Buenos Aires – 5 to 9 September, 2016 Acoustics for the 21st Century…

PROCEEDINGS of the 22nd International Congress on Acoustics

Acoustics of Worship Spaces: Paper ICA2016-815

Mexico City’s cathedral: An archaeoacoustical and musicological analysis

Braxton Boren(a), Guadalupe Caro(b), Diana Calixto(c), Julio González(d), Víctor H. Mendoza(e) ,Francisco Salazar(f), Pablo Padilla(g), Gabriela Pérez(h), Alejandro Ramos(i), Alberto Rivera(j), Rodrigo Tapia(k), Carlos Paz(l), Jezzica Zamudio(m)

(a) Princeton University, USA, [email protected], (b)Instituto Tecnológico y de Estudios Superiores de Monterrey, México, [email protected] (c) Universidad Nacional Autónoma de México, México, [email protected] (d) Instituto Tecnológico y de Estudios Superiores de Monterrey, México, [email protected] (e) Universidad Nacional Autónoma de México, México, [email protected] (f ) Instituto Poltécnico Nacional, México, [email protected] (g) Universidad Nacional Autónoma de México, México, [email protected] (h) Centro Nacional de Investigación, Documentación e Información Musical Carlos Chávez , México, [email protected] (g) Instituto Tecnológico de Estudios Superiores de Monterrey, [email protected] (h) Instituto Tecnológico de Estudios Superiores de Monterrey, [email protected] (i) Universidad Nacional Autónoma de México, México, [email protected] (j) Instituto Tecnológico de Estudios Superiores de Monterrey, [email protected] (e) Instituto Poltécnico Nacional, México, [email protected]

Abstract

In this paper, we discuss the need to study colonial architectural spaces and their relationship with aspects of acoustic design. Other research groups have addressed issues such as the importance of acoustics in the architectural design of churches; how much the composers of a certain era took into account the acoustic of the spaces and venues where their compositions would be played; and how intelligible were the texts of complex polyphonic compositions of the time in certain enclosures, etc. In order to address these questions, they have used mathematical models and digital audio engineering to reconstruct the acoustics of these spaces and give tentative answers to the above questions. Our research group has also considered other topics such as the possible reconstruction of sonorities corresponding to polychoral musical practices, and the Iberian and Latin American musical characteristics of the colonial era. Initially we propose the study of the Cathedral of City and we present the results of impulse-response analysis of the building and describe our methodological framework and progress made so far.

Keywords: archaeoacoustics, ’s Cathedral, music.

22nd International Congress on Acoustics, ICA 2016 Buenos Aires – 5 to 9 September, 2016

Acoustics for the 21st Century…

Mexico City’s cathedral: An archaeoacoustical and musicological analysis

1 Introduction

Motivated by the basic question of understanding the acoustics of Mexico City’s Cathedral in the past and hopefully contributing to its improvement in the present we performed a first study as a starting point of an on-going research project. This project is part of previous efforts to incorporate sound as an important component of archaeological studies (see [2]).

Mexico City’s Cathedral, as any other iconic building, possesses or has been given many symbolic and practical functions. Many of these functions involve sound and speech, as it is clear from the fact that this building became the most important religious centre in New and one of the most important in the Spanish Empire. It was built basically in the same place where the former Major Temple of the Aztecs once stood and using stones and material from this construction, which adds, from the very beginning, to its meaning as a symbol of the religious conquest and at the same time as a symbol of spiritual continuity. It has “been there” for several centuries, even when its construction itself was a complex and long process. It is perhaps from this permanence that the same immutability is tacitly assumed of the acoustics of the building. It is nevertheless now clear that the acoustical features of buildings change as it has been shown by several authors and that even at a certain historical moment the acoustic response of a building could change depending on diverse circumstances. The conditioning of a church for certain festivity with different decorations and ornaments and the very fact that there were more people inside the building in important celebrations radically affected the sound features.

