AERÓFONO DE PIEDRA NEGRA
ENGLISH
AEROPHONE OF BLACK STONE
Roberto Velázquez Cabrera
Firts version May 2000. Last update March 2002
The Spanish version of this paper was presented in the Computing Internacional Congress CIC-2000, IPN, Mexico, November 16/2000.
Introduction and background
The objective of this work is to prove the viability of a previous study recommendation [Velázquez-Cabrera, 2000], taking advantage of a proposed methodology, to help in the analysis of relevant Mexican aerophones. The case is an extraordinary aerophone of black stone collected by the deceased anthropologist Francisco Beverido Pereau, who realized important archaeological discoveries and was the photographer of the “Museo de Antropología” of Xalapa, Veracruz. He was also the photographer of the book “Caritas sonrientes” [Paz, 1971], with texts from poet Octavio Paz and a description from archaeologist Alfonso Medellín. Beverido took the pictures included in Charles Boiles´s article “Flauta triple de Tenenexpan” [Boiles-Lafayette, 1965], and he has other important publications.
The Beverido family let me look for pictures and studies of aerophones from Gulf Zone in the anthropologist’s office and library. They gave me a book “Estética Olmeca” [Beverido-Pereau, 1996], several beautiful pictures of Totonacan clay sculptures and they lended me the book “Cerámica de Totonacapan” [Medellin-Zenil, 1970]. In this search, it was found the little black stone, together with several beads. It had not any archaeological information of origin and description, but maybe the construction and material called the attention of the anthropologist. It seems that he did not considered it to be relevant, since he did not take pictures, neither it was analyzed and catalogued as other archaeological goods collected by him and provided to the museum.
When I saw it, I identified it as a possible aerophone. When it was played, it generated loud sounds similar to noise and wind (but distinctive from aeolian tones). The simple visual analysis indicates that it is an ancient aerophone, for several reasons: one is the shape of its holes or tubes that could not be made with a common conical bit. The most important criteria for its particular and exact structure is unknown. In other words, there is not an ancient artifact of this type from which we could make a copy.
It was a pleasant surprise to find this drilled little stone, since I had a special interest in this kind of Mexican wind aerophones (which appear to the untrained ear cacophonous, although they work with air and generate wind). I had been looking for an ancient aerophone to make a study. I did not look to find one in the office of a professional anthropologist and photograper.
More than 50 years ago, I made my first aerophone with a “corcholata” (metallic plug for soda and beer bottle), flattened, bent and with two holes near the center, like the one shown in Figure 5. The metallic plug (with out the cork), was lightly flattened with a hammer and then fixed (with a chewed gum) on railroad, to be very well flattened by the wheels of iron. Kids from my home town (Tequila, Jalisco) used to play with this “zumbador” (buzzer) or “gallito” (little cock), operated with a cord introduced in the holes and tied. The cord was sustained with the annular fingers of the two hands, with a circular movement the cord was twisted and when it was stretched and relaxed the flattened plug rotated to a great velocity in one direction and then in the contrary. The game was between two players, face to face, to cut the cord of the adversary. These toys folded (with out the cord and with the two holes located in a near distance face to face) to become another toy. The new play was a competition to see who could make the loudest sound. This sound is very rich in composed of high frequencies, maybe due to its special small simple, flattened and open resonating chamber and its two holes of small length (or thickness of the wall).
Some years ago, when I started the study of Mexican aerophones, I realized that these toys were similar to those used in Ancient Mexico (actual zone from south of USA to Nicaragua). In my opinion, the Florentine Codex illustrates one of this type, that can be seen in the upper left corner of Figure 1.
During the last two years, I have researched more than one hundred experimental wind aerophones (a family that may be called Mexican noise generators) of several shapes and structures, some of them with similar design, but none exactly like this drilled little black stone, which seemed unique. There are some artisans (as Gregorio and Mario Cortéz brothers, from Santa Cruz de Arriba, Municipio de Texcoco, Estado de Mexico) who know how to make aerophones of this type although of a different design.
To a researcher who has most studied this family of aerophones – José Luis Franco [Franco, 1962]- this artifacts were “aerófonos con fuelle de aire” (aerophones with spring of air). He also studied aerophones of the Gulf Zone [Franco, 1971].
This family type of aerophones had been directly analyzed by other researchers who had access to them, like Susan Rawcliffe [Rawcliffe, 1986], who has been analyzing ancient flutes, and built and playing her sound sculptures for 25 years. In her article was included a set of drawings with views of sections of aerophones of several museums and collections, made by the artist Jim Grant on the base of a careful visual analysis of the aerophones made by herself. Included is a brief analysis of an extraordinary aerophone with thee chambers, the “Gamitadera”, called by her a “chamberduct flute”. Rawcliffe comments: “The sound of this type of instrument is extraordinary, varying from a raspy throat gurgle to wrenching cry, depending on construction and on performance practices”. There are many other flutes that have a chamberduct. The author has analyzed replicas of the “Gamitadera” in a previous study [Velázquez-Cabrera, 1999]
Jorge Dájer included in his book [Dájer, 1995] a picture of one, described as an “ocarina” (figure 2), similar to one included in Florentine Codex (Figure 1). Dájer provides the following comments:
“The free intonation in this ocarina made of bone is controlled by the tongue changing the mouth cavity, forming with this a chamber, needing practice to acquire the knack of playing. It comes from Araró (Michoacan) and is part of the State Museum’s special collection where it has been classified as shuttle (Num. 4749)”.
