Computer Acoustic Analysis: Digital Audio Modelling with Odeon
A digital model of Stonehenge IIIc was obtained from Imigea digital modelling company’s virtual museum.[1] This model was then acoustically analysed using Odeon software. The model is still being analysed and will be presented in more detail in a future publication. Initial results are discussed here. The acoustic model lacked detailed figures for the reflective qualities of the stones. The model was given the reflective qualities of marble, as this was the closest material available in terms of acoustic properties. The model was tested with rough concrete surfaces, and similar results were produced, which indicates that the choice of which hard reflective surface to use was not critical for these measurements. It also indicates that the concrete model at Maryhill has some validity despite the concrete construction. Figure 7 shows reverberation that varies between different frequencies and in different positions.
The acoustic model uses ray tracing, and is therefore likely to be inaccurate at very low frequencies. However a substantially larger reverberation than other positions and frequencies is shown at 125Hz at the edge of the circle, and at this frequency the order of difference is significant, and results will be at least partially accurate. Here the reverberation time is 3.2s, compared to 0.9s inside the circle at the same frequency. This shows a strong low frequency resonance probably caused principally by the outer sarsen ring of uprights and lintels. It also shows that this low ringing would happen far more strongly at the edge than anywhere else.
Figure 7: Reverberation Time T30 at different frequencies, purple is at the entrance to the space by the bluestone ring, grey is central in the entrance a few metres in, red is at the heel stone.
Figure 8 shows the powerful acoustic effects at the centre of the space. Sound leaving a soruce reflects back to the centre from all directions, bouncing off the stone circle and coming back again. One can see that reverberation and early decay time are much higher at low frequencies (as at the circle edge). Volume levels (SPL) are also higher at the edge. Clarity (C80) and Definition (D50) are correspondingly higher at high frequencies, the reverberation makes clarity worse at low frequencies.
Figure 8: Acoustic calculations for the centre of Stonehenge
Figure 9: Binaural Impulse Response
The impulse response in figure 9 shows a number of spikes after the initial sound, showing echoes in the space. A reverberation with no echoes would have a smoother curve. Mapping of Clarity (C80) in the space shows that there are lines of clear sound, much like lines of sight, along which sound transmits (figure 10). These show sound being transmitted. Particularly interesting was the way the sound was transmitted out of the entrance down the ceremonial approach to the site. Sound
Figure 10: Clarity at 1kHz at the centre
Figure 11: Speech Transmission index above 0.9 indicated by black lines.
escapes the outer bank at Stonehenge in the Odeon model only at specific points, this is illustrated by the dark lines in figure 11. The line leaving at the top seems to head off towards the Cursus Barrows. On the right there are four lines. The lowest may aim towards Durrington Walls or the Cuckoo Stone, the next upwards is aimed straight at the space (or stone) next to the Heel Stone. The next aims towards the western end of the Cursus. It is interesting to consider whether sound from Stonehenge could be heard in these places, this warrants further investigation. Extremely low frequencies can travel particularly long distances.
Figure 12: LG80 envelopment mapped out in the space
LG80 is a measure of how much an acoustic gives a sense of envelopment in any specific position. The map of envelopment (figure 12) shows clearly how within the stone circle, LG80 is higher (red) than that outside, as high as 21.6 near the centre. This seems to illustrate the social stratification of the space. In concert hall environments LG80 is used to identify the seating positions where tickets are most expensive, the positions with the highest figures for envelopment are the most desirable and significant.[2] Akutec[3] give typical ranges of acoustical parameters for concert halls, and these are indicated in figure 13, along with appropriate values for musical source material, where available. Skålevik[4] provides comparisons with results produced by Odeon for digital models of existing concert halls (Olso, Elmia and Vienna). Odeon also provides guidance in its manual for recommended figures for symphonic music (music column). It is interesting to compare these to figures provided by Odeon for the Stonehenge digital model. Stonehenge is loud; has figures for reverberance and source width for musical sounds that are as good as the three concert halls. It has poor clarity and definition but acceptable speech intelligablility, and envelops the listener in an extreme fashion.
