Yaxchilán's clay frogs

C-405 clay dual whistle

Roberto Velázquez Cabrera
Virtual Research Institute Tlapitzcalzin

Firs version April 8, 2002. Last version January 7, 2003
(Consultation paper)

Versión en Español
Short popular version


A short version of this study was presented in the 1st Special Sessions on Acoustics of Ancient Sounding Instruments included in the 1st International Joint Meeting: 9th Acoustic Mexican Congress (IMA), 144th Meeting of the Acoustic Society of America (ASA) and the 3rd Acoustics Iberoamerican Congress (FIA) in Cancun, Mexico in December 2-6, 2002.

A Lay Language Paper is posted in the ASA World Wide Press Room Yaxchilan's Whistles

Introduction

The objective of this project is to analyze a set of eighth ancient clay whistles found in the temples of Yaxchilan, Chiapas, in the Small Acropolis or West Acropolis. It is estimated that the site's structures are from the late classic period (650 - 800 b.C). The Yaxchilan's whistles were discovered during excavations by INAH (Instituto Nacional de Antropología e Historia) from 1989 to 1991 and they have not been archaeologically classified nor analyzed and they rest in a storage room of Cuicuilco site, in the south of Mexico City.

The paper includes the first analysis of three dual whistles of that set with their body shape resembling frogs. It is not known if the whistles were made in Yaxchilan nor if there are other clay aerophones of that community or similar whistles of other Mayan sites.

A simple methodology has been applied to experimental clay models and aerophones from other ancient cultures [1, 2 & 3]. The intention in this study is to improve that methodology with the incorporation of additional interdisciplinary analysis.

The selected case is relevant because the clay whistles are the most abundant in explorations and discoveries of sonorous archaeological goods that were designed and used in the remote times of ancient cultures, but they are the least analyzed, published and promoted, despite of being the least complex in their organological structure. The Mayan culture is one of the best known but it's sounds were lost with it's extinction and they have not been rediscovered with clarity even with the existence of several hundreds of ancient clay sonorous artifacts in operable conditions to get their millenary sonic secrets.

Background

Important groups of small Mayan sculptures have been analyzed from the aesthetic and archaeological point of view, considering mainly their form, figure or external iconography as those that have been included in publications of Mayan figures [4] and of Jaina Island [5 & 6] which include whistles, but the internal analysis and their substantial sonorous function has not been formally realized. Some Mayan sonorous artifacts have been of interest for museographers and researchers of ancient art for their originality, singular elegance, beauty and external designs and have been displayed in diverse museums and especial exhibitions, but it is frequent to be presented as figurines. The investigation about the Mayan organology just begins. A study is being conducted in Guatemala about 49 Maya instruments [7]. Maya whistles have been found in diverse archaeological explorations but their information or analysis has not been provided. In the web the most displayed are some pictures of Mayan whistles and Yaxchilán ¹.

Diverse publications exists in which pictures or drawings are included and general descriptions of some whistles and other relevant Maya aerophones [8 & 9] but the rich organology found has not been analyzed formally, systematically and in depth. In most cases of the literature, at the most it is mentioned if the whistles have amorphous, zoomorphous or antrophomorphous figure and when the form of a recognizable being is specified.

The only known study about an important group of Mayan whistles is precisely on 356 whistles, mainly from the Jaina Island [10]. It includes some organological data about the analyzed whistles, which gives a good idea of their dimensions and structural forms, but the analysis has limitations and basic methodological errors, which were, commented in detail in a previous study, openly available [11].

Formal studies about Mayan whistles or from other cultures are nonexistent. In the international context, the only known formal study on ancient whistles is about the Peruvian Whistling Vessels [12]. The majority of the rest of the studies produced are general or introductory types, but do not include the application of modern techniques for the acoustical or organological analysis or have been realized with the alien criteria of the ancient cultures, which has impaired to know the own secrets of their sonorous functions.

Generally, the whistles are underappresiated, because they are considered simple or elementary. Also, ancient whistles are underestimated, because they are considered toys, but it seems that it is not realized that even the toys can reflect the profound spirit of a culture. In reality, no studies exist about their ancient use. But their simplicity is only a superficial appearance, because it has been found that they have special characteristics and can generate complex sounds and effects, which are not well known nor well analyzed. It is necessary to study the functioning of the whistles to be able to understand the aerophones of greater complexity. In previous studies [1], it was found that the ancient music had a very wide concept. It could be related with sounds from nature and used to honor their gods, in shamanic rites, in communications, to improve the physical and mental health of persons, in hunting and many other applications.

There are many Mayan whistles and from other ancient cultures in national museums and collections and from the exterior, but unfortunately their physical possession prevails over for their investigation. Many organological treasures were only changed from one burial to another, without even being analyzed archaeologically.

Some representations of sonorous artifacts remain, mainly in drawings of the Maya iconography, as in Codex's: Dresden (lamina 21), Troano (plana XX) y Cortesiano (Lamina 21), in paintings as in the Bonampak's murals and in polychrome vessels, but unfortunately they do not show enough detail as to be able to reproduce and to study them. Also writings exist about similar instruments, which were played in big ceremonies or events up to the conquest, but the clay whistles do not appear in any of them whith clear descriptions or detailed indications of their possible ancient uses.

About the sonorous artifacts from Yaxchilán, no reference has been found, neither much archaeological literature exist in the web about this Maya site, however there are some pictures of their buildings and views of its surroundings. It appears that most of the emphasis of the best publicized studies have been centered in the analysis of the glyphs of the lintels and steles, mainly with relation to the governing elite persons, dates and events represented in the main Maya communities like Tikal, Piedras Negras, Palenque, etc. The artisans in charge to tell in stone the events of the governors must have had lots of work in Yaxchilán. It is estimated that 130 monuments were carved in stones, a paradise for students of epigrapy and iconography [51].

