Virtual Analysis of Maya Trumpets
Case 1. Hom-Tahs of Bonampak

The best and last reproduction of the Bonampak's mural, by BDP-Yale University (1)

Roberto Velázquez Cabrera
Virtual Research Institute Tlapitzcalzin

Consultation draft in process of refinement
First version: 12.19.9.5 5 or November 1, 2002
(584,283 correlation)
Last version: April 29, 2005
(Versión en Español)

A Power Point version was presented as a special contribution in the 1st Special Sessions on Ancient Sounding Artifacts of the First Pan-American/Iberian Meeting on Acoustics, Cancun, Mexico, 2-6 December 2002.

Other new short version was published in the Bulletin "La Pintura Mural Prehispánica en México". Instituto de Investigaciones Estéticas. UNAM. Year VIII. Num. 17. December 2002.

Introduction

This exercise is a virtual analysis of the Hom-Tahs 1 (gourd trumpets, horns, megaphones, cornetas, bocinas or sacabuches) painted in the very well known North Wall mural, Room 1, Structure 1 at Bonampak, Chiapas, Mexico. The famous and beautiful murals of Bonampak are considered one of the most important discoveries (1946) in Mesoamerica by the modern western culture, are the best frescos of Ancient America and had been studied from the point of view of many disciplines like archaeology, epigraphy, iconography, painting techniques, reconstruction, esthetics, dance, etc., mainly in the last decades (1, 2, 3 & 4). The history represented in the murals was deciphered and its events begin on 9.18.0.3.4 10 K'an 2 K'ayab in the Maya system or December 14, 790 b.C, 658 years before Leonardo de Vincy, at the time of the called Dark Age of Europe. The frescos were painted at the end of the splendor of the Bonampak reign, in the Late Classic period (800-850 a.C.). The murals of Bonampak have the best graphical representation of the Mayan classic sonorous instruments and their performers, which were the heart of many celebrations, rites, combats and other social events. Also, there are several explicit representations of sonorous artifacts in other murals, codices, carvings and ceramic artifacts like vases. Unfortunately, the rich ancient sonorous iconography is a matter for future systematic research. The great interest and main focus on the visual, monumental and temporary spaces of ancient cultures has prevented to explore the universe of their sounds. Many very fine, difficult and relevant works were realized in the last century with visual analysis, like the decipherment of Mayan hieroglyphic writing (24), calendar and numeric system, but the breakthrough of the Maya sounds code is waiting to be initiated. This paper shows that the available paintings, carvings and drawings with images of trumpets can be useful to explore the unknown Maya sounds.

The Maya master on musical/sonorous instruments/artifacts Ax Pax Chul disappeared from this world, as similar masters from other Mexican cultures like the Purepecha Curinguri and the Mexica (Aztec) Tlapitzcalzin. The last institutions interested in the Mexican organology and its music were the Mixcoacalli and the Cuicacalli, that were destroyed (1530 a.C.) along with tens of thousands of priests, temples, sculptures and codices, after the massacre (drawing by Armando Ramirez Nava, copy from Duran Codex) in the Great Temple Precinct of Tenotchtitlan (the sacred place where the two deities of the Mexica people: Huitzilopochtli and Tlaloc were worshipped) during the last Mexica song with their sacred instruments like the Huehuetl and the Teponaztli shown in the drawing, when "the dance was loveliest and when song was linked to song" the watching Spaniards rushed forward into the courtyard and slaughtered the celebrants who carried "nothing in their hands but flowers and feathers", according to Duran, in The History of the Indies of New Spain. First, the musicians were killed, then the dancers and the rest inside the Cuatepantli "Muro-Vibora" (Snake-Wall). The killers destroyed the Mexica sacred sonorous instruments, because "they were from the devil". After that, millions of indigenous from the rest of the continent were decapitated in the name of god and against the evil, in the interest of the invaders or were killed by the new pests.

In Mexico, the globalization, dependency and exploitation from the exterior were initiated since the XVI century with the force of weapons. The frontiers of Mexico were opened to all kind of policies, cultures, products, services, etc, but many doors to the rich Mexican past were closed. Up to now, in the practice, many ancient native arts and technologies are forbidden or excluded, even to be academically analyzed. The modern Mayas, their basic human rights and culture have been attacked by the paramilitary squadrons of the dead and the leaders of the right. The powers of the new nations have not represented the interests of the indigenous people.

The prohibition was stablished in the educational system of the new nations. For example, an MS thesis on Mexican aerophones could not be presented in any cultural and humanistic educational institution, because interested and qualified professors and available laboratories were not found. It could be presented in the Centro de Investigación en Computación (CIC) of the Instituto Politécnico Nacional (IPN), but it was necessary to expend five years convincing some revisers of the precedence of the new field of research and surpassing administrative procedures, because some technical specialists and administrators were not interested in the Mexican culture and technology and were opposed to accept the research as a thesis on computing. Finally, a letter to the President Vicente Fox was sent and the precedent was established, the first MS thesis on ancient aerophones was accepted on June 7, 2002, but in the actual context an advanced research on the same field and place is more difficult. The new proposed Law of the IPN ("Propuesta de Nueva Ley del IPN") of August 26, 2002, does not include the mexican culture in the educational objectives and programs. The moral is that new studies on ancient organology, like this one, only can be realized independent of the existing educational and research institutions, because the humanistics are not interested in the required technology and the technologists are not interested in the Mexican sonorous culture. The best system to present papers on this forbidden matter is Internet, because the only requirement is to learn how to do it and it is open to visitors from all the world.

The rich and millenarian Mexican organology and its music were matter of state and sound government, because they were promoted and used by all kind of authorities (religious, military and civil), but they were destroyed, forbidden, substituted and forgotten during and after the conquest, colonization, evangelization and inquisition, since more than five centuries ago. Unfortunately, similar policy was continued with effectiveness, in despite of the independence, the revolution and the orderings of the law (including the Constitution) to research and promote the Pre-Hispanic and indigenous cultures and the national technology.

Secrets of thousands of discovered and recovered sonorous artifacts that escaped the destruction, because they were underground, remain buried in storage rooms from many museums, collectors and explorations, which seem modern tombs. With very few exceptions, administrators and investigators related with the sonorous patrimony were not interested and are opposed to their formal research, even without any legal or technical justification. It is said that it is impossible to get something relevant in the analysis of the main utilitarian function of the ancient sonorous artifacts, as if modern human beings were deaf and formal acoustical techniques were not available. Western musical instruments had been scientifically analyzed since the beginning of the last century. Furthermore, formal analysis (19) and virtual reconstruction or simulation of European trumpets (20 & 21) exist in the literature, but Mexican ancient instruments like the trumpets are waiting to be deeply analyzed.

The ancient sonorous artifacts are highly appreciated and commercialized in the international markets of fine antiques, but they are not studied and published. The result is the same with the artifacts found by authorized explorations. The ancient organology found by authorized explorations and by sackers is not deeply analyzed in the open literature and the public do not know it.

The real opposition to formal studies on the ancient musical instruments is very strong by most of the administrators and regulators of the Mexican sonorous patrimony. For example, in the middle of the 1980s a contract was signed to study the musical instruments from the Museo Nacional de Antropología by the Instituto de Física, UNAM, but it was not realized because the researchers had not access to the ancient instruments. In last years, it was not permitted to have access to some clay sonorous artifacts from the museums of Mexico City, to apply the methodology of a thesis. The study of the ancient musical instruments is a monopoly assigned to the responsible of the explorations and the official researchers, but the formal studies on the found musical instruments are unknown, and the reports of many of those archaeological explorations are not published. For many sonorous artifacts found and stored in museums their exact origin is unknown, qualified interested experts and specialized areas on ancient organology were not found and the access to their few descriptive information, like their cedules, is restricted to the public because it is said that "they are confidential"!.

Some famous scholars were opposed to great Maya findings influenced by ideological factors, like Eric Thomson against the very important decipherment of Mayan glyphs by Yuri Valentinovich Knorosov and Tatiana Prouskouriakoff (24), but in the case of the opposition to study the ancient organology the enemy is unknown, apart of ignorance, laziness, envy, racism and ethnocentrism. Some studies are centered in the history of the elite and other try to explore the preterit way of living of common people, but the ancient organology was extensively used by rich and poor people and it has not been deeply analyzed.

