Virtual Analysis of Maya Trumpets
Caso 2. Model in wood Hom-Kooché


Photo 1. Maya vase K7613 with trumpets
A photo of Justin Kerr Maya Vase Archives

Roberto Velázquez Cabrera
Virtual Research Institute Tlapitzcalzin

Consultation document.
Firs version in English: June 1, 2004.

(Versión en Español)
Introduction

The purpose of this document is to analyze a model of wood trumpets used in the great cultures of Ancient Mexico and were represented in iconography of maya murals and vases. The maya wood trumpets were mentioned in the study of the Hom-Tahs of Bonampak painted in the North Wall of Room 1, made of gourds or Lagenaria Ciceraria. Those trumpets were used at the most explendorous time of the maya culture. They were painted in the Bonampak murals 800-850 years B.C., eighth and half centuries before the arrival of Columbus, six and half centuries before Michael Angelo and Leonardo da Vincy, during the so called dark age of Europe. The trumpets were used by the maya royalty and by all the powers in great celebrations and wars. In Bonampak, they appear in the paintings of the three rooms, which represent two ceremonies and a battle. The exact original use of the maya trumpets is not known even though it is known that they were used in their numerous celebrations and dances that they were close to 5,000. Iconography also shows that they were ritualy used, like in sacrifices.

In the few writings where ancient maya trumpets are mentioned are very superficial, insufficient to know their structure, construction and possible uses. Even if it is supposed that they were made of wood, stucco covered canes, clay and palm leaves or cloth strips. They were decorated with tapes, glyphs or feathers. However there are several general evidences in the literature about maya trumpets that they were still being used when the colonizing conquerors arrived. One that mentions the use of wood trumpets is of the burning of maya codices by Diego de Landa, included in his Relations of Things of Yucatan (Relacion de las Cosas de Yucatán):

"...and they have long thin trumpets, of hollow wood and at the end twisted gourds (Rukuyultun or Hom-Kooché-Tah?).....and their lugubrious and sad sound".

That comment could be applied to the painted trumpets in the North Wall N of Room 3 of Bonampak (Photo of Arqueología Mexicana) and in some maya vases like the K594 of Justin Kerr.

The maya trumpets disappeared many years ago. In the last century, the few trumpets used in celebrations of rural maya zones were made out of metal, such as those used in some regions of Guatemala. Ethnomusicologist Alfonso Arrivallaga Cortez informed that in the Rabinal Achi a pre-Columbian Drama still being played, is accompanied by trumpets but these are made of brass and they resemble an European type. Among the K'ich'e of Totonicapa also a long brass trumpet was used with embouchure of cane reeds "cañuelas" such as the one used in the "chirimias". An ancient use of the maya trumpets is narrated in the recordings of the Calchicueles. At the end of the representation K'iche'-Achí is scarified.

The same thing happened to the maya trumpets as the rest of the millenary and singular ancient Mexican organology, which was destroyed, prohibited, proscribed and forgotten, since five centuries ago as a result of the conquest, the colonization, the dependence, the racism, the malinchism, the ignorance and the laziness; even with the independence and revolution and the ordinances of our laws to investigate and promote the pre-Hispanic and indigenous cultures.

The last institutions interested in the Mexican organology and its sounds were destroyed during the great massacre of Tenotchtitlan in 1530 A.C. Persons that study ancient goods have said that they do not have the technology and methods for the analysis of recovered sonorous artifacts and for those appearing in the iconography. Some academicians who have musical education say that it is impossible to know how the ancient musical instruments were played, because they are not played any more and there are not known writings or recordings of their original sounds.

In this presentation, it is shown that even without the real ancient trumpets, with a little investigation and using mathematical and experimental physical models it is possible to revive and study the wood trumpets that only appear in the iconography and explore some possible uses of the extraordinaey sounds they can produce.

The selected trumpet design for the analysis is like the three ones shown in the right of the picture of maya vase K7613. The resonator is almost of tubular structure similar to the didjeridu or yidaki from the north of Australia, which is still being made of eucaliptus branches perforated by white ants or termites. The trumpets of the Maya vase K7613 have tubular embouchure and possible a bell at the exit, but such organological elements can be experimentally examined, but it was seen that the embouchure is tubular and it only helps the player to have more comfort in the lips having larger contact surface in its extreme disc. The bell affects the produced sounds, but mainly it improves the tube's efficiency and strengthens the harmonics.