The best works of research on the Mayan history were realized visually, like those developed during the last century to read the Mayan glyphs, but the sounds of the ancient cultures belong to an unexplored space.

In previous studies [1], it was found that the millenary and rich organology of Ancient Mexico was destroyed, forbidden and forgotten during and after the Spanish conquest, since more than five centuries ago. Secrets of thousands of sound artifacts still remain buried in old and modern tombs (cellars with discovered artifacts).

The big problem is that experts and administrators related with the ancient cultures and artifacts, with very few exceptions, say that it is impossible to get something relevant in the analysis of ancient sonorous artifacts, and many of them are opposed to any formal investigation on the matter.

In this project, we will try to show that it is possible to get relevant findings in the unexplored ancient Mayan sonic space, even with the analysis of few clay whistles (which are stored, unknown and underappresiated) and without any (financial or technical) support.

Presentation and justification

The study is a methodological investigation project. It is to support a MSc thesis on Mexican aerophones [13] to test and to enrich the suggested method. It has been recommended to analyze as deep as possible each one of the different types of the relevant ancient aerophones that have been discovered to be able to detect the characteristics and substantial qualifications of each one, which will allow to correlate them. This project follows that recommendation and was organized in several stages.

The first stage was to select a type of whistles from those stored in Cuicuilco, which were analyzed with the available resources and methodology, without incurring in additional marginal costs. This document is the report of the study realized in the first stage and it's results are described in the rest of this document. In other stages the analysis of these whistles and/or the rest of this lot could be performed deeply, incorporating additional studies that could be made.

The technical justification is based in the lack of a formal methodology for the analysis of ancient aerophones. Without a formal methodology it is not possible to realize systematic studies nor train personnel nor select and acquire technologies and the necessary equipment to carry them out. This limitation is one of the main technical reasons for the lack of formal studies in the matter.

The beginning of the analysis of old aerophones could bring additional elements to identify and characterize the sonorous wind artifacts and provide additional knowledge to more comprehend the ancient cultures in their basic aspects as their sonorous art/technology. To promote this new field of investigation it could help to discover organological and acoustical secrets and possible uses of these ancient sonorous artifacts.

This study, considered a pilot project, is to support the report about the corresponding exploration and could be a guide for the elaboration of reports and studies of other explorations in which relevant ancient wind artifacts have been discovered.

The study of each one of the relevant aerophones discovered and the corresponding monograph could help to define the terminology for their adequate analysis, description and classification, considering that the existing systems in the international context are not well adapted to the rich and varied prehispanic organology.

To find organological and acoustical characteristics of the aerophones from each archaeological site could bring additional elements for the origin identification of other similar wind ancient artifacts.

The registry and the acoustical and organological analysis of each ancient sonorous artifact is a previous task to the adequate diffusion.

The study of each one of the relevant aerophones found is a tough job, but it has to be initiated some day. In Peru, a project ² began to study and catalogue Pre-Columbus musical instruments, but their advances or results are not known.

A previous work project ^{3 & 4} was presented to Daniel Juárez, responsible archaeologist of the exploration from the INAH. In the first stage, the archaeological information and data were not provided, because the report of the exploration of Yaxchilán Project remains to be published. Nearly 500,000 clay artifacts were discovered in Yaxchilan, but its exact knowledge is unknown [51].

In the first stage, it was proposed to reach the following objectives and goals:

Objectives

1. To analyze a type of whistles from Yaxchilán, Chiapas using the available proved methodology.

2. To determine and present feasible recommendations for other stages of the project according to the interest and possible available support.

Goals

1. To analyze 3 dual-whistles, stored in Cuicuilco and catalogued as C-466, C-381 & C-405.

2. To generate a report of the realized studies.

3. To detail the recommendations for other stages.

Main hypothesis to be investigated

The intention is to prove that those Mayan dual whistles can produce complex sounds and different to those in western music and that they have a closer relation with the beings chosen to form their body, meaning that they can produce sounds similar to their models in nature: frogs. Their possible use could have been related to the imitation of natural frogs in rites or ceremonies. Also it is possible that the dual-whistles can generate special effects like beats or phantom sounds.

Technical main activities realized in the first stage:

1. Visual analysis of the whistles.

2. Obtain general and organological measurements of the whistles, at least those required by the Helmholtz's equation for globular resonators.

3. Analysis of the fundamental frequencies and determination of quality factor of the sounds using the Helmholtz's equation and computer programs.

4. Take digital pictures of the basic sounds of the whistles with: front, rear, top, bottom, the sonorous mechanism views & artistic take of 3/4.

5. To register digitally the basic sounds of the whistles at their place of storage using a Laptop computer with sound card and microphone.

6. Analysis of the available information of the whistles and of their archaeological surroundings using mainly the open information available in Internet to facilitate the consultation of the utilized references and not to incur in marginal costs.

7. Tonal and spectral analysis of the sounds of the whistles, using digital spectrograms. The necessary computer programs to analyze the sounds have been acquired and proven in previous studies.

8. Elaborate experimental replicas to get a first idea of how they can be build and to make additional measurement tests, like the sonorous intensity and acoustical radiated power estimation and to acquire spectrums of complex forms of operation.

The main results of the realized works in the first stage are now presented:

Visual analysis

The whistles have no glyphs nor drawings on their surface and the finishing is not very fine and no sign of decorative paint is visible, but their three-dimensional zoomorphous figure is very useful to extract relevant information.

The most noticeable of the analyzed whistles from Yaxchilán is their shape of frogs or toads in singing position with their erected head. This indicates a special taste for the amphibians and their singings, which must have been very abundant in the selvatic environment of that community. There is a clear evidence that the clay frogs are singing. In two of them their throat is inflated (whistle C-405 and whistle C-381), but it seems that their mouth is almost closed. The natural frogs do not sing like the humans with the mouth very open, they sing with the front of their mouth closed most of the time, because the pulsating sounds emerge by the two sides (which can be seen in the previous two photos) to generate the very special vibrating and profound singing.