It is said that the study of the Mexican organology is useless, because its exact original use or way of playing and its music were lost. But, similar situation exists in many archaeological sites and monuments, like the murals of Bonampak and their three Rooms. It is difficult to know their exact original use, but fortunately that fact did not prevented to develop in the last decades the long term projects to reproduce the beautiful paintings and to study their possible original techniques, like those admirable works realized by Diana Magalony and Tatiana Falcon (2), and the advanced works to reconstruct the murals by the BDP, directed by Mary Miller.

Experimental archaeology had been applied to ethnomusicology in a study (22) of an Ancient Maya Friction Drum from a vase (Kerr number K52332, MS Number 1720) through various lines of evidence from the literature. However, the techniques are not very useful to study Mayan trumpets, because the acoustical analysis was not reported and trumpets work in a very different way, but the Tigrero is a good example on ancient uses. Similar drums and their roars still are heard, in the South-East of Mexico to call the puma for hunting, and the Teconte in dances of The Devils in Santiago Collantes, Oaxaca.

There are many publications with photos of the mural of Bonampak (North Wall, Room 1) or its reproductions, but in most of them the organology was not the main interest, because the attention was centered in some personages like the animal-men, the iconography, the hoods, the masks, the dresses, the feathers, the composition, the decorations, the jewels, etc., but there are images of the trumpets to support the first analysis. Some photos are in small format and were amplified. (photo copyrights by the publishers).

Some years ago, Maria Teresa Uriarte Director of the IIE and Beatriz de la Fuente (when she was the Coordinator of the PMPM) informed that in the multidisciplinary technical team experts on Mexican instruments and their sounds were not included, because they were not found and those fields are very difficult, but it was recognized that they are very important to understand the Pre-Hispanic cultures. The result of that limitation is that in the beautiful publications of the Bonampak murals (2) the instruments painted in Room 1 were not analyzed, described or even listed in the cedule and the studies of that mural, as were included the dresses, the adornments, the jewels, the glyphs, the postures, the headdresses, etc. of the personages. This paper is a contribution to the Pre-Hispanic murals projects. It shows that it is possible to make use of the beautiful photos of the murals and their reproductions to study their trumpets shown so clearly.

The lack of interest on the ancient sonorous instruments and artifacts is a long and wide tradition in the archaeology and in the best literature on ancient cultures. Many beautiful Mayan whistles had been presented in museums, expositions and publications as "figurines" and only the iconography, dresses, adornments, jewels, etc. from their exterior were visually analyzed, like the Maya figurines analyzed by Linda Shelle in a publication with introduction of Piña Chan and many beautiful photos (31). Usually, the whistles are treated as any other clay artifact, and their main sonorous function is not explored, and in many cases it is not described.

The Mayan vases are a good example of the availability of other images of trumpets. The best public information system on circular vessels is the remarkable Kerr database from Famsi (21). In a search using the string "trumpet" 20 photos of Maya vases were available. Descriptive information and data are provided and in some of them short comments are included. For example, in the vase K594 (photos copyright by Justin Kerr2), MS number 1729 or Ratinlinxul Vase, the comment is: "In an article, The Last Journey, I explain that this is a dead individual being carried to his burial, accompanied by his throne cushion, dog messenger to the other world (bundle, way and trumpeters)". Justin Kerr believes that it is a funerary procession (23) and comments that the same vase was described in various ways: in the fourth edition of The Ancient Maya the noble is identified as a merchant and the three trumpets as canoe paddles!. There are not remarks on the trumpets or their sounds, but the Maya vases show the variety of their trumpets. The three trumpets from vase K594 have their own structure, shape, construction, dimension and they have embouchures and could be played at the same time.

A replica of ancient art is undervalued when it is called apocryphal, but in this case, the analysis must be virtual or indirect using replicas, because it is the only and best way to study the Hom-Tahs and other similar Maya trumpets of Bonampak. The few available evidences in the literature are very general to know how they could be made and played, like the words from a famous codex incendiary, Diego de Landa (15): "....and they have long and thin trumpets, of hollow sticks, and in their end long and wrongly gourds (rukuyultun?)...and their sound is lugubrious and sad". The comment could be applicable to the trumpets of Wall North of Room 3 (4) or figures 46, 47, 48 and 49 (2) and on some vases like the K594. It is difficult that the writers from the conquest and colonization could known the Hom-Tahs from Bonampak, because they were played and lost 800 years before the arrival of Columbus. But, the murals of Bonampak were discovered since the middle of last century and the modern literature does not provide studies on their sonorous artifacts like the trumpets. In the few available descriptions (20) the instruments are listed, in addition to a photo or drawing.

There is a booklet on musical instruments from the Mayas by Roberto Rivera (29), but its main object is the classification of some instruments derived from the Sachs-Hornbostel scheme. In relation to Maya trumpets the data provided is limited to the following codes: wood trumpets without embouchure 423.121.11 and with embouchure 423.121.12. Gourd, gourd-wood and clay trumpets are not included in the publication and Maya trumpets (other than conch sells) are not stored in museums. A short comment on the trumpets from Bonampak is included: "In the frescos of Bonampak it can be seen two trumpets but it is not clear if they have mouthpiece...".

The only known study about an important group of Mayan instruments is on 356 whistles by Felipe Flores and Lorenza Flores (36), mainly from the Jaina Island. It includes some organological data about the whistles, which gives a good idea of their dimensions and structural forms, but the analysis is not useful to study ancient sonorous artifacts, because it has several limitations and errors, which were commented in detail in a previous Virtual Analysis of Mayan Whistles, openly available (41).

The booklet and the study on Mayan whistles show with clarity the level of analysis and the usefulness of the few literature on Mayan organology. The personnel that had access to ancient Maya sonorous artifacts stored in museums did not have the knowledge and the tools to analyze them formally, systematically and acoustically.

The investigation about the Mayan organology just begins. A study is being conducted in Guatemala about 49 Maya instruments from the Popol Vuh museum (39), which have been analyzed by the ethnomusicologist Alfonso Arrivillaga Cortés, but the results will be published in a book. It could be relevant, because usually those with musical education are more interested in the music that still is played, recorded or written. It seems that trumpets still are played in Guatemala, but their studies were not found in the literature and those that subsist they are of brass 15.

There are images of trumpets in different structure, shape and dimension up to more that 2 m long like the one of vase K7613, but each known instrument must be analyzed as deeply as it is possible. The extraordinary reproductions of the mural of Bonampak can be useful to get relevant information and data to analyze the Hom-Tahs, because they are shown with realism and how they were played in a celebration. Now, the best way to make use and enhance the murals and their reproductions is analyzing their images not only to see their beauty and to know the represented history, personages, objects and glyphs, but to understand and recover the rest of the lost culture, like the art and the technology of their users, in this case, their organology and acoustics. The images from the murals and vases are better than any available description in the literature on Maya trumpets to be able to know their structure and millenary sonic secrets using models. The trumpets were very important in Bonampak, because they were painted on walls of the three Rooms.

The analysis is several times virtual, because Maya trumpets made on perishable material were lost, their images in the mural are deteriorated, and the available published photos of the reproductions of the mural are used to make experimental replicas and mathematical models to get the findings. The use of public images is the only way to realize independent studies on the Mexican organology, but it seems that the analysis is a difficult work for specialized detectives.

The main assumption of the analysis is that the copies of the trumpets in the mural and their reproductions were made accurately, which seems reasonable because the ancient and modern painters used their best art and techniques.

The music is the soul of people, but if the music of ancient cultures was lost, it is impossible to know directly the soul of their people. Also, their dances and singings were lost, which were part of the best music to honor their gods and very important, because ancient people lived by and for their gods. However, it is possible to know the ancient sounds, which is the soul of the music, with the analysis of discovered instruments or their replicas. Furthermore, it is possible to know the soul of instruments or artifact with the study of their sounding mechanisms that produces the sounds, which are the first cause of their creation, making and use not only in music, but in combats, communications and signaling, magic, healing, hunting, and many other applications. For example, the red trumpet painted in the upper register of Wall East, Room 2 of Bonampak (4) or figure 7 (2), decorated with bones (symbol of dead and killing), clearly shows that it was not for music or pleasure, but for battles or combats. In the same Room and combat there are other two trumpets used to fight (figures 8 and 35). It seems that they were used in the same way up to the conquest, because in several Spanish documents it is mentioned that the Mayas used trumpets and other instruments and sounds during their battles.