The designation “Ocarina” was, however an inaccurate description of these artifacts, since they do not have closed resonating chambers, or tone holes.
The round stamp or button with a glyph, about 22 millimeters, was included in his pictures to give an idea of the artifacts size. They told me that it was stolen in an exposition (The author appreciates this design so much he uses similar one for making drawings and clay artifacts).
The few analysis made of this family of “Mexican noise generators” includes only very general descriptions, pictures and drawings. The “Museo Nacional de Antropología”, in México City, shows one x-ray negative picture of a Maya artifact of this type.
General Analysis
Beverido family lended to me the little black stone to make the first direct study of a Mexican ancient aerophone, considered original and relevant, using tools and procedures previously proved with experimental replicas. The most recent case was the Virtual Analysis of Gamitadera [Velázquez- Cabrera, 1999].
The aerophone of black stone illustrated in Figure 3 is relevant for several reasons: most important, it constitutes the first aerophone discovered of this type crafted with hard stone (it also contains metal becausing a high specific weight); secondly, it clearly revels it’s internal structure, making x-ray examination unneeded, as it is current practice for other complex aerophones of this type; thirdly, it is the smallest known of this general style and; fourth, it is drilled with round holes or channels (with an interior shape like a tube with round holes or channels), which relates to other Mexican aerophones of wood, bone, metal and stone, similar to the one included in Figure 1 and other different (whistles, ocarinas and flutes), but with their windows, edges and chambers made with 4 conical drillings of different sizes.
Design structure
Figure 4 shows a draft with the principal views and sections of the aerophone. The frontal view shows the part where the sound is generated. The section A-A´ shows the detail of the resonating central cavity and the exit, and one lateral hole (or channel), equal and face to face to one of the opposite side (4 mm in diameter), where the sound is generated). The section B-B´ shows the detail of these holes (in the upper an lower part) and the resonating cavity viewed from the top. This section is used to show the playing tecnique (Figure 6). The three short channels or tubes are centered horizontally but a tittle lower vertically. The front view indicates the anterior diameter (9 mm) of the exit hole. It is bigger than one in the back (5 mm).
This simple sketch is relevant, since with this information it is possible to elaborate very similar replicas of the original. A similar sketch or drawing was nor discovered in the literature, among the thousands of ancient aerophones that had been found. In the best drawings, only one section view is provided without the dimensions, capable of providing insufficient information for the purposes of explanation.
I made replicas of the original aerophone of black stone aerophone on several materials like clay and wood (Figure 5) that can produce similar sounds. This work proved that it is possible to build good replicas, if we have the original artifact, the ability to work the required materials, and the systems to measure and analyze their sounds. This exercise is relevant because no similar studies seem to have been recorded.
Main element and functioning
Figure 6 shows the elements and scheme of functioning of the aerophone, to produce the loudest sound. It must be played as shown in cutting B-B´ of Figure 4, located inside the mouth, between lips and teeth, and the tongue closing the back hole. The organological elements of this aerophone-mouth system are:
• Mouth channel 1, formed between palate and tongue, to input the air flow (showed by the arrow);
• Aerophone with the main resonating cavity B (as an open tube) and two holes (tubes A and C), located face to face, in a vertical axis. The inner circle of this holes may be two especial circular edges, where the sound is generated.
• Mouth cavity 2 (that may work like a Hemholtz´s irregular resonator)
In the beginning, the sounding mechanism might works as follows:
1. The strong flow of air (coming from mouth channel 1 and showed by the arrow), goes into the upper hole (channel) A.
2. In the exit of hole A the compressed circular air flow may be expanded, because the main chamber B is open and has less pressure. And may occur diffractions, because the aperture is small.
3. The expanded waves go to the opposite side of chamber B and to the circular edge of hole C, generating reflections to the back.
4. The main strong flow of air, that is coming from hole A, pass throw hole C and go to mouth cavity 2, that acts as a mass-spring system, generating resonating reflections to the back.
5. When these reflections cross to the hole C more refraction are generated inside the main resonating chamber B.
6. In few milliseconds, the combination of reflections and refractions (and expansions), in both directions, with the two circular edges in a reduced space, may generate a complex and turbulent dynamic of waves, pressures and sounds, that produce the noise than is showed with virgules (Mexican graphical symbols for all kind of waving being and phenomenon, like sounds).
7. Two groups of frequency components of the noise are amplified by the two resonating chambers, as it can be seen in the two wide peaks of the spectrograms (figures 7, 8, 9 and 10)
It can produce other sounds, if it is played in other ways. For example, rotated 90 degrees and set outside in front of the lips with the air flowed by his back hole, and closing with afinger its front hole, their lateral holes are converted as exit holes for the sound.
