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Inside the Hydra: Taking the Ancient Water Organ Seriously

In: Greek and Roman Musical Studies
Author:
Stefan Hagel Austrian Archaeological Institute, Austrian Academy of Sciences Vienna Austria
Institute for Classical Philology, University of Vienna Vienna Austria

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Abstract

Although ancient sources describe the mechanism of the ancient water organ’s wind supply in considerable detail, modern attempts at recreating such a device have remained unsatisfactory. A study of the relations between the shape of the pressure chamber, its size, possible water levels and the ensuing usable air pressure and volume suggests that the true hydraulis played at much higher pressures than has been commonly assumed. Such pressures would support reed pipes much more readily than flue pipes; this, in turn, can explain the sound volume that we must expect from an instrument that was used in open spaces and inherently noisy environments.

1 Introduction: What We Know

As seems to be clear enough from its name, the ancient hydraulis, invented by engineer Ctesibius in Alexandria, worked with water. Its basic mechanism is described in Vitruvius and Heron of Alexandria: the wind pressure was held more or less constant by a submerged pressure chamber, filled with air by means of a system of pistons and valves.1 Keys operated sliders that controlled the openings between the windchest and the pipes. When there were several registers, additional sliders at right angles to the key sliders or, alternatively, taps gave access to different rows of pipes.2 The details of such an upper part are well known from a rescue excavation in Aquincum of an organ dating to the early third century AD, which revealed all its metal elements, including the labial pipes together with their feet, which directed the air stream against the edges of the pipes.3 However, there was no trace of the lower part, the wind supply mechanism, which ought to have comprised even more substantial metal parts. From the start, therefore, it has been suspected that this instrument was operated by bellows instead.4 But the Latin inscription that had once adorned it referred to it as a hydra; consequently many people preferred to view it as the more exotic ‘real’ hydraulus, a water organ, which also makes for more spectacular reconstructions. However, attempts to supply a musically reasonable instrument with a water tank of a reasonable size – especially given the small dimensions of the extant part – have failed.5

Much the same is true for the magnificent remains of an organ found more recently in Dion.6 Apparently equipped with only a single register of labial pipes, it also lacks a wind mechanism. The existing modern reconstruction with such a mechanism seems hardly to support playing more than one note at once.7 This would be a poor record for a newfangled Hellenistic device that bears the name of the aulos, the age-old two-voiced instrument, in a musical culture whose non-monophonic nature is now universally recognised among experts.8

The problem is twofold. Firstly, one or a few mid-sized labial pipes cannot create the sound volume we must expect from an organ that accompanied gladiator fights in the arena together with trumpets and horns, instruments noted precisely for their loudness.9 Secondly, the reconstructed hydraulis wind mechanisms, as long as they stay within the transmitted parameters, could not sustain a stable supply of air sufficient for many such pipes; their hydraulic buffer was just too small for the required intense pumping.

This might be different with other kinds of organ pipes, such as reed pipes, which have theoretically been considered but, as far as I know, never practically tried. After all, both the Aquincum and the Dion organ had labial (‘flue’) pipes, which have also been discerned in the iconography. But both were small and were likely intended to be used as indoor instruments. Can we really assume that they reflected the design of an arena organ?

2 Water and Air

So far, these issues have been the subject of general discussion and trial-and-error experiment, necessarily based on modern organ-maker experience informed by the sparse finds. It is the purpose of the present contribution to take a numerical approach, outlining the ranges of the physical parameters within which the ancient water organ must have operated, and to ask what this might imply for its reconstruction.

The two essential parameters are air pressure and the (average) air flow. The latter is conveniently measured in litre per second (1 l/s = 10–3 m³/s), while air pressure in organs is traditionally specified in terms of the height of a water column (1 mmH₂O ≈ 9.8 Pa), which is especially useful for the water organ, where it reflects the actual means by which pressure is maintained and can thus be read directly from the object or its mathematical model. Modern organs typically play at pressures between 55 mm and 120 mm. The usable air volume is ultimately defined by the wind supply, which, on the hydraulis, is typically a pair of pistons, each operated by one person. The pairing ensures that air can always be provided from one piston while the other is drawn back, which drastically reduces the requirement for buffering air pressure by the hydraulic mechanism. But even in this way, no constant air flow can be achieved from the pistons alone. In addition, air consumption could almost certainly vary greatly even within short time spans whenever different numbers of pipes were activated, contrasting ‘chords’ with single notes or even rests.10 Such differences could hardly be balanced or even anticipated by the persons at the pistons. The hydraulic pressure chamber was therefore indispensable for levelling out the inevitable (and unsynchronisable) irregularities concerning the air flow on both ends of the system.

In order to uphold a stable sound, the buffer mechanism furthermore needs to minimise pressure differences: a pressure drop of 10% during a loud ‘chord’ may not affect the functionality of the organ pipes much, while a difference of 50% would be hardly tolerable. A variation of 10%, on the other hand, translates to different variations in water column height at different pressure levels. When starting from a typical modern playing pressure of 100 mmH2O, it would be exhausted by only a single centimetre difference, while an original pressure of 200 mmH2O allows for two centimetres, and therefore a reserve of about twice as much air. Within a water column of a given cross-sectional area, therefore, higher pressures translate to similarly larger reserves and, in turn, to similarly longer time windows within which the pistons can catch up. Conversely, there are basically four ways in which a hydraulis engineer can optimise that time window: (a) by increasing the area of the pressure chamber along with the water tank engulfing it, which leads to a proportional increase of the available air volume for a given pressure drop; (b) by increasing only the area of the water tank, a procedure that yields up to twice the original air volume when the area approaches infinity (e.g. when the pressure chamber is placed in a lake); (c) by increasing the playing pressure by adding extra water and/or (d) by minimising the air consumption of the pipes. In the following we will consider these factors in the light of the extant literary and iconographic testimonies.

Before turning to absolute numbers, we need to consider the general geometry of the pressure chamber, called the pnigeus (πνιγεύς), which was situated inside a bronze vessel called the ara (βωµίσκος). Vitruvius likens the shape of the former to that of an inverted funnel (infundibulum, 10.8), whence illustrations based on his text often realise it as a cone. Heron, in turn, calls it a hollow hemisphere (κοῖλον ἡµισφαίριον, Pneum. 1.42). Indeed, such a shape is also suggested by the term pnigeús itself, originally a furnace cover, which invoked comparison with the sky forming a dome above the earth (Ar. Nu. 96; Av. 1001) or with oyster shells (Aristot. PA 654a7). The apparent discrepancy between the ancient authors is merely a misunderstanding. Roman funnels were typically not conical but rounded, forming more or less perfect hemispheres.11

In order to understand why a hemisphere is close to the optimal shape for the pressure chamber, it is useful to consider alternatives. The most straightforward idea might involve a simple cylindrical pnigeus, placed inside a similarly cylindrical ara, as in Figure 1.12 With a constant amount of stored air, pressure differences are here minimised when the lowered water surface inside the pnigeus and the raised surface outside it are of the same size, which demands that .

