The Frequency Spectrum and Geometry of the ¯H¯alSaflieni Hypogeum Appear Tuned

Kristina Wolfea, Douglas Swansonb, Rupert Tilla

aUniversity of Huddersfield bIndependent Researcher

Abstract The ¯H¯alSaflieni Hypogeum is a unique subterranean Maltese Neolithic sanctuary with a -documented history of interest in its acoustics [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. Previous studies have noted its unusual strongly-defined frequency spectrum [2], but it is unknown if this was coincidental. In this paper, we present evidence that the Hypogeum’s creators shaped the site’s geometry to create or amplify its frequency spectrum, or another property closely correlated with the spectrum. Specifically, we show that the observed spectrum required jointly fine-tuning the dimensions of multiple non-contiguous walls across multiple independent chambers, to a degree that seems unlikely to be coincidental. We also note that the peak frequencies are evenly spaced and resemble a whole-tone scale in music, which is also unlikely to be coincidental and suggests the spectrum itself might have held some cultural significance. Taken together, it suggests acoustic or spectral properties may have played a motivational or cultural role for the site’s Neolithic creators. This work identifies one of the earliest known examples of a manmade structure with a significant musical element to its interior architecture. Keywords: ¯H¯alSaflieni Hypogeum, , Neolithic, sound archaeology, archaeoacoustics, cave acoustics, acoustic modeling

1. Introduction a perturbed version of the full non-rectangular geometry. Our results suggest the aggregate spectrum across the The ¯H¯alSaflieni Hypogeum is a subterranean Neolithic Hypogeum middle level required jointly fine-tuning the structure and UNESCO World Heritage Site in Paola, Malta dimensions of multiple non-contiguous chamber walls to [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]. It is among the old- within 10-25 cm. This seems unlikely to have come about est and best-preserved manmade structures with an in- by coincidence, and suggests that the Hypogeum’s Ne- tact interior. Hand-carved with stone and bone tools, it olithic creators shaped the site’s geometry to create or am- is believed to have been a sanctuary and then an ossuary plify its frequency spectrum, or another property closely [6, 8, 9]. Previous studies have noted its unique acoustic correlated with the spectrum. properties, such as low-frequency amplification, long rever- beration times, and well-defined peak frequencies [1, 2, 3], but it is unknown whether these properties were coinci- 2. Methodology dental. The Hypogeum consists of three levels: upper (3600- In this paper, we present the first comprehensive mea- 3300 BC), middle (3300-3000 BC), and lower (3150-2500 surements of the frequency spectrum of the Hypogeum BC) [13]. The field work in this paper was undertaken arXiv:2010.13697v1 [cs.SD] 26 Oct 2020 middle level. We identify strong well-defined peak frequen- in the inner chambers of the middle level. A diagram of cies common to multiple non-contiguous chambers. We the middle level is shown in Figure 1(a). A well-known show that these peak frequencies can be reproduced by early 20th century photograph of Chamber 26 from [10] a simulation of the 3D wave equation incorporating only is shown in Figure 1(b) as an example of the hand-carved the site’s geometry, suggesting they represent room modes. ornamentation and smooth Lower Globigerina limestone We further show that prominent peaks can be modeled an- surfaces common to middle level chambers. Additional alytically as the modal frequencies of individual chambers photographs and descriptions of the site and its material treated as rectangular boxes, even though the chambers composition may be found in [6, 8, 9, 10]. Virtual video are in reality highly non-rectangular. We use this simpli- tours to help visualize the site layout may also be found fied “box model” to estimate the distances that individual in [11, 12]. chamber walls could be perturbed before prominent peaks We measured the frequency spectrum using standard would shift by human-noticeable amounts. We validate acoustic methods. Impulse responses were generated us- these estimates by re-simulating the 3D wave equation in ing the sine sweep measurement method [14] at several

Preprint submitted to Journal of Archaeological Science: Reports October 27, 2020 Figure 1(a): Diagram of the Hypogeum middle level from [9] with approximate positions of experimental sound sources and receivers. Chamber numbering is from [8].

Figure 1(b): A well-known early 20th century photograph of Chamber 26 from [10]. Additional photographs and descriptions of the site and its material composition may be found in [6, 8, 9, 10]. Virtual video tours to help visualize the site layout may also be found in [11, 12].