Analysis of sounds.
In the following, the spectrograms are shown in 2 and 3 dimensions (2D and 3D) of Figures 7 and 8, respectively, of a sound or noise, played in a simple way. The sound was registered with a microphone and a personal computer with a sound card type “Sound Blaster”, in a file format Wav compatible with Windows 95 operating system. The spectrograms were generated with programs downloaded from Internet [Horne] and [Volkner], that uses a routine of FFT (Fast Fourier Transform), applied to the digital file. The graphs show that there are frequency components (Hz) and relatively high intensities (dB) very complex. The maximum level of their peaks or crests are given near 2 kHz and 6 kHz but the generated frequencies cover a wide range from less than 20 Hz to more than 10 KHz similar to a colored noise.
In Figure 8, we can observe that the resulting signals in the lower frequencies have considerable magnitudes. To observe characteristic details of the signal, Figure 9 shows the power spectrum of the same sound. In these graphs the scales are not linear, the Hz are duplicated each octave as it happen in music. This is because the used program [Volkner] is a tuner for musical instruments. The intensities are given in dB, in a logarithmic scale relative to the perception properties of human being neither represents a linear scale.
Using other programs [Sat 32], it was possible to elaborate other graph (Figure 10) in which the frequencies and amplitudes are given in linear scales and units (like EU**2 instead of dB), the greater frequencies in intensities are noted with better clarity, since lower levels are reduced considerably.
Conclusions and recommendations
• This exercise proves that the proposed organological and acoustical analysis may be effective to analyze original (authentic) Mexican aerophones and can be of utility to support opinions on the authenticity of archaeological sound artifacts.
• As the spectrograms obtained are similar to other members of the family “aerophones of spring of air” or “of wind” analyzed previously, in intensity and in frequency components, it confirms that the unknown little black aerophone is an original (authentic) ancient artifact, and belongs to this group of noisy aerophones. Also, It was proved that the spectrograms can be used to evaluate the sound fidelity of copies or replicas with complex non periodic sounds.
• Spectrogram is the best technique to make visual analysis (in frequency domain) of non periodic complex signals like these Mexican sounds, that I could find available openly in Internet.
• It is important to make an analysis of all known parallel aerophones in stewardship of museums and collectors, to expedite be their comparison and correlation. The method is applicable by others, is easy, simple and cheap (because requires only a personal computer and the programs are openly available in Internet).
• It is necessary to inform the museum of Xalapa, to see if they are interested in the analyzed aerophone of black stone and its possible exhibition and explanation.
• The detailed dynamics of the sounding mechanism of this family of complex “Mexican noise generators” is unknown. Its determination is a work for advanced research. From the mathematical point of view, it seems that this system may be represented by a stochastic-non linear-dynamic model operating with a wide range of non periodic vibrations of pressure and sound waves, with two resonating chambers (one of them very small) and two special circular edges, as a chaotic and turbulent process. This kind of models are in the frontier of the research of several advanced techniques, as fluid vortex dynamics and scientific visualization.
• Also, the anthropological and cultural elements of these noisy aerophones are unknown, from their original name to their ancient use.
Notes of some advanced techniques, found in Internet.
There are advanced techniques to analyze complex systems of fluids, as those of the generation of sound in tubes (organs and flutes), using digital computers and elaborated mathematical models and numeric solutions. But they are not easy to adapt in Mexico for complex aerophones analysis.
Advanced Techniques using computers
A good example of this is the following: Panayotis Skordos in his extraordinary doctoral dissertation at MIT [Skordos, 1995] made simulations of a 20 cm long soprano recorder (without tone holes), using 20 computer workstations in parallel during three days, to obtain 25 milliseconds of isocontours of vorticity after startup of the a tone produced near 400 and 1100Hz (Figure 11).
After I read his study, I sent an e-mail with my congratulations for his research and to inform him about my thesis in Spanish. I asked him for permission to use some of his graphs and to know how difficult it would it be to use his program to analyze complex aerophones with several irregular chambers, in other computer networks. He wrote his answer:
“Thanks. As I do not know Spanish, I will have to wait for your English paper later. Yes, you can include graphs, pictures, etc. from my stuff (it’s an honor for me) as long as you have a reference and say where you took it from. The model is direct simulation of compressible subsonic fluid flow (the full Navier Stokes equations), and it can certainly be applied to complex sound artifacts. However it will take some work to do it correctly and lots of computer time. I expect it will be a lot easier in 10-20 years with much more powerful computers. To use my programs in other networks, I assume you mean to run my fluid-flow simulations in other computer networks. If I was doing it, it would not be too difficult (especially if it was a UNIX network). But for someone else it would be very difficult, and require very good computer skills. You are talking about setting up an advanced CFD simulation system. It is not trivial. Also I am not working on this anymore so I can not help. Best wishes on your research.”
