Ehekachiktli with wind way or air duct and open resonating tube
An ancient generator of chaos, sounds and complex noises called: double diaphragm aerophone, bellows flute, of air spring, oboe or Maya clarinet..



Roberto Velázquez Cabrera
Virtual Research Institute Tlapitzcalzin.

(Consultation document)
First version November 10, 2003.

(Versión en Español)

Introduction.

The purpose of this virtual and experimental study is to analyze the Ehekachiktli with air duct and open tubular resonator. It is one of the developed members of the extraordinary family of Mexican aerophones that produces signals with noise, their mechanism or sonorous heart is that of the ancient bucal Ehekachiktli analyzed in other study [1]. Its design is similar to the Ehekachiktli with air duct [2] or air whistle, but it is different from this in its inlet's angle to the noise generating chamber and instead of the bell it has an open resonating tube, occasionally with one or two tonal holes.

Engineer José Luis Franco [3] was the first to start to study the so called double diaphragm or air bellows aerophones. Unfortunately, only one of his studies was published in a newspaper of national circulation. The world diaphragm does not apply well in this case, because the two holes that the sonorous mechanism has in these aerophones is of fixed diameter, they are perforations in the clay, and a diaphragm is an aperture that can change similar to that used in photographic cameras.

The internal structure of these sonorous goods can be shown with clarity using a didactic clay model or a drawing of Jose Luis Franco.


Didactic model Ehekachiktli with air duct and open resonating tube.


Drawing of José Luis Franco, published by Samuel Martí. INAH [4].

The organologic components of the "bellows Maya flute" can be listed using a drawing and the numbers: 1) air-duct where the air excitation current is introduced; 2) first input hole to the chaos generating chamber, which is formed between holes 2 and 3; 3) second hole to the globular resonator; 4) globular resonating chamber that functions as a Helmholtz resonator; 5) tonal hole and; 6) output resonating tube. In the zone painted yellow between the two holes, 2 and 3, the small chamber generator of chaos and noise is formed. It operates as described with certain detail in the study of the ancient bucal Ehekachiktli bucal, but in this case it functions inside the aerophone.

Several investigators published texts of Franco's discoveries and some published other drawings and pictures of sonorous artifacts stored in museums. One of these is Samuel Marti [4] in 1962, another is Pablo Castellanos [5] in 1970. Also, Guillermo Contreras CENIDIM investigator and professor at the National School of Music of the UNAM in his book of 1988 [5] he comments on these aerophones and provides cut-drawings. Ceramist, musician and independent investigator Susan Rawcliffe in her 1992 article [7] provides a drawing of Franco along with others aerophones of the same family.

However, in the literature, the acoustical analysis of these aerophones has not been included or recordings or studies of their sounds, neither the antique iconographical representations of this case are known, but it is known that several exists in national museums and in the exterior. Years ago, there was one in the Maya Room of the National Anthropology Museum with an x-ray, before it was closed for remodeling, That x-ray was very important, because beside showing with clarity the internal structure of a Maya-air-bellows flute, it was the only one exposed in a public room, from the thousands of ancient aerophones stored in museums.

The lack of interest and the opposition by museums administrators and curators to deeply analyze the Mexican organology and to obtain information of its description and functioning is so strong that even with the law's authorization it has not been possible to take x-rays requested by the author. According to the analyzed publications it appears that the archaeological analysis is reduced to the external visual aspects of the antique goods, even if these are sonorous, like when they are considered as "figurines" or they are included in expositions, publications and museums only because they are tridimensional pictures of antique personalities, rich in their iconography or beautiful in their external finishing

In Mexico City museums they have not allowed even direct analysis, because they say that activity concern to the responsible archaeologists or argue that the rules do not allow it, but the museum rules with these prohibitions have not been found and in the official literature no formal studies has been found about the sonorous substantive function of any of the thousands of ancient aerophones stored in museums, explorations, collections and explorations by any archaeologist . Practically, all it takes for a museum administrator or curator is "not to agree" with the legal authorization presented in official paper to deny its practical execution.

