VIRTUAL ANALYSIS OF "GAMITADERA"
Roberto Velázquez Cabrera
paper in Spanish will be presented in the VII Mexican Congress on Acoustics, in
This study is an illustrative example of
recommended actions included in a previous study [Velázquez-Cabrera, 1999], to
prove the effective and relatively simplicity of a proposed methodology,
analyzing specific cases of Mexican relevant aerophones. The first selected
case is an extraordinary aerophone of clay that is in exhibition in the
The information obtained of the original "Gamitadera" is the following:
It was discovered by the anthropologist
Marco Antonio Reyes López, former researcher of the
Employers of the
The only known public document with mention to this extraordinary aerophone is an article of Susan Rawcliffe [Rawcliffe, 1965], who has been analyzing ancient flutes, and constructed and plays her sound sculptures for 25 years. In her article it is included a brief analysis of the Gamitadera, called by her as "chamberduct flute". She comments: "The sound of this instrument type is extraordinary, varying from a raspy throat gurgle to wrenching cry, depending on construction and on performance practices"
In her article was included a set of drawings with views of sections of aerophones (called by her flutes) of several museums and collections, made by the artist Jim Grant on the base of a carefully visual analysis of the aerophones made by herself, including the "Gamitadera". The drawing of the "Gamitadera" (that I did not know) and the Susan Rawcliffe´s comments, motivated my trip to Xalapa.
Don (used to give respect) Brigido Lara [Vacio, 1996], one of the best sculptor of Mexican ancient art replicas with near 50 years of artisan experience and now working for the Museum of Anthropology of Xalapa, opined that the clay used in the original "Gamitadera" is from the same place and similar material used by him. Also he mentioned that it is not easy to make replicas that sound well.
Having seen the original "Gamitadera" in the show case of the museum and with the help of Susan Rawcliffe´s drawing and the help of Don Brigido Lara I elaborated a drawing with the view of a section, showing the structure and interior components (figure 3)
1. Firsts resonating chamber in a donna shape flattened at the center.
2. Second chamber of globular shape. Principal resonator or oscillating chamber.
3. Third resonating of tubular shape.
4. Small hollows.
5. First central hole, for the input of blowing or insuflation.
6. Second central hole, for the input to the globular resonating chamber.
7. Output cannel to the resonating tube.
8. Exit hole.
In base of the drawing, I made a set of replicas (figure 4) using several types of clay, including one provided by Don Brigido Lara and other by Mario and Gregorio Cortéz of Santa cruz de Arriba, Texcoco, from State of Mexico (they are the most experimented Mexican clay flute makers), and one from Oaxaca state available commercially in Mexico City. The three are very good. The first two are sandy, excellent to minimize la possibility of cracking in big pieces. La last one, is good for small pieces with delicate details and to obtain shined or polished surfaces.
The replicas where made with the help of spherical molds, to form the principal chamber (2) and with the help of a cane and the hands it was molded the resonating tube (3). The rest was finished with clay pinding and sticking of the pieces. The holes were made and finished with a bit and a round stick. It was tried to obtain replicas with small variations in shapes and dimensions, to see their effects.
The generation of sounds is similar to those
"of wind" or "spring of air" as are called by Jose Luis franco [Franco, 1962, 1], whom
analyzed them by more than 10 years. He is one of the few who written about the
Totonacan (ancient culture from center the
The air stream is introduced through the input hole (a) and it goes to the input hole (b) and to the oscillating chamber (2). Inside the air is then compressed to a limit when the pressure inside the chamber is equal to the air blowing pressure, then no more air inputs the chamber (2), but the inputting air pulls more air and the time comes that the inside the chamber (2) there are less pressure than the blowing air; then more air enters inside the chamber (2) until it equals the equilibrium of pressure with the blowing air. This cycle is repeated indefinitely generating the sound.
The previous is not sufficient to explain the differences between the sounds generated by the "Gamitadera" and those of conventional spring of air, since they differs noticeably. Neither it includes the other organological elements included in the draft. It has to be explained, at least, the possible effect of the first chamber (1). It is necessary to note that the oscillations of this spring of air would have to function at the same time in a wide range of frequencies, bigger than the audible. Until the availability of technology exists to simulate and to analyze in detail the dynamic behavior of the air and the sound waves in high frequencies in multiple and irregular chambers, it will be possible to know the detailed behavior of complex aerophones like the "Gamitadera".