Figure 1
Figure 1

An ‘optimal’ cylindrical pnigeus within a cylindrical ara. Left: zero pressure; right: maximal pressure

Citation: Greek and Roman Musical Studies 11, 1 (2023) ; 10.1163/22129758-bja10055

Clearly, however, such a design does not take full advantage of the area within the ara because the pnigeus can hold hardly more than half of the air volume that it might store if it extended almost to the walls of the ara. Also, pressure differences are enormous, ranging between zero and the full height of the pnigeus. Even if a pressure difference of 30% is tolerable, only the upper 15% of this range might therefore be used. For an organ playing with maximally 100 mmH2O, this would just be 1.5 cm: when the water rises 1.5 cm inside the pnigeus, it falls 1.5 cm outside it, resulting in a total pressure difference of 30 mmH2O. Even in a large ara of 1 m diameter, the resulting air reserve would amount to less than 6 l, hardly a few seconds even with only one labial pipe playing.

A considerably more efficient design would take advantage of almost the full cross-sectional area of the ara, leaving just enough clearance between pnigeus wall and ara wall for the water to flow unhindered (Figure 2). With zero pressure, the water must here cover the upper edge of the pnigeus, so that it rises above it when air is blown into the system. The rising surface is thus once more effectively equal to the falling surface – the small differences are negligible, especially because the slightly greater width of the ara is roughly cancelled out by the air ducts above the pnigeus, here sketched as a single tube. Once more the overall pressure difference translates to half its height within the pnigeus, but the area is now twice as large. The height of the pnigeus therefore equals half the maximal pressure. A playing pressure of maximally 120 mmH2O thus requires a pnigeus of only 6 cm height. Pressure drops by 30% when the water level inside the pnigeus rises from 0 to 18 mm, providing 14 l of air to the pipes with a similar ara diameter as above.

Figure 2
Figure 2

A large cylindrical pnigeus within a cylindrical ara. Left: zero pressure; right: maximal pressure

Citation: Greek and Roman Musical Studies 11, 1 (2023) ; 10.1163/22129758-bja10055

This is still not a lot, even though it already depends on the rather optimistic assumption of 30% tolerable pressure difference. However, the pressure difference as a percentage can be reduced by increasing the initial pressure, either by providing a higher pnigeus or, since the upper part of it, which is filled with water only near zero pressure, cannot anyway be used for playing, by adding some extra water, so that the pnigeus becomes more deeply immersed. The air duct thus effectively becomes part of the pnigeus (Figure 3).

Figure 3
Figure 3

A large cylindrical pnigeus within a cylindrical ara and initial water level above the pnigeus. Left: zero pressure; right: maximal pressure

Citation: Greek and Roman Musical Studies 11, 1 (2023) ; 10.1163/22129758-bja10055

The air reserve rises proportionally with the pressure. At 200 mmH2O maximal pressure and an acceptable drop of 30% it becomes 23.5 l for a pnigeus of 1 m, and still almost 8 l for a 10% drop. However, such pressures are radically higher than those we find on later organs.

The rectangular top edge of a cylindrical pnigeus causes an additional problem. When the instrument is completely depressurised, the total rising water surface hits the ceiling of the pnigeus simultaneously, which must cause significant noise, prolonged by unpleasant gastrophonic sounds created by air bubbles that escape after having become caught between the ceiling and the inevitable waves on the water. Such effects were hardly compatible with the representative function of the organ. Consequently the shape of the pnigeus would need to be modified, so as to avoid any strictly horizontal parts. In fact, the area right at the centre of the ceiling, where almost no air is left to be expelled, may remain almost horizontal, while the wall needs to become increasingly steep when moving outward, where greater diameters entail much greater amounts of air, finally maintaining an upright shape towards the bottom. Furthermore, any sharp edges in the construction would always cause a disturbance when met by the rising surface. The optimal shape therefore would come close to a hemisphere, or perhaps a flattened hemisphere with a cylindrical prolongation at its lower end, very much like an inverted Roman-period funnel, precisely as the sources have it (Figure 4).

Figure 4
Figure 4

A large hemispherical pnigeus within a cylindrical ara and initial water level at pnigeus top. Left: zero pressure; right: maximal pressure

Citation: Greek and Roman Musical Studies 11, 1 (2023) ; 10.1163/22129758-bja10055

Notably, the problem that necessitates producing a substantial curved vessel of hammered bronze sheet, instead of conveniently soldering parts of straight and bent sheet together, only occurs when the water level at zero pressure lies very close to or above the top of the pnigeus. This expensive construction detail alone should therefore caution us that any interpretation involving a lower water level lacks credibility and, consequently, that the maximum playing pressure was not lower but considerably higher than the height of the pnigeus. The height of a truly hemispherical pnigeus would of course be identical to its radius; neither can it have been much smaller for a shape with a cylindrically prolonged bottom end. At the very least it is to be expected that the water level was still above the upper end of the pnigeus when the system was depleted to the point of lowest usable playing pressure. Otherwise the behaviour of the instrument would change abruptly and precariously when the plummeting surface reaches the near-horizontal roof of the pnigeus, from which point on the pressure would fall much faster due to the swiftly shrinking external, and subsequently also internal, cross-sectional areas.

A hemispherical or funnel-shaped pnigeus has the additional advantage of diminishing the overall pressure for a given radius in comparison with a cylindrical construction, while maintaining a similar air reserve. This is because the useable air reserve concerns the lowest zone, where the walls are practically vertical. The upper part, in contrast, holds considerably less volume, so that less initial pumping is required to get the system up to working pressure. In turn, the overall water level is raised less. Since a hemisphere holds only two thirds of the volume of a cylinder with identical radius and height, the maximum pressure with initial water level not lower than the pnigeus top drops from pmax≥2r for a cylindrical pnigeus to pmax≥5/3r for a hemisphere.

The height of a cylindrical pnigeus can be chosen freely while exploiting the full area of the ara. The same is not true with a hemisphere, whose height is by definition half of its diameter. In order to play with 120 mmH2O, the height of the pnigeus would thus amount to merely 7.2 cm if narrowly enclosed within the ara and not much more even if the ara is much wider. With a volume of less than 3 l in total even in the later case, such a pnigeus would be useless. The conclusion seems inevitable that a true water organ required a significantly larger and therefore taller pnigeus and consequently played at much higher pressures.

3 Sizes

So what are realistic ara and pnigeus sizes? In general, “up to a metre high, rather less in diameter”, as Martin L. West summarised the evidence.13 However, the iconography appears to present different shapes: sometimes the entire row of pipes fits easily on the ara; in other instances, the windchest protrudes left and right. Is this distinction due a difference in ara sizes, to different numbers of pipes in a row (or pipes of different diameter), or both? Not many sources offer us the opportunity to assess absolute sizes by comparison with human figures; players are mostly hidden behind their instrument, and other musicians may appear closer to the foreground,14 while, in those cases where the organ functions merely as a symbol15 or its image is cramped into a small space,16 we can hardly even count on a realistic representation of its own proportions.

