## Preliminaries The word [[Archaeoacoustics|acoustics]] is originated from the Greek word _akouein_ (ἀκούειν), Joseph Sauveur coined the term for the science of sound he pioneered in 1701 [1]. ## Introduction of Archaeoacoustics Archaeoacoustics, also known as Auditory Archaeology, is an emerging interdisciplinary field that combines [[Archaeology|archaeology]] and acoustics. It focuses on studying archaeological spaces by examining their acoustic properties and characteristics. [2-4] According to Navas-Reascos et al. [^2], 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 following measurements. ### Measurements #### 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: $$ \label{t60} T_{60} = 0.161 \frac{V}{A} $$ 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): $$ \label{spl} L_{SPL} = 20 \log_{10}{\frac{P}{P_0}} $$ 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: $$ \label{edt} EDT = 6(t_{-10}) $$ or $$EDT = \frac{60}{A(0 \text{ dB} \to - 10 \text{ dB})}s$$ 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: $$ \label{g} G = 10 \log_{10}{\frac {\int_{0}^{\infty} P^{2}(t) dt} {\int_{0}^{\infty} P^{2}_{A}(t) dt}} $$ #### 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] : $$ \label{alcons} \text{Alcons} \approx 0.652 (\frac{r_{LH}}{r_{H}}T_{60})^{2} \% $$ 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. $$ \label{sti} STI = \frac{(\overline{S/N})_{ap} + 15}{30} $$ 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, the following evaluation scale for 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 | < 0.30 | | 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 $$ \label{c} C_{t} = 10\log_{10} \frac{\int_{0}^{t} P^2(t) \, dt}{\int_{t}^{\infty} P^2(t) \, dt}\, . $$ 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 ($C_{50}$) The $C_{50}$ was developed by Ahnert and it measures the clarity or intelligibility of speech and specifically related to the sound energy that arrives at a listener within 50 milliseconds: $$ \label{c50} C_{50} = 10\log_{10} \frac{\int_{0}^{0.05} P^2(t) \, dt}{\int_{0.05}^{\infty} P^2(t) \, dt} $$ where $P(t)$ represents instantaneous sound pressure in Pascals. ##### Definition ($D_{50}$) The $D_{50}$, also known as the degree of definition, is equivalent to $C_{50}$ to some extent. 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: $$ \label{d50} D_{50} = \frac{E_{50}}{E_{\infty}}= \frac{\int_{0}^{0.05} P^2(t) \, dt}{\int_{0.05}^{\infty} P^2(t) \, dt} $$ This ratio can be further related to $C_{50}$ (eq:c50)., which is defined as: $$ C_{50}=10\log_{10}\left( \frac{D_{50}}{1-D_{50}} \right) \,. $$ ##### Clarity80 ($C_{80}$) The $C_{80}$ 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: $$ \label{c80} C_{80} = 10 \log_{10} \frac{\int_{0}^{0.08} P^2(t) \, dt}{\int_{0.08}^{\infty} P^2(t) \, dt} $$ where $P(t)$ represents instantaneous sound pressure in Pascals. By employing some former mentioned formulas (eq:g), we can extend $C_{80}$ to this form: $$ C_{80} = 10 \log_{10} \frac{10^{G_{0-80}/10}}{10^{G_{80-\infty}/10}} = 10 \log_{10} \frac{E_{0.08}}{E_{\infty} - E_{0.08}} = G_{0-0.08} - G_{0.08-\infty}\,. $$ ### Technologies #### Ambisonics [[Ambisonics]] technology has been one of the most important technology of the spatial sound production since 1970s. It refers to a method that is based on the representation of the [[sound field]] excitation as a decomposition into [[Spherical harmonics|spherical harmonics]] [12]. In Ambisonics each channel has information about certain physical properties of the acoustic field, such as the pressure or the acoustic velocity [13]. ### 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](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. [12] Frank, Matthias & Zotter, Franz & Sontacchi, Alois. (2015). Producing 3D Audio in Ambisonics. Proceedings of the AES International Conference. 2015. [13] Arteaga, Daniel. (2023). Introduction to Ambisonics. 10.5281/zenodo.7963105. [^1]: 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. [^2]: This entry mainly developed its structure and content from Navas-Reascos et al.'s essay. Navas-Reascos, G.; Alonso-Valerdi, L.M.; Ibarra-Zarate, D.I. Archaeoacoustics around the World: A Literature Review (2016–2022). Appl. Sci. 2023, 13, 2361. https://doi.org/10.3390/app13042361