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Preface

The word acoustics is originated from the Greek word akouein (ἀκούειν), and Joseph Sauveur coined the term acoustics for the science of sound he pioneered in 1701 [1].

Introduction of Auditory Archaeology

Archaeoacoustics, also known as Auditory Archaeology, is an emerging interdisciplinary field that combines archaeology and acoustics. It focuses on studying archaeological spaces by examining their acoustic properties and characteristics. [2-4]

According to Navas-Reascos et al., Archaeoacoustics has had a wide variety of study aims, including socio-political studies to obtain information among different cultures.

Acoustical analysis procedures of Archaeoacoustics

The acoustical analysis procedures of Archaeoacoustics researches have been standardized to ensure similar quality characterizations of archaeological spaces, [5-6] general measuring parameters of Archaeoacoustics researches are described as follows:

Reverberation time $T_{60}$

Reverberation time $T_{60}$ is regarded as the most basic and important objective parameter of the Acoustics study, which can be used to measure how long a sound remains after the sound source is turned off. It was first proposed by W. C. Sabine (1868-1919), and it marked the beginning of modern room acoustics. It is measured in seconds and is obtained when the sound energy reduces by 60 dB. Sabine’s formula is:

T_{60} = 0.161 \frac{V}{A} \tag{1}

where $V$ represents the analyzed room volume (in cubic meters), and $A$ denotes the equivalent absorption surface of the room (in square meters).

Sound pressure level (SPL)

The sound pressure level (SPL) or acoustic pressure level (APL) quantifies the magnitude of a sound field and is expressed in decibels (dB):

L_{SPL} = 20 \log_{10}{\frac{P}{P_0}}

where $P$ denotes the SI unit of root mean square sound pressure mesured in Pascal (Pa), $P_0$ represents the reference sound pressure in air, set at a value of 20 $\mu$ Pa ¹. SPL can be measured using a microphone in air and with a hydrophone in water.

1 Pa = an SPL of

20\log_{10}{\frac{1}{2 \times 10^{-5}}}\text{dB} \approx 94 \text{dB}

Early decay time (EDT)

Early decay time (EDT) is derived from the reverberation time decay $T$ , measures the rate of the decay. The difference is the EDT value is evaluated from the initial part, namely the interval between 0 and −10 dB. EDT can be defined by two ways:

EDT = 6(t_{-10})

EDT = \frac{60}{A(0 \text{ dB} \to - 10 \text{ dB})}s

It is considered as a better descriptor of reverberance than $T_{60}$ [7].

Sound strength $G$

Sound strength ( $G$ ) relates closely to loudness and represents the difference in sound pressure level (SPL) between an omnidirectional sound source at a specific point in a room and the SPL produced by the same source in an open field, measured at a distance of 10 meters.

This measurement is crucial as it reflects the influence of the space on perceived loudness. Specifically, it quantifies the difference in dB between the level of a continuous, calibrated sound source measured in the space and the level generated by the same source in anechoic surroundings at 10 meters. [7] The formula for calculating the sound strength $G$ is as follows:

G = 10 \log_{10}{\frac {\int\limits_{0}^{\infty} P^{2}(t) dt} {\int\limits_{0}^{\infty} P^{2}_{A}(t) dt}}

Articulation loss of consonants (%ALcons)

The %ALcons, also known as the articulation loss of (spoken) consonants, was developed by Victor M.A. Peutz, and was presented in the march of 1971 at the 1st central Europese AES convention in Cologne [8]. %ALcons is an objectively indication of the loss of speech intelligibility that occurs in complex acoustic environments, which is decisive for the evaluation of speech intelligibility in rooms [9] :

\text{Alcons} \approx 0.652 (\frac{r_{LH}}{r_{H}}T_{60})^{2} \%

where $r_{LH}$ is the distance sound source-listener, $r_{H}$ is the reverberation radius or critical distance $r_{R}$ when in case of directional sound sources.

Speech transmission index (STI)

The speech transmission index STI was developed by Tammo Houtgast and Herman Steeneken in 1971, and has become the most common measurement predictor to assess objectively speech intelligibility in rooms. The STI scale ranges from the value of 0 to 1 (1 represents perfect intelligibility), indicates the speech transmission quality [10]. STI’s approach considers the source/room/listener as a transmission channel and measures the reduction in modulation depth of a specialized test signal which replicates the burst nature of real speech [9]. It is widely accepted that the STI is the most accurate of the intelligibility measures.

STI = \frac{(\overline{S/N})_{ap} + 15}{30}

where $(\overline{S/N})_{ap}$ represents the total apparent signal-to-noise ratio.

Scale

According to “The Audio System Designer Technical Reference” by Peter Mapp, published by Klark Teknik, the following evaluation scale for Speech Transmission Index (STI) is provided:

Evaluation	Sti	%ALcons
Bad	0.20 to 0.34	24.3 to 57
Poor	0.35 to 0.50	11.3 to 24.2
Fair	0.51 to 0.64	5.1 to 11.2
Good	0.65 to 0.86	1.6 to 5.0
Excellent	0.87 to 1.00	0.0 to 1.5

Additionally, the Common Intelligibility Scale (CIS) proposed by Barnett et al. [11] categorizes intelligibility as follows:

Intelligibility	Sti
Bad
Poor	0.30 to 0.45
Fair	0.45 to 0.60
Good	0.60 to 0.75
Excellent	0.75 to 1.00

Clarity

Clarity is a property complementary to $T_{60}$ , which describes the ratio between early and late energy in the impulse response. The general formula of Clarity is

C_{t} = 10\log_{10} \frac{\int_{0}^{t} P^2(t) \, dt}{\int_{t}^{\infty} P^2(t) \, dt}\, .