Figure 5 shows the most promising images in this respect.17 Although it features representations created in entirely different media, ranging from a large mosaic panel to a tiny ‘medal’, the two-dimensional depictions of the instrument appear based on the same iconographic prototype, with a frontal view of three panels of the octagonal prism, the cover of which is partially visible in front of the pipes, and pistons of specific size and placement. Note, however, that the inclination of the pipe ends is unusual on the mosaic; normally bass notes are at the left side of the player, as is still customary on keyboards.

Figure 5
Figure 5

Guessing sizes from the iconography. Contorniate Alföldi et al. 1976 no. 221, Mosaic from Nennig (3rd cent. AD), contorniate Alföldi 205 (British Museum R.4865), British Museum 1965,1011.1 (frontal and back view), all scaled for similar ara span

Citation: Greek and Roman Musical Studies 11, 1 (2023) ; 10.1163/22129758-bja10055

In the figure, the span of the ara is compared with its height as well as with the body heights, underarm lengths and shoulder widths of the musicians, where feasible. Though it is difficult to assess the level of the bottom of the water tank – does it extend within the bronze-coloured basis of the ara or is this actually the ‘basis assembled from wood’ that Vitruvius mentions? – it appears that the height of the ara is roughly equal to its span, producing a square frontal view. Scaled to typical ancient body heights of about 168 cm, a comparison between body parts and ara span (Table 1) suggests about a width of 79.5 cm for the latter, with a standard deviation of 7.9 cm. If outliers deviating more than a standard deviation are removed and averages for each item are calculated from the rest, their average suggests an ara span of 80.9 cm.18 Since its bronze walls must have been quite thin, this would be close to the incircle of the ara; the excircle would be somewhat larger. Notably, the large protruding windchest of the oil lamp does not imply that the water tank below was any smaller than on the other instruments.

Table 1
Table 1

Guessing ara sizes from the iconography: evaluating Figure 5. Outliers in italics

Citation: Greek and Roman Musical Studies 11, 1 (2023) ; 10.1163/22129758-bja10055

A hemisphere within an octagonal prism might provide a technically perfect solution for securing the pnigeus tightly in place, assuming that it abutted against the walls of the ara. The corners of the octagon would thus serve as ducts for the water that was ejected from and subsequently returned into the pnigeus. With a diameter of 80 cm and consequently a height of 40 cm, the pnigeus would hold no less than 134  l. A pressure drop of 30% from maximum would only occur after using up 50  l of air reserve (without any pumping). A loss of 17 l air, in turn, would only cause a drop of 10%. This would indeed form an excellently buffered system – but it would work at a maximal pressure of enormous 653 mmH₂O, five to ten times that of typical modern organs.

We need to pause here for a moment and examine the credentials of our results more closely. Firstly, the iconography is considerably later than the texts, later by easily two centuries and more. However, there can be no doubt that the depicted instruments are indeed functional water organs, which can only have used the same principles as described in the texts – all the more since we have seen that the attested pnigeus shape is already very close to the mechanical optimum in the early sources and was therefore not liable to significant further development. Time as such is hardly a factor, as long as there is no evidence of change – and especially when we cannot even imagine why and how the crucial factors would have changed. At the very least, the iconography allows us to study a specific kind of functional hydraulis.

Secondly, is it really necessary to install a pnigeus that uses up the full area of the water tank? Perhaps not, but if it was not done, it is difficult to see why the ara would have been made that large in the first place. Though it is true that pressure differences are smaller for an identical pnigeus placed in a larger tank, the relatively small effect may not be worth the effort. Anyway, as we have seen, a functional hydraulis cannot play at modern low pressures because this would render the pnigeus useless. So much we can assert with confidence, thanks to the fact that changes in the single dimension of height, when applied to a hemisphere, are inevitably raised to their cubes when it comes to volume differences. In this way, any decrease in height and therefore in maximal pressure causes a much more substantial loss of air reserve.

A supportive argument might furthermore be derived from Vitruvius’ text. When describing the placement of the pnigeus, the author takes pains to mention ‘dice’ of three fingers height (10.8.2 taxilli alti circiter digitorum ternum), which are placed underneath, in order to create the required clearance between the bottom of the water tank and the lower rim of the pnigeus. Conversely, we are not informed how the pnigeus is supposed to be held in place in the other dimensions. Such an omission would be all but natural if the circular lower end of the pnigeus was, in fact, fitted tightly between the faces of the octagonal prism that formed the ara.

The decisive argument, however, concerns the height of the ara, which is very well attested in the iconography. How tall does it need to be? With the model we have derived above, the water level needs to lie at least 653  mm above the lower rim of the pnigeus in fully pumped state. Below, Vitruvius places a gap of about three fingers, so that the total water height from the bottom becomes 70.5 cm. Above, a few centimetres of clearance are required in order to prevent waves on the water surface from lapping against the ceiling of the ara, and probably also to accommodate the horizontal air ducts from the pistons, taking us to perhaps 76 cm internal height, which is almost identical to the incircle of 80cm diameter from which we started. Our reconstruction therefore vindicates the practically square impression of this part in the iconography; the average data also suggest only a minimal difference (Table 1). At the same time, the iconography generally implies that there was hardly any room for extra water, so that the initial water level must have been very close to the top of the pnigeus. Apparently the large-ara type of hydraulis was optimised by incorporating the largest possible pnigeus for a defined working pressure, and therefore air reserve.

Finally, if this pressure would have been lower than we have concluded, there would have been no need for the high arae we observe. A lower ara would not only be preferable for economical reasons, but it would also have been much more practical. The representations either show or, where the player is largely hidden by the instrument, imply that she or he could not stand on the ground or on the same base as the organ while playing. Instead, the player could access the keys – and obtain an uninhibited view over the pipes – only by mounting a small raised platform.19 Consequently, there must have been a genuine necessity to make the ara so inconveniently tall, and it is hard to come up with any reason other than creating a water column of precisely that height.

Assuming that the possible pressure was not confined within a very narrow range by purely mechanical reasons, we may wonder whether a typical hydraulis design might have reflected Roman-period units of measurement. Anyway, such a connection may be established only very tentatively, not least because the instrument contains several lengths that derive from each other, each of which might have been used as the starting point: the diameter of the pnigeus, which was probably identical with that of the incircle of the octagonal ara, but also its outward span (i.e. the incircle diameter plus twice the width of the ara wall) and its excircle. Starting from our span of very roughly 80.9 cm, no plausible internal measurements can be derived. However, the excircle of such an ara would measure 80.9 cm/cos(π/8) = 87.6 cm, which falls only about 1.4% short of two ancient cubits. On balance, it appears quite possible that the construction of a typical ara started from a circle with the radius of one cubit.