The paper tries to show that it is possible to get relevant finds on the ancient organology, even in this difficult case. The work was based on: a simple method applied to Mexican aerophones in previous studies, included in an MS thesis; data and information from the mural and its published copies; studies from similar trumpets from Australia (6 & 12); an experimental replica; speech theory (7); software for the visualization of signals (8); acoustical metrology; simple calculations; some experiments; a scanner and; information or tools from other disciplines.

Preliminary finds

It was necessary to estimate the approximate dimensions of the trumpets to be able to make use of mathematical and physical experimental models. The literature of the murals (2) provides detailed dimensions on the Structure 1 of Bonampak and its Rooms, but the dimensions of the natural beings and objects painted on the walls are missing. The human beings are the most important figures of the Bonampak frescos, but basic information on the painted people was not found like their real tallness and their musical instruments were ignored or evaded. However, several well known experts related with the murals and the Mayas kindly provided some data by e-mail to realize this first exercise: Mary Miller 3, the murals of Bonampak are 60% of the natural size, or a scaling factor of 1.666; Leticia Staines 4, the personages in murals of Rooms 1, 2 and 3 are between 80 cm and 95 cm or in reality nearly 133 cm and 158 cm of tallness; Vera Tiesler 5, the average ancient Maya male tallness was 160 cm.

The best and last reproduction of the murals from the DBP donated by Yale University could not be used to get more accurate measurements of the figures, because they are not available to the public in the Fototeca Nacional 6, as it was announced by Conaculta (32). Also, the published photos of the mural can not be used to get exact measurements, because the images are not very clear due to the deterioration of the frescos and the size of the available photos.

The estimation of the trumpets dimensions could not be exact, because their main reference, the known tallness for the Mayas is an average, the technical bases of the scaling factor estimation for the frescos are unknown, the size of the trumpeters and trumpets from the mural are not provided and there are differences in the dimensions of the painted figures between several reproductions of the frescos from Room 1. The only available size of the musicians from the mural is from the drummer, the player of the Zacatán, figure 56 from Room 1 (2), that it is equal to 63 cm. If 63 cm is multiplied by the scaling factor 1.666 his estimated natural tallness is 105 cm, which seems very small in relation to a good reference, the possible size of the Zacatán. Its natural size is unknown, but other similar ancient drums exist in museums and were studied and measured since the beginning of the last century. In 1930, Daniel Castañeda, the first engineer interested in the Mexican organology, realized the first study on Mexican percussion instruments (30). It was found that the Huehuetls are 80 cm - 100 cm high. For example, the Huehuetl of Malinalco (37) is 97 - 98 cm high (37). It means that the tallness of the player of the Zacatan must be more than 105 cm and the scaling factor more than 1.666, because the drummer is nearly 34 % bigger than his Zacatan. It is interesting to note that the study of some known Mexican instruments from the frescos could provide references to have better estimate of the scale of the mural and their figures and the possible real tallness of the personages and size of other figures presented in the murals like the unknown trumpets. This exercise shows that the detailed study of ancient organology is not only useful to explore the ancient sonic space, but to know more about the ancient people and their artifacts, which are main objectives of the archaeology and physical anthropology.

Other way to test the given scaling factor is with the estimated average size of the personages from the murals, which is 85 cm (2) or 141.6 cm (85 * 1.666) in the reality. It is very small, if it is compared with 160 cm, the average tallness of male Mayas, and even for their females, less than 150 cm, also estimated by Vera Tiesler. In the first exercise, the average tallness (160 cm) will be used as a reference for the trumpeters, because it is from real Mayan skeletons and it is congruent with the possible minimum size of the Zacatán. Using the first reproduction from Mary Miller (3), simple arithmetic proportions, a projector or Photoshop the dimension of the trumpets can be estimated. For example, if the projected image of the mural is adjusted to the reference size of the Maya trumpeters (160 cm), the external dimensions of the trumpets can be measured directly from the projected image or from the actual dimensions of the trumpets on the mural multiplied by 1.88 (160/85), or the average tallness of the Mayas / the average size of the personages on the mural. Then, the mural could be painted at 53.2 % (100 / 1.88) of the natural size. The length of the two trumpets was estimated in 100 - 101 cm and 104 - 105 cm, including a part of the feathers.

The previous estimations could be refined if it is possible to get the real sizes of the figures from the murals or from their best reproductions like those from the BDP, skeletons from Bonampak, better estimations of the tallness of the Bonampak people or the dimensions of the Zacatán. However, there are evidences that the given average natural tallness of the people painted on the murals could be larger that 160 m, because they were from the elite of Bonampak (rulers, priest, musicians, dancers, singers, martials, etc). Vera Tiesler informed that the skeletons from the Maya elite are larger that those of the average tallness of Mayan people. Some skeletons from Mayan rulers were found like those from the King Pakal, and his tallness was estimated in 165 cm by Arturo Romano, the only living anthropologist that found the Pakal tomb 50 years ago, and the tallness of the Red Queen is 154 cm, data provided by Vera Tiesler and published by Arnoldo González (34), archaeologist from Palenque. Also, the tallness of the musicians of Bonampak could be bigger if the size of the sacred Zacatán (112 cm using the scaling factor 53.2 %), was similar to the Panhuehuetl (that was bigger than the Huehuetl) a large hollow tree trunk drum, used in big ceremonies. The Tlapanhuehuetl was the largest of the tree trunk drums (250 cm), which was used to announce the combats and big ceremonies at long distances, up to 12 Km. If the average tallness of the people from the murals of Room 1 is 165 cm, the scale of the murals is 51.5% of the natural size and the Zacatán could be nearly 115 cm and the trumpets 3 or 4 cm larger than their previous estimation. The last numbers give an idea of the possible range of the natural dimensions and errors in their estimations.

The selected scale for the frescos indicates that the ceremony could not be realized inside the Room 1. One possible cause of the selected scale of the murals is the final wished size of the Structure 1 and its Rooms. A scale 1:1 could be very impressing, but it requires a structure two times bigger.

The inside diameter of the trumpets are difficult to know exactly, but it was determined as d1 = 3 cm, similar to the maximum diameter of trumpets from Australia like the didjeridu, didjeridoo or Yidaki 7 made of a branch of Eucalyptus hollowed by termites. And d2 = 13 cm (it is the diameter of the available material to be able to make experiments and comparisons), but it is different in the two trumpets and could be up to 20 - 25 cm, if the trumpets were made of a thin material like gourd.

Professor Neville Fletcher 7 found (5) that the didjeridu can be modeled (in passive acoustics) as a truncated conical trumpet of length L and provided the approximate expression 1 for the frequencies, that could be applied to the Hom-Tah, because its organological structure is similar:


Where, in this case:
Fn = frequency of mode n
L' = L + 0.3*d2
c = speed of sound in the air (38,000 cm/s, used in previous studies)
d1 = diameter at smaller end (3 cm)
d2 = diameter at larger end (13 cm)
L = length of the trumpets (L1 = 100 cm and L2 = 104 cm)

Making use of equation 1 and dimensions of the ideal trumpets it is possible to estimate their fundamental frequency F1, in nearly 144 Hz and 139 Hz (between a musical pitch of C#3 and D3, in the tempered scale with A4 = 440 Hz). It means that the tubes were not tuned or designed to a standard pitch, but to produce beats. In several ancient sonorous artifacts the exact pitch was not relevant, as it was the relation between the sounds and the ability to play other effects like micro tonalities, and, in several cases, to be tuned during the operation. The resulting beats or phantom sounds could be in the infrasonic band (less that 20 Hz: 144 Hz - 139 Hz = 5 Hz), if the two trumpets were played at the same time, as it is shown in the mural. In some cases, that feature is a distinction of ancient music, in relation to modern music, because now the beats are normally forbidden and very often they are called disharmonies. Studies from the point of view of modern musical analysis devaluate and misunderstand some ancient instruments, when they are not tuned, but it prevents to recognize the beats and other special acoustic characteristics as an aim on the design of ancient instruments and their use.

Phantom sounds can not be measured with metrology equipment; they are generated inside the human head and could be considered magic by their effects. It is known that infrasonic beats can produce special effects, like synesthesia, a psychedelic or superior state of conscience may be due to the physical vibration and excitation of neurons from the cortex of the brain. Infrasounds could be considered from the infraworld, because they can not be listen by normal human beings due to their F1 is below 20 Hz. Now, there are patented methods of sound healing to improve the mental and physical health of human beings using beats (9), but it is interesting that those effects could be known and used in the past, as it was found by Garret and Statnekov (42) in their paper on Peruvian Whistling Bottles.