In order to be able to simulate and evaluate the importance of these factors, a computational model has to be built. Here we present the first steps in this direction. Namely, the results of acoustic measurements performed in the cathedral and the drawings of the building. We also discuss the historical (especially musical) background, since we believe that it is essential to have a reasonable understanding of the musical practices, repertoire and traditions if we intend to gain a clear understanding of its acoustics. This is especially relevant if we try to incorporate polychoral music into consideration, which is known to be present in the repertoire of the cathedral (see [4]). This historical and musical discussion is presented in section 2. Immediately afterwards, in section 3 another important topic is discussed, which is the architectural background. It is really the cornerstone of our study and the logical technical prerequisite. Later on, in section 4, we describe in detail the acoustic measurements

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that were performed. In section five we sketch work in progress which consists in the development of a computational model based on the results of the previous two sections. This model will enable us to create different acoustic scenarios and to explore different research questions. Moreover, it will allow us to provide the Chapter of the Cathedral and the architects responsible for the maintenance of the building with practical advice in order to improve the acoustical features during religious festivities as well as other activities, including concerts and plays.

2 Historical and musical considerations

Mexico Cathedral is more than a simple building, it embodies a very complex set of historical, political, social as well as artistic relationships. It would be impossible even to summarize these, but the reader is referred to [7] for a complete overview of these subjects. As any other space or building that has been constantly used since its construction, Mexico Cathedral cannot be considered as a finished or immutable structure. This is probably even more so in this case, for the soil on which the cathedral is based is very unstable. One has to recall that Mexico City lied originally on a lake and that major engineering works have been carried out in order to keep the building in a suitable state. The same can be said to a great extent of its acoustic features. Architectural restorations, modifications and additions have modified the acoustic response and, perhaps more importantly, the kind of music that is performed both for religious services and as part of the musical activities of the church has been continuously changing and adapted to the artistic taste and needs of each period. In this section we want to briefly outline the early repertoire that we know was performed in Mexico Cathedral. This is due to the fact that, as a starting point, our study aims at reconstructing the original acoustics of the building, although of course, we do not limit ourselves to a specific period and it is important to have an overall perspective of its acoustic evolution. However, we believe it is essential to have a precise idea of the musical corpus that constituted the core of the standard musical practices during the first years.

More specifically, we initially restrict ourselves to the music found in the Cathedral until 1589 for a very simple reason: there is an inventory which was recently rediscovered [4]. In what follows we sketch the main composers and musical forms that are listed in this inventory. Among the polyphonic pieces Masses, Magnificats, antiphons, hymns, psalms and motets can be found as part of the imported repertory. Several composers, are represented. We mention Tomás Luis de Victoria as probably the most representative, but pieces by Cristóbal de Morales, Pedro and Francisco and Pierre Colin and most interestingly Josquin. Concerning the local composers we find motets, masses, music for the Holy Week, Passions, Lamentations, Vespers, Mass and Office of the Dead, psalms, alleluias, etc. As it is expected, much of the local production was written by the chapelmasters of the cathedral. Among the latter, Hernando Franco is the best represented one in the period under consideration. Other genres listed in the inventory include villancicos and other devotional forms as well as chanzonetas and ensaladas.

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22nd International Congress on Acoustics, ICA 2016 Buenos Aires – 5 to 9 September, 2016

Acoustics for the 21st Century…

3 Architectural background

Mexico City’s Cathedral is the most important Catholic temple located in the Plaza of the Constitution of Mexico City. It is built with gray stone and has 5 naves and 16 side chapels, measuring 55 meters wide by 110 long with a height of 30 meters in the central nave. It is dedicated to the Assumption of the Virgin Mary and is considered the mother church of the Archdiocese of Mexico. The cathedral was built over a period of more than two centuries, between 1573 and 1813. Its design is a blend of three architectural styles that prevailed during colonial times: Renaissance, and neoclassical. Construction began with the designs and models created by Claudio de Arciniega and Juan Miguel Aguero, inspired by the Spanish cathedrals of Jaen and . He later promoted a contest to finish the facade. The winning project was the neoclassical proposal of Jose Damian Ortiz de Castro, who proceeded to finish the towers of the dome and works inside the cathedral. His death would leave the works on hold for a short time until 1793, when the Valencian architect Manuel Tolsa was appointed to finish the construction of the Cathedral, which was concluded in 1813.

On the facade three reliefs are observed in white marble, the central one represents the Ascension of the Virgin Mary. The left side shows the delivery of the keys of Heaven to Saint Peter and finally the right, a ship represents allegorically the Church. The temple consists of five naves. The plant is covered with a cylindrical dome transversely intercepted by other cone-shape structure. This vault is supported by 16 stone columns. The two processional aisles have spherical vaults. Thus the two extreme chapels are divided by robust masonry walls. A cylindrical vault transept crosses the temple, and at its intersection with the main nave the large central dome rises. The primary building material is a kind of concrete composed of stones and tezontle volcanico andesitas, bounded by a mortar of lime and sand. The composition of this material, and therefore their volumetric weight and mechanical properties vary according to the constructive elements and the times when each part of the construction was made.

