meg2αS Meg2αL Meg2βI Meg2βS Meg2βL 207.8 198.5 145.5 150.0 140.5 102.5 106.5 187.6 211.2 143.5/142.5 106/103 201/195.5 140.5/136.5 105.0 206 188.3 178.5 124.5 131.5 124.0 89.0 90.0 171.1 195.7 124.5/123.5 85.0/82.0 179.0/174.5 124.5/119.5 87.5 183.5 171.3 162.5 109.5 115.5 105.0 73.0 75.0 164.5 186.7 108.5/107.5 71.0/68.0 162.5/158 108.5/103.5 71.5 167 42.5 39.2 35.5 33.0 17.5 17.5 18.0 = Pl.L = Pl.L 28 16.5 30.0 = Pl.L = Pl.L 33.5 14.8 13.8 12.8 13.8 16.8 13.8 12.8 4.8 6.8 14.0 13.0 15.5 14.0 13.5 15.0 25.8 28.3 27 24.5 25 26.3 22.5 14 13.2 18 23 28 26 24.5 36 11.8 14.5 (14.8) 11 8 12.5 (9.7) (9.2) (6.4) 14 10 14 12 11 22 16.3 16 16 16.5 14 14 15.5 9.3 9.5 16 15.5 17 16 16 17 O.L.: SlU – E: SlL – E: CL – E: Sl.L: C.L.: G.L.: Pl.L.: in bold: Overall length slot internal upper edge – plate end slot internal lower edge – plate end rod constriction lower end – plate end slot effective length rod constriction length roof-shaped guide length plate length corrected dimensions Greek and Roman Musical Studies 10 (2022) 15–77 68 Terzḗs and Hagel table 5 Megara Auloi: adjusting sliders to their side holes (mm) Slider hole Pin lower edge – hole upper rim ± from Pin upper edge – SlL – E hole lower rim Meg1αS1 Meg1αS2 Meg1αS3 Meg1βS1 Meg1βS2 Meg1βS3 Meg2αS1 Meg2αS2 Meg2αS3 Meg2βS1 Meg2βS2 Meg2βS3 108.85 + 3.5 = 112.35 69.7 + 3.5 = 73.2 168.85 + 3.5 = 172.35 (βFii = 71.1) 105.8 [8.1 − 1.1] + 68.2 = 75.2 [6 − 1.1] + [71.1] + 87.8 = 164.8 107.5 68.1 159.5 103.8 74.5 167.6 2.85 0.2 0.95 0.9 0.2 2.3 0.0 0.1 1.5 0.3 3.0 0.6 table 6 Aulos Meg1: Distances in mm related to sýrinx sliders. Discrepancies assuming that the hole, when closed, should be covered by more than 1 mm of plate. Meg1α/Sy1 Meg1β/Sy2 p.s.: f.R.: SlU: s.h.: PlL: Plc: s.R.: ± from Slider SlU – E 120.25 + 3.5 = 123.75 81.1 + 3.5 = 84.6 180.25 + 3.5 = 183.75 (βFii = 71.1) 116.7 [8.1 + 1.1] + 77.7 = 86.9 [6 + 1.1] + [71.1] + 97 = 176.5 119.2 78.3 170.7 116.6 84.4 178.2 −0.75 −4.4 −3.55 −7.3 −3.1 −2.0 −4.3 −3.7 −3.8 −2.9 −3.1 −5.3 I1 S1 L1 I3 S2 L2 αI αS αL βI βS βL Pipe p.s. – f.R. Slider SlU – s.R. Pipe /Slider discrepancy Pipe f.R. – s.h. Slider s.R. – PlL s.R. – PlC Pipe/Slider discrepancy 76.45 103.8 78.8 105.5 2.35 1.7 76.2 71.7 76.0 71.7 80.65 76.45 1.3–4.45 1.5–4.75 sýrinx pin (upper edge) fixed Ring (upper rim) slot internal (upper edge) sýrinx hole slider plate lower end slider plate centre slider Ring (lower edge) Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara plate 1 Auloi Meg1 (Δ1965αβ) and Meg2 (Δ1964αβ); original restoration by the Museum Greek and Roman Musical Studies 10 (2022) 15–77 69 70 plate 2 Terzḗs and Hagel Meg1α bone sections; scale: 2/3 Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara plate 3 Meg1β bone sections; scale: 2/3 Greek and Roman Musical Studies 10 (2022) 15–77 71 72 plate 4 Terzḗs and Hagel Meg1 slider keys: long (L.1–2), intermediate (I.1–3); scale: 2/3 Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara plate 5 Meg1 slider keys: short (S.1–2), sýrinx (Sy.1–2); scale: 2/3 Greek and Roman Musical Studies 10 (2022) 15–77 73 74 plate 6 Terzḗs and Hagel Meg2α bone sections; scale: 2/3 Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara plate 7 Meg2β bone sections; scale: 2/3 Greek and Roman Musical Studies 10 (2022) 15–77 75 76 plate 8 Terzḗs and Hagel Meg2α slider keys: long (L), intermediate (I), short (S); scale: 2/3 Greek and Roman Musical Studies 10 (2022) 15–77 Two Auloi from Megara plate 9 Meg2β slider keys: long (L), intermediate (I), short (S); scale: 2/3 Greek and Roman Musical Studies 10 (2022) 15–77 77