Three whistles with the shape of frogs or toads in a lot of eight represent a very high percentage, more than 30%. The whistles are dual, which indicates that they liked to play whistles in pairs surely to generate and listen sounds with special complex sounds like beats or phantom sounds (not physically real) that are brain detected and can not be detected nor measured with acoustic or metrology equipment. Beats are generated as a result of listening two or more sounds with close fundamental frequencies and the resulting perception is the numerical difference of the two originated frequencies. Generally, the musicians prohibit the generation of beats but it has been found that in antiquity some Mexican employed them.

It is noticeable that the most common and distinctive organological characteristic of the Yaxchilan´s whistles (with the exception of a transverse whistle), is the design of their sonorous mechanism, the mouths or sonorous holes are of similar form and size, with the bevel in arch or semicircular form (as it can be seen in the dual whistles (C-466, C-381, C-405 and in other single whistles), the size and form of the air ducts are also similar, which is important as this is in accord with the form of the whistles of this lot. The common characteristic of the sonorous mechanism could be an organological stile, distinctive of the wind artifacts with curved embouchures from Yaxchilán. It is not know if these whistles are originally from this site but the similarities of their sonorous mechanism indicate that they were made with the same organological technique, which means that they could have been constructed by the same artisan community. They could belong to Yaxchilán, because it is difficult that all the whistles were brought from other Mayan community to be buried.

Only one sonorous artifact (shown in the center of other four single whistles) from the lot of eight differs in the form of the embouchure by having a round sonorous hole and being a transversal tubular whistle. The organologic design of this side whistle was found in several great cultures from America. Several similar tubular and globular aerophones were found in the Ancient Mexico and in the Andean zone. A good example is a set of 32 bone tubes from Caral, Sucre, Peru (~2,600 bC), which is included in a previous study [16]. This relation means that the rich ancient cultures from America had very similar sonic technology and culture.

Whistle C-381

The most important in the sculptoric representation of this whistle is that it tell us that the frog is singing like frogs in nature. It has the trout so inflated that it forms a small sac. This could also indicate that the clay frog was made to sing and therefore it is possible that it can generate sounds like the natural frogs.

It is possible that the makers of these Maya whistles knew that the sounds of the frogs are generated by the vocal cords and are amplified and modulated in the interior of the mouth and the vocal sac. Also, it is noticeable that this whistle has shoulders.

This whistle is the one that looks more complete and in good condition to be played and analyzed in its sonorous function. In the first stage, the analysis was centered in this clay frog.

The whistle measures 7.8 cm L, 6 cm W & 6.6 cm H and it has two tonal holes. The clay is slightly dark brown.

The main dimensions of the whistles are given en Table 1. including those to estimate the fundamental frequencies with the Helmholtz's equation and to make approximate replicas.

The most noticeable is that the difference of the volume of their two resonators is significant (8.6 & 12.4 cm²) which indicates that the resulting beats can be easily perceived.

Whistle C-466

This whistle is the largest one (10.8 cm L, 7.5 cm H & 6. cm W) it has a baby frog on its shoulder with a broken head. It has two tonal holes, one on the front of each whistle. The clay color is clear yellow.

When first analyzing this whistle it was found with sand in it's interior, it was cleaned with a small stick but it was not well cleaned.

It is noticeable that the resonators' volume of the whistle is slightly different (11 & 10 cm²), This means that they can produce low frequency beats and it could be that they cannot be well perceived.

Whistle C-405

This whistle is the most beautiful; it has a baby frog on its back with its complete body. The representation with the frog with the baby on its back is very meaningfully and has a much relation with Maya culture, costumes and uses and with animals of that area, like monkeys. For example, in the Dresden Codex (pp 13-26) drawings show women with diverse beings on their back. There are females of several Maya jungle species that carry their babies on their back. In this way the babies maintain a very close relation with their mother during the first years of their lives. The baby figure also tells us with more realism that they belong to the frog family. The singing mother' body had to be altered in her body to facilitate its handling when being played. If the legs were integrated they could interfere with the player's hands and if it's four extremities were formed with more realism, they would become fragile or make the whistle very thick and heavy.

The whistle also shows it's inflated trout and with more realism tells us that it is singing, which emphasizes the possibility that they can produce sounds similar to those of frogs. The fact that of the three frog whistles, two are singing, also could indicate that they may sing in chorus, like the natural frogs.

Unfortunately, this whistle has a broken insuflation channel. It cannot be operated in a dual mode nor the resulting sounds analized.

Table 1. Main dimensions of the whistles

Silbato	V	l	d	Wl	Iw	Oh	Ih	Oh
C-381-L	8.6	0.2-0.7	0.7	18	1.0	1.1	0.4	0.2
C-381-R	12.4	0.1-0.6	0.7	19	1.0	1.0	0.4	0.1
C-466-L	11	0.3-1.7	1.0	1.8	1.0	1.5	0.3	.15
C-466-R	10	0.3-1.7	1.0	1.7	1.0	1.6	0.3	0.2
C-405-L	5.8	0.2-0.5	1.0	1	0.9	0.8	0.4	0.2
C-405-R	5.2	0.15-0.5	1.0	-	-	-	-	-

Concepts: V = Resonator volume (cm³), l = Thickness of the wall (min-max in cm), d = Mouth diameter(cm), Wl = Wind way length(cm), Iw = Input wind way wide(cm), Ow = Output wind way wide(cm), Ih = Input wind way high(cm), Oh = Output wind way high(cm), R = Right and L = Left.

Construction techniques

The construction of Maya aerophones or from other ancient cultures has not been studied nor divulged and no publications about this organological technology are known. The only study where it is shown with detail and photos the probable making process of an ancient aerophone is about four Mexican (Aztecs) tlapitzalzintlis (little flutes) from Templo Mayor Museum [19].