The archaeological information of the sonorous goods could give clues about their possible original utilization, but it is very limited. No publications are known about the explorations in which ancient aerophones were found. The most important information that has been given about the museum's "double diaphragm aerophones" is the ones given my Marti [4], with texts of Franco [3] and the drawings and pictures of Contreras [6]. Franco commented that these aerophones could belong to al least to the eight century B.C. in an Olmec context without defining the exact place of origin. It appears that some figures of "big belly animals" are from the Maya zones, like the Jaina Island, according to Marti [4], but because in that Island there were burials of personalities with objects from several maya zones, their exact origin is unknown.


"Air spring or bellow Maya flute with double diaphragm" published by Martí [4], courtesy of the New York Natural History American Museum. The photo was patined and the background retouched to give a classic look.

It appears that a below flute with double diaphragm and the rest of Marti collection are stored in the San Jasinto Museum at Oaxaca City, where in matter of sonorous artifacts, they prefer to display old radios, even if they are not of Oaxaca origin.

There are other noisy mesoamerinan aerophones no so well known that have similar sonorous mechanism and coupled resonating tubes like the extraordinary Olmec Gamitadera, in exposition at the Xalapa Anthropology Museum, but this one do not have tubular air duct and its resonator tube is closed with a lateral-inferior exit hole, for that it could be classified as a Ehekachiktli with closed tube and without tubular air duct.

The members of this singular family of aerophones could have been build in an infinite amount of sizes and external forms such as the some hundreds of experimental clay models made by the author .


Sample of experimental model with skull.

Construction.

The construction of these artifacts is not easy. If it is intended to generate strong sounds, the construction of hundreds of models shown that it is more effective to initiate the process my molding the sonorous mechanism heart. If it is pretended to generate complex sounds the globular resonator's holes diameter must be slightly larger than the firth input hole. If this the sounding mechanism is well molded and it left to dry a little, it is probable that the rest of the parts will function correctly. The air-duct tube and the tubular and globular resonators con be molded separately to be attached with clay to the noise. One way to align the sonorous mechanism holes is to make two outside large holes, one in the air duct and another in the globular resonator, to align the two holes, 2 and 3, with a little round stick, rod or wire and glue the assembly. To test its operation, cover the large holes with your fingers and blow through the air duct 1.

Clay is the best material to make this type of sonorous mechanism. It could be very complicated to make them out of rigid materials like wood, metal, bone, etc. due to the complexity of their internal design. Models can be made with parts using canes and nut shells even if ancient artifacts made in such way have not been found, possibly because these materials are easily degradable.


Experimental model with cane and macadamia nut shell resonator over a mountain cat skin.

Spectral sonorous analysis of experimental models.

The execution of experimental organology exercises are not known in the traditional archaeology, because the analysis using physical replicas and mathematical models are not used, which are used in the design and evaluation process of engineering and scientific investigations. Neither has been of interest to explore the ancient acoustical attributes, because not a single aerophone rescued and stored in national museums has ever been to travel to a good laboratory with metrology equipment nor to other places where they could be played in the past to analyze their sonorous properties in controlled situation or in ancient spaces and contexts. The author's experimental models have done so, at times finding administration difficulties, because guards say that "it is not permitted to play musical instruments in the archaeological sites". It occurred to some administrators of the ancient national patrimony to reinstall this prohibition initially imposed during the conquest and colonization by others who also depreciate the Mexican sonorous artifacts and their sounds.

As it has not been possible to have access to the sonorous artifacts in museums and collections the analysis can only be done using experimental models. With experimental models it has been proved that the basic operation of these aerophones is very simple, because they have an air duct, but they can produce complex sounds if the input air flow is complex. Some of then have tonal holes, but their fundamental F0 operation is altered a very little. Greater alteration comes with greater input air and pressure or by forming another resonator with the hands around the resonator tube output, changing its size and output aperture.

There is no use in applying views of musical analysis to these sonorous artifacts, because their sounds are not musical in the modern occidental sense, even if some investigators have tried to apply musical concepts to these sounds like when they say that they are tuned to a certain musical note and that their scales are very rudimentary. It only take to see the face expression of an actual musician when he listen to see how far they are with their imported modern mentality and musical uses.