2 source (loudspeaker) and receiver (microphone) positions ber peak frequencies to deviate noticeably from the Hypogeum- throughout the middle level. Measurements were taken wide mean spectrum, we modeled the chambers analyti- following guidelines for the acoustic analysis of rooms and cally as rectangular boxes. This “box model” was cho- performance spaces outlined in ISO-3382-1 [15, 16]. This sen for its simple and analytically-solvable room modal was deemed most relevant given the archaeological record. frequencies. Approximate rectangular dimensions (length, Although ISO-3382-1 is primarily focused on analysis of width, height) for each chamber were estimated using Mesh- music performance venues, its acoustic quantities can also Lab [25] and resulting room modal frequencies were calcu- characterize other forms of listener experience [17, 18, 19]. lated using the standard equation: Ambient environmental conditions during the field work s 2 2 2 including temperature and humidity were provided by Her- c nx ny nz f = 2 + 2 + 2 itage Malta in order to estimate the speed of sound for use 2 Lx Ly Lz in simulations and modeling. Source and receiver positions where n , n , and n are modal indices, L , L , and L were chosen based on archaeological context, recommen- x y z x y z are box dimensions, and c is the speed of sound [27]. Dif- dations from archaeologists, and results ferentiating with respect to L leads to a similar equation from previous field work [1]. For each source and receiver i governing the response of a room modal frequency to a position, a 45-second 48-kHz 32-bit exponential sine sweep perturbation in a box dimension: was generated within the range of 20Hz to 22.5kHz with a tail length of 17 seconds. The sound source was a Bang & −c2n2 ∆f = i ∆L Olufsen Beolit 12 loudspeaker [20]. Sweeps were recorded 3 i 4fLi using two omnidirectional microphones (Neumann KM- D digital microphone with Neumann KK-131 diaphragm) We calculated the perturbation size ∆Li needed to pro- and an ambisonic sound field microphone (Sennheiser Ambeo- duce a modal frequency deviation ∆f of 3 Hz, the ap- proximate just-noticeable difference for modern humans VR), through two MOTU Ultralight sound cards. Impulse 1 responses were recorded and processed using the HAART for frequencies below 500 Hz [29]. We calculated this per- [21] library in Max [22]. turbation size for each chamber wall that the box model Frequency spectra were extracted using the Fast Fourier predicted was related to a prominent frequency peak in Transform over the entire 17-second impulse response, and the Hypogeum-wide mean spectrum. This produces es- smoothed using a Savitzky-Golay filter to improve visual timates of the distances that individual chamber walls display [23, 24]. Mean frequency spectra were calculated could be perturbed before prominent spectral peaks in the for each chamber by averaging all impulse responses from Hypogeum-wide mean spectrum would change by human- source-receiver pairs in that chamber, and then extracting noticeable amounts. In other words, it produces bounds the frequency spectrum of the mean impulse response. A on how much individual chamber wall dimensions could Hypogeum-wide mean spectrum was calculated by averag- change before the Hypogeum-wide mean spectrum would ing the mean impulse responses from chambers 18, 20, 24, be noticeably affected. 25, 26, and 27, so that all chambers contributed equally re- Finally, to validate the box model predictions, we per- gardless of their numbers of sources and receivers, and then turbed several chamber wall dimensions by the amount extracting the frequency spectrum of this Hypogeum-wide predicted by the box model, and re-simulated the 3D wave mean impulse response. This Hypogeum-wide mean spec- equation in a perturbed version of the full non-rectangular trum provided a quantitative representation of the acoustic geometry. Perturbations were generated by translating behavior of the site. and then remeshing individual chamber walls in MeshLab To reproduce the observed frequency spectra and ex- [25]. The perturbed spectra were compared to the unper- plore the effects of perturbing the site’s geometry, we sim- turbed spectra to look for the predicted frequency peaks ulated the 3D wave equation. A high-resolution digital shifting by approximately 3 Hz, as predicted by the box geometric model of the site provided by Heritage Malta model. was simplified and remeshed using MeshLab [25]. Simula- tions were implemented in C++ using libigl [26] following 3. Results the approach of Bilbao and Hamilton [27, 28]. Simula- tions modeled rigid wall boundary conditions and Kro- Figure 2(a) shows measured and simulated mean Hypogeum- necker delta initial conditions and did not incorporate any wide frequency spectra. Agreement between measurement material properties, absorption coefficients, or viscother- and simulation is reasonable, both qualitatively in over- mal relaxation, as they were not found to be necessary all spectral shape and quantitatively in several prominent to reproduce the experimental spectra. Simulated impulse responses were generated and simulated frequency spec- 1We note that 3 Hz is likely a conservative estimate for the mini- tra extracted in the same manner as the experimental fre- mum frequency deviation that a human could notice. A more aggres- quency spectra. sive estimate might be the full-width-at-half-maximum of the promi- nent measured frequency peaks, which as shown below are closer to To estimate the perturbation size (the change in cham- 1 Hz, and would lead to bounds three times tighter than the ones ber wall dimensions) necessary to cause individual cham- presented in this paper. 3 frequency peaks, to within the precision of the measure- ments. This helps to motivate our use of simulation to probe the effects of perturbing the site’s geometry, which is the only purpose and application for our use of simulation in this paper. However, we note that our measurements are only able to resolve the amplitudes of prominent fre- quency peaks to within 10 dB in most cases, which may mean we are not sensitive to some potential amplitude ef- fects, as we will discuss further below. Prominent frequency peaks include 37.2, 41.0, 46.1, 50.4, 57.1, 64.3, 72.7, 81.8, and 92.5 Hz. Previous studies had identified resonances at 70 and 82 Hz [2, 3], which are close to the 72.7 and 81.8 Hz peaks we identify, although our resolution is considerably higher. These peaks repre- sent strong well-defined characteristic frequencies common to multiple non-contiguous chambers in the Hypogeum middle level, and can therefore be understood as acous- tic features of the middle level as a whole. Figure 2(b): Mean measured spectrogram of the Hypogeum middle level.