With exponential decay, Clarity can be expressed as

C_{\text{exp}} = 10 \log_{10}\left[ \exp\left( \frac{1.104}{T_{60}} \right) - 1 \right] \, \text{dB}\,.

Clarity50 ( $C_{50}$ )

$C_{50}$ was developed by Ahnert and measures the clarity or intelligibility of speech and specifically related to the sound energy that arrives at a listener within 50 milliseconds:

C_{50} = 10\log_{10} \frac{\int_{0}^{0.05} P^2(t) \, dt}{\int_{0.05}^{\infty} P^2(t) \, dt}

where $P(t)$ represents instantaneous sound pressure in Pascals.

Definition ( $D_{50}$ )

$D_{50}$ , also known as the degree of definition, is equivalent to $C_{50}$ . It represents the ratio of sound energy received within 50 ms after the direct sound arrival to the total sound energy, expressed as a percentage:

D_{50} = \frac{E_{50}}{E_{\infty}}= \frac{\int_{0}^{0.05} P^2(t) \, dt}{\int_{0.05}^{\infty} P^2(t) \, dt}

This ratio can be further related to $C_{50}$ , which is defined as:

C_{50}=10\log_{10}\left( \frac{D_{50}}{1-D_{50}} \right) \,.

Clarity80 ( $C_{80}$ )

The $C_{80}$ was developed by Abdel Alim, it describes the temporal transparency of musical performances (defined for an octave center frequency of 1000 Hz). Similarly, it related to the sound energy that arrives at a listener within 80 milliseconds, and expressed in dB:

C_{80} = 10 \log_{10} \frac{\int_{0}^{0.08} P^{2} (t) dt}{\int_{0.08}^{∞} P^{2} (t) dt} = 10 \log_{10} \frac{10^{G_{0 - 80} / 10}}{10^{G_{80 - ∞} / 10}} = 10 \log_{10} \frac{E_{0.08}}{E_{∞} - E_{0.08}} = G_{0 - 0.08} - G_{0.08 - ∞}

C_{80} = 10 \log_{10} \frac{\int_{0}^{0.08} P^2(t) \, dt}{\int_{0.08}^{\infty} P^2(t) \, dt} = 10 \log_{10} \frac{10^{G_{0-80}/10}}{10^{G_{80-\infty}/10}} = 10 \log_{10} \frac{E_{0.08}}{E_{\infty} - E_{0.08}} = G_{0-0.08} - ~~G_{0.08-\infty}~~ G_{0.08-\infty}

where $P(t)$ represents instantaneous sound pressure in Pascals.

References

[1] R.B. Lindsay, Acoustics: Historical and Philosophical Development, Dowden, Hutchinson & Ross, Stroudsburg, PA 1973, p. 88, Translation of Sauveur’s paper. https://archive.org/details/isbn_0879330155

[2] Valenzuela, J.; Díaz-Andreu, M.; Escera, C. Psychology Meets Archaeology: Psychoarchaeoacoustics for Understanding Ancient Minds and Their Relationship to the Sacred. Front. Psychol. 2020, 11, 550794.

[3] Debertolis, P.; Bisconti, N. Archaeoacoustics in Ancient Sites. A New Way to Analyzing Archaeological Locations. In Proceedings of the 1st International Virtual Conference on Advanced Scientific Results SCIECONF 2013, Žilina, Slovakia, 10–11 June 2013; pp. 10–14.

[4] Aletta, F.; Kang, J. Historical Acoustics: Relationships between People and Sound over Time. Acoustics 2020, 2, 128–130.

[5] Ramos Amézquita, A. Metodologia de Analisis Acustico de Sitios Arqueologicos de Mesoamerica; Universidad Politécnica de Madrid: Madrid, Spain, 2015.

[6] Ramos-Amezquita, A.; Ibarra-Zarate, D.I. Acoustic characterization of three archeological sites in the state of Guanajuato, Mexico. Proc. Meet. Acoust. Acoust. Soc. Am. 2013, 19, 040100.

[7] M. Schroeder, Thomas D. Rossing, F. Dunn, W. M. Hartmann, D. M. Campbell, and N. H. Fletcher. 2007. Springer Handbook of Acoustics (1st. ed.). Springer Publishing Company, Incorporated.

[8] Peutz, V. M. A.; 1971; Articulation Loss of Consonants as a Criterion for Speech Transmission in a Room [PDF]; Akoestisch Adviesbureau Ir. V.M.A. Peutz N.V., Nijmegen, The Netherlands; Paper ; Available from: https://aes2.org/publications/elibrary-page/?id=2108

[9] Ballou, G. (Ed.). (2015). Handbook for Sound Engineers (5th ed.). Routledge. https://doi.org/10.4324/9780203758281

[10] Carrion, A. Diseño Acústico de Espacios Arquitectónicos, 1st ed.; Universitat Politècnica de Catalunya: Barcelona, Spain, 1998.

[11] Barnett, P. W., Knight, R. D., & Institute of Acoustics. (1995). The Common Intelligibility Scale. In Reproduced sound (Vol. 17, issue 7, pp. 201-206). The Institute.

The reference sound presssure $P_0$ is often considered as the threshold of human hearing. It is notable that in an underwater environment, the $P_0$ is set at a value of 1 $\mu$ Pa. ↩

Revision from March 18, 2025 14:10:03 by Yu

MAN Wiki Archaeoacoustics (Rev #7, changes)