It has been mentioned that the sounds of those aerophones can be guttural and is for that reason that they have been compared with the modern reed interments, but no signal analysis has been provided to show this similarity. It appears the performed studies have been only by ear without using acoustical tools or signal analysis. It is not intended to underestimate our aural system. A well trained ear is excellent to analyze audible sounds in a very wide band of frequencies an amplitudes, but the musical language is poor in describing complex sounds like those produced by the artifacts in our case and of some ancient musical instruments.

The frequency components of complex sounds can be analyzed using modern equipment and systems or signal analysis. For example, the dynamic spectral analysis of the clay experimental model and the one made of cane and macadamia nut shell can be shown with spectrograms. For the first one a 3-D ( intensity in dB, F0 and time) spectrogram 1 is used to see its performance in time and others spectrograms 2 and 3 for their projection in 2-D to see the signal intensity detail with noise in all of its spectral band. In graphs 1, 2 and 3 the intensity is different . In the fist one it is given in dB scale, and in the second one in a decimal one. Also, the frequency is presented in different forms, because a logarithmic musical scale is used in the first one and in the second and third a linear scale is used.


Spectrograma 1 in 3 dimensions of a noisy sound from a clay model.


Spectrograma 2 in 2 dimensions of the same noisy sound.


Spectrogram 3 of a sound from the cane and macadamia model.

It can be clearly seen in the previous spectrograms (1, 2 and 3) that these are not musical sounds. It is well noted that wide signal peaks with low Q factor (sharpness of sounds) and noise in a wide band are produced, where the highest peak is not in the lowest frequency. Besides it is very different to assign the equivalent note in the conventional musical scale to the sound that resembles roars of unknown animals or generated by natural phenomena or from the underworld, which contains noise and timber not known in music.

Now it is not possible to analyze the sounds of the Maya "oboes" because they are not available for that purpose, neither an European oboe is available to analyze its sounds, but it is possible to make other exercises. With the spectrogram 4 it is easy to show with clarity that the signals from the reed instruments (including the simplest and oldest) have great amount of pure harmonics well defined with a high Q (quality factor) without noise between them, which shows the cleanliness and intensity of the Fn frequencies in their sounds and that they are very different to the complex signals previously shown.


Spectrogram 4 of the sound from a little tube of cane with reed.

In all the experiments done with similar aerophones it has possible to observe that main effect of the resonator tube is that it has an influence in which the frequencies associated to their dimensions are generated with greater intensity in one of their wide peaks of low Q. They can generate guttural noises or whistling, but not like the conventional notes, they resemble animal cries or noises from unknown beings as it has been clearly shown in the roaring Tlemaitl, sahumador generator of creepy cries.

Some characteristics and properties of sonorous mechanism are described in the study of the bucal Ehekachiktli [1], but the exact effect in the variation of its dimensions is a mystery, because with a small change in its design it is possible to generate very diverse e impressing sounds, similar to those of suffering animals, like that of an experimental clay model can produce. See spectrogram 5.


Spectrogram 5 of a sound from the clay model similar to that of a desperate pig.

It has been seen that those noise generators of sounds can be coupled to large tubes like the one used in Maya trumpets, shown in the study of the Trumpets of Bonampak.

Acoustic radiated and perceived power.

Another important factor in the analysis of artifacts generators of sounds is their acoustic power to determine their possible range and spatial surrounding for their best utilization. The real radiated acoustic power of these aerophones can be as high up to 1 Watt (109 dB at 1 m y 0 degrees) in the best experimental models, even if generally the impedance of the complex sonorous mechanism attenuates the power down to about 0.5 Watts.

The radiated acoustic power was estimated with the formulas 1 and 2 expressed in MS Excel format:

I = + (10 ^-12) * 10 ^ (dB/10)             (1)
W = 4 * PI() * I                                      (2)

Where,
I = intensity of the sound (W/m2)
dB = sonorous pressure measured with a sonometer (dB), in this case at one meter and 0 degrees.
PI = 3.1416....
W = radiated acoustic power (Watts)

The perceived power of these sounds is even grater, because they have peaks and noises in the band of greater audible impact of humans (1-6 kHz).