Figure 13: Comparative acoustic values
High Transparency or speech intelligibility is indicated by low values of the centre time Ts.[5] According to Rumsey[6] subjective ‘clearness’ relates closely to the measured concert hall acoustics parameter D50 (Definition or Deutlichkeit), and is an indication of direct to reverberant ratio. D50 (intended for speech) above 0.5 is ‘excellent’, and C80 should be above 0, aiming for 15, which is good. Although the averaged figures for D50 and C80 at the centre of Stonehenge are not good compared to the concert halls, values vary at different positions, and are good in places.
In figure 14, the results are as at positions 1, 2, 3 etc. (P1, P2, P3 etc.). There is also a set of results with the source at the heel stone (heel) instead of the centre, where it is for P1 – P7. O/E/V are the range of values in the Olso, Elmia and Vienna Concert Halls. R is the Akutek suggested range of values from figure 13. Values of STi (speech transmission index) of 0 – 0.3 are bad (subjectively), 0.3 – 0.45 are poor, 0.45 – 0.6 are fair, 0.6 – 0.75 are good, and 0.75 – 1 are excellent.[7] T30 (for rock music) should ideally be 0.8 to 1s.[8] EDT for speech should be 0.3 – 1.2s and for orchestral music should be 2.2s.[9] SPL(A) is equivalent to G in this case.
Figure 14’s results show that the space is louder than a concert hall, and very loud for an outdoor space. T30 across the space, and even when standing at the Heel Stone, was close to ideal (at least close, ironically enough for a stone site, to the requirements of rock music). Most of the results (P1 – P7) are based on software modelling with a sound source placed at the centre of the space. When a source is placed at the heelstone, and readings are taken in the centre, results are mostly good, better for speech than for music. Thus if sound was made at the heelstone, with the intention of it being heard in the centre of the circle, the acoustic properties of the space would support speech better than music. Figures of T30, reverberation time, are fairly uniform, in all positions between 0.8 and 1. This is within the ideal range for rock music. This is significant, as this shows that the reverberation at Stonehenge would naturally fit loud, rhythmic music. Quiet, or orchestral, or harmonically rich music, is generally performed in a venue with a longer reverberation time, reflected in larger values of both T30 and EDT, perhaps 1.5 – 2.2s.
Figure 14: Acoustic values in different measurement (listening) positions (central source at 1kHz, values in suggested range R are in bold).
We are also used to hearing vocal music in highly reverberant spaces, the acoustics of churches being designed in order to provide long reverberation for singing. Hearing the reverb tail of the previous note allows a singer to pitch the next note in tune, and is generally considered to flatter the sound of the voice. This is because it helps to hide the small intonation (pitch) inaccuracies and variations that are a natural part of vocal production, by mixing them with the direct sound, producing a chorus effect, which reduces the accuracy of the listener’s perception of the pitch of the sung note. This is true to such an extent that large reverberant spaces are routinely added to dry popular music recordings made in studios using electronic reverb units.
Figure 15: Results positions P1 – P7 for figure 14.
It is not helpful however for loud, rhythmic music to be performed in highly reverberant spaces. This is because percussionists need to hear the exact timing of the previous note(s) in order to know the exact moment at which to play the next rhythm. Thus concert spaces for popular music tend to have relatively dry acoustics, with EDT or T30 about 0.8 – 1. We can see from the Odeon results that the acoustic in the centre of the circle would make speech clear, well-defined and intelligible, especially in the central area enclosed by the trilithons and the entrance to the space. We can also see that if there were music in the space, singing voices and pitched instruments would not be as well supported as rhythmic music. Singing or instruments would have sounded better to those outside of the circle, especially at the heelstone, where there would have been particularly strong musical enhancement and acoustic effects. Sound made at the centre would have been very much enhanced acoustically at the heel stone, and sound made at the heel stone would have been enhanced, but not quite as much, when heard in the centre, speech being better transmitted in this case.