It is possible to calculate the fundamental frequency of the same trumpets, if more accurate dimensions and scaling factor are available, and if other trumpets with different dimensions are analyzed, but all the parameters of equation 1 affect the pitch. It can be seen from the equation 1 that if L1 or d1 are risen or the difference d2-d1 is reduced, the pitch is lower. Also, it is possible to analyze hypothesis. For example, if d2 = 20 cm, F1 = 168 Hz and if d2 = 25 cm, F1 = 181 Hz, which could be the maximum pitch. A similar trumpet of L2 = 170 cm (like those of some Mayan vases) produces a F1 = 86 Hz (which is lower of the musical note F2), if other parameters of the equation remains unchanged. If the length of the two trumpets is 4 cm bigger (104 cm and 108 cm), their F1 is 139 Hz and 134 Hz and the resulting beat is maintained in 5 Hz. The beats may be audible (more that 20 Hz) if L1 = 100 cm (144 Hz) and L2 = or more than 117 cm (124 Hz). A big trumpet with d1 = 3 cm, d2 = 30 cm and L = 200 cm has a F1 = 100 Hz.

A mature and dry gourd called Lek or Home' (in Maya), guaje, bule, calabazo, gourd bottle or Lagenaria siceraria, family Cucurbitaceae (45) is the material selected to make the experimental replica. Lagenaria siceraria is a climbing vine and it was grown in several continents, but since thousands of years ago it was used to make the acocote (acocoti in Náhuatl) to extract the juice from the maguey to ferment the Mexican pulque and other containers. It was used to make many musical instruments: idiophones, aerophones, membranophones, chordophones, mixed and other, like the gourd rattles, maracas and guiros or scraper, trumpets, special ancient Mixtec wind instruments shown in Becker Codex (L. VIII), for wind bands in Chilacachapa, Guerrero (23) in the 1940s, drums, and to form the resonating chamber other artifacts. That gourd has similar size, shape, color and weight as the two trumpets shown in the mural of North Wall, Room 1, and it grows in all zones of Ancient Mexico. The original material of the Maya trumpets painted in the mural must be very light, because they are easily sustained with the hands and arms in the air without any other support to be played, and they could be carried in processions and sustained with one hand only like those of vase K7613, even the bigger one. There are trumpets and horns made of other material like wood or clay, but in big size they are heavy and to be played they must be rested on the floor or on a table, like the yidaki from Australia (48), Central Africa (49) and Perú (44). Some details were not considered in the experimental replica, because they are shown different in several available copies like those on the larger end of the trumpets that look like feathers.

This is the experimental replica on gourd, with dimensions L = 100 cm, d1 =3 cm and d2 = 13 cm. It was necessary to eliminate the seeds and to put the trumpet in water, more than two weeks to soften the gourd's skin to scrape away the offending matter with a knife and to remove the pithy material inside the gourd, and several hours in the sun light for its drying. The final material is hard, the thickness of the wall is 3 mm, the external surface is smooth and the interior is a little wrinkled. The final weight of the replica is very light 300 g (0.3 Kg). It means that some light trumpets (like those commented by Landa and from mural and vases) could be made with Lagenaria and light wood like the trumpet tree or Cecropia peltata (46 & 47). The curvature of the available tube does not affect the sounds, as it happens with instruments for wind bands. The main difference is the bell and its diameter, which could affect the sounds. For that reason and the estimated dimensions, the exercise is a first approximation and the numerical results could not be exact, but they are useful to get other relevant acoustical and organological findings. If the tube is not conical, the mathematical model is more complicated, but it could be modeled founded upon electronic analogies as a dissipative transmission-line (16).

The internal shape of the blowing end in the Hom-Tah is unknown, but seeing the trumpets of the mural it seems that the shape is similar to the Yidaki, which does not have an embouchure or filter cup. Usually, its blowing end is coated with a rim of resinous gum or beeswax to improve playing comfort and to make a good coupling with the player lips. The beeswax coating in the blowing end and the simple tube seem to be the main special organological characteristics and distinctions of those kind of trumpets, usually without pitch holes.

The experimental trumpet can produce flat notes with fundamental frequency under the bandwidth of 141 Hz and 144 Hz if the pressure of blowing is changed. The last pitch is equal to the F1 of L2 calculated with equation 1 and the lower is near to the F1 of L1. The range of sounds shows that those tubes were not made to produce one pitch only. It is very difficult to find two guajes of equal dimensions. Even with flat notes, (like this, in wav format) the produced sounds are lugubrious and sad, as was commented by Landa (15), but dull like the lowing or bellowing of a bull, ox or cow. There are evidences that those kind of sounds may have a especial effect in big animals like livestock. Big animals have a hearing more sensitive to low pitch sounds. Angel Mendoza informed that horns still are used in dances of the Rubios, as it can be seen in the photo of the caporal (Arturo Olivo Carrasco) and the Diablos (on their masks). A diablo dancing. Horns are played to call the livestock at Juxtlahuaca, from the Mixteca Baja, Oaxaca. Also, his father used horns to call the livestock flock during their long traveling from the coast of Oaxaca to the coast of Veracruz. The livestock can listen the horns up to 2 Km or 3 Km, in a line of view.

It is possible to see the sounds of the replica in the frequency domain, using software for the visualization of signals like the program by Richard Horne (9). This is the spectrogram of the signal of a pulsating sound generated with amplitude variations and the number of harmonics, that were produced changing the size of the vocal tract rising the tongue to constrict the vocal tract in a periodic way. The fundamental is powerful and there are several harmonics with considerable and variable magnitude (dB in colors) and a wide band of frequencies (Hz).

This is a complex signal generated with voiced and noisy sounds (that seems from other world). The signal shows similarities with the human speech and singing, but it is notable the enhancement of harmonics, filtering of the signal and great variations in pitch.

The selected range of dimensions of ancient trumpets is relevant because they can produce sounds in many sizes. It is pertinent to note that the calculated fundamental frequency of the two trumpets (144 - 139 Hz) is in the range of the frequency of the glottal excitation of voiced sounds from males (80 - 200 Hz), which could be the main cause of the trumpets size. In other words, those two trumpets and other similar trumpets (between 70 cm and 185 cm, if L1 = 3 cm and L2 = 13 cm) were designed and made to work very easy and very well with the glottal excitation of people, because their resonance is in similar pitch. Other possible cause of the selected dimensions of ancient trumpets is to facilitate the production of beats of low frequency, when they were played in groups due to the difficult to make two equal tubes of gourd or branches of trees. The trumpet can not produce melodies, because it does not have pitch holes but it can be used to speak and to play histories. The beeswax coating facilitates the lips vibration and production of sounds of F1 in a very easy way, even with very low pressure of air. The first mode is the best way of operation, if the long notes are required.

The superior modes are difficult to be produced and in that case the sound is loud and thunderous, but short, because it is necessary a larger volume of air and pressure due to a higher tension of the lips. The measured pitch of the mode 2 is 282 Hz (between C#4-D4) or exactly at an octave of the lower F1. The trumpet can produce many different sounds, some of them very complex in frequency components, timber and rhythms. The magnitude and richness of the harmonics mean that the sounds could be impressive, even if their pitch is not in the band of maximum hearing sensitivity of the human being (1 - 4 kHz).

Other great advantage of the use of experimental models is that it is possible to evaluate hypothesis:

The perceived acoustic power of the trumpet indicates that it was adequate to be used in Mayan bands, as it is shown in the mural, but it could be used in other kind of ceremonies and rites in open and closed spaces. In closed spaces, the effect in the people is very impressive. For example, the trumpet was tested in the Observatory of Xochicalco, Morelos and the sonorous effect was as expected and the experiment was successful, but the guard sent the researchers away.

When the trumpet was played in a closed room divided with screens, the sound was heard in several rooms of the same floor, because its low pitch and considerable power.

It is impossible to realize acoustic experiments in open spaces on the original situation at Bonampak, but last year similar trumpet and some Mexica whistles and flutes were tested in the main plazas of Teotihuacan's Sun, Moon and Quetzacoatl pyramids. The sounds were heard very well inside the plazas and up to 250 m, which means that those instruments and plazas could work acoustically very well together. But, recently (August 21, 2002), it was not possible to realize sound level measurements of the replica on the same plazas, because "it is forbidden to play musical instruments in Teotihuacan site"10. The experiment was prohibited without any known justification10. It is an example of the arbitrary actions to maintain "killed" and unknown the Mexican organology and its music, by those that have the legal obligation to research and promote them. In this matter, the modern native inquisitors are worst that those from the colonization.