was unexpected given the highly non-rectangular shapes of the chambers. This motivates our use of the highly- simplified box model to estimate chamber wall perturba- tion sizes below, which is the only use to which we put the box model in this paper. Several prominent peaks that appear in measurement and simulation but that do not appear in box-model pre- dictions are room modes of other chambers. For example, Figures 3(a) and 3(c) both show a prominent peak at 37 Hz that does not appear to be a room mode for either chamber 27 or 25. This peak is actually a room mode of nearby chamber 20. Similarly, Figure 3(c) shows a promi- nent peak at 41 Hz for chamber 25, which can be seen in Figure 3(b) as a room mode of chamber 18, and is also a mode of chamber 20. Table 1 shows prominent measured frequency peaks Figure 2(a): Mean measured (red) and simulated (blue) frequency spectrum of the Hypogeum middle level, weighted so that all cham- from the mean Hypogeum-wide spectrum, with the box- bers contribute equally. Prominent peaks in the measured spectrum model modes and implied bounds on individual chamber are labeled. Error bars (black) shown for prominent measured fre- wall dimensions associated with each. Associated box- quency peaks reflect measurement-to-measurement spectral varia- model modes are determined by selecting the closest box- tion. model mode within a 3 Hz just-noticeable difference of the measured peak frequency. The tightest bounds on indi- Figure 2(b) shows a measured mean Hypogeum-wide vidual chamber walls are generally in the 10-15 cm range, spectrogram, showing that the prominent characteristic indicating that those chamber walls could not be moved by frequency peaks are largely time-independent. Character- more than 10-15 cm before a human would notice a change istic peaks are present for between 5 and 8 seconds, and in the chamber’s frequency spectrum. The chamber would were audible during the field work. then sound “out of tune” with the rest of the Hypogeum Figure 3 shows measured and simulated mean indi- middle level chambers and mean spectrum. vidual chamber frequency spectra for three representative Each of the prominent measured frequency peaks from chambers: 27 (a), 18 (b), and 25 (c). Agreement between the mean Hypogeum-wide spectrum come from box-model measurement and simulation is qualitatively reasonable, room modes from at least two separate chambers, and suggesting the prominent frequency peaks in the measure- sometimes as many as five. Although in cases such as 41.0 ments represent room modes, since the simulations incor- Hz this comes from three separate chambers happening to porate only geometry, with no material properties or ab- have a single wall of approximately 420 cm in length, more sorption. Box-model modal frequencies are also shown, commonly the peaks come from the coincidence of multiple and agree reasonably with prominent measured and simu- box modes involving multiple walls of differing lengths in lated frequency peaks. The degree of box-model agreement 4 involving eight walls in total.