The acoustic characteristics of these sonorous artifacts makes them ideal to be used in ancient rites or ceremonies like those related to the wind, death and the underworld and to imitate sounds of animals. It has been observed that their sounds can be very impressive in closed spaces like rooms and caves. They can generate very special effects when are played in large groups of these artifacts or with whistles, because they produce frequency beats, interferences, and cause vibrations and neuronal stimuli, that con not be generated in any other way.

Final comments.

It has been shown that it is possible to study complex sonorous artifacts and to analyze some of their sonorous or acoustic attributes even without having direct access to the real ancient sonorous goods as it has been shown in other studies of the author (in English) [8].

With this study it is possible to integrate the complete fundamental structure of the tree or branch of Mexican famuly of noisy aerophones that have been denominated as Ehekachiktli in honor to the wind god and by the characteristics of their sounds. The integration of this sonorous family is a relevant goal for the Mexican organology, because it has been found that even the experts who study our ancient instruments and other goods they do not know them. Ideally, every branch of the tree in the rich Mexican organology must be analyzed in similar form, considering the ancient artifacts that have been recuperated, complemented with experimental.

With the divulgation of the complete structure and the most important elements of this mesoamerican sonorous family even the existing organological classification can benefit. They were not included in any of them, because they were not well known. With the experimental models that were made it is possible to analyze other possible cases, even if they have not been found in the reality.

This family of aerophones is the clearest sample that the ancient musical practice and concept were much wider than actual ones and it is an evidence of their singularity in the known universal organology as far as designs, sounds and uses. This type of Ehekachictli and other more developed members of the family have not been found in other zones and cultures of the exterior. This family can be a tree separated from the rest of the known organology, because the heart of its sonorous mechanism is very different to the ancient and modern aerophones.

However, it has been commented that even if there are modern technologies, mathematical models (like partial differential equations of Boltzmann), advanced laboratories (of fluid dynamics) and tools with high technology (supercomputers and networks of computers) for the analysis, visualization or simulation of turbulent or complex chaotic systems we do not even know the exact and detailed functioning of the sonorous mechanism of the simplest and oldest bucal noise aerophones with two holes, which were designed and made al least 3000 years ago.

Now, even with the great medical, neurological and psychological development, we do not know either the original use of these extraordinary and singular artifacts that can generate strong complex signals with noise and with possible special physical and mental effects in human beings. There is no doubt that the complete comprehension of their functioning and the determination of their possible utilization, represent challenges to the advanced investigation.

The principal methodological limitation is that no evaluation protocols exist for the evaluation of ancient aerophones and less for those that produce noise. The most advanced that has been done to the few modern aerophones since the beginning of the last century is trying to understand their functioning, to begin to model them with detail and rigor their sonorous behavior and to know their effects, but the same has not been tried with thousands of ancient Mexican aerophones that have been rescued and much less has been done with those that generate chaos and noise.

There is no doubt, this extraordinary family of Mexican aerophones can be subject of more advanced investigations, but the greatest limitation is that no institutions nor experts of the related specializations have been found who would be interested to support its development. Nor even in the education and/or investigation sectors have been any interest to know more about our own, sonorous technologies that are unique in the history of the humanity, like those of the millenary mesoamerican Ehekachictli.

Referencesas.

1. Velázquez-Cabrera, Roberto. "Ehekachiktli bucal".

2. Velázquez-Cabrera, Roberto. "Ehekachiktli con aeroduto".

3. José Luis Franco C. Musical Instruments from Central Veracruz in Classic Times.Ancient Art of Veracruz. Exhibition Catalog of the Los Angeles County Museum of Natural History, 1971.

4. Martí, Samuel. "Instrumentos Musicales Precortesianos". INAH. 1968

5. Castellanos, Pablo. "Horizontes de la Música Precortesiana". FCE, 1970

6. Contreras Arias, Guillermo. Atlas Cultural de México. Música. , SEP-INAH-PLANETA, 1988.

7. Rawcliff, Susan. "Complex Acoustics in Pre-Columbian Flute Systems". EMI. Vol. 8. # 2, 1992. (http://www.windworld.com/emi/). (http://www.artawakening.com/soundworks/)

8. "Aerófonos mexicanos".(http://www.geocities.com/rvelaz.geo/spanish.html)