However, some experiments on perceived acoustic power were made in the open field of the same zone, with the help of Gonzalo Sánchez11. The trumpet can be heard very well up to nearly 270 m (300 steps), even if the player and the listener were not in a line of view, with trees in between. Also, the trumpet was tested in a long grotto (~ 40 - 50 m) in the underground of the recreational park "Tlalocan" from the "Barrio Purificación", near Teotihuacan, with the permission of Ponciano, the land owner, because he liked the gourd trumpet and its sounds. The sounds could be transmitted and heard very well inside the irregular grotto and even in its exterior it was possible to listen sounds from the underworld, because the grotto has a hole to see the sun light like the Observatory from Xochicalco. The Maya trumpets were very effective to be used in rites or ceremonies in open fields, grottos and caves, because their sounds can be transmitted in irregular spaces and the natural physical obstacles do not stop the sonorous waves, due to their low pitch.

Those experiments indicate that the trumpets could be heard very well inside the plaza (~ 87 m x 110 m) of Bonampak, if they were played outside and in front of the Structure 1 or in any other place inside the plaza.

There are evidences that many archaeological plazas were well designed acoustically to transmit the sounds of ancient sonic artifacts and vice versa, ancient sonorous instruments were designed to function very well in ceremonial plazas. There are many acoustical secrets in the ceremonial spaces. For example, it is possible that the very special roof crest constructed on the Structure 1 and other structures of Bonampak and some Maya sites like Yaxchilán could produce sounds with the wind. Uli Wahl informs that in Europe there are aeolian whistles on the roof of some old buildings (48). Aaeolian whistles need an edge and a cavity as a resonator to produce sounds and it does not need a wind way because the wind in the air is laminar. The flow of the wind could be considerable to excite the possible aeolian whistles of the crest, because the Structure of the murals was constructed on a promontory and its front is oriented to the North-East, to use the air flows coming from the North or the East. Similar situation and orientation exist in structures with crests from other sites like Yaxchilán. The chorus produced by hundreds of big aeolian whistles exited and played by nature at the same time could be very loud and extraordinary.

It was possible to realize experiments with acoustic metrology equipment in the Laboratory from the ESIME, Instituto Politecnico Nacional (IPN), with the help of Sergio Beristain 12. Using the experimental replica operated in its first register and a professional sonometer or sound level meter it was found that the maximum sound pressure was 102 dB at 1 m and 0 degrees and 97 dB at 90 degrees. Using equations 2 and 3 (in Excel format), the equivalent radiated acoustic power was estimated in 0.2 and 0.06 Watts. In the upper register at 0 degrees the maximum sound pressure level was 108 dB or a radiated acoustic power of 0.8 Watts.

I = + (10 ^ - 12) * 10 ^ (dB / 10)            (2)

W = 4 * PI () * I                                      (3)

Where,
I = Sound intensity in W/m2
dB = Sound pressure from the sonometer in dB
PI() = 3.1416...
W = Radiated acoustic power in Watts

In the last experiments it was found that the power in the low mode is 650 mWatts at 90 degrees and the maximum power is 2 Watts, at the front, with an maximum average power of 1 Watt. The fundamental is of 140-143 Hz, with a great quantity of harmonics, up to 30, which has fluctuations in their level and timber, in function of the excitation. The graph shows the intensity of the main harmonicas in the low mode (Series 2 and 4) and in the second mode (Series 3 and 5). The most relevant is that main intensity in dBs is produced with the low pressure, which means that in the low mode the trumpet operates with the best efficiency (output radiated power/input air pressure).

As it was expected, the estimated radiated acoustic power is considerable to be heard in open and closed acoustic spaces and with good response in several degrees. It is difficult that those trumpets could be used for long distance communications or signaling, if they were not played in groups or in their upper mode. For that purpose it is necessary to have a higher radiated acoustic power and/or pitch (1-5 kHz). With the radiated acoustic power it is possible to make comparisons. Some modern brass wind instruments have a higher radiated acoustic power like the tuba (6 Watts). And sounds from whistles and small flutes can be heard at long distances, even if they have a lower acoustic power. A clay replica of a Mexica Tlapitzalzintli (little flute) from Templo Mayor Museum, with a power of 0.02 Watts and F1 of 1 - 3 Hz could be heard up to 500 m in Teotihuacan, from the top of the Moon Pyramid to the mural of Jaguar. The previous examples shows that each acoustic parameter of the instruments, like the radiated acoustic power and the pitch, can provide signs to find their possible ancient use and range of the sounds in the reality.

The mural shows that some instruments used to play rhythms, like the Tunkul or Teponaztli (in Náhuatl), three Boxel ac (conch turtle) and three pairs of Zoots (maracas) are not played, most of the dancer-animals are seated or resting and the rest of the K'ayomms 8 (musicians/singers) and personages of the ceremony seem very relax. It could mean that the produced sounds are not very loud and rhythmic, like those required to dance. It is like an interlude, but with sounds from the two Hom-Tahs, two pairs of Zoots, the Zacatán played with low acoustic power considering the image of the player's hands (he was a short person) and that at the same time he is talking with other K'ayomms. Also, a globular whistle is being operated and played with one hand in a very delicate and soft way.

The sounding mechanism is very complex and must be analyzed from the interior of the vocal tract of the player and the trumpet, because it is related with the speech system and its coupling with the resonating trumpet. This is a section of the vocal tract and the conical tube that shows the very special sounding mechanism. It can be analyzed and explained with signal analysis and speech techniques, physics theory and studies of similar trumpets. Experts on signal analysis had described the speech production anatomy, as a very complex system for the generation of sounds. For example, Dale E. Veeneman (7) provides a good description:

The best information on similar ancient trumpets came from experts on physics of musical instruments like Fletcher, Hollemberg, Smith & Wolf (6). In their last paper on the didjeridu or Yidaki include a general description that also could be applied to the Hom-Tahs:

Several relevant finds of their analysis that may be applied to the Hom-Tah, with small variations derived from the differences in dimensions and shape, are included. Some extracts of them, mainly related with the way of playing and the sounds produced are the following :

Also, the previous features could mean that many Mayan plosive words and phonemes can be spoken and sung with the trumpets in an impressive way. And sounds of animals, the nature and other beings from the Mayan world (and infraworld) could be produced very well by the performers and their trumpets, in addition to the musical drones. The sounds of the Hom-Tah could be related with those of animals, because in the mural it seems that the lobster-man is listening and following the sounds that are generated by the two trumpets. The group of animals-man with hoods and masks indicates that the music/sounds, dances and singings could be related with those animals and beings, as it was used in many other Mexican ancient dances with masks of tigers, snakes, deers, devils, birds, etc.

A fully integrated mathematical model for the coupled system between the vocal tract and the tube still is in development by experts 7 in the didjeridu (12). This is a diagram of the speech-trumpet system that shows the possible elements of a digital model, considering studies from experts on speech (7) and on physics of trumpets (11) to give a general idea of the possible required broad modules of the basic system. It seems that the real system could be more complex, when those trumpets are operated by a skilled player.

It was possible to analyze some hypothesis, like the effect of an embouchure in the tube, but they could not be exact because it is difficult to know its exact shape, surface, dimension and material (wood, bone, clay, etc.). In general, as the cup is a filter, the sound is more clean with less noise, and if its dimensions are reduced (like the internal diameter), the pitch in higher, strident and rich in harmonics. Those effect are well known, because many embouchures were designed to be used in modern wind musical instruments, like those of brass bands and many trumpets and horns.

However, Prof. Fletcher commented 5 that the embouchures of some Maya trumpets (like those of vase K594) do not appear to be a mouthpiece cup, as in modern brass instruments, but rather just supports for the lips. It is possible to analyze that relevant observation on the sounding mechanism of the Maya trumpet, because there are some images of ancient sacred conch shell trumpets that show the embouchures with more clarity, like those of The House of Butterflies or The Palace of Jaguars at Teotihuacan. Two Quetzalteccitli (divine conch shells) are carved on the wall and other is in a photo of the mural with a jaguar that "holds in one paw a snail-trumpet decorated with long tail feathers of exotic quetzal bird playing the shell trumpet", according to the plaque in the courtyard. It seems that the embouchure of those conch shells trumpets is a circular tube, but the shape of the interior cavity of the tube is not shown.