The columns, arches and some decorative elements are of ashlar stone quarry and chiluca. It was found that there remains a core of poor masonry, whose contribution to the resistance is insignificant. The towers of the cathedral have a height between 64 and 67 meters. Each has a bell-shaped top and symbolize the communication between God and men. Between the two there is enough space to accommodate 56 bells, but today thirty have been placed.

Inside the temple you can see three main areas: the Altar of forgiveness. Located in the choir, it is the work of Jerome Balbas (1735), in colonial style, this structure in mahogany and red cedar is covered with gold leaf (hoja de oro). The Choir, covers an area of about 324 squared meters, consisting of quarry walls 3.35m high, where the stalls are made of mahogany with 120 seats are at the center. It has two levels: the higher one for Canons and the lower one for obispillos. At the top, it has carvings in half relief, bishops and other figures. At the center of the choir, between the gate and stalls, there is a mahogany stand, decorated with ivory figures, one of which is a crucifix that crowns the whole work. It is also used to hold singing books and it consists of three bodies: the support in mahogany, and two bookshelves.

At the top of the choir there are two organs which were built by the Spanish Joseph Nassarre who worked in Mexico from 1734 to 1736. The organ of the gospel of the Metropolitan Cathedral, measures fourteen meters high by ten wide and three meters long is located six meters above the floor.

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The instruments were subjected to a complete restoration: to reconstruct the organ of the gospel and repair damage caused by water leaks. This, together with the deterioration of the leather parts affected the functioning of the organs, forcing a more comprehensive restoration. In 2007 a thorough study of the structure, mechanisms and parts of the instruments in order to perform a restoration with strict adherence to the construction practices of the time they were built, was held in order to have the same appearance and the same sound quality as originally. Except for the addition of a few fans for air supply, they were not "modernized" or modified. The restoration was completed in 2009, when the organs of the Cathedral of Mexico sounded again.

The Altar of the Kings, is in the apse of the church, behind the altar, and is the masterpiece of Mexican Baroque or Churrigueresque. It measures 25 meters high, 13 meters wide and 7 meters long; rises to the bottom of the Cathedral occupying the altar. This altar is composed of three parts: two lateral and one central section. This altar was made in polychrome precious woods, in a composition of columns and foliage garlands and cherubs. The set is adorned and covered with gold leaf.

4 Acoustic measurements

In order to measure the impulse response of the building, four Beringer ECM800 microphones and a fulminant gun were used and recorded at a sample rate of 96Khz and 24-bit depth. Although several microphone configurations were used placing the gun at different source points, due to space limitations only results for one microphone configuration are presented in this paper. For this configuration, the microphones were placed in the center nave; from the door of the choir and down the middle aisle with the source placed at the entrance of the choir section. Placement of the microphones were as presented in table 1, and distances were measured taking the choir’s door as the origin. The following figure shows the placement of the microphones and sound source.

Table 1 - Microphone placement configuration.

Microphone Distance Height 1 3.5 m 1.2 m 2 18.5 m 1.2 m 3 32.27m 1.2 m 4 40.65 2.18 m

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CATEDRAL METROPOLITANA

s

s 40.65 32.27 18.50 3.50 61.54

s

s

118.48 123.83

Figure 1 – Microphone placement for configuration 1

Humidity at the time of the measurements ranged between 34% and 35%, and the temperature was of 21º Celsius. The background noise ranged from 35.8 to 40.5 dB SPL on average. Signal processing of the Impulse Response was performed in Matlab, a band-filtered analysis (up to 8 kHz) of the different IRs we obtained to get base parameters - EDT, T30, T20, C80, and D50 for the different source-receiver combinations. Decay curves for octave bands are also presented for microphone 2. Table 2 presents results for microphone 2, as representative of the measurements obtained.

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22nd International Congress on Acoustics, ICA 2016 Buenos Aires – 5 to 9 September, 2016

Acoustics for the 21st Century…

Figure 2 - Decay curves for octave bands a) 63 Hz Octave (upperrow left); b) 125 Hz Octave (upper row center); c) 250 Hz Octave (upper row right); d) 500 Hz Octave (middle row left); e) 1 kHz Octave (middle row center); 2 kHz Octave (middle row right); 4 kHz Octave (bottom row left); 8 kHz Octave (bottom row right).