About Maya culture, only few general commentaries about the construction of the clay figurines that exist in the museums have been found, like the words of the mayist expert Linda Schele [4]. Linda thought that there were other Maya areas more developed in that beautiful art that she considered sculptoric and she comments about the clay burning, its decoration and she recognizes that some of the figurines were ritual musical instruments, but she does not provide any organological details.

Master Ramon Piña Chan also briefly comments about the making of the Maya figurines [4]. His descriptions help to have an idea about how the Maya figurines were elaborated, but they are not enough to know how the Maya whistles were made in each one of the ancient artisan communities.

Now, it is not possible to know exactly how the whistles of this study could have been made. The interior of the whistles has not been analyzed nor have x-rays taken, however it is supposed that they were made in several parts and stages, probably some details used in their fabrication can be mentioned, according to the visual analysis of the Yaxchilán whistles and the making of the first experimental replicas (like this one).

The whistle with the broken embouchure shows that it's air duct was molded with the aid of a small pointed stick to form the air channel adhering small flat clay pieces. The analysis of the airway's interior from the rest of the frog-whistles indicates that they were formed with similar little stick.

The frog's heads were hand modeled in several parts then attached, the mouth and jaws, the eyes and the head's superior part, the frog's body were also hand modeled and attached to the resonator's body.

The tonal holes are made with a round stick of the corresponding diameter.

The analyzed whistles are of semi fine clay possibly burned at low temperature, specially the brown ones. No traces of decorative paint appear at plain sight.

The organological design function very well in several sizes, smaller and bigger.

The good construction of the dual clay frogs is not easy. Dual whistles were produced after a very long development by the ancient makers of clay singers. For example, It was found that it is more difficult to learn how to copy a Mayan dual whistle than to learn how to carve (in soft stone), to draw and to paint copies of Mayan glyphs.

However, the best way of making was found.

Techniques for the sonorous analysis

The analysis of sonorous archaeological goods in their substantive function is important because that is the reason for their existence and because it adds another space of real variables to the traditional visual analysis of the ancient artifacts.

Experimental archaeological studies applied to ethnomusicology have begun to be done, as in the case of the friction Maya drum [42] which appears in the vase K5233 or number MS-1720 from which replicas were constructed for their analysis. Unfortunately, the acoustical analysis techniques have not been used and it is very difficult to elaborate precise experimental replicas with reference to the illustrated Maya images, as far as dimensions, materials, ancient construction procedures which allow to reproduce sounds very similar to the originals.

This paper shows that the direct analysis of the ancient whistles and replicas supported with ancient and modern techniques can help us to obtain secrets of their properties, capacities and possible uses and very importantly, can provide additional associated elements to enrich the knowledge of the past, if the technical analysis are complemented with multidisciplinary information of the objects in the study analyzed in its own context. In this study it was not possible to realize some comparative analysis with other whistles, because acoustical studies of similar dual-whistles were not found. It is relevant to be able to study ancient dual-whistles, because the characteristics of their sonorous function can be useful aid in the analysis of later similar studies.

To gain the most effectively and objectivity possible, the sonorous analysis of the whistles has to be done initially and fundamentally with technical or scientific methods related with their basic substantive sonorous function, with tools for organology, acoustic and signal analysis, which have been used in other studies about Mexican aerophones, where they have demonstrated to be effective to analyze simple and complex sounds. The only variation permissible and desirable is to try to adapt a Yaxchilanian point of view.

The spectral techniques for voice recognition and biological acoustic (which studies the animal's sounds) are adequate due to the kind of sounds that the ancient aerophones can produce.

It is possible to make some simple exercises with Helmholtz's equation (1). It is convenient to mention that this equation was applied with success to whistling vessels from Peru [12] to determine their fundamental frequency. Garret & Statnekov found that the whistles from the cultures of the high mountains zones were different from the ones of the valleys, which can be taken into consideration to determine the possible origin of similar Peruvian whistles of unknown origin. They also found that the whistles played in groups could produce beats and special effects in humans as states of superior conscience. Helmholtz's equation has been also applied with success to other Mexican globular whistles in previous studies [1]. This equation has not been used to design or analyze modern earphones, because they are tubular, except ocarinas.

The exercises of sonorous analysis were realized based in the recordings made in a first session at the storage room in Cuicuilco. The main observed effect of the sounding mechanism (embouchure-mouth) is a noisy sound.

Applying the equations (1 & 2 in Excel format) the fundamental frequency F0 and the quality factor Q can be estimated, as shown in Table 2, which also includes the measured frequencies F0: minimum (Fmin) and maximum (Fmax). The sound generated by each one of the individual whistles was produced in a simple closed form, as flat musical notes.

F0 = (17000/PI)* (S/(((L+0.7*D)*V)) ^1/2          (1)

Q = 2*pi()*(V*((L+0.7*d)/S)^3) ^1/2                   (2)

Where:
F0 = Frequency in cycles per second = Hz
Q = Quality factor
V = Volume of the whistle's resonating chamber in cm³
S = Area of the mouth's section in cm²
L = Thickness of the mouth in cm
d = Mouth diameter in cm
1700 = Sound speed/2 (as it was used in previous studies)
PI() = 3.1416
0.7 = Correcting factor

Table 2. F0, F, Fmin, Fmax (in Hz) and Q

Whistle	F0	F	Fmin	Fmax	Q
C-381-L	1,096	1115	880	1,400	88
C-381-R	1,010	962	885	1,185	78
C-466-L	1,201	1010	988	1,198	52
C-466-R	1,259	1049	992	1,257	50

As it was expected, the calculated fundamentals F0 are in the range of frequencies generated by the whistles played individually, closed to the Fmax. The higher produced sounds comes out between C#6 (1,108 Hz) and E6 (1,396.9 Hz) of the tempered musical scale with the diapason A4 = 440 Hz. That is the only relation that the sounds of the whistles have with modern music.