Ten clay artifact (4-7 cm high) of unknown use were found by Alfonzo Medellin (28) in Vertedero excavation from the Totonacan zone seem to be very similar to clay embouchures for trumpets. Then, Prof. Fletcher could be right, because it seems, from the photo, that the interior of the tube has a constant circular section, different than a mouthpiece cup for modern wind brass instruments and too big to be an ancient earflap or earmuff, usually made in hard stones. The consequence of that finding is very important, because the uncertainty of the internal shape of the embouchure it may be eliminated and the methods and mathematical models applied to the didjeridu and the Hom-Tah can be applied to images of other Maya trumpets from the murals of Bonampak and vases. In other words, the breakthrough of the Maya trumpets' sounds code already began. It is possible to recreate, study and reuse the Maya trumpets and their sounds that were generated and listened before 1200 years ago.

In the unknown Mexican sonorous universe there are endless possibilities to explore hypothesis, even without the help of balche (Maya drink), peyote (divine cactus) or the master Ah Pax Chul. For example, this is a short (60 cm) trumpet of gourd and a Mexican noise generator decorated with a mono saraguato. This is the resulting noisy sound, very adequate to be used in secret rites of H-men, shamans, healing, magic or funerary. Its sound is frightful or hair-raising, if it is played in closed spaces like caves or in the darkness. Similar noisy artifacts were made and used by several Mexican cultures, like Olmec, Maya, Mexica, Totonaca, etc., but they are not registered in the known iconography and literature on open ceremonies. A small model on clay of this type can produce real sounds of dead, like the sound of a pig when is been killed. Several members of this family generate sounds of animals that were abundant in the Maya jungle. The example again shows that simple ancient trumpets coupled to complex ancient aerophones can produce very complex sounds of unknown uses and effects. These noisy artifacts will be analyzed in other paper, but the deep analysis of each member of this family of Mexican sonorous artifacts could be matter of advanced research, because the techniques to analyze their sounding mechanism is in the frontier of several fields as scientific visualization and simulation of chaotic systems.

Conclusions and recommendations for future works

  1. The extraordinary studies and acoustical findings on the didgiridu are useful to analyze the Hom-Tah. It is possible to study other ancient trumpets with similar methods and findings, from the mural of Bonampak and from vases. Also, the speech and signal analysis tools can be useful in these cases.

  2. From a dynamic mathematical model of the system vocal tract-trumpet it is possible to generate syntactical sounds for experimentation and multiple applications. As in voice processing there is syntactical voice, it is possible to open a new discipline called SYNTACTICAL ANCIENT SOUNDS.

  3. It seems that the Yidaki, the Hom-Tah and similar ancient trumpets were designed to be easily coupled with the vocal mechanism of the people and the pitch of their basic sounds. These cases show that simple sonorous artifacts can produce a very wide range of acoustical possibilities, if they are coupled with the human tract and played in an ancient way as many other Mexican aerophones like the Yaxchilan's clay frogs (18) and Olmec whistle on black stone (ilmenite) that has very special sonic properties. Some years ago, more than 4.5 ton or 140,000 similar Olmec multi-drilled little stones were found in San Lorenzo Tenochtitlan by Ann Cyphers (40) and Michael D. Coe and Richard A. Diehl reported (41) the first finding of similar artifacts in the 60s, but the sonorous function of the black stones was not known.

  4. Hom-Tahs could produce complex signals, some of them very well related with biological sounds like from people and animals from the Maya jungle, as well from the underworld, a notable characteristic and distinction of music from some great ancient cultures.

  5. With the aid of experimental trumpets and acoustical metrology other measurements could be made, like impedance, etc. to know more their acoustical characteristics, as well as experiments with human beings.

  6. Other known instruments painted in the mural could be analyzed, but more accurate scaling factor of the mural or the tallness of ancient Mayas will be necessary.

  7. The sounds from experimental replicas or dynamic mathematical models could be used to make more realist the analog or digital visual representations of the mural of Bonampak (4) to make a better simulation of the ancient history of Bonampak, in virtual museums, representations and performances 9, because it is impossible to imagine its real combats and ceremonies in silence.

  8. Finally, there is a question about the possible relation between the special infrasounds effects in the cortex of the brain and the special oblique head shaping (10) and geometry (in the cortex) widely practiced in the pre-Hispanic time by the Mayans as it is shown in the mural of Bonampak and in diverse human figures on rock carvings of that zone. It could create a line of investigation for the new field of research ARCHAEOLOGY OF PEOPLE (as it is called by Vera Tiesler) and for other new field of research: ARCHAEOLOGY OF SOUNDS, ANCIENT ACOUSTICS or Sounding Instruments and Pre-Columbian Sounding Instruments Sessions, which already were included in the First Pan-American/Iberian Meeting on Acoustics, in Maya land. It is the first time in the history that the experts on acoustics had the opportunity to know about the organology of Ancient Mexico through a very narrow window of few papers and sounds of ancient instruments and experimental replicas like the trumpet of Bonampak and similar instruments from other zones like the Ancient Celtic Horns by Murray Campbell16, Professor of Musical Acoustics, Department of Physics and Astronomy, University of Edinburgh. Also, the first formal analysis on Mayan whistles was presented. Its Lay Language Paper Yaxchilan's Whistles (Clay Frogs) is posted in the Acoustical Society of America World Wide Press Room.

New works (in Spanish)

    Some death whistles with craniums as resonators were made, including a aerophone with a mayan deformed cranium. It was found that they works very fine to generate chaos and noise of ancient unknown exact use.

    It was found that the branches of the cecropiaceas are very good to make mayan trumpets of wood Hom-Kooché.

    A maya trumpet model of a branch of the cecropiaceas and a guaje Hom_Kooche_Tah was made and analized (in Spanish).

    Maya trumpets models of quiote de maguey (agave) Incus_Utop_Chek were analized (in Spanish).

It means that now it is possible to analyze experimental models of all the maya trumpets that are shown in the ancient iconography.

Notes and relevant remarks from experts

The consultation draft was posted in several forums and some related experts and organizations13 & 14 were informed. Several pertinent remarks were obtained and included in the text.

  1. Pablo Castellanos in his book (15), gives some musical terms of the Nahuas and Mayas, including the Hom as trumpet and other ceremonial instruments like those of Bonampak. Luis Perez Ixonestli informs that Mayan gourd trumpets were called Hom-Tahs. In other references the Maya trumpet is called Hub' and the globular Lagenaria siceraria is Lek, Lec or Homa'. Gourd trumpet could be called Hom or Homa'. But Hom has different meanings. In the John Mongomery´s dictionary from Famsi (38) there are other meanings for the glyph HOM like T218 "to end", T672 "to trow down" or "to destroy", but the only trumpet included is JUB´ T579v, "shell" or "shell trumpet". The Maya glyphs of gourd trumpets are unknown, but their images were painted in the frescos of Bonampak and they can "speak" like the glyphs, but with real sounds.

  2. Justin Kerr. Mayanists, photographer, expert in vases. He participated in the Bonampak Documentation Project and gave permission to use images from his remarkable Database (22), included a link to the article in his web page with open studies on Maya vases, and he commented that the flat sound from the replica is almost identical to the sound of a ceramic trumpet from Veracruz. The Kerr's database is an extraordinary example to make openly available to the public the images and data of found ancient artifacts, which contrasts with the absence of similar official information systems.

  3. Mary Miller. The Vincent Scully Professor of History of Art at Yale University. Director of the Bonampak Documentation Project (BDP). Miller produced the first digital reproduction on the murals of Bonampak with Adobe Photoshop and she commented that:

    • She has been reading the work with interest;
    • She recommended to visit the Kerr Database to study the Maya trumpets;
    • A vase from Australia shows that the feathers can be used to mute the horns;
    • The paintings are probably range from 1/2 to 2/3 life size, so 53% would be reasonable, but not all the walls have the same precise scale -- for example, the family in the throne in Room 1 is a little too small for the rest of the figures in that Room;
    • They say that the BDP reconstructions were painted at 50%, but they are technically 49.5%, and;
    • The Room 1, as reconstructed, will be put on display in New Haven.

    If it is possible to get the requested copies of the BDP reproductions of the Bonampak musicians, it will be possible to refine this exercises.