There are other limitations: the cost of the workstations ($50 k US dollars), the programs are not available, the simulation was made only in two dimensions and not in real time. It seems that this extraordinary study was not continued or followed by others.
Other advanced methods.
There are other methods, that have been used, from the beginning of this century, to analyze the vortex dynamics in real time of wind musical instruments as tubes of organs, flutes and whistles, that could be used to study complex aerophones. They used smoke and stroboscopic pictures, but these facilities were unavailable in Mexico for such experiments.
There are also important studies related with the recognition of musical notes and human phonemes and words from speech, but the equivalent elements of complex ancient aerophones and their possible meaning, are unknown.
I did not find any literature on these methods, or any other, applied to complex ancient aerophones.
I found only one study [Garret and Statnekov, 1977] of ancient aerophones, that includes the Hemholtz´s equation for globular resonators. They used a spectrum analyzer but it seems that their main conclusions were obtained with physical measurements of the sounds.
Magazines interested in ancient sound artifacts
On Internet, I found only one magazine with few articles on ancient aerophones. “Experimental Musical Instruments”, but last year they decided to end the publication of the magazine. (http://www.windworld.com/emi/). The former Editor, Bart Hopkin, told me that he does not know any other magazine interested in ancient sound artifacts.
In a Hopkin´s book [Hopkin, 1999] is included one equation applied to globular resonators as ocarinas, whistles and horns with al least one circular tone hole, in addition to the mouth. He informed me that this equation was provided directly by Dr. John W. Coltman*, who told me that its derivation is in a book [Fletcher & Rossing, 1991] and how to interpret and use the formula.
f =(c/2*PI)*square root [((a1/te1) + (a2/te2) + ….)/v]
Where:
f = resonance frequency
c = velocity of sound on air
PI = 3.1416
v = volume of resonator cavity
a1 = area of mouth and a2, a3, etc. are areas of additional tone holes.
tei = effective length of holes or thickness of the wall = L + k * d , k may vary between .75 to .85
d = diameter of circular hole
L = Length of hole or thickness of the wall
It seems that this equation can not be applied to resonators with complex non periodic sounds, but is adequate to estimate the frequency of globular resonators with several circular tone holes, that can be made in any location on the chamber wall.
The Hemholtz´s equation is very important for ancient aerophones because many whistles and ocarinas have a globular resonator.
Situation in archaeology.
The state of the art for the analysis of ancient aerophones in archaeology, can be shown with an extraordinary discovery and study of six 9000 years old flutes, made of bird’s bone, found in an excavation at Jiahu of the Neolitic site in Henan Province of China [Zhang, Juzhong Harbattle and German, 1999], published in Nature magazine, on September 23 of 1999. The project was supported by the National Natural Science of China, the Department of Science & Technology of China, The Chinese Academy of Science and the Structure Research Laboratory at USTC. Research at Brothaven National Laboratory, supported by the US Department of Energy.
During research at the Brothahaven National laboratory, (which is supported by the US Department of Energy), it was found that important archeological information and material (dated with C14 technique), and cultures originated the aerophones. For the analysis of the sounds they used a “stroboconn” to measure the pitch of the sound of the best preserved instument (which was free of cracks) that remained playable. They found that their notes and scale are similar to those of familiar music. Ergo, their ancient users could be Neolithic musical performers. In addition, they conclude:
“It should be possible, by constructing exact replicas of the Jihau flutes in material whose density approximate bird-bone, to study the tonal sequence of all these instruments without endangering the valuable artifacts themselves”.
To use of replicas was a method long adopted by the author to study Mexican ancient aerophones (however, independent researchers were not permitted to study the museums’s own ancient artifact directly).
To study the tonal sequences of flutes is important anthropological and archaeological imperative; and the stroboscope (now part of the history of the technological examination of sound) measures accurately the pitch of a musical note. II found a picture also on the Web of one strobosconn (technology developed in 1936) located at (href=”http://www.wallickmusic.com/photo5.html). In México, too, there is a stroboconn is in a museum of metrology, having been previously used in the “Escuela Nacional de Música”.
With the Wav file of an ancient song from China “little cabbage” played with the flute (available in Nature magazine) and the program Gram (used in the paper), it is possible to obtain the spectrogram of a 9,000 years old striking sound, recorded with more noise of lower frequencies (figure 12). The spectrogram of the bitonal musical phrase seems a Spartan ancient Greek or classic signature, as a graphical symbol used to represent all kind of waving beings and phenomena, like the sound.
There are similar bone flutes in other countries as Peru and México, but their technical analysis remain to be done. Similar situation exists in the rich oganology of thousands of ancient wind artifacts from all over the word, with the exception of modern wind musical instruments.
Conferencia para el Congreso Internacional de Computación CIC-2000.
IPN, México, noviembre 13-17 de 2000.
Roberto Velázquez Cabrera
Palabras clave: aerófonos, acústica, visualización, multimedios, espectrogramas.
Resumen.