But what about the instruments whose arae give a more slender impression, sometimes almost like columns that bear the windchests? Are these merely stylised depictions of instruments that ultimately worked much as those do in the detailed representations? If they are real, they would clearly not have accommodated a similarly large pnigeus. Would they, therefore, have played at considerably lower pressures, even though these pressures were still way above the level of modern organs? This seems unlikely because a reduction in pressure compounds the problems associated with the reduction in air volume, which, as we have discussed above, already reflects the decrease in diameter at the power of three. The effects become clear from Figure 6,20 which allows determining the air volumes associated with various pressure differences for systems of different size operated with the respective minimal amounts of water, which in unpressurised state just covers the pnigeus.21 Note that this figure models an octagonal ara, neglecting only the small and antagonistic effects of the pnigeus wall and any plumbing.22

Figure 6
Figure 6

Pressure and air volume inside octagonal pnigeus for various ara radii with initial water level at pnigeus top. The three configurations would require 212 l, 89 l and 27 l water, respectively

Citation: Greek and Roman Musical Studies 11, 1 (2023) ; 10.1163/22129758-bja10055

A narrower pnigeus would therefore always work more efficiently at higher pressures. Figure 7 shows how adding some extra water increases the air reserve available before the pressure drops by a certain percentage. Also, the iconography appears to imply that narrow arae, if they were a thing at all, were just as tall as their wider relatives, which, as has become clear above, suggests that they played at the same pressure.

Figure 7
Figure 7

Pressure and air volume inside pnigeus of 50cm diameter inscribed within octagonal ara, with different levels of extra water above the pnigeus top. Points of 50% – 40% – 30% – 20% – 10% below maximal pressure are indicated. The three configurations would require 102 l, 77 l and 52 l water, respectively

Citation: Greek and Roman Musical Studies 11, 1 (2023) ; 10.1163/22129758-bja10055

Ensuing relations in such high-pressure systems of smaller diameter can be gleaned from Figure 8. It emerges that, although a pnigeus of half a metre diameter contains only a quarter of the volume of one of 80 cm, it has still 40% of its efficiency, which may be sufficient for most purposes, especially when balanced by well-trained personal at the pistons. At the same time, such a smaller organ requires only about half the water and, more importantly, half the bronze,23 which also results in a significant weight reduction.24

Figure 8
Figure 8

Pressure and air volume inside pnigeus inscribed within octagonal ara for various radii, with levels of extra water above the narrower pnigeus tops that ensure similar maximal pressures as with a radius of 400 mm. The three configurations work with 212 l, 153 l and 107 l water, respectively

Citation: Greek and Roman Musical Studies 11, 1 (2023) ; 10.1163/22129758-bja10055

4 Pipes

If it appears inevitable to accept high playing pressures in the hydraulis as a fact, what does this imply for the technology of its organ pipes? One might presume that higher pressure and therefore a faster stream of air increased the loudness of the instrument, and that the higher speed of the air jets allowed for a reduction in the volume of the air flow. Unfortunately, this seems not to work for labial pipes. In the course of the experimental construction of a large hydraulis in the course of the European Music Archaeology Project (EMAP)25 between 2013 and 2018 conducted by Justus Willberg in collaboration with the author, modern specialists have been unaware of a technology that might employ high pressure in such a way. Indeed, medieval organs achieved their acclaimed volume by installing rows of identical pipes, driven by multiple bellows.26

Above we have considered pressure and air reserve for compensating irregularities in the airflow caused both by pumping action and playing techniques, but not the possible average air flow, which would have been limited by the efficiency of the pistons and the stamina of their operators – who are sometimes represented as children. Representations of the proportional size of comparatively small details such as the pistons are probably considerably less accurate than those of the general dimensions of the ara. An evaluation of the iconography in Figure 5 yields an average diameter of 27.5 cm and an average height of 38.5 cm, with considerable variation (sd = 6 c m; sh = 10 cm). Such a piston would contain about 23 l, only part of which can however be exploited.27 Assuming that the end of the internal cylinder must not be pulled closer to the end of the piston than at least one third of its diameter, the maximal volume of air supplied per cycle and piston would not exceed about 17 l. In spite of substantial uncertainties, and though the capacities of individual instruments may have varied considerably, this figure nonetheless ought to give at least a rough impression about the scale of the maximal average air flow.

Labial pipes, in which the stream of air passes continuously through a small opening, may easily consume several litres of air per second, depending, of course, on their size and design. If each piston was operated once every two seconds, the estimated air might suffice to sound up to five pipes of the Aquincum type at once, and perhaps twice as many with very swift action at the levers. However, as far as modern experiments have gone, this would apparently be possible only at low pressures, unlike those of a real water organ. Higher pressures result in higher velocity of the air stream, which cannot be compensated by reducing the volume of the stream (as any flute player can confirm). Evidently, ancient water organ pipes were different from modern labial pipes. Were they labial pipes at all, of a lost technology? Or were they of a different kind altogether, reed pipes in fact?

Aquincum and Dion cannot help us here; if they represent bellows organs, they were rather precursors of our modern instruments. Remain the texts and the iconography. The latter appears to speak in favour of labial pipes: the semicircles at the bottom of the pipes depicted at Noheda may represent labia; the pipes on the lamp in the British Museum28 look very different but may be taken to represent Aquincum-type separate ‘feet’ with nozzles, or perhaps a separate, short rank of pipes of equal length, tuned internally; those on an oil lamp from Carthage29 look uncannily like modern church organ pipes but might also represent another attempt at rendering the same reality as does its sibling in the British Museum; the same is true for a lamp in Copenhagen30 and perhaps a sarcophagus from Saint-Maximin-la-Sainte-Baume,31 while a tomb slab in San Paolo fuori le Mura32 tilts the odds of all these in favour of labial pipes. Other representations show no trace of an exciter, just as we would expect for reed pipes. Arguing from an absence of evidence is all the more dangerous where it is so likely that the detail might just have been omitted, for instance as a result of the limitation of the medium – but would we not, at least, expect some shadow in the Nennig mosaic, for instance?

The texts are similarly ambiguous. Philo of Byzantium, writing in close temporal proximity to the invention of the hydraulis by Ctesibius, defines the instrument as a sýrinx:

ἐπὶ τῆς σύριγγος τῆς κρουοµένης ταῖς χερσίν, ἣν λέγοµεν ὕδραυλιν

on the kind of sýrinx that is played with the hands, which we call hýdraulis

Philo Mech. Bel. 61, 77.42f. Thévenot

Since the term sýrinx typically denotes the panpipe or some other kind of flute, this may be taken as a testimony to labial pipes, a series of which would indeed imitate the sound production on a panpipe. However, the multiplicity of pipes – one per note – as well as their graded appearance might provide sufficient similarity without any recourse to the mechanism of sound production.

The opposite is true for the very name of the instrument. The terms hýdraulis and, even more strongly, hýdraulos/hydraulus refer to the aulos, typically a double-reed doublepipe. But the stem also appears in the more general sense of, about, ‘woodwind’, as in the composite plagíaulos ‘transverse aulos’ for the transverse flute. In addition, the water organ would have been able to produce more than a single note at once, a musically decisive characteristic it shared with the doublepipe but not the panpipe.