Table 1: Prominent measured frequency peaks common to multiple individual chamber spectra, with associated box-model modes and implied bounds on chamber wall dimensions. Box-model modes are chosen to be within 1 just-noticeable difference (3 Hz) of the mea- sured peak frequency. Peak Chamber Box-Model Implied Frequency Mode and Bounds on (Hz) Modal Box-Model Frequency Wall (Hz) Dimensions (cm) 41.0 18 (0,1,0), 40.4 424 ± 31.4 20 (0,1,0), 40.8 420 ± 30.9 24 (1,0,0), 40.1 428 ± 32.0 46.1 18 (1,1,0), 47.9 670 ± 146.8 424 ± 37.2 27 (1,0,0), 47.6 360 ± 22.7 50.4 18 (2,0,0), 51.2 670 ± 39.3 26 (1,0,0), 51.2 335 ± 19.6 57.1 20 (1,1,0), 55.3 459 ± 54.6 420 ± 41.8 24 (0,0,1), 56.6 303 ± 16.1 64.3 18 (2,1,0), 65.2 670 ± 50.0 424 ± 50.7 25 (1,0,0), 66.2 259 ± 11.7 26 (0,1,0), 63.5 270 ± 12.8 27 (0,1,0), 66.0 260 ± 11.8 72.7 20 (2,0,0), 74.7 459 ± 18.4 24 (0,1,1), 70.7 405 ± 47.9 303 ± 20.1 26 (0,0,1), 73.0 235 ± 9.7 27 (0,0,1), 73.0 235 ± 9.7 81.8 18 (0,2,0), 80.9 424 ± 15.7 20 (0,2,0), 81.7 420 ± 15.4 24 (1,1,1), 81.3 428 ± 65.0 405 ± 55.1 303 ± 23.1 26 (1,1,0), 81.6 335 ± 31.3 270 ± 16.4 27 (1,1,0), 81.4 360 ± 38.7 260 ± 14.6 92.5 18 (2,0,1), 93.3 670 ± 71.5 220 ± 10.1 Figure 3: Measured (red) and simulated (blue) frequency spectra for representative middle level chambers 27 (a), 18 (b), and 25 20 (0,1,1), 91.0 420 ± 68.7 (c). Box-model modal frequencies are shown as dashed grey ver- 211 ± 8.7 tical lines. Prominent peaks in the measured spectrum are labeled. 24 (1,2,0), 93.7 428 ± 74.9 Error bars (black) shown for prominent measured frequency peaks 405 ± 15.9 reflect measurement-to-measurement spectral variation. 25 (0,1,0), 92.7 185 ± 6.0 27 (2,0,0), 95.3 360 ± 11.3 multiple non-contiguous chambers. For example, the 72.7 Hz peak is from the coincidence of three distinct modal Figure 4 shows simulated perturbed and unperturbed arrangements involving four walls in total, the 81.8 Hz frequency spectra for two representative perturbations (or peak is from three distinct modal arrangements involving variations) made to two different walls in chamber 27. In six walls in total, and the 92.5 Hz peak is from five dis- Figure 4(a) one wall dimension was perturbed from ap- tinct modal arrangements found in five different chambers proximately 360 to 385 cm, and in Figure 4(b) one wall 5 dimension was perturbed from approximately 235 to 245 4. Discussion cm. As shown in Table 1, the box model would predict a 3 Hz peak shift from 47.6 Hz to 44.6 Hz for Figure 4(a), There are three pieces of evidence that suggest the fre- and from 73.0 Hz to 70.0 Hz for Figure 4(b). Simulation quency spectrum of the Hypogeum was not coincidental. results agree well with these box-model predictions, and First, our results in this paper indicate the geometry of the validate the use of the box model for estimating bounds Hypogeum middle level is remarkably finely-tuned. The on individual chamber wall dimensions. aggregate Hypogeum spectrum required jointly fine-tuning the dimensions of multiple distinct walls in multiple non- contiguous chambers to within 10-25 cm, sometimes as many as 6 to 8 walls across 4 to 5 chambers contributing to generate a single aggregate frequency peak. In other words, there are multiple individual cave walls where if one such wall was moved from its current position by more than about 10-25 cm it would affect the overall frequency spectrum, moving one chamber “out of tune” with the other chambers enough for a human to notice. This de- gree of fine-tuning seems unlikely to have come about by coincidence, and suggests that the Hypogeum’s frequency spectrum, or another property closely correlated with the spectrum, strongly influenced how the Neolithic creators shaped the site. The second piece of evidence is that the frequency spec- trum itself looks highly non-random and unusual. Surpris- ingly, the ratios of the frequencies of consecutive promi- nent peaks from 37.2 Hz to 92.5 Hz are nearly all close to the whole-number ratios 9:8 or 10:9, which both char- acterize the musical “whole tone” interval, as though the Hypogeum’s spectrum defines a musical scale similar to a whole-tone scale. The Hypogeum therefore appears “tuned” both in the physical and the musical sense. A whole-tone scale is notably symmetrical and evenly-spaced, not at all what would be expected for a randomly-generated spec- trum, and suggests the frequency spectrum held cultural significance. The third piece of evidence is that the frequency spec- trum is a highly unusual and conspicuous feature of a culturally significant site. The acoustic properties of the Hypogeum have been readily audible even to untrained visitors since the site’s excavation [6, 8, 9, 10], and it is reasonable to assume Neolithic people would have been closely attuned to the acoustics of the site. The process of hand-sculpting the Hypogeum using stone and bone tools and without natural light was likely very loud, and would have excited the acoustics of the site. Moreover, a fre- quency spectrum with 30-50 dB peaks would be consid- ered undesirable in a modern room [30, 31]. Indeed, the Hypogeum looks spectrally more similar to an instrument like a bell, gong, or lithophone than to a room or theater [32], and the process of shaping the Hypogeum was similar to the process of tuning a bell or gong [8, 9, 32]. The Hy- pogeum was a culturally important site that required sig- nificant human effort to carve over many generations and hundreds of years [13]. It seems likely therefore that its Figure 4: Simulated unperturbed (red) and perturbed (blue) fre- quency spectra for chamber 27. Perturbations are (a) to move length unusual conspicuous instrument-like frequency spectrum dimension from 360 to 385 cm, and (b) to move height dimension was a culturally-desired feature, or else it would have been from 235 to 245 cm. disruptive to any activities that might have taken place. This requires no assumptions about the kinds of activities