The pitch of the sounds from the Yaxchilan's whistles is located in the superior part of the median arithmetic 721 Hz (over F5) of the sounds from Maya whistles from other zones previously analyzed [11] mainly those from Jaina Island. 97 % of those Mayan whistles are from 277 Hz (C#4) to 1480 Hz (F#6). See figure.

The frequency F in Table 2 was calculated using the equation found for mayan whistles from Jaina Island F = 2642*V^-0.4011. The F is a good aproximation even if it is function only of the resonator volume V.

Even if it was not possible to have a portable sonometer to take measurements in their place of storage, it was perceived that the power of the sounds is not high, as it happens with the sounds of other Maya whistles in similar irregular forms and sizes.

The quality factor Q is higher for the resonators of whistle C-381. F0 and Q are broad approximations, because the mouth or sonorous hole is not circular and the measurements of S, d and l are approximate, because they do not have constant values due to the irregularities in the clay structure of the mouth.

Spectral analysis.

The best-known modern technique to analyze simple and complex signals is realized with the spectral analysis. The spectrums are mathematical transformation or mappings of signals from the time domain (in the case of sounds) to the frequency domain, using the Fourier Transform or the Fast Fourier Transform. Several automatic procedures exist to obtain this purpose. One is an analogic method using spectrum analyzers, but that kind of equipment is very expensive and have not been available for our studies, Other method is digital, using computer programs, which was used in the first stage of this project. For the digital analysis all that is required is a personal computer, with sound card and microphone and the programs to obtain the spectrograms. Previously, several programs, which are adequate for the required analysis, were selected and proved like "Gram" by Richard Horne [49]. Spectrums are used to analyze stationary signals and spectrograms when the signal varies during the time. Usually, the spectrograms show the signal's evolution in time in the superior part and in the bottom the components of the sound's frequencies in the axis of time (seconds) and frequencies (Hz). The level of the signal components (dB) is shown as the degree of black or color intensity of the graph.

About the spectral components of the frequencies, it was observed that the lowest sounds are generated without or with few weak harmonics and the high sounds include several overtones of certain intensity. In the following paragraphs we will concentrate in the analysis of more complex sounds that the clay-frogs can produce and are notably different from the performance and normal way of playing conventional wind musical instruments.

In the spectrogram 1 are shown the frequency components of the sounds from the whistle C-381 played in dual mode, in flat form and piano or soft (with a low pressure of excitation air). Two strong fundamental frequencies are present with some noise and weak harmonics. The sounds produce beats, even when playing the whistles in that simple way.

In the spectrogram 2 the frequencies' components of the short sounds of the same whistle C-381 are shown, played in dual mode and somewhat complex: uncovering the two tonal holes and very soft or low piano to imitate a little frog. It is seen that the pitch of the fundamental increases a little, no harmonics are generated and the signals in the time and frequency domains are similar but not equal.

The spectrogram 3 shows the frequency components of the short sounds of the whistle C-466 played in similar way to the previous one, dual and soft, imitating the frog. The two fundamental components are not well distinguished, there are no strong harmonics and differences exist in signals, in the time and frequency domains.

As it was expected, the two previous exercises show that the clay frogs can produce sounds similar to the natural frogs and the whistle C-381 is the one that can produce more complex sounds that can be detected audibly, because it has tonal holes and the difference in the volume of it's resonators.

It was seen that the clay frogs can produce other type of complex sounds like those generated by fast movement of the tongue to create cyclic variations in the amplitude of the sounds or "turulatos" sounds, as they are called by Guillermo Contreras, but the recordings came out defective, because they were obtained with the microphone at a very short distance and the signals were saturated and maximum values were clipped (spectrogram 4. However, it was possible to note that in such mode the sounds were strong and of some complexity.

In this stage, it was not possible to make some spectral comparison with the sounds of natural frogs, but it is possible that a great variety of sounds exists among frogs. It is possible that singing frogs still exist in Yaxchilán, because in the rural places where rains or water remains it is frequent to listen frogs sings. As an example, Angel Mendoza got a recording in a river at the edge of his home in Nican, Oaxaca, using a portable recorder (spectrogram 5).

Analysis with experimental replicas

Other important reasons for which it has not been possible to acoustically analyze the Mexican ancient aerophones are: a) due the administrative difficulties so they could be taken from museums to equipped laboratories; b) due to the difficulties to take metrology equipment into museums and c); lack of trained personnel, acoustical installation and equipment in museums. One way to alleviate this vicious cycle is to use experimental replicas.

An example. It was possible to make and take a replica of the singing frogs to the ESIME-IPN Acoustic Laboratory and with the aid of Sergio Beristain, a sonometer (Bueger & Kjaer, Type 2230, of reference level 1, with a microphone of the same reference level. The measurements were obtained at a distance of 1 m, at 0 degrees, in front of the microphone) and an educational anechoic chamber. The real sound pressure measurements and radiated power W calculation of several experimental aerophones were obtained (equations 3 & 4 in Excel format), to be able to make comparisons, which appear in Table 3.

I = (10^-12)*10^(dB/10)          (3)

W = 4*PI()*I                                (4)

Where,
dB = Sound presure measurement in dB
I = Sound intensity (Watt/m²)
W= Radiated power (Watt)

Table 3. Real sound presure (dB) and radiated acoustic power (W)

Aerophone, mode
dB
W
Yaxchilán frog, closed	67	0.0005
Yaxchilán frog, "turulato" open	73	0.003
Mayan whistle, closed	65	0.0005
Mexica flute M2, open	92	0.02
Olmec mouth whistle	104	0.3

It is seen that the obtained values for the Maya frogs are low if they are compared with others of higher sonorous power such as the Mexica little flute model M2 operated in open form which could be heard at a distance of 500 meters in Teotihuacan site or a louder Olmec mouth whistle. But the frog-whistles may be more powerful than other whistles like other Mayan and the Zapotecs possibly due to the irregular design of their sonorous mechanism and size.