  4. Leticia Staines. Researcher of the IIE (Instituto de Investigaciones Estéticas), UNAM (Universidad Nacional Autónoma de México) and expert in Mexican art and murals. Vice-Director of the project "La Pintura Mural Prehispánica en México" (PMPM) and Editor of its bianual Bulletin. A set of the Bulletin was provided and a new short version of this paper in Spanish was published in the number 17 of December 2002. The exercise could be improved if it is possible to make use of better digital reproductions of the murals from the PMPM, that were requested.

  5. Vera Tiesler (10),. Prof. and researcher at the Universidad Autónoma de (UAY), Mérida, Mexico. Mayanists, expert in Mayan bones, head shaping, dental decoration, skeletons, osteology or "esquelética", a new field that will be included in postgraduate courses in the UAY. Tiesler provided relevant data on the size of Maya skeletons:

    • Average size of the skeletons of ancient male Maya is 160 cm and female less than 150 cm.
    • The skeletons of the Maya elite are larger than the average.
    • The skeleton of the Red Queen from Palenque is 154 cm.

    Tiesler commented that the paper is interesting and in the Mayan zone of the Usumacinta river the oblique head shaping is more notable.

  6. A search was necessary to know where the BDP reproductions are stored (or buried). In the office of the Sistema Nacional de Fototecas (SINAFO) at Mexico City it was informed that they do not have the pictures and the original material donated by Yale University (on May 15, 2002) could be in the central office at Pachuca City. Rosa Casanova García, Directora of SINAFO, informed that the BDP´s reproductions are in the Museo Nacional de Antropología (MNA). An e-mail was sent to the Director of the MNA, Felipe Solis, to ask for permission to get the measurements of the trumpets, because the Secretario Técnico informed that it is a requisite. The request could not be delivered, because the MNA e-mail (museo@internet.com.mx and atencion.mna@inah.gob.mx) published in the MNA and INAH web sites are out of order. It will be a waste of time to send a letter, because previous requests to the MNA were not answered. The MNA has the biggest modern tomb of ancient sonorous artifacts with tens of thousands of other archaeological goods. The MNA reproduction of the Structure 1 and the murals of Bonampak could not be analyzed, because the last two years the Maya (and Gulf Coast) Halls have been closed to the public.

  7. Neville H. Fletcher. Prof. of the Research School of Physical Sciences and Engineering, Australian National University. Expert in acoustics of musical instruments. He is co-author (with Thomas Rossing) of one of the best and most complete formal books on the physics of musical instruments (11) and he is the responsible of Musical Acoustics for the Journal of Acoustical Society of America. The studies on the didjeridu are very important for the ancient organology, because it is the only ancient aerophone that is subject of research in departments of physics of several universities (12) and their findings will support the understanding of similar trumpets from other preterit cultures from Africa and América like the Maya. Prof. Fletcher sent an e-mail with fine words and additional information and data on the didgeridu and its unique research:

    Dear Roberto

    I have now had a chance to read your paper on Mayan horns. Very interesting. It seems that instruments somewhat like the didjeridu may have been fairly widespread in ancient cultures, and presumably the size and shape was determined by what was naturally available. In the case, the fact that termites ate the inner parts of many small tree trunks meant that gently flaring tubes up to 1.5 or 2 meters in length were readily available in that part of Northern Australia. Incidentally, while most didjeridus flare from about 20 or 30 mm diameter at the blowing end to about 50 mm at the open end, some of them remain about 30 mm along their entire length, while others flare to as much as 100 mm.

    Your idea of recreating ancient instruments based upon old paintings and drawings is a very good one. I don't think you actually mention how old the paintings are, which would be interesting to know. It is fortunate that the instruments were shown so clearly --- I expect they were considered really important to the ceremony. You mention mouthpieces on the horns in Figure 2 (vase K594), and indeed they are clearly evident. From what I can see of them, however, they do not appear to be mouthpiece cups, as in modern brass instruments, but rather just supports for the lips.

    We are continuing with our study of the didjeridu, both experimental and theoretical, and I hope we will have something to report in the literature by the end of this year.

    Best wishes with your study.

    Neville
    _____________________________________________________

    Prof. Neville H. Fletcher
    Department of Electronic Materials Engineering
    Research School of Physical Sciences and Engineering
    Australian National University
    Canberra 0200, Australia
    _____________________________________________________

  8. Stephen D. Houston, Mayanists and expert in glyphs from Brigham Youth University, in his paper on "Cantantes y Danzantes de Bonampak", published in the reference (4) PP 54 and 55, remarks on glyphs from the mural of Bonampak about the k´ayoom (who sings) and its relation with the virgule of the world, and the ch´ok (young dancers) related with their dresses or singings of the k´uk (quetzals).

  9. Julia Sanchez, Chair, Music Archaeology Study Group, ICTM, Assistant Director, The Cotsen Institute of Archaeology and expert in Maya monumental art at UCLA and Archaeology of Performance among the Ancient Maya (26) recommended to use trumpets instead of horns, because most of the ethnohistoric Spanish documents translate them as "wood trumpets" and commented that "the paper is fascinating.... and it's wonderful to know that people with detailed knowledge of acoustics are beginning to study the ancient instruments".

  10. The INAH's guard/porter said that the prohibition to go into the site with the trumpet was from the "Director de la Zona Arqueologica" (Arturo Zarate Ramírez), but he was not in his office to ask for a permit to realize the acoustic experiment. The responsible of that office was the "Jefe del Depto. de Mantenimiento" (David Ibarra Vega), unfortunately he confirmed that "it is forbidden to play musical instruments in the archaeological site", but he could not provide the requested permit and the legal or technical justification for the negation, even for an accredited academic work. In that zone there is a Centro de Estudios Teotihuacanos and its responsible (Jesús Torres Peralta) kindly tried to provide help to realize the experiment with the trumpet, but the negation subsisted. That prohibition is irregular, arbitrary and disastrous for the Mexican organology. There is a library in that Center, but reports or books on many clay musical instruments found in that important archaeological zone are not included. Similar situation exists in other zones and archaeological sites.

  11. Gonzalo Sánchez, student of ethnomusicology, Escuela Nacional de Música, UNAM, member of the Virtual Research Institute Tlapitzacalzin. He is studding and posted some papers on zapotec instruments.

  12. Sergio Beristain, MSc, is lecturer at the ESIME, IPN and President of the "Instituto Mexicano de Acustica" (IMA). IMA is the only Mexican professional association interested on Mexican ancient acoustics and instruments. They realized and included conferences on that matters in their two recent annual international congresses and proposed to include that new field of research in the First Pan-American/Iberian Meeting on Acoustics at Cancun. The "Centro de Investigación en Computación", from the same IPN, provided the required computers, scanner and the use of the network for the digital works.

  13. Getty Institute13, one on the organizations that provided financial support to develop the BDP at Yale Yniversity14, welcomed the consultation draft.

  14. It was difficult to find good images to take more accurate measurements of the trumpets and the musicians, because original reproductions are also restricted to the public. Images from the murals of Bonampak can be provide by eographic Image Collection (http://storysys.ngs.org/yearofpub/1995/bonampak.htm) but the rate is too expensive for an independent project. NGS also provided financial support to develop the BDP at Yale University.

  15. Alfonso Arrivillaga infomed that in the Rabinal Achi, a pre-Columbian drama that even dance, is accompanied by trumpets, but these are of brass and they seem of an European type. Between the K'ich'e of Totonicapa, also they accustom a long trumpet of brass, with reeds of cane like the used ones in chirimias. In old stories it is mentioned that the trumpets were of wood.