Speech transmission index (STi) at the side of the heelstone (P6) was excellent, as was clarity and definition. Impressively, these figures are substantially higher than if standing in the central part of the circle. There is also a considerable difference compared to standing 1m to the right of the heel stone. ‘The Heel Stone … was originally one of a pair’,[10] and it seems that sound was aimed in particular either at this missing stone or the space between the two stones. Further research will investigate the effect on the acoustics of including this other stone in the simulation.
Also remarkable are the figures for D50, STi and C80 in the centre of the space. They are considerably higher than the concert hall figures, and it is clear that speech would have been very clear in the central area of the space. This would not be as unusual if the space was small and/or had little reverberation or obvious acoustic effects present, like a modern living room, but this is not the case. Within the stone circle there are very high figures for envelopment, substantially higher than the figures for the concert halls, and it is clear that those within the space would feel enclosed and enveloped by it.
In addition Odeon allows one to produce auralisations of the space, sound examples that allow one to hear how audio (for example someone clapping or singing) would have sounded in the space when the listener is positioned at a given point. These auralisations illustrate a distinct reverberation that changes in tone and character in different positions within the space. Odeon also shows how the sound travels around the space and arrives at the receiver (listening) position. Figure 15 illustrates this, and shows how the sound arrives directly and indirectly to the listener, producing reverberation and listener envelopment. Results varied in some cases metre by metre, with the acoustics depending on precise position of listener or sound source, much like Maryhill. Indeed, results agreed with and largely confirmed those from Hardy, Watson, theoretical investigation and Maryhill.
Figure 15: Reflections (purple) from a centre source (red) to receiver (blue)
[1] You can walk around the model at http://www.3dancientwonders.com online (2005) [accessed 20th March 2009].
[2] ‘Spatial Impression is known to be an important part of good rated concert hall acoustics and it is now well established that spatial impression is composed of at least two components: apparent source width (ASW) and listener envelopment (LEV). ASW is defined as broadening of the apparent source width of the sound source, while LEV refers to the listener’s sense of being surrounded or enveloped by sound.’ Soulodre, G. A; Lavoie, M.C; Norcorss, S.G., Temporal Aspects of Listener Envelopment in Multichannel Surround Systems, AES Convention Paper 5803. 114th Convention, The Netherlands, Amsterdam, March 22-25, 2003. ASW equates to LF80, as seen in figure 8, LEV is described by LG80.
[3] ‘Concert Hall Acoustics: Parameters’, Akutek.info: The WWW Center for Search, Research and Free Sharing in Acoustics, October 2008, http://www.akutek.info/concert_hall_acoustics.htm, (1st April 2009).
[4] Skålevik, M., ‘Room Acoustic Parameters and their Distribution over Concert Hall Seats’, Papers: Akutek.info: The WWW Center for Search, Research and Free Sharing in Acoustics, October 2008, http://www.akutek.info/Papers/MS_Parameters_Distribution.pdf, (1st April 2009).
[5]Heinrich Kuttruff Room Acoustics, (Taylor and Francis, London, 2000) p. 211.
[6] Francis Rumsey, ‘Subjective Assessment of the Spatial Attributes of Reproduced Sound’, Proceedings of the AES 15th International Conference: Audio, Acoustics and Small Space, Copenhagen, Denmark, Oct 1998, pp 122–135.
[7] Chris Lynge Christensen, Odeon Room Acoustic Program User Manual, (Lyngby, Denmark, 2008) p. 7-86.
[8] Niels Werner Larsen, Esteban Olmos, Anders C. Gade, Acoustics in Halls for Rock Music, Joint Baltic-Nordic Acoustics Meeting 2004, 8-10 June 2004, Mariehamn, Åland, http://www.acoustics.hut.fi/asf/bnam04/webprosari/papers/o18.pdf (2nd April 2009), p.4.
[9] Sabine Von Fischer, ‘Scenic and Sonic Structure’, December 2002, http://e-collection.ethbib.ethz.ch/eserv/eth:26421/eth-26421-01.pdf (2nd April 2009), p.3.
[10] Julian Richards, Stonehenge: The Story So Far, (English Heritage, Swindon, 2007), p. 18.
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