This simple exercise also shows the usefulness to obtain sonic parameters. The sonorous power of an artifact is one of the most important parameters to determine their utilization, because allows to imagine its real coverage and possible utilization surroundings, as will be seen when analyzing the possible uses of Yaxchilán clay frogs.

With the replica it was possible to record a "turulato" sound, similar to the one of the natural frogs and to obtain in spectrograms with more clarity (spectrogram 6), where we see it's highest power than when it is played with flat notes.

Whistles' possible uses

It is impossible to know exactly and with certainty the old ways and uses of how the Yaxchilan's dual-whistles were played. But with certainty, whistles are not conventional musical instruments, because they cannot produce music similar to the contemporary.

It is possible that the ancient whistles could be used as toys, but the requirements for the good construction of the dual whistles and the Mayan culture indicate that if they were used as toys the "games" were not as those of a child.

Possibly, the whistles and their sounds, similar to those of the real frogs, were used in festivities and celebrations related to the rain god, in shaman rites or by the H-men. The inference of these possibilities was made considering the following evidences found in a first investigation in several associated fields, inside the context of the natural frogs, the Mayan and other Mexican cultures, Yaxchilán and its surroundings:

The frogs were directly associated with two fundamental aspects of great ancient cultures. Our ancestors lived by and for their gods and were nearly related and harmonically cohabit with their natural world. Amphibians were venerated and represented in the art of Ancient Mexico, like this toad on the mural of Cacaxtla [53].

In the ancient figurative art the representations of the rich fauna of the Maya zone, like jaguars, sakes, fish, turtles, armadillos, deer, alligators, frogs (like this tree frog) and many other species are very noticeable and impressing. These representations are evidence of the importance that the zoological surrounding in the old societies had. The frogs appear in diverse and multiple iconography and sculptoric representations and were very abundant in the shores of lakes and rivers. In several archaeological sites, representations of frogs still can be seen which survived the conquerors, colonizers and sackers destruction as well as the abandonment and the pass of time.

Relevant clues have been found which show the taste and veneration that the Maya had for these amphibians:

In the Yaxchilán site an important archaeological evidence was found related with frogs. Figures representing frogs are seen in the huipil, huipilli or k'ub of Lady Na Xok in the lintel 26 photo from Mesoweb by Teobert Maler [31]. The frog can be seen in the superior part of the Lintel, which was not damaged, between her arm and the back. Also, it is in the drawing by Peter Mathews in his book of Yaxchilán [51]. This beautiful lintel is one that escaped the foreign ransacking and was in exhibition at the Maya room of the Anthropology Museum in Mexico City, before it's closure for remodeling some years ago. It appears that those amphibious figures were used very much for decorating of textiles [32]. Some archaeologists say that the figures of the kúd of lady Na Xok are stylized flowers and other experts in iconography have not recognized them as frogs, but rural people who know frogs very well, say that they do look like frogs.

It is also relevant to know that the frog (zac) appears in the glyph of one of the 18 ulinales (months) of the 20 kinels (days) plus 5 wayels (days) at the end of the Maya calendar of 365 days (haab). The symbol of the 11th month is a frog, called in some references zac [33] and in others uo. Also, they call it constellation frog, night jaguar or jaguar of the infraworld, keep in mind that the jaguar is one of the most respected and venerated beings by the Mayas and the Maya calendar had much importance in their agriculture, daily life, ceremonies, festivities, religious and cosmos vision.

It is very important to note that a frog appears in the first breakthroughs in the extraordinary decipherment of the Maya hieroglyphs [34] which was realized by Tania Proskouriakoff [35] in the Pacal tomb, when finding the glyph in frog form (classified as T740) "birth", which she (and Erik Thompson) called "upended frog" for it's position. Also Linda Schele discovered other glyphs in frog form [32] in the Alfardas of the Sun's Great Temple in Palenque, which she called "touch earth" or "be born". Peter Mathews and Linda Schele recognize [37] the glyph that Tania found and it's meaning as the birth date of lords like Pacal T740.181:125 o 246 o 125(88). According to Tania [45] the "upended frog" glyph also appears in lintel 29 of Yaxchilán associated to the birth date of Bird-Jaguar (9.13.17.12.10) and in Shield - Jaguar II in lintel 13 (9.16.0.14.5 1) Chicchan 13 Pop. Also, it appears in several carved stones like in stele 3 at Piedras Negras, drawing from a book of Prof. Michael D. Coe [52], by the artist John Montgomery.

When carefully analyzing glyph T740, we see clearly that the animal is singing, it's head is in upright, in a singing position and it's mouth slightly open so the singing sound comes out by the two sides, as it is shown by Yaxchilan's clay frogs. The image of this glyph also indicates that the frog's singing comes out of it's mouth, because the glyph used to represent the voice, word or song is shown and comes out in the inferior part of it's moth, as it is shown with color in the glyph T740). It's ears are amplified, possibly to indicate that they amplify sounds, with some other signs still undesiphered. When frogs first come out from their auto-burial in subsoil or "are born" is when they can sing in our world. This analysis supports and reinforces the idea of "birth" associated to the glyph T740 and enrich it's meaning at the center of the Maya philosophical context. Now, the glyph T740 could be called "upended singing frog".

Some investigators say that the glyph T740 is an iguana [34] but the iguanas have a much longer body than the one shown in that glyph and do not sing up standing as the frogs. It is understandable that different interpretations exist for some Mayan glyphs, because they are not realistic representations. In general, the non-realistic representations are like mirrors, frequently when trying to interpret what they mean, more is said about what they think than what is in reality. The psychologists take advantage of that to know something about those who see stained drawings in the Roscharch's test. In that sense, what is relevant to glyph T740 is that the experts who were pioneers in the deep study of Maya culture, in it's context and in deciphering it's hieroglyphs, they associated that glyph to the frog's figure and the birth idea.

Today, the most clear and unquestionable evidences about the taste of the Yaxchilán Mayans for the singing frogs are the clay whistles themselves in the form of frogs.