The two authors who explicitly describe the construction of the hydraulis take the mechanism of sound production for granted and are only concerned with how the pipes are connected to the windchest. Both mention some kind of seat into which each pipe was inserted:

supra tabulam foramina〈que, per〉 quae ex canalibus habent egressum spiritus, sunt anuli adglutinati, quibus lingulae omnium includuntur organorum.

Upon the board and the holes through which the air from the channels takes its exit, rings are soldered, within which the lingulae of all the instruments are enclosed.

Vitruvius 10.8.4

It is clear that some sort of receptacle was required to ensure an airtight connection between the mechanism and the pipes, and it is natural enough that Vitruvius calls it a ‘ring’. But why would he refer to the lower end of the pipes as lingulae, ‘small tongues’? The term is otherwise found for the double reed of the aulos/tibia, the diminutive somewhat indistinctly alternating with lingua, reflecting the Greek forms glōssís/glōttís and glôssa/glôtta.33 It has consequently been taken as a testimony to the use of reed pipes on the hydraulis.34 Alternatively one might point to 8.6 tubuli ex una parte sint lingulati, where the term refers to spigots in the junctions of earthenware water pipes, or to Columella, where lingula denotes a kind of tenon at the end of a post that was inserted into a hole (Rust. 8.11.4). But the semblance remains doubtful. In both cases, the tongue-like quality is evidently imparted by an overall narrow part ‘sticking out’ from a wider body from which they are demarcated by a clear step, while the feet of metal pipes are more reasonably constructed either cylindrical or conical.

Fascinatingly, Heron invokes the same associations in a totally different way:

ἐν ᾧ ἐπικείσθωσαν οἱ αὐλοὶ συντετρηµένοι αὐτῷ οἱ ͵Α καὶ ἔχοντες ἐκ τῶν κάτω µερῶν καθάπερ γλωσσόκοµα συντετρηµένα αὐτοῖς

upon which the auloi (A’) are placed, which open into it and have at their lower ends sort of glōssókoma, which open into them

Hero, Pneum. 1.42

While he does not address the lingulae directly, Heron refers to their seats not by their ring shape but likens them to glōssókoma, which literally translates ‘reed cases’ but, together with its variant glōttokomeîon, came to denote small boxes for various purposes.35 Does Heron use the term precisely because actual reeds protruding from the ends of the pipes were inserted into these parts? Or is he merely referring to some typical cylindrical form, analogously to Vitruvius’ anuli? At any rate, we find reed-related vocabulary in both authors – and, what is more important, in so diverse ways that the coincidence cannot be explained by a common source.

Much later, Simplicius mentions sound generators of ‘the water organs’:

ἐν γὰρ ταῖς ὑδραύλεσιν ὅταν µεσταῖς οὔσαις ἀέρος ἐγχέηται ὕδωρ, γλῶσσαί τινες σαλπίγγων ἢ αὐλῶν ταῖς ὀπαῖς προστιθέµεναι δι᾿ ὧν ἔξεισι τὸ πνεῦµα διὰ τοῦ ψόφου τὴν ἔξοδον διελέγχουσι τὴν δι᾿ αὐτῶν τοῦ ἀέρος·

In the water organs, when these are filled with air and water is poured in, there are kinds of reeds (‘tongues’) of trumpets or auloi attached to the openings through which the air exits, which reveal the fact that air passes through them by their sound.

Simp. in Ph. 9.681.7–9 Diels

Although the sound tools in question are expressly called hydraúleis, the reference to their mechanism is awkward: a hydraulis is not typically sounded by pouring water into it, even though the described effect would actually happen in the course of filling up the instrument. Conversely, pouring water into vessels is the mode of sound production in some automata that are also described by Heron. Possibly Simplicius confused the two cognate contraptions. At any rate, he perceived their vibration-generating mechanisms as trumpet and aulos ‘tongues’. Trumpets, of course, do not come with reeds; the latter’s function is performed by the player’s lips. It is true that glôtta sometimes meant any kind of ‘mouthpiece’ including the cup-shaped trumpet mouthpieces.36 Without any lips it might support, however, a trumpet mouthpiece would have been useless on an organ.

Nonetheless, the items Simplicius refers to are already mentioned by Heron, precisely in the context of sounding automata, which are equipped with ἡ σάλπιγξ ἔχουσα τόν τε κώδωνα καὶ τὴν γλωσσίδα (Pneum. 1.16 and 1.17), ‘the trumpet with bell and glōssís’. At face value, therefore, Simplicius attributes a sound mechanism to the ‘hydraulis’ that was otherwise part of automata, which appears to be perfectly reasonable. Unfortunately, we do not learn from his wording whether Simplicius considered a ‘trumpet mouthpiece’ and an ‘aulos mouthpiece’ as two different devices or as essentially the same thing. Since actual trumpet mouthpieces are not an option, automaton ‘trumpets’ might, in principle, have sported any other kind of exciter. However, since labial pipes produce a sound so unlike that of a trumpet, some kind of reed is again the more likely option.

5 Reeds

Modern lingual organ pipes are necessarily designed so that their metal ‘reeds’ speak at the same pressures as their labial counterparts. Standalone reed instruments, on the other hand, both those with double reeds such as the bassoon and the oboe and those with single reeds such as the clarinet and the saxophone, play at significantly higher pressures. Actual values vary with pitch and dynamics, from player to player, and with the individual characteristics of the reeds. Modern measurements, however, indicate that the ranges for reed instruments, and especially those with double reeds, are compatible with the pressure we have predicted for the ancient water organ.37 Of course, at the time when it was invented, only ‘real’ reeds would have been known. Ancient double reeds differ from those in the modern European orchestra: while the latter consist of two blades tightly joined over a cone, ancient reed makers flattened one end of a cylindrical length of cane. It is, therefore, of interest to examine how the differences in manufacture and geometry affect possible playing pressures.

Recently, there has been a concerted effort to play reconstructed auloi, which, in turn, has introduced the need for suitable and functional reeds. As a result of these projects, our understanding of reed production has deepened by developing practical, hands-on knowledge on the basis of ancient literary, iconographic and (limited) material evidence, as well as surviving organological parallels in Central and East Asia. For the present purpose, I was thus able to measure the playing pressures of three reconstructed aulos pipes of different bore diameters, using suitable reeds of my own manufacture. On reconstructions of the Paestum aulos38 and the Louvre aulos,39 I have produced notes in their respective bass regions; for an extra-low pitch and wide bore I have used a model of over 60cm length, composed from parts found in the Oxus Temple.40 For all these, I have measured the minimum and maximum pressures at which my reeds would speak, exploiting their full dynamic range. Since all these are double-reed instruments, I have also evaluated launeddas generously provided by Pitano Perra, a specimen of the famous Sardinian triplepipe instrument with single reeds, the last remnant of a tradition that appears to go back to antiquity and have once spanned a much larger geographical region up to the British Islands.41 As is typical for clarinet-type reeds in the ethnographical record, launeddas reeds are not controlled by the lips and have therefore a limited dynamic range.