6 that might have occurred in the space, given that during of the observed peak amplitudes beyond noting their mag- our field work, even minimal human motion like shuffling nitude and prominence. In particular, our measurements of feet, sniffing or coughing, or clearing one’s throat trig- are only able to resolve the amplitudes of prominent spec- gered audible frequency responses from the site. tral frequency peaks to a precision of 10 dB, a level within Taken together, the evidence suggests that spectral the bounds of human perception [29, 30, 31]. It is there- properties played some cultural or motivational role in the fore possible that the Hypogeum’s Neolithic creators might Hypogeum’s hand-carved geometry. None of these pieces have been attentive to specific amplitude effects that we of evidence necessarily prove that the Neolithic people are unable to resolve in this paper. Further work is re- carved the Hypogeum initially with acoustics in mind. For quired to increase the measurement precision in order to example, perhaps the creators came upon some naturally- resolve peak amplitudes to less than 10 dB, and to inves- occurring spectral protofeatures and chose to amplify them tigate any perceptual, acoustical, or archaeological impli- (such as the naturally-occurring fissures and bedding planes cations of the observed peak amplitudes. that outline some walls and floors [33]), or perhaps they This work identifies the Hypogeum as one of the ear- created or amplified the frequency spectrum while using liest known examples of a manmade structure with a sig- sound as a heuristic for optimizing some other geometric nificant musical element to its interior architecture. The or spatial features. Nor can we ascertain the significance of Hypogeum is one of the earliest surviving manmade struc- what acoustic properties might have meant to them. But tures of any kind, and is unusual among similarly-aged we do think they preclude coincidence. manmade structures because its intact interior allows sonic One potential objection to this work is that modern architectural elements to be studied. Although there is acoustic measurements (and models constructed from them) evidence that prehistoric humans identified, decorated, or may not be representative of historical conditions. In par- culturalized sonically-resonant locations within [19, ticular, modern acoustic measurements are made after the 34, 35], this provides remarkably early evidence of prehis- archaeological clearing process undertaken in the early 20th toric humans building such an interior space. century, and the ancient site may not have been bare rock free of archaeological deposits. This is a limitation of our 5. Acknowledgements methodology. However, although it is difficult to know for certain given that early excavations of the site were The authors wish to thank Heritage Malta for helpful under-documented, there is some reason to believe several support and access to the site. This work was funded by of the chambers studied in this work may not have had de- the European Commission through the Marie Sklodowska- posit prior to excavation. According to the first published Curie Actions program under grant number REP-750618- documentation on excavations of the Hypogeum by Zam- 1. mit in 1910, “nearly all the caves, passages, and chambers contained old deposit varying from a few centimeters to over one metre deep” [9]. However, Zammit also specifies 6. License that “the deposit was wanting in the series of caves which (c) 2020. This manuscript version is made available un- are elaborately cut and finished, and in the small caves der the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by- in the lower storey.” Most of the chambers studied in this nc-nd/4.0/ work could reasonably be described as “elaborately cut and finished”, including chambers 18, 20, 24, 26, and 27, which Zammit characterizes using words like “painted”, References “elaborate”, “finished”, and “ornamented”. Among these [1] R. Till, An archaeoacoustic study of the ¯H¯alSaflieni Hypogeum chambers, Zammit notes that chamber 18 “was found full on Malta, Antiquity 91 (2017) 74–89. doi:10.15184/aqy.2016. of old material,” but specifically does not mention any- 258. thing similar for any of the others. Furthermore, Zam- [2] P. Debertolis, F. Coimbra, L. 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