El extraordinario aerófono de piedra negra, sujeto del estudio, se localizó en el despacho del finado antropólogo Francisco Beverido Pereau, de Xalapa, Veracruz. Su familia me lo prestó para hacer el primer análisis de un aerófono antiguo usando técnicas modernas. En general, se describe la estructura y el funcionamiento del aerófono. Se aprovechan programas de computadoras disponibles en Internet, para analizar los sonidos que produce la piedra negra mediante el uso de espectrogramas digitales, mismos que son adecuados para analizar señales no periódicas. De acuerdo a los resultados del análisis, el artefacto sonoro considerado pertenece a una familia de aerófonos que se pueden designar como generadores mexicanos de ruido coloreado. No es un instrumento musical, porque no produce sonidos musicales. Para repetir el ejercicio, sólo se requiere de una computadora personal y de los artefactos sonoros a estudiar. El ejercicio prueba que las técnicas usadas pueden ayudar a analizar bienes sonoros antiguos y a opinar sobre su autenticidad. Las técnicas utilizadas también pueden servir para analizar sonidos menos complejos como los de los instrumentos musicales. Se incluyen varias recomendaciones como la de analizar los generadores de ruido similares en poder de los museos, para poder hacer correlaciones entre ellos. El estudio es original a nivel nacional e internacional, ya que no se ha encontrado en la literatura uno similar.
Introducción y antecedentes.
Aerófono mexica del Códice Florentino.Libro XII. Instrumentos de MIzcoacalli. Lam. 70. Foto de Guillermo Contreras [5].
“Ocarina”de Araró según Dájer. Foto de Jorge Dájer[4].
Fig. 3. Foto del aerófono de piedra negra, sobre un tamborcito maya de Mario Cortés y con una pintura de un paisaje de Tepoztlan de fondo.
La familia Beverido me permitió buscar en su estudio fotografías o estudios sobre aerófonos de la Zona del Golfo. Me regalaron un libro sobre “Estética Olmeca” [6], unas fotografías de esculturas de barro y me prestaron un libro sobre “Cerámica de Totonacapan” [7]. En esas tareas de búsqueda, se encontró casualmente la piedrita negra junto a unas cuentitas. No tenía ninguna información arqueológica, como su origen y descripción, pero seguramente llamó la atención del antropólogo, por su construcción y material. Parece que no lo consideró relevante, ya que no lo fotografío ni analizó o catalogó como los bienes arqueológicos que recolectó y que fueron entregados al museo.
Fig. 4. Boceto con dos vista y dos cortes
Al verlo, lo identifiqué inmediatamente como un posible aerófono. Al tocarlo, se comprobó que podía generar sonidos fuertes parecidos al ruido o al viento (pero diferentes a los sonidos aeolianos). El simple análisis visual indica que es un aerófono antiguo, por varias razones. Una, es la forma de sus hoyos, que no se pueden hacer con una broca normal de forma cónica. Pero la razón más determinante, es que su estructura exacta particular es desconocida en la actualidad. En otras palabras, no se conoce un artefacto antiguo similar para poder hacer una copia.
Fue una sorpresa agradable encontrar esa piedrita perforada, ya que he tenido un interés especial por ese tipo de aerófonos de viento (esta designación parece una cacofonía, pero esa familia de aerófonos funcionan con aire y producen sonidos parecidos al viento). Recientemente, he buscado y deseado encontrar la posibilidad de estudiar un aerófono antiguo. Nunca esperé encontrar esa posibilidad al descubrir uno en el estudio de un antropólogo-fotógrafo profesional.
Fig. 5. Réplicas de materiales rígidos
Hace cerca de 50 años hice mis primeros aerófonos con corcholatas de refrescos y cervezas aplanadas, dobladas con dos hoyos cerca del centro, como la que se ve en la Figura 5. Las corcholatas sin el corcho y un poco aplanadas con un martillo se colocaban en las vías del ferrocarril pegadas (con un poco de chicle), para que se aplanaran muy bien con las ruedas de fierro. Los niños en mi pueblo (Tequila, Jalisco), jugábamos con ellos haciendo “zumbadores” y “gallitos”, operados con una cuerda o cincha introducida en los hoyos y amarrada. La cuerda se introduce en los dedos anulares de cada mano, con un movimiento circular se tuerce la cuerda y al estirarla y aflojarla con las manos la corcholata aplanada da vueltas a gran velocidad en una y otra dirección. El juego era entre dos, colocados cara a cara, para cortar la cuerda del adversario. Esos juguetes doblados (sin la cuerda) convertían en otros juguetes ruidosos. El juego era ver quien podía hacer que sonaran más fuerte. Ese sonido es muy rico en componentes de altas frecuencias, por sus pequeñas y simples aplanadas cámaras resonadoras y sus dos hoyos de pequeña longitud (grueso de la pared).
Fig. 6. Esquema de funcionamiento del sistema boca-aerófono
Hasta hace unos años, cuando empecé a estudiar la organología mexicana, me di cuenta que esos juguetes, eran similares a los que se usaban en el México Antiguo (actual Zona entre el Sur de los EUA y Nicaragua). En el Códice Florentino se incluye uno de este tipo, que se ve en la esquina superior izquierda de la Figura 1.