Figure 9 compares all these empirical playing pressures with those of modern organs and with our predictions for the ancient water organ. Evidently all reed instruments, though powered by lungs, cheeks and tongue, require significantly greater pressure than the bellows-driven organ. Clarinets, both those of the Western orchestra and the beating reeds of the launeddas, are on the lower end of the spectrum. The latter, however, whose reed tongues vibrate freely within the player’s mouth cavity, operate within a narrow range in comparison with reeds, both single and double, that are controlled by the lips (I have not measured any freely vibrating double reeds).

Figure 9
Figure 9

Empirical playing pressures of modern and ancient reed instruments compared with the prediction for the hydraulis. Data: Fuks, Sundberg 1999 for Clarinet, Bassoon, Oboe; the author’s for launeddas made by Pitano Perra as well as reconstructions of the Paestum aulos, the Louvre aulos and a model from parts found in the Oxus Temple, all made by the author

Citation: Greek and Roman Musical Studies 11, 1 (2023) ; 10.1163/22129758-bja10055

The predicted operating pressure of the hydraulis is, by comparison, sharply delimited towards its upper end by the estimated pnigeus height while its lower margin depends on what pressure drop the individual pipes would tolerate. At any rate, it falls squarely within the range shared by all double reeds, while apparently exceeding those of the clarinets. This does not necessarily imply that beating reeds that play at higher pressures cannot be produced; certain bagpipes, in fact, combine single and double reeds, and these must evidently be constructed so as to speak at the same pressure. High-pressure competition bagpipe reeds are reported to require 750–900 mmH2O, depending on pitch, but to be played at even higher pressures up to 1000 mmH2O.42 Bagpipe pressures are therefore comparable to aulos pressures, which is not surprising considering the close relation of the two traditions,43 singularly but undeniably expressed in a catalogue of Nero’s musical aspirations: αὐλεῖν τῷ τε στόµατι καὶ ταῖς µασχάλαις ἀσκὸν ὑποβάλλοντα ‘piping (auleîn) both with the mouth and by placing a bag under the armpit’ (Dio Chrys. 71.9). We do not know for how long bagpipes had been around by that period, but at least it is clear that in the Mediterranean of the first century AD freely vibrating reeds were known and used.

Such reeds would form natural candidates for true water organ pipes. They would reflect technologies that had been perfected for centuries, speak at the right pressure levels to be driven by a pnigeus of useful size, and ultimately also justify the name of the instrument somewhat better than labial pipes.

Perhaps most importantly, they would also account better for arae of smaller diameter, thanks to their considerably smaller air consumption. I have found it not too difficult to sustain a note from a single aulos pipe for at least 40 seconds, which corresponds to an air consumption of approximately 1/8 l/s. Even if freely vibrating reeds are granted a higher flow rate, it remains about ten to twenty times smaller than what labial pipes require. A rough extrapolation for the 50 cm-pnigeus instrument of Figure 7 may illustrate the potential. As we have seen, its reserve can supply 7 l of air before the pressure drops by 10%. This might support a single labial pipe only for a couple of seconds, but a reed pipe for a full minute. More realistically, it might sustain 5 such pipes for ten seconds, in addition to what the pistons would supply. As a result, the number of sounding pipes might be doubled for such a short period (even though the sound would have to be reduced again in order to allow the pistons to catch up). If a pressure loss of 20% was tolerable – which is more than likely because a hemispherical pnigeus would make little sense if not even that range was exploited – the effect would be almost twice as large, providing 13 l of extra air or approximately 100 pipe seconds.

What are the potential disadvantages of reeds? Above all, they are tricky to control, especially when there are many of them which all need to work at a common pressure range. Here single ‘beating’ reeds may provide more stability than the curved blades of double reeds that may take a long time until they assume a stable shape. Also, single reeds are more easily produced in greater numbers and lend themselves to comparatively straightforward adjustment by movable wrappings and/or placing lumps of wax on their blades. Humidity, on the other hand, is not an issue that we might expect, in spite of the presence of water in the mechanism. Since the surface inside the pnigeus is hardly disturbed – bubbles from excess air from the pistons escape outside the pnigeus into the ara and from there into the environment – it is only by normal evaporation that some moisture might get into the pipes.44 For several reasons, its amount must be much lower than in mouth-inflated bagpipes. First, all the air that passes through bagpipe reeds would come from the player’s lungs, having been exposed to dozens of square metres of humid surface instead of half a square metre as in the hydraulis. Second, while all bagpipe reeds are constantly subjected to that air during the entire performance, each hydraulis pipe would sound only intermittently, in total only for a fraction of the time. And finally, most of the air that passes through hydraulis pipes does not arrive from the reserve inside the pnigeus at all but, rather, directly from the pistons without coming anywhere close to the water surface. As a result, the humidity of the air in the windchest should hardly differ from the outer air, so that no significant impact on reed response and tuning can be expected.

6 Bellows

Bellows, albeit arguably less elegant, have considerable advantages over a piston-driven pnigeus.45 Since their geometry is only restricted by available space next to the instrument and their maximal height not in any way geometrically tied to their area, they can be made in any size, capacity and pressure. On the one hand, this paves the pathway to organs with low-pressure pipes throughout, precursors of the modern tradition. Larger or multiple bellows would allow for increasing the number of simultaneously sounding pipes, overcoming volume restrictions associated with small instruments and, at the same time, eliminating pipes precariously excited by actual reeds. On the other, the use of bellows does not preclude building high-pressure systems quite as well, which would furnish the water organ’s musical potential with a different and potentially more effective air supply without ridiculously increasing the instrument’s size and weight. Most importantly, however, a bellows system maintains a constant pressure right until it is depleted, unlike the water organ, in which, as we have seen, the pressure becomes the smaller, the more air is consumed without immediate repletion from the pistons.

In organ bellows, the required pressure is generated by weights placed on their top surface. While modern specimens combine pump and pressure chamber in one piece and must therefore be paired, ancient depictions show an inflatable air bag on the top of which several small bellows are mounted. The major part of the required weight is here conferred by the operators themselves, who stand on top of the air reservoir, working the small bellows with their feet.46 Reusing personnel as weights is very economical in terms of transport (generally not an issue for modern organs) but, in order to obtain a predefined working pressure, it would require people of standardised weight. In practice, this problem is easily overcome by building the system for the maximal expected operator weight, adding additional weights when needed.

Unfortunately, the realism of the only depiction from which the size of an ancient bellows system may be gleaned, the famous mosaic with various musicians from Mariamīn,47 is doubtful in this respect, especially because the people at the bellows are Erotes (or children dressed up as such). Nonetheless, it is instructive to start by taking the image at face value, and considering how it might deviate from ancient reality in a second step. The method employed above, starting from height, cubit length and shoulder width of the organ player, suggests a diameter of about 68 cm for the roughly cylindrical pressure chamber,48 with a height of perhaps 13 cm between its top and bottom plates, enclosing a volume of nearly 50 l. This is just as much as the largest pnigeus we have considered might provide at a pressure drop of 30%.