Some formal studies about trumpets being analyzed by experts in physics of musical instruments few are known about ancient aerophones. Departments of Physics of three universities from Australia are studying their didjeridu and one of Scotland about Celtic trumpets. It is known that in several world zones existed ancient wood trumpets, like Some in Peru, Africa and New Zealand, but their formal studies are not know.

Estimation of f1 o F0 of the experimental model.

Professor Neville H. Fletcher, first investigator who formally studied the didjeridu, found that it can be modeled (in passive acoustic) as a truncated conical trumpet of length L. He provided the approximate expression 1 for the frequencies of each mode n, which was also applied to the Hom-Tahs, because its organological structure is similar. Dimensions of the model are included:


Where:
fn = frequency of mode n (Hz)
L' = L + 0.3 * d2 (cm.)
c = velocity of the sound in the air (38000 cm/s, used in other studies)
d1 = diameter of the embouchure (3 cm.)
d2 = diameter of the larger end (4.8 cm.)
L = trumpet's length (147 cm.)

Due to the fact that the dimension of the wood model are approximately the same as the ones the typical didjeridu, the result published by the investigator Fletcher can be used in this case.

Using the equation 1 and the dimensions of the experimental trumpet, it was possible to estimate the fundamental frequencies f1 or F0 in 69 Hz, close the musical pitch of C#2 (69.296 Hz) of the tempered scale with A4 = 440 Hz. Even if the wood model used does not represent exactly any ancient maya trumpet, what is important about equation 1 is that it can be used to make estimation of the pitch of any similar model with variations in their dimensions. For example, if length L of the model is 200 cm, the fundamental frequency would be close to 51 Hz.

Selected material for the experimental model.

After a long search in the botanical field of Mesoamerica and some tests, it was found that an ideal material to make "wood" trumpets, is the branches of Cecropia Obtusifolia in the family of the Cecropiaceas which has close to 200 species like the one shown in the photo of the Cecropia Peltata. It meets the necessary physical and structural characteristics, the branches are of monopodic trunk, cylindrical, straight and hollow, so the construction procedure is simple. Its light, when it is dried. It is also soft which facilitates the work. The inside surface is thin dark brown layer which is not hard nor water sealed. It has sectional discs like bamboo. The wood is clear gray color and fibrous structure (Foto 2).


Photo 2. Cut view of a branch of Cecropia obtusifolia from Colima State, Mexico.

The low weight of the material is very important, because it was one of the distinctions of the maya trumpets. The available iconography shows that they were so light as to be hand held in the air and easily carried in processions. It appears that the material of similar trumpets from other zones like Africa, Australia and the Andes was of greater specific weight, reason enough to be played resting on the ground or in other supports, specially if they were played for long periods of time.

The Cecropia obtusifolia tree grows naturally from the north part of South America to the north of Mesoamerica at the altitude of 0 to 500 m, in hummed, semihummed, tempered and semitempered zones. In Mexico it is widely known and distributed, in all the Gulf from Tamaulipas to Yucatan states, in the Pacific from south Sinaloa to Chiapas states. The low maya zones are ideal for its growth, which means that it could have been easily used by those living in that area; it has many common names in the zones it grows: Kooché y Koochlé (in Yucatán peninsula), Guarumo (Chiapas), Guarina (Tabasco, Chiapas), Chancarro (Veracruz, Oaxaca), Yaba, Yabioo, Yava, Yaga-gacho, (Oaxaca, zapotec), Hormiguillo (Puebla), Sarumo (Michoacán), Sushanguji (Veracruz, popoloca), Tzulte (S.L.P., hustec), Juaquequistli, Quiquiscuahuitl, Tequescuahutl, Jarilla, Palo de violín, Trompeta, Trompetilla (S.L.P.), Trompeta (Sinaloa), Guanacaste, Trompetilla, Trompetero, (Nayarit, Jalisco, Colima). The designation in West Mexico shows that its sonorous use was well known. The English name for this tree is "Trumpet Tree" which means that its organological use was also well known in other external areas.

Close to thirty medicinal uses have been found for this tree, one is antidiabetic, its milky sap attack the skin and in its branches live ants of the Aztec gender .

Construction of the experimental model.

This project was possible with the help of a great friend from our childhood, engineer Ignacio Montes Rodríguez, who lives in Colima state. He found, cut, dried in the shade for several months some branches of guanacaste (troumpetero o trompetilla). When the branch is dry, the thin fibrous outside layer is removed to smooth and polish the exterior, which is somewhat porous, the surface can be painted, sealed and lacquered. The internal discs have to be eliminated using a metallic tube, a ribbed steel rod and or a round stick or thin tree branch. To avoid cracks, the model can (and should) be wrapped at intervals with whatever is available or desired (like cotton or plastic strings). Some trumpets in the iconography appear to be crisscross tied with cloth or palm strips. The interior wall can be sealed as protection against humidity. Models build in such a simple way, are very light, The one shown in the Photo 3 weights only 500 grams (1/2 kilo). The external finishing was oleo painted toad green and transparent orange mixed with the sealant and the varnish which were applied by hand with a sponge in several thin layers, like lacquering.