Durante los últimos dos años he elaborado más de cien aerófonos de viento (familia que podría ser llamada Generadores Mexicanos de Ruido Coloreado) experimentales de diferentes formas y estructuras, algunos de diseño muy similar, pero ninguno exactamente como esa piedrita negra, ya que no lo conocía. Hay algunos artesanos (como los hermanos Gregorio y Mario Cortés de Santa Cruz de Arriba, Municipio de Texcoco del Estado de México) que saben elaborar algunos con principios de funcionamiento parecido pero son de diseño diferente.
Fig. 7. Espectrograma en 2D del sonido del aerófono de piedra negra.
El investigador que más estudió este tipo de aerófonos fue José Luis Franco [8], que los llamó “aerófonos de muelle de aire”. Él también estudió los aerófonos de la Zona del Golfo [9]. Esos aerófonos han sido analizados directamente por otros investigadores que han tenido acceso a ellos, como Susan Raucliffe [10] que los llama de “chamberduct flute”. Jorge Dájer incluyó en su libro [11] una fotografía (Figura 2) de un aerófono de hueso que él llama ocarina, similar al del Códice Florentino, sobre la que comenta lo siguiente:
“La libre entonación en esta ocarina de hueso es controlada lingualmente al cambiar la capacidad de la cavidad bucal, pues ésta forma la cámara, de la que carece este instrumento de difícil técnica ejecutoria. Proviene de Araró (Michoacán) y forma parte del acervo del Museo del Estado, donde de halla(ba) clasificada como lanzadera (núm. 4797)”.
Análisis general.
Fig.8. Espectrograma en 3D del mismo sonido
La familia Beverido me prestó la piedrita negra para hacer el primer estudio sobre un aerófono mexicano antiguo, que se considera original y relevante, usando herramientas y procedimientos probados anteriormente en réplicas experimentales. El caso estudiado más reciente por el autor es sobre la Gamitadera [3].
El aerófono de piedra negra se muestra en la Figura 3. Es relevante por varias razones como las siguientes: La primera, es que constituye el primer aerófono detectado de este tipo elaborado en piedra (contiene algún metal, ya que es de peso específico alto); La segunda, es que muestra con claridad su estructura interna, factor importante, ya que no se requiere de una radiografía para conocerla; La tercera, es su tamaño, ya que es el más pequeño conocido de su tipo; Y la cuarta, es que al estar elaborada con hoyos y canales redondos (cuya forma interior se parece a la de una bala) se puede maquinar en cualquier material rígido en una sola pieza. Esa posibilidad sólo se ha visto realizada en México, con unos cuantos casos de aerófonos de madera, hueso y piedra similares al de la Figura 1 y otros diferentes con embocadura de pico.
Fig. 9. Espectro de potencia del mismo sonido
No se sabe como podían hacer esas obras de arte lapidarias. Aun en la actualidad no es fácil su elaboración en piedra dura, ya que se requiere de herramientas de corte de diamante para hacer sus hoyos.
Diseño y estructura.
En la Figura 4 se muestra el boceto con las principales vistas y cortes del aerófono. La vista superior muestra la parte donde sale el ruido. El corte A-A´ muestra el detalle de la cavidad central resonadora y de salida, así como uno de los dos hoyos laterales. La vista lateral y su hoyo (o canal) son iguales a los del lado opuesto. El corte B-B´ muestra el detalle de los cortes de las cavidades laterales (las de la parte superior e inferior), así como de la cavidad resonadora y canal de salida con su hoyo correspondiente (colocado a la izquierda) y su hoyo de obturación posterior (colocado a la derecha). Ese corte es el que se usa para ilustrar como tocarlo, como se muestra en la Fig. 6. Los tres canales y hoyos están centrados horizontalmente, pero un poco abajo verticalmente. La vista superior indica que el diámetro anterior (9 m) de la cavidad central o de salida del frente es un poco mayor que el posterior (5 m).
Este sencillo boceto es relevante, ya que con él se pueden elaborar réplicas muy parecidas a la pieza original. No se ha encontrado un boceto o dibujo similar en las publicaciones disponibles, sobre ninguno de los cientos de los aerófonos mexicanos antiguos que se han descubierto. En los mejores dibujos sólo se proporciona el dibujo de una vista o corte y en la mayoría de los casos no se dan sus medidas, necesarias para su reproducción.
Ya se elaboraron réplicas en varios materiales como barro y madera (Figura 5), que pueden producir sonidos similares a la original. Con eso se prueba que es posible recuperar el conocimiento necesario para elaborarlas, si se tiene un poco de habilidad para trabajar los materiales y los sistemas para medir y analizar sus sonidos. Ese ejercicio es relevante, ya que tampoco se conocen otros casos en donde se hayan hecho réplicas de aerófonos antiguos que emitan sonidos similares, debido a que los sonidos de los artefactos antiguos no se han estudiado formalmente y no ha sido posible elaborar réplicas precisas porque sus poseedores no tienen la información necesaria y no han permitido estudiarlos formalmente.