What about the pressure? A circular surface of 68 cm diameter has an area of 0.36 m². The Erotes appear about 96 cm high (precisely the average three-years old), which would correspond to a median weight of just over 14 kg each.49 Standing together on the estimated area, they would exert a pressure of about 78 mmH2O – actually a bit more, being rather on the chubby side (unless they flap their wings, of course), and the board itself also adds some weight. At face value, therefore, the Mariamīn scene implies a pressure that is very much in the range of a modern church organ, far below what we have deduced for a water organ.

How much may ancient reality have deviated from what we seem to discern in the image? Typical three-year-olds are hardly reliable assistants in a musical event. Even if the bellows were operated by children, these would have been older and consequently heavier, thus increasing the pressure. There is also some reason to believe that the pressure chamber in the image is represented as being too small. A technically necessary but little representative part, even when promoted by celestial helpers, might easily be shown compressed within as little space as possible. Omitting it by implicit relegation to a hidden background would have been possible, but the symbolic value of the winged sidekicks, whose kind is often shown engaged in musical activity, must have provided a strong motivation to keep it in sight. A real bellows system may therefore have needed more room than the artist would have wanted to dedicate to it. After all, two larger persons would hardly find place on a space that small, especially not while engaged in their continuous dance on the bellows. Might the artist have shrunk the wind supply system along with its operators in relation to the rest of the scene? On such an assumption, the pressure would get somewhat higher: if we reckon with proportional scaling, the volume and therefore weight of the figures would have to increase at about the third power, while the area of the pressure chamber would only be scaled by the power of two. Increasing the lengths by half, for instance, would more than double the stored air volume, but a pair of subadult humans of suitable size, about eleven years old, would typically weigh twice 37 kg, boosting the pressure to 90 mmH2O. On the other hand, we may obtain a minimal value by enlarging the container as much as may seem credible while keeping the operators as small as possible. Expanding the former by two thirds and entrusting it to typical eight-year-olds of 26 kg results in a pressure of 51 mmH2O, which is just a bit too low for modern organs. Conversely, maximal pressure may be achieved by two fully-grown males cramped together on bellows as small as depicted. With 75 kg each, they would exert a pressure of 410 mmH2O, which is in the range of reed instruments but significantly below the level we have derived for water organs. But two adults sharing the small space is hardly conceivable; it would at least be necessary to increase the diameter of the bellows by half, which reduces the pressure to a mere 180 mmH2O, much closer to modern levels than to the real hydraulis.

7 Conclusion

When taking the water organ seriously as a musical instrument and the geometry of its mechanism into account, we must reckon with much higher pressures than modern organ builders are generally comfortable with (except sometimes for very special registers, which would need a separate blower). Such pressures would require either reed pipes or labial pipes of a different construction than those known from the Aquincum find or later periods (unless one would want to consider ranks of pipes that were always overblowing to higher harmonics). While technical considerations, most of all their efficiency regarding the intake of air, suggest reeds, the iconography appears to show labial pipes.

Given the presence of at least four and up to eight registers,50 implying a variety that is incompatible with the idea that each register reflects one of the six musical tónoi that are attested for the hydraulis,51 together with the fact that labial pipes of different design, both open and closed, are even found on the bellows-driven instrument from Aquincum, it is advisable to anticipate a high degree of diversity in this highly advanced instrument. On balance, it appears probable that a typical large hydraulis, especially an open-air instrument such as those used in the arena, combined labial and reed registers. If so, the ranks of labial pipes would optimally be placed at the extremes: since they generate their sound by directing a stream of air against a sharp edge, they are vulnerable to any kind of perturbation as would ensue when the outward deflected part of the jet strikes against a close object. As a result, the labia are best placed facing outwards. This, in turn, would inevitably lead to the observed bias in the iconography, where we can only ever see the outermost ranks.

With a combination of both general types of pipes, the hydraulis could still play multiple notes in several registers at once, especially whenever no more than a single labial register was active. A large instrument of about 80 cm pnigeus diameter, as suggested by many of the depictions, would have considerable potential. With 17 l reserve at 10% pressure tolerance, it would, for instance, have been possible to sound about four extra labial pipes plus twenty extra reed pipes for a second, and (almost) proportionally more for greater tolerances. In this way, the organ would indeed have been able to compete with trumpets and horns in the din of the arena.

On the other hand, the evidence for ancient bellows organs, scarce as it is, points to pressures right in the range of later instruments with labial pipes, pressures that have also been found useful in reconstructions of the Aquincum instrument. When constructed to be no larger than necessary to hold a comfortable air reserve, their wind supplies would have needed to be operated by children in order to generate a sufficiently low pressure.

Acknowledgements

Part of this publication is based on research conducted within the European Music Archaeology Project (EMAP) funded by the Education, Audiovisual and Culture Executive Agency (EACEA), now European Education and Culture Executive Agency, of the European Commission under the Culture Programme 2007–2013 (project no. 536370). The views presented here, however, reflect only those of the author; the European Commission is not responsible for any use that may be made of the information contained.

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1

A splendid visualisation of the mechanics is provided by van Haarlem 2020 (caution is however due concerning the pressure – apparently, the figures indicate more than three metres of water column – and the hypotheses about tuning).

2

The sources are conveniently collected in Perrot 1965; Markovits 2003; for its historical and cultural context, cf. also Dessì 2008. For a very concise account, see West 1992, 114–18; for broader assessments especially of the Hellenistic evidence, Beschi 2009; Catalano 2018.

3

Walcker-Mayer 1972; Jeans 1971; Szigeti 1971; Kaba 1976; Hagel 2009, 364f.; Fényes 2017.

4

With confidence e.g. in Perrot 1973, 101; Catalano 2018, 76f. Bellows organs are mentioned in Pollux 4.70.

5

I am deeply indebted to many years of conversations with Justus Willberg, who has spent considerable time and skills on making an Aquincum reconstruction work as a true water organ – but in order to do so, had to implement a layout that diverges from the historical sources. Other reconstructions have avoided questions of practicality by using an electric blower; cf. Rühling 2013a; Rühling 2013b; Rühling 2013c.

6

Pandermalis 1992; Karasmanis 2005.

8

Gaining prominent track once more with Barker 1995. The term πολύφωνος ‘many-voiced’ in Pollux 4.70 sets the organ apart from both the pan flute and the doublepipe, which are capable of producing one and two simultaneous pitches respectively; therefore, the ancient organ would typically have sounded at least three and probably considerably more pipes simultaneously.

9

Cf. Markovits 2003 Taff. 6; 13a; 13b; 17; 19. This is especially true for narrower pipes, cf. Stroux 2009, 268f.