Photo 3 of the model build with a branch of Cecropia obtusifolia of 147 cm length.

Sonorous mechanism.

The sonorous mechanism is formed by a truncated conical trumpet and the human speech system. Both elements are well known and have been studied by experts in trumpets and the voice. What now is being investigated is the behavior of both and the lips' dynamics, but there is no known model that simulates their integrated behavior in their most complex operational forms. However, some peculiarities are known of this case under analysis: A) This trumpet has no embouchure such as those of the wind instruments; B) The low resonating frequencies of the trumpet is close to the vibration's low frequencies of the vocal cords; C) The coupling is good due to the impedance (~ air' s specific density/tube's section), because the human mouth section and the tube's input are a good match, and ; D) The trumpets acts as an efficient line impedance transducer. Some of these peculiarities and some others more detailed ones about the effects in the vocal tract and tongue of the didjeridu operator, have been published by professor Neville H. Fletcher and several Australian investigators.

Sonorous analysis.

The timber of the sounds produced by the model is similar to that of the Bonampak trumpets, even if its pitch is lower because the resonator is longer. The simplest sounds obtained in the first mode of operation are similar to bull's roars or other large animals and its frequency components can be seen in spectrogram 1. The black intensity shows the dB level.


Spectrogram 1 of a flat and simple sound.

The sound is produced in the usual way that is used to produce musical notes in trumpets, vibrating only the lips, but in this case very loose, floating and separated from the teeth and with the slaps inflated. The F0 is ~ 70 Hz (very close to the calculated with equation 1 of 69 Hz) and the sound is very clear and rich, it generates more than 30 harmonics. Not everybody can hear sounds of that low F0, but they can hear the higher ones. These sounds cab be heard at considerable distances (~ 300 m) in a open field. Due to their low F0 propagation of these sounds is not affected much by obstacles like trees, caves , etc.

The trumpet can generate diverse special sounds. The first mode is modifying the vocal tract configuration to change the impedance and adjust it to that of the trumpet. Another is generating composite sounds. For example, as shown en spectrogram 2, where the frequency components of a three phonic sound is produced (with three strong components), this is accomplished by vibrating the lips and the vocal cords at the same time. This operation is basic among the good didjeridu players in Australia.


Spectrogram 2 of a sound of troat and lips.

In the power spectrum, three different equally strong frequency components can be seen and none of the three is harmonic. The signal level is given in lineal energy units.


Power spectrum with three strong peaks.

The power perceived by the ear is not high, because its low F0, but the real and the perceived power by the body is greater. The low pitch of the sounds is felt with more intensity in several other parts of the body like in the stomach. Using the equation 2 and 3 (in Excel format) the maximum radiated acoustic power in one direction is of 0.01 Watts or 89 dB at 1 m and 0 degrees.

I = + (10 ^-12) * 10 ^ (dB/10)             (2)
W = 4 * PI() * I                                      (3)

Where,
I = sound intensity in W/m2
dB = sonometer sonorous pressure in dB at 1 m and 0 degrees.
PI() = 3.1416....

The equivalent power of the model is lower than the Bonampak (0.8-1.0 Watts) due to the internal structure difference, the model is almost tubular, which means that the Bonampak model is acoustically more efficient. It is known that trumpets with a greater widening factor such as those get closer to the hyperbolas, catenary or exponential functions, are the most efficient ones. For that same reason the gigantic trumpet in vase K7613 also can be very effective. The three trumpets on the right side of the photo of the vase K7613 are not played with a similar power to the larger one, but when they are played at the same time their sonorous power is added and amplified.

It has been noted that the maya trumpets are more efficient in its first or low mode of operation, reason why that pitch have been the preferred way to play them if long notes or phrases with a single lung-air excitation. It is known that experts didjeridu players can generate very low continuos sound, because they have the ability to blow continuously using the very difficult circular respiration technique.