Fig. 10. Otro espectro de potencia del mismo sonido.
(Con coordenadas lineales)
Elementos y Funcionamiento.
En la Figura 6 se muestra el esquema de funcionamiento del aerófono, para producir el sonido más fuerte. Debe tocarse en la posición que se muestra en la figura 4, con el corte B-B´, colocado dentro de la boca, entre la parte interior de los labios y la lengua, misma que cubre el hoyo posterior. Los elementos organológicos del sistema boca-aerófono son:
Canal bucal 1, formado entre el paladar y lengua, para generar la corriente aire de insuflación (mostrada con la flecha)
Aerófono con la cámara resonadora principal B (como un tubo abierto) y dos hoyos (tubos A y C), localizados cara a cara, en un eje vertical. El circulo interno de estos hoyos pueden ser dos biseles circulares especiales, donde se genera el sonido.
Cavidad bucal 2, que puede actuar como un resonador de Hemholtz irregular.
Al principio, el mecanismo sonoro puede trabajar como sigue:
La fuerte corriente de aire proveniente de la cavidad bucal 1 se introduce por el canal superior A (del aerófono)
En la salida del hoyo A el flujo de aire comprimido se puede expandir, porque la cámara principal B es abierta y tiene menor presión. Y pueden ocurrir difraxiones, porque la apertura es pequeña.
Las ondas expandidas se dirigen al otro lado de la cámara B y hacia el bisel circular de C, generando reflexiones hacia atrás.
El fuerte flujo principal de aire, que viene del hoyo A, pasa a través del hoyo C y va hacia la cavidad bucal 2, que actúa como un sistema de masa-resorte, generando reflexiones hacia atrás.
Cuando esas reflexiones cruzan el hoyo C se generan más refraxiones dentro de la cámara principal B.
En pocos milisegundos, la combinación de reflexiones y refraxiones (y expansiones), en ambas direcciones, con dos biseles circulares en un espacio reducido, pueden generar una compleja y turbulenta dinámica de ondas, presiones y sonidos, que producen el ruido que se muestra con vírgulas (símbolo gráfico Mexicano para toda clase de seres y fenómenos ondulares, como el sonido)
Las dos cámaras resonadoras amplifican dos grupos de componentes de frecuencias, como se pueden ver en los dos picos amplios de los espectrogramas (figuras 7, 8, 9 y 10)
Puede producir otros sonidos, si se toca de otras formas. Por ejemplo, rotado 90 grados y colocado fuera y enfrente de los labios con el aire introducido por el hoyo posterior, y cerrando con un dedo el hoyo frontal, sus hoyos laterales se convierten en salidas del sonido.
Análisis de los sonidos.
El análisis de los sonidos se realizó con sus espectrogramas. En las Figuras 7 y 8 se muestran los espectrogramas en 2 y 3 dimensiones de un sonido o ruido corto (1 segundo), tocado en forma muy simple. Los sonidos se registraron con el micrófono de una computadora personal con tarjeta de sonido tipo “SoundBlaster”. Los espectrogramas se obtuvieron usando programas bajados de Internet de [12 y 13], mismos que usan una rutina para calcular la Transformada Rápida de Fourier de la señal grabada y registrada en formato Wav (para Windows).
Las gráficas muestran que se generan componentes de frecuencia e intensidades relativas (en dB) muy complejos. Los niveles máximos de sus picos o crestas se dan alrededor de 2 kHz y 6 kHz, pero las frecuencias generadas cubren un rango amplio desde menos de 20 Hz hasta más de 10 kHz.
Como esos espectrogramas se parecen a los de otros aerófonos de fuelle o de viento analizados con anterioridad, en intensidad y en componentes de frecuencias [1, 2, 3], es muy probable que esa piedrita negra sea un artefacto de viento antiguo.
En la Figura 8 se observa también que los componentes de las frecuencias bajas también tienen magnitudes audibles. Para ver más en detalle las características de la señal, se muestra el espectrograma para un tiempo dado, que se llama espectro de potencia (Figura 9). Es conveniente hacer notar, que en estas gráficas la escala de frecuencias no es lineal, ya que se duplica en cada octava, como sucede en la música. Lo anterior se debe a que el programa utilizado es un afinador de instrumentos musicales. Y como las intensidades se dan en dB, en una escala logarítmica, representación cercana a las propiedades de audición del ser humano, tampoco representan una escala lineal.
Usando otro programa [14], se elaboró otra gráfica (figura 10) en la que las frecuencias y amplitudes se dan en escalas lineales, usadas con frecuencia en análisis técnico-cientificos de señales. Con esta escala y el uso de otras unidades de amplitud (EU2 en lugar de dB), se notan con mayor claridad los componentes de frecuencias de mayor intensidad o sus picos mayores, ya que los niveles bajos se reducen considerablemente. Se notan 4 picos que corresponden a las 4 cámaras resonadoras del sistema boca-aerófono (2, C, B y A de la Figura 6). El pico más grande corresponde a la cámara principal B.