Table 2 - Acoustic parameters for microphone 2 Configuration 1

CONFIGURATION 1 MIC2 Column1 Column2 Column3 Column4 Column5

Bands Center Frequency C80 (dB) D50 (%) EDT (s) T20 (s) T30 (s) 63.0957 Hz -4.0368 0.2097 10.4471 7.5312 7.5311

125.8925 Hz -9.2698 0.0863 45.5516 19.4455 19.4138 251.1886 Hz -8.7106 0.0911 34.4603 33.345 33.0877

501.1872 Hz -6.4409 0.1012 7.1158 13.5088 14.4446

1000 Hz -5.1315 0.1565 6.9788 7.0246 7.1863 1995.2623 Hz -5.1883 0.1585 6.5636 6.4315 6.4189

3981.0717 Hz -3.5405 0.2196 5.1191 5.428 5.4658 7943.2823 Hz -3.8072 0.2369 3.1493 3.411 3.5683

5 Mathematical and computational modelling

In order to develop a mathematical and computational model of the acoustics of the building, it was necessary to first develop a 3D model. A 2D AutoCAD floor model was received from the Cathedral

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22nd International Congress on Acoustics, ICA 2016 Buenos Aires – 5 to 9 September, 2016

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officials, and from it a 3D model was developed by taking laser measurements of the heights of the sections of the building. This turned out to be quite time consuming, due to the fact that the 2D model did not take into account the fact that the Cathedral has been sinking unevenly throughout the centuries and therefore the measured heights did not coincide with the model. The following figures present a comparison of the rendered space versus de actual one.

Figure 3 – a) Picture of the Choir taken from the Altar; b) Render of the Altar’s view of the Choir (center); c) Render of the Top view of the Mexico City Cathedral (right);

After completion of the 3D model (i.e. materials, floor adjustment, etc.), the next step is to develop the Acoustical Computational model, in order to compare the computational and experimental acoustics parameters. Due to time limitations, such step is not presented at the present work.

6 Analysis and Conclusions

Analysis of the Decay curves show an RT60 of approximately 6 seconds for most Octave Bands. However, the acoustical parameters obtained show some irregularities for the Decay Time of the 63, 125 and 500 Hz bands. A Longer EDT than T20 or T30 might suggest that the frequency response of the pistol used is slightly uneven in one or several of the lower bands. Results of D50 show poor intelligibility for all octave bands and negative results for C80 in every octave band, that range from -0.1308 dB down to -12.1772 dB suggesting that only slow Organ Music is favored at the venue.

A closer analysis on the normalization of the decay curves and a characterization of the source are in order to be absolutely certain that no methodological error has been made. Also, once the 3D model is completed, computational modeling could help to compare simulated results to experimental ones.

Acknowledgments

We would like to thank the authorities of Mexico Cathedral for their help in this project as well as the authorities from the National Institute of Anthropology and History (INAH) and the City Government. We would also like to thank professor Guadalupe Caro Cocotle from the Instituto Tecnológico y de

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22nd International Congress on Acoustics, ICA 2016 Buenos Aires – 5 to 9 September, 2016

Acoustics for the 21st Century…

Estudios Superiores de Monterrey (Campus Estado de México) for her valuable musicological advice, and Diana Calixto and Gabriela Pérez for their help and support.

References

[1] Aguilera Jiménez Patricia. Catedral Metropolitana, hundimiento y rescate. Instituto de Ingeniería, UNAM. 2013, México D.F. [2] Garza, Clara; Medina, Andrés; Padilla, Pablo; Ramos, Alejandro and Zalaquett, Francisca. La necesidad del estudio sistemático de efectos acústicos en sitios arqueológicos. Estudios de Cultura Maya, MAYA XXXII, 2008. [3] Harris, Cyril. Handbook of noise control. McGraw-Hill. 1979, USA. [4] Marín-López, Javier. The musical inventory of Mexico Cathedral, 1589: a lost document rediscovered. Early Music, Vol XXXVI (4), 2008, pp 575-596. [5] Recuero, López Manuel. Acondicionamiento Acústico. Paraninfo, 2001, España. [6] Toussaint, Manuel. Arte Colonial en México. UNAM. Instituto de Investigaciones Estéticas. 1990, México D.F. [7] Turrent, Lourdes. Rito, música y poder en la Catedral Mtropolitana. Mexico 1790-1810. Fondo de Cultura Económica, El Colegio de México, 2013.

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