It is estimated that the acoustic efficiency of these trumpets is considerable, even if their internal surface is not smooth, due to the fact that their sonorous power is significative and that very little pneumatic excitation power (blowing pressure x air flow volume kPa x m3/s) . Professor Fletcher has mentioned that to operate the low mode of the dudjeridu, it is only required 1-2 kPa (10-20 cm of water) of blowing pressure

Sounds with two or more F0s were very much used in songs of ancient cultures in several zones of the world, which have been called songs with the trout, biphonic, with harmonics, with overtones, khoomei, Steve Sklar, Huun-Huur-Tu, etc., such as those still being used Tibet and Tuba y Mongolia. The archaeologists/anthropologist Dr. Margaret Bruchez, when listening to the sounds by lips and troat of this experimental model, noted their similarity with the trout songs of Tuba. Spectrogram 3 shows the signal of a Tuba sound generated with the trout. The F0 is higher and can vary, but has less harmonic and power than the similar sounds of the experimental trumpet.


Spectrogram 3. Tuba song generated with the trout.

The truncated conical trumpets such as the maya ones allow the sounds with several F0s and overtones to be generated with greater acoustic power, possibly due to the excitation force vibrations of the lips and of the vocal cords associated to the F0s, the resonator tube greater efficiency in the range of the fundamental frequency of the vocal cords and their greater harmonic richness. It has not been possible to know estimations of the radiated acoustic power of the biphonic songs. It is estimated that they are similar to those of monophonic songs, even if for these, their measurements in Watts have not been found either. The few known analysis are mainly for F0s, spectral or of sonorous pressure in dBs. To give a reference level, it can be mentioned that the radiated acoustic power of a normal conversation is around 0.000001 Watts.

With the variation of the F0 of the vibration of the vocal cords while maintaining constant in time the lips vibrations, it allows to generate beats of variable pitch, because the numerical subtraction among them can have variations. That possibility makes them ideal to stimulate the cerebral neurons in a range of frequencies inclined in the infrasonic ones. That property can be the reason why similar trumpets like the didjeridu are still being used in meditation practices or to generate special state of conscience. It is known that some aerophones can produce infrasonic beats specially if they are played at the same time in a group, because usually whistles have small differences in their resonator volume, but ancient trumpets like the maya ones, can generate those effects even if they are played individually. However, the circular respiration technique can not be maintained with sound generated by the vocal cords, because their vibration has to stop while air intakes to the lungs. To produce beats in a continuous way for long time it is required several trumpeters so at least one is playing when other or others are momentarily breathing in. Possibly that might be the reason why in several maya iconography representations several trumpeters appear with their trumpets.

It is also known that some ancient songs that were performed in groups like the Gregorians could produce infrasonic sounds, but for sure the maya trumpets played in a group, like it is shown in the maya iconography, generated those sounds called "phantom sounds" with greater power and effects in the audience as well as in the players.

It has been proved that it is possible to produce a great diversity of sounds if all the acoustical possibilities of the vocal tract are used when coupled to the maya trumpets as when they are used to talk, sing, scream as well as to generate biological sounds like roar, rumble, grunt, growl, howl, hould, etc. or of nature or of other unknown, imaginary beings or phenomena.

Conclusions

With a little practice, the experimental wood trumpet can function very well and without much effort. That shows that the hollow branches of Cecropiaceas are adequate to make ancient trumpets. Because of their acoustic efficiency, this material could have been used to make trumpets in zones where it grows naturally.

With experimental model of Lagenaria Ciceraria and Cecropiaceas it is possible to analyze the behavior of maya trumpets and from other cultures of Mesoamerica that appear in the ancient iconography. It is only required to estimate their approximate dimensions, to find the branches or cultivate the required gourds to build the models, analyze them and start to decipher the sonorous code of all the ancient trumpets, including those made with two materials, wood and gourd or Hom-Kooche-Tah.

Being able to build experimental models of ancient designs makes it possible to initiate projects to operate the most complex forms of trumpets and to know their effects in humans beings as well as to be able to play them at once in a group, in different spaces like in open archaeological sites, their rooms, caves, etc.

The most relevant properties found in the realized studies about maya trumpets is the indication the besides being used to honor their gods in ceremonies as well as in dances, battles, communications and signaling sacrifices, etc., also they could used their sounds to generate special state of conciseness, for therapeutic, mental or physical treatments, to produce special effects in shamanic rites and perhaps to represent magical-religious dramas.

Similar trumpets were used by ancient people of other zones of the world, but the diversity of trumpet images appearing in the recuperated maya iconography, even if it represents only a very small fraction of what exited, indicates that mayas used them intensely, and their sonorous applications posses one of the greatest developments in history at that time, but all of it was condemned, proscribed, and has been forgotten for five centuries.