  16. Prof. Murray Cambel has been studing the sounding mechanism of trumpets, horns and cornets in the University of Edimburgh's Acoustic Group (54). He said (57) that "the physics of brass instruments are not well understood. You´d be surprised how little is known about the relatinship between a brass player does with their lips, what the instrument tries to do and the note that actually comes out". His last studies include ancient Celtic Horns. Some beautiful photos of iron and bronze horns of Scotland, Ireland and England are posted and commented in the Web site PREHISTORIC MUSIC IRELAND(59).
Refereces The links (URLs) were used in 2002

  1. Miller, Mary Ellen, (1986) "The murals of Bonampak" Princeton University Press.(http://www.yale.edu/bonampak/references.html)
  2. De la Fuente, Beatriz and Staines, Leticia, (2001) "La Pintura Mural Prehispánica en México, II Area Maya, Vol. I Catálogo y II Estudios. Instituto de Investigaciones Estéticas, UNAM, Mexico.(http://www.esteticas.unam.mx/)
  3. Miller, Mary, (1995), "Bonampak" Revista Arqueología Mexicana, Vol. III, Núm. 16 (nov.-dic), pp. 48-55.
  4. Miller, Mary, (2002), "Reconstrucción de los Murales de Bonampak" Revista Arqueología Mexicana, Vol X, Núm. 55 (mayo-junio), pp. 44-55.
  5. Fletcher, N. H. (1996) "The didjeridu (didjeridoo)" Acoustics Australia, 24, pp. 11-15. (http://www.phys.unsw.edu.au/~jw/dij/dij.html)
  6. Fletcher, N., Hollenberg, L., Smith, J., and Wolf, J. (2001) "The didjeridu and the vocal tract" Proc. International Symposium on Musical Acoustics, Perugia. D. Bonzi, D. Gonzalez, D. Stancial, eds, pp. 87-90. (http://www.phys.unsw.edu.au/~jw/ISMAdidjpaper.pdf)
  7. Veeneman E. Dale, "Speech Signal Analysis", included in the book edited by Chen, C.H. Signal procesing habdbook. Ed. Marcel Dekker, Chapter IV pp. 511-549
  8. Horne, Richard, Spectrogram V 5.0.9, Shareware (http://www.visualizationsoftware.com/gram.html)
  9. Monroe Institute (http://www.monroeinstitute.org/research/index.html)
  10. Tiesler, Vera, (1999) "Head Shaping and Dental Decoration Among the Ancient Maya: Archaeological and Cultural Aspects". Paper presented in the 64 Meeting of the Society of American Archaeology, Chicago.(http://www.mesoweb.com/features/tiesler/)
  11. N. H. Fletcher and T.D. Rossing, (1991) "The Physics of Musical Instruments" Spring-Verlag, New York.
  12. Hollemberg, Lloyd. "Didjeridu acoustics" Dept of Physics, University of South Wales, Sydney, Australia. (http://www.unsw.edu.au)/~jw/didjeridu.html
  13. Castellanos, Pablo, (1970) "Horizontes de la Música Precortesiana", Presencia en México, 14, Fondo de Cultura Económica, Mexico. P 90.
  14. Precolumbian instruments. (http://auralia.com/auralia/ixoneztli/pages/instrum.htm)
  15. Landa, Diego, (1936) "Relacion de las cosas de Yucatán" Introducción y notas de Hector Pérez Martínez, De. Porrua. P. 109. Tambien en Edición XI (1978) con Introducción de Angel M. Garibay. P. 38.
  16. Rodet, X. And Verguez, C. "Physical Models of Trumpets-like Instruments Detailed Behavior and Model Improvements" (http://www.ircam.fr/equipes/analyse- synthese/listePublications/articlesRodet/ICMC96NLO/ICMC96NLO.HTML/index -e.html)
  17. Simulation of Brass Instruments (http://iwk.mdw.ac.at/Forschung/english/simulation/simulation.htm)
  18. Tronchin, L & Cocchi A. "Virtual Reconstruction of trumpet" (http://www.ciarm.ing.unibo.it/researches/trumpet)
  19. Donahue, J. "Applying Experimental Archaeology to Ethnomusicology: Recreating an Ancient Maya Friction Drum through Various Lines of Evidence" (http://www.famsi.org/mayavase/jkarticles/friction_drum/friction_drum.htm)
  20. Martí, Samuel, "Instrumentos musicales precortesianos", INAH, 1968. PP 68-a.
  21. Martí, Samuel, "Canto, danza y música prehispánica" FCE, 1961. P 50.
  22. Kerr, Justin, Maya Vase Archives. (http://famsi.saiph.com:9500/dataSpark/maya/)
  23. Kerr, Justin. The last Journey (http://www.mayavase.com/jour/journey.html)
  24. Coe, D. Michael, (1994) "Breaking the Maya Code". Duke University Press.
  25. Kerr, Justin, Open articles on maya vases (http://www.mayavase.com/articleopen.html)
  26. Sanchez, Julia. "Studying the Archaeology of Performance among the Ancient Maya" (http://www.sscnet.ucla.edu/ioa/pubs/backdirt/fall01/julia.html)
  27. Mesoamerican Photo Archives (http://www.mesoamerican- archives.com)
  28. Medellin, Z. Alfonzo, (1987) "Napiloa. Exploraciòn Arqueològica", Universidad Veracruzana.
  29. Rivera, Roberto, (1980) "Los instrumentos musicales de los Mayas" INAH.
  30. Castañeda, Daniel y Mendoza, Vicente, (1933) "Tomo1. Intrumental Precortesiano. Instrumentos de Percusión" Conservatorio Nacional de Música. Reedición de 1991, UNAM.
  31. Schelle, Linda. (1997), "Rostros ocultos de los Mayas". Impetus Communications.
  32. El Universal (http://www.el- universal.com.mx/pls/impreso/version_imprimir?id_nota=23116&tabla=cultura_ H)
  33. Hueuetl de malinalco (http://www.humanities- interactive.org/splendors/ex048_08g.html)
  34. Mesoweb. Reina Roja (http://www.mesoweb.com/palenque/features/reina_roja/11.html)
  35. Villagra, Agustín. (1949), Bonampak, la ciudad de los muros pintados, INAH, SEP, (Suplemento al tomo III de los Anales del INAH).
  36. Flores-Dorantes, Felipe y Flores-gGarcia, Lorenza, (1981) "Organología Aplicada a Instrumentos Prehispánicos. Silbatas Mayas", INAH, MNA, Coleccioón Científica, Arqueología, Instrumentos Musicales Prehispánicos. Mexico.
  37. Announcement from Conaculta (http://www.conaculta.gob.mx/saladeprensa/2002/16may/murales.htm)
  38. Dictionary of John Montgomery (http://www.famsi.org/montgomery/dictionary/index.html)
  39. Popol Vuh (http://www.popolvuh.ufm.edu.gt/Vocesmayas.htm).
  40. Cyphers, Ann and di Castro, Anna, 1966 "Los artefactos multiperforados de ilmenita en San Lorenzo", Arqueología, Revista de la Coordinación Nacional de Arqueología del INAH/Segunda época, 16, Julio-diciembre.
  41. Michael D. Coe and Richard A. Diehl, (1980) In the Land of the Olmec, two volumes plus maps. Volume I, The Archaeology of San Lorenzo Tenochtitlan, 416 pp.; Volume II, The People of the River, 198 pp. The University of Texas Press, Austin, Texas.
  42. Garret, S and Statnekov, D. (1977). "Peruvian Whistleing Bottles", The Journal of Acoustical Society of America, Vol.62. No. 2. August. (http://www.statnekov.com).
  43. Wahl, Uli, Aeolian (Kite) Musical Instruments. (http://members.aol.com/winem1/index/index.htm)
  44. The Art of Ancient Peru (http://www.howardnowes.com/pcpe.html)
  45. BotanischerGarten.ch. Lagenaria ciceraria(http://www.botanischergarten.ch/jpegs/317_flaschenkuerbis.jpg)
  46. Area de Conservacion Guanacaste. Cecropia peltata(http://www.acguanacaste.ac.cr/bosque_seco_virtual/bosque_seco_images/images_de_especies/cecropia_peltata/arbol.jpg)
  47. USDA. Cecropia peltata L. (http://www.na.fs.fed.us/spfo/pubs/silvics_manual/volume_2/cecropia/peltata.htm)
  48. Yidaki of Australia(http://www.gingerroot.com/oztrip/yirrkala/yidaki/17play.jpg)
  49. Musical instruments of the world. Wood trumpets from Africa (http://www.eyeneer.com/World/Af/Instruments/wood.trumpet.html(
  50. US Departement of State. Bureau of Educational and Cultural Affairs. Wooden Trumpets Moche, Huari from Perú. (http://exchanges.state.gov/culprop/peru/Perishab/00000012.htm)
  51. Dary F., Claudia. El combate representado en las danzas de origen prehispánico: El Rabinal Achí. (http://www.icrc.org/icrcspa.nsf/c71a2d6bd91c8c47c12564670035ecb8/9819aff8431ac92241256732003ab673?OpenDocument)
  52. The Acoustics and Fluid Dynamics Group. University of Edimburgh. (http://www.ph.ed.ac.uk/fluids/Homepage.html)
  53. Campbell, Murray. "Latex Lips Blow Own Trumpet". TPO. (http://www.trumpetplayeronline.com/latex_lips.html)
  54. Prehistoric Music Ireland. Bronze Horns Uses (http://homepage.eircom.net/~bronzeagehorns/index.html)