10

For evidence for multiple notes, see West 1992, 117. Some sort of ‘polyphony’ beyond parallel movement by using multiple registers simultaneously is explicit in Hero Pneum. 1.42, elevated above any palaeographical doubt by a dozen of plural forms: ὅταν βουλώµεθά τινας τῶν αὐλῶν φθέγγεσθαι, κατάξοµεν τοῖς δακτύλοις τὰ κατ᾿ ἐκείνους ἀγκωνίσκια· ὅταν δὲ µηκέτι φθέγγεσθαι βουλώµεθα, ἐπαροῦµεν τοὺς δακτύλους, καὶ τότε παύσονται τῶν πωµάτων ἐξελκυσθέντων. ‘Whenever we want some of the pipes to speak, we use our fingers to draw their respective keys downwards; and whenever we no longer want them to speak, we raise our fingers and then they will stop because the lids are drawn outwards’.

11

So already Perrot 1965, 68 with n. 2; curiously, Perrot later works with a conical pnigeus (1965, 200–4). Cf. http://www.pompeiiinpictures.com/pompeiiinpictures/r1/1%2020%2005%20p2.htm, accessed 2022-01-17; https://www.pinterest.com/pin/498492252490484250/, accessed 2022-01-17; https://www.pinterest.de/pin/386605949239652787/,accessed 2022-01-17; https://bbarakat.com/product/roman-herodian-glass-funnel-infundibulum/, accessed 2022-01-17; https://www.invaluable.com/auction-lot/published-roman-glass-funnel-rare-38c-c-0ac40c1a00, accessed 2022-01-17. For a rare conical counterexample, although with cylindrical rim, see https://de.m.wikipedia.org/wiki/Datei:Roman_Kitchen_Funnel_Saalburg.jpg, accessed 2022-01-17.

12

Of course the cylinders might be replaced with any configuration of prisms with similar cross-sectional areas – such as the typical octagon for the ara, with a circumference diameter equalling the radius of the simpler cylinder times .

13

West 1992, 116. Cf. Perrot 1965, 256: “la hauteur moyenne de la cuve allait de 0,80 à 1 mètre et le diamètre de 0,60 à 0,80 m”.

14

E.g. Markovits 2003 Taff. 13a; 13b; 14.

15

E.g. Markovits 2003 Taff. 15b; 16; 20; 31.

16

E.g. Markovits 2003 Taff. 21; 31.

17

Unfortunately, the otherwise quite detailed mosaics from Noheda cannot be evaluated in a similar way because its figure sizes are not realistically scaled: although the organ seems to be positioned in the foreground, the head of the player on Panel B is much smaller than those of the persons next to him (the player on Panel E, which may have formed the model for Panel B, is destroyed). Cf. Tévar 2013.

18

The rough sketch of a hydraulis with trumpeters from San Sebastiano fuori le Mura in Rome (Perrot 1965, 111 Fig. 3; Markovits 2003 Taf. 17) would not a priori inspire great confidence. When evaluated in the same way, it yields a similar ara width of 79 cm, but a greater height of 112 cm.

19

Markovits 2003 Taff. 6; 10b; 11b; 12b.

20

The three configurations would require 212 l, 89 l and 27 l water, respectively (cf. the very rough estimate in Perrot 1965, 256: “la capacité utilisée pouvait être d’une centaine de litres”).

21

Note that the diagram does not account for air compression and is therefore slightly inaccurate when comparing volumes at large pressure differences. At maximal pressure, the compression rate is 6.3% for the 80 cm pnigeus (as well as all configurations in Figure 8), 4.7% for one of 60 cm, and 3.1% for 40 cm.

22

For instance, a wall of 1 mm thickness forming a pnigeus of 80 cm diameter would cancel out the effect of a cylindrical air duct of 57 mm diameter, and 45 mm, for a 50 cm pnigeus.

23

Ara and pnigeus walls together cover about 3.95 m² for an 80 cm pnigeus of 71 cm height, and 1.98 m² for a 50 cm pnigeus.

24

With an average wall thickness of 2 mm, the large ara with pnigeus would weigh about 65 kg empty and 275 kg ready to play.

26

Cf. e.g. Catalunya 2021.

27

Cf. Perrot 1965, 257: 24 cm diameter and 45 cm height for the item from Carthage, also holding 23 l.

28

Inv. 1965.1011.1, above Figure 5; Markovits 2003 Taf. 11.

29

National Museum inv. 885.1, Markovits 2003 Taf. 10.

30

National Museum inv. ABb 96, Markovits 2003 Taf. 12.

31

Markovits 2003 Taf. 31.

32

Markovits 2003 Taf. 36.

33

Cf. Pliny HN 16.172: … comprimentibus se linguis … apertioribus earum lingulis ad flectendos sonos … ‘… when the reeds close up … their reeds being more open in order to bend the sounds …’. For the Greek terms, cf. e.g. Phryn. 208: ‹Γλωσσίδαςαὐλῶν ἢ ὑποδηµάτων µὴ λέγε, ἀλλ᾿ ὡς οἱ δόκιµοι γλώττας αὐλῶν, γλώττας ὑποδηµάτων.

34

Perrot 1973; West 1992, 115; Markovits 2003, 53; 421; similarly, without further discussion, Catalano 2018, 34.

35

Cf. Phryn. PS 58 De Borries: γλωττοκοµεῖον· ἐπὶ µόνου τοῦ τῶν αὐλητικῶν γλωττῶν ἀγγείου. ὕστερον δὲ καὶ εἰς ἑτέραν χρῆσιν κατεσκευάζετο, βιβλίων ἢ ἱµατίων ἢ ἀργύρου ἢ ὁτουοῦν ἄλλου. καλοῦσι δ᾿ αὐτὸ οἱ ἀµαθεῖς γλωσσόκοµον.

36

Pollux 4.85.

37

Fuks, Sundberg 1999.

38

Psaroudakēs 2014; Reichlin, Reichlin-Moser 2015; Hagel 2021.

39

Bélis 1984; Hagel 2004; Hagel 2014.

40

Litvinsky 1999; Litvinsky 2010.

41

Brown 2006; Brown 2018.

42

Gibson 1979.

43

For possible continuations from antiquity, cf. Ahrens 1987.

44

In contrast, humidity may become a problem when the instrument is left unplayed without either removing the water or shutting the connection between pnigeus and windchest; cf. Perrot 1965, 208.

45

Cf. Perrot 1965, 263f.

46

Cf. Markovits 2003 Taff. 27–9.

47

Markovits 2003 Taf. 29. For its context, cf. Gavrili 2010.

48

Cf. Perrot’s (1973, 104) 70 cm.

49

According to data from the World Health Organisation (WHO), available at https://cdn.who.int/media/docs/default-source/child-growth/child-growth-standards/indicators/weight-for-length-height/cht-wfh-boys-p-2-5.pdf, accessed 2022-02-03. Perrot’s assumption of “38 kg.” combined weight, in turn, implies an age of at most 5 years. However, these 19 kg are wholly incompatible with his height estimate of 82 cm, because practically all 5 years-old are significantly taller than that, while even the stoutest boys of such a small size hardly weigh more than 13 kg.

50

Vitruv. 10.8.2.

51

Anon. Bell. §28.

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