Conclusiones y recomendaciones.
El ejercicio, original en el ámbito nacional e internacional, demuestra que las herramientas y técnicas utilizadas son efectivas para analizar aerófonos mexicanos antiguos y sus sonidos complejs.
Se ha mostrado que el análisis organológico junto al acústico de los sonidos puede ser de utilidad para dictaminar sobre la autenticidad de bienes muebles arqueológicos sonoros. Esas técnicas no han sido aprovechadas por la arqueología ni la etnomusicología tradicionales.
Se ha visto que los espectrogramas también han servido para evaluar la fidelidad sonora de las copias o réplicas elaboradas.
Es recomendable analizar en forma similar los aerófonos de fuelle existentes en poder de los museos, para hacer comparaciones y correlaciones.
Es necesario informar del estudio al Museo de Antropología de Xalapa, para ver si tienen interés en el aerófono de piedra negra analizado y en su posible exhibición o divulgación.
Se desconoce la dinámica detallada del mecanismo de producción de sonidos de este tipo de aerófonos, misma que requiere de investigación avanzada. Su sistema pertenece al campo de modelos dinámicos no-lineales, ya que operan en un rango amplio de vibraciones de presiones y ondas de sonido no periódicos, dentro de dos cámaras (una de ella muy pequeña) y dos biseles especiales circulares, como un proceso caótico y turbulento. Esta clase de modelos matemáticos está en la frontera de varios campos avanzados del conocimiento, como dinámica de vórtices y visualización científica y de flujos turbulentos.
También se desconocen los elementos antropológicos y organológicos de los generadores de ruido Mexicanos, desde su nombre original hasta su uso antiguo.
Las técnicas empleadas, pueden servir para analizar sonidos menos complejos como los de los instrumentos musicales antiguos y modernos. Eso ya se probó con un análisis del sonido musical más antiguo, de una flauta de hueso de China de 9,000 años [15].
El presente estudio ya fue puesto en Internet en las páginas del autor con otros estudios, entre los que se incluyen los listados en las Referencias siguientes.
Referencias.
Velázquez-Cabrera, Roberto, “Estudio de Aerófonos Mexicanos Usando Técnicas Artesanales y Computacionales. Polifonía Mexicana Virtual”, Proyecto de tesis de Maestría en Ciencias de la Computación, CIC, IPN, Marzo 2000
Velázquez-Cabrera, Roberto, “Analisis de Aerófonos Mexicanos”, Ponencia presentada en el Congreso Internacional de Computación CIC-99, IPN, México, Nov. 17 de 1999.
Velázquez-Cabrera, Roberto. “Análisis Virtual de la Gamitadera”, Conferencia para el 7º. Congreso Mexicano de Acústica, Veracruz, Ver. Mexico, octubre 2000.
Paz, Octavio, Medellín, Francisco y Beverido Francisco. “Magia de la Risa” Sep/Setentas, 1971.
Boiles-Lafayette, Charles. “La Flauta Triple de Tenenexpan”. La Palabra y el Hombre, II, Epoca 34, Revista de la Universidad Veracruzana, Abril-junio de 1965.
Beverido, Francisco, Pereau. ” Estética Olmeca”, Biblioteca Universidad Veracruzana, Xalapa, Veracruz, México.
Medellín-Zenil, Alfonzo, “Cerámicas de Totonacapan. Exploraciones Arqueológicas en el Centro de Veracruz”. Universidad Veracruzana, Instituto de Arqueología, Xalapa, Ver. México, 1960.
Franco, José Luis, “Flautas de Muelle de aire”, Excélsior, México, 14 de octubre de 1962.
Franco, José Luis, “Musical Instruments from Central Veracruz in Classic Times”, Ancient Art of Veracruz, Exhibition Catalog of the Los Angeles County Museum of Narural History, 1971.
Raucliffe, Susan. “Complex Acoustics in Pre-Columbian Flute Systems”, Experimental Musical Instruments, Organology, Vol. III, #2, 1986. Publicado también en el libro “Musical Repercussions of 1942: Encounters in Text and Performance”, Smithsonian Institution Press, 1992
Dájer, Jorge. “Los artefactos Sonoros Precolombinos, Desde su Descubrimiento en Michoacan”, FONCA-ELA. México. 1995.
Horne, Richard, Spectogram V 5.0.9, Freeware, Gram Atentamente, ha autorizado a utilizar y mencionar su excelente programa en mis estudios. El programa es gratuito (freeware). (http://www.monumental.com/rshore/gram.html).
Volkmer, D., “TUNE!IT”. Es un programa de uso compartido (shareware), que se uso en el tiempo de pruebas. (http://www.zeta.org.au/~dvolkmer/tuneit.html.)
Liangson He, Signal Analyzer Toolkit V.2., Sat32. Sharaeware, usado en tiempo de pruebas. (http://www.userworld.com/users/hlingso/remote.htm).,
Figuras.
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