In ancient Mexico's cultures, frogs and their sounds were directly associated with their most important gods of life like those of the rain and water. People who prefer to analyze and show the archaeology of war, death, blood, gold or jade, disregard the god of rain because it was the god of poor peasants, of the corn growers. It looks like that they have not realized its importance and usefulness to study ancient cultures. Many evidences exist about the relevance of the water gods and their relation with frogs and their sounds, among which the following stand.

It is said that of the twenty big celebrations in the mexica calendar [25], "five were dedicated to Tlaloc and its woman Chalchiutlicue (the one having skirt of green stones), which symbolized waving water, floods and rivers. During these celebrations the priests dived into the lake and imitated the movements and the croaking of frogs, with the intention to bring rain themselves". In the precinct of the ceremonial center at Tenochtitlan have been found several sculptural representations that show the veneration that mexicas had for the frogs, cueyatl or cuiyatl (pl. cuecueya). Some of them can be seen at the museum of the great temple and others in the exterior at the original placement.

Mayas believed that the uo or uoob (frogs) were companion of their rain god Chaac. According to remaining Maya peasants in the rural areas [26] "frogs call or ask for the fall of rain, for which it is believed that frogs are associated to Chaac's deities that produce rain emptying their pumpkins and their companion and act as rain enunciators."

In a written description about Maya lushes [27] toad chorus are mentioned imitated by children: "...afterwards, the prayers start, selecting four or six children who will represent frogs and toads, which are the messengers of the rain god. These children are tied with their hands on their back and are placed around and under the table. They start with a cry and later the (Ah)Men tells them how they are going to sing, imitating the sounds that the toads make and when all sing together is as if the toads reunited."

The Maya corn growers also make their Cha-Chaac [28] ceremony, which includes the children croaking, "The H-men (witch man) must match the works to see if they are doing well. Even the children can participate, as such (toads), which are going to croak so it rains, or like mountain birds imitating their croak. There will be zacá vessels under the trees, the ritual corn drink sweetened with honey. In other vessels will be the balché, sacred liquor made from the bark of the tree of the same name, fermented with water and honey for several days. Once the altar is finished, with logs a cross will be formed, the drinks will be brought up and the H-men will ignite the incense and will pray helped by the sacristan of the ceremony. The children will surround the altar and will croak in different ways. The ceremony lasts three days and three times a day zaca and balche is drunk."

The knowledge of ancestral ceremonies with frog songs has been mentioned also by the Chiapas Zapatistas natives [29] "if the rain does not show then we will have to place, ourselves, like our ancestors, in squatting position and sing like the frogs do before the rain, and agitate branches as if the storm's winds would hit them and some one will represent a Kunu-Chaac, the main rain god."

Every one that has been in a dense tropical forest like the Maya around the Usumacinta river has listened the impressive sounds of the multiple animals forming it's fauna. For sure that sonorous biological richness was greater in antiquity, the "symphonies" songs and chorus of night animals must have been very much listened, admired and imitated by our ancestors.

Even today, the lacandon jungle is abundant in it's frogs & toads fauna, even with the terrible destruction of its biosphere. In a SEMARNAP page [30] it informs "In the particular case of amphibians and reptiles we must point out that no political entity with similar dimensions has a faunistic diversity similar to the one of Mexico, which is 10.5 % of the amphibians and reptiles species of the world. At present, 77 species are registered for the lacandon jungle, belonging to 55 genera, grouped in 24 families of amphibians and reptiles. From these species, 23 are amphibious, however, it is considered that up until now only 65% of the potentially present species has been registered. The most numerous group is integrated by serpents with 28 species, the second is formed by frogs and toads with 21 species,"

According to the Mayas, during the night the spirits of divine beings (benigns and maligns) come up of the jungle. One of the most noticeable jungle choruses that are listened at night is from frogs. Besides frogs were considered beings from the underworld, possibly because during winter they bury themselves underground or in the mud looking for humidity and to resist the cold. Frogs come out in spring, when the sun and rain warms up the environment, resurgent life and songs from spring animals. For sure those frog chorus were more noticeable at the shore of a great river like the Usumacinta and in an abundant jungle, humid and warm, at less than 500m above sea level and with six months of heavy rain, like at the site at Yaxchilán. The characteristics of the terrain at the Yaxchilán site, a peninsula situated in an omega form surrounded by the most mighty river in Mexico and the longest in Central America with abundant residues of earth an sedimentary mud carried by the river and accumulated at it's shores for thousands of years, must have been a paradise for the proliferation of amphibians. Their biological nocturnal chorus must have been very impressing in contrast with the deep silence of the jungle.

It is not known the type of frogs that could have been the models in Yaxchilán but it is known that the sonorous chanting of the frogs are similar in variety to those of the singing birds. It is estimated that there are close to 3,000 different species of frogs and they produce different sounds with several purposes, such as calls to females, danger warning, etc.

The frogs stay quiet and in silence when there are strange sounds generated by humans, by their artifacts or celebrations. Therefore, if the Mayas wanted to include frog chorus in their festivities and celebrations to their god Chaac to ask for rain, they had to substitute the real frogs with similar chorus produced by humans or with their clay frogs. It has been seen that it is possible to produce sounds similar to those of natural frogs, generating "turulato" sounds, with the Yaxchilan's clay dual-whistles.

Frogs also are associated with fertility symbols and rites, possible because in a single season some species can produce tens of thousands of eggs.

As the sound produced by clay frogs could produce beats in the brain, it is possible that they had been used in shaman rites to generate special states of conscience possibly in closed spaces due to the low power of the artifacts and to be more efficient in closed or near fields.

It is not probable that the Yaxchilan's whistles, due to their low power, had been used in conjunction with other more sonorous Maya instruments like the ones shown in Bonampak murals, in big plazas or open spaces, unless they were played in big groups or sets at the same time. Small whistles are more sonorous but it is not known if there were smaller clay frogs.

Dual and multiple whistles are the most noticeable evidence that our ancestors liked to play whistles simultaneously to produce beats and interferences. It is difficult that they had been used to produce melodies.

The Small or West Acropolis of Yaxchilán is formed by thirteen structures and is located on a hill east of the main plaza. It's two relatively small plazas must have been an adequate place for the acoustic utilization of similar clay frogs, because they were surrounded by several edification or temples designed with numbers 42, 42, 44, 45, 46, 47, 48, 49, 50, 51, & 52. The great plaza of the Small Acropolis measures nearly 20 m x 40m. The characteristics of restricted complex away from the main ceremonial center, allows to suppose that in there it was possible to make ceremonies for a selected group. The closed quarters of temples and caves are also acoustically ideal to listen the clay frogs' chorus and aid in the realization of rites in reduced and selected groups of shamans or H-men priests.

Finally, some hypothesis can be made about the significance of the fact that the analyzed whistles were found in refilled sites and were not destroyed. The fact that they were placed in construction refills means that they were made and used before the construction of the Small Acropolis or in the stage previous to the Yaxchilan's full development or before the highest growth of it's population and the deterioration of it's biosphere, when the natural frogs must have been more abundant. The fact that the clay frogs were buried complete means that they are not trash or that they were not "killed" and buried as it happen in many other cases of ancient clay artifacts. Having placed the whistles among the refills of temples could be considered as a kind of offering to the gods venerated in that complex of buildings and/or as a way to venerate the natural frogs of that site. As the majority of these whistles were buried complete they could live and be played by the habitants of Yaxchilan's underworld and they were adequate to be used in the Labyrinth's rites or ceremonies.

To have discovered these whistles means, in a Maya sense, that they were reborn in our world, but their deep analysis allows us to truly rescue and recognize them or revive them in our reality.

Recommended activities for other stages

It is possible to realize additional studies to the same three clay-frog whistles and or to other of the same Yaxchilán lot, if interest exists with the necessary resources. Among the additional possible works, the following can be mentioned:

- Whistle C-466, it is necessary to perfecttly clean it's inside so a precise acoustic analysis can be made.

- Whistle C-405, it is recommendable to seee if it can be repaired so it can produce sounds and be analyzed in it's original form.

- Take conventional pictures for publicatioons in paper.

- X-ray the whistles, this is necessary to know the internal structure of the whistles and be able to make more precise experimental replicas.

- With the sounds of the original whistles as a reference, the replicas can be tested and calibrated precisely.

- Learning to make experimental replicas alllows to know the possible construction procedures of the whistles and show with pictures in detail the whole process, as it has been demonstrated in previous cases [12].

- It has been demonstrated that with repliccas or experimental clay models it is possible to analyze hypothesis that can not be done easily with original whistles like their performance in archaeological sites, in specialized laboratories and by flute players to see what sounds they can get.

- The analysis of whistles' materials is a study that requires the support of other specialists.

- If experts, installations and better recoording equipment are available, it is feasible to register the whistles' sounds with better quality, and if installations and special equipment (anechoic chamber, spectrum analyzers, etc.) are available, it is possible to realize other acoustic measurements.

- It is possible to realize exercises with Multimedia tools to store in CDs the records of pictures and sounds and to exemplify presentations of the artifacts in 360 degrees to help in their diffusion in virtual museums.

- Still, to analyze the archaeological infoormation available about the whistles, their detailed origin, their stratigraphic context and their exploration surroundings.

- It would be possible to record and analyzze the sounds of the Yaxchilan's natural frogs to make comparisons with the clay-frog-whistles.

- Also, it is possible to make the acousticcal experiments at original archaeological site.

- A relevant task is to investigate if therre are other Yaxchilán whistles in museums or collections and if there are similar whistles from other Mayan sites.

- The study result must be revised and publlished. It is recommended to distribute the study at least in the archaeological and acoustic media. Several possibilities have arisen to publicize the study in international congresses ⁵.

Notes.

1. In Internet there are very few sites with pictures of ancient whistles. One of them is about an exploration of objects found in caves [39], other is an international system of protection to cultural property [40]. It is noticeable the little information available in the web about Yaxchilán, even if that site has been investigated for more that a century. The web pages on that Mayan site have pictures [43]. Conaculta posted a miniguide for that site [50] . The literature about the Mayan culture is very extensive, but in a web search (http://www.amazon.com/) about Yaxchilán word only three books were found, the most recent is of Carolyn Elaine Tate [44] and the INAH publications store had one [45], edited by Roberto García y Daniel Juárez. The best analysis of the epigraphy of Yaxchilán is by Peter Mathews [51]. Yaxchilán is in the WMF List of 100 Most Endangered sites in 2002.

2. In the site [41] of the Peruvian National Museum of Archaeology, Anthropology and History it was informed that since two years ago they have been developing an investigation project about "Sounds of the past" to obtain the inventory, classification and sonorous registry of 700 prehispanic musical instruments. But they have not published detailed information about it's contents or results.

3. This study's work plan was formulated in September 2001 based in an index provided by mayist investigator Dr. Vera Tiesler Bloss.

4. The project was suggested by the archaeologist Jesus Ignacio Mora of INAH and by the interest of Daniel Juárez, archaeologist responsible of the related Yaxchilan's excavations, in which these whistles were discovered. The technical studies were left to members in charge of The Virtual Research Institute Tlapitzcalzin [1] Roberto Velázquez, Gonzalo Sánchez y Angel Mendoza.

5. A new short version of this essay was presented in the 1st Special Session on Acoustics of Ancient Sounding Instruments [48] to be included in the 1st International Joint Meeting: 9th Acoustic Mexican Congress (IMA), 144th Meeting of the Acoustic Society of America (ASA) and the 3rd Acoustics Iberoamerican Congress (FIA) in Cancun, Mexico in December 2-6, 2002.

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