What it can be affirmed, is that the resonating tube is an amplifier of their corresponding frequencies of its dimensions. As the majority of aerophones with a hole (d) it can modify the frequencies, if it is partially covered or if an additional chamber is formed with the hands. If the holes (a), (b) and (c) coincide in a line, it is possible to improve its sonority, and facilities its adjustment from outside. Also helps the sound generated to flat a little the upper globular surface around the input hole (b). Of course, The general principles of resonators are maintained: The frequencies most amplified are those related to the dimension of the principal chamber (2) and the resonating tube (3). If their dimensions are increased, the stronger sounds are of lower frequencies and these are higher when the size of their internal cavities are reduced.
It was necessary to make several replicas to be able to generate audible sounds. We had "to kill" several silent replicas before its possible burning. Angel Mendoza, who has been a companion in these experiences, also elaborated two replicas that specked when they were made but become mute when they were burned.
It is very difficult to make ones that generate strong and clear sounds. The elements that affect more are: The distance, aligning (of centers) and dimensions of and between the upper blowing hole (a), that must be of smaller diameter, and the hole (b) of the spherical resonating chamber (1). Also affect, in lesser extent, the dimensions, the finishing, the aligning and surface of the output channel (c) from the two first chambers (1 and 2) and the resonating tube (3). It seems that the small cavities (4) in the end part of the resonating tube (3) do not very much influence in the sound produced. It was tested with the three used professional clays than it is possible to make replicas that can "speak", "sing" or "cry".
This type or artifact can not be catalogued as musical instrument, because it does not produce musical sounds. Even if some researchers, as Samuel Martí [Martí, 1968), had tried to analyze and adjust them to musical concepts and criteria, like when they say that they are tuned to some musical note.
The sounds of the replicas were recorded with a personal computer, with a sound card (Sounblaster type) and a microphone. The recorded sounds are very short, of less than a second and were stored in wav format. This type of format is used by Windows system. There are methods to analyze signals on the time domain, but they are complex for the purpose of the work.
In the following it is included a visual comparison of spectrograms from five replicas made, to show some differences in their frequency components. A spectrogram is a graph of the power spectrum of the frequency components of a signal, for different times. The spectrograms are helpful to analyze sounds, like those of this case, that have a complex combination of frequencies and intensities, in a wide range of frequencies. There are spectrum analyzers but they are expensive and I have not found laboratories with them available to me.
To obtain the spectrograms I used the last version of the Richar Horn´s program "Gram", openly and freely available in Internet [Horn]. This program generates and shows the spectrograms in two dimensions: frequency (kHz) and time (sec). The colors correspond to the amplitude of the signals (dB), variable of dimension 3. In this case a scale of 60 dB was selected (figure 5).
In the upper part of the graphs (figure 6) includes the signal of the waves in the time, that appears spots by their frequency components.
It is observed that the replicas produce sounds with frequencies in ranges of certain amplitude, with its strongest picks between 1-5 KHz. The first two produce additionally notes with fundamentals and harmonics, determined in function to the resonator size. In the last three, all the frequencies are of larger amplitude and their noise components have wider ranges. This shows that with small variations of the structure they can generate different sounds, but it is possible to make groups of replicas that generate spectrums of certain similarity.
Each of the previous signals can be seen with more detail. For example, selecting the last signal (of previous figure 6) a spectrogram can be produced by changing the background color, the frequency window or the sampling rate (to 44.1 KHz), the time scales and the amplitude (in this case of 30 dB9) of the graph. This makes us to use the colors of the upper part of figure 5, what shows now that maximum levels are shown with colors red, orange and yellow on the spectrogram of figure 7.
This figure 7 shows the sonority cause of the replica, since it includes a wide range of high intensity signals. The frequency range exceeds the maximum frequency range of audible sounds for humans being (20 KHz). However, the shown frequencies over 12 KHz are questionable, due to the used microphone, since it is of common capacitor for personal computers.
This same signal can also be visualized in its 3 dimensions (amplitude, frequency and time), using the program Tunit [Volkner], as it is shows in the spectrogram of figure 8. In the spectrogram can be seen that the minimum frequencies also exceed (down) the limit that the human being can hear (20 Hz). It is noted that in all the frequency range the signals are of significant magnitudes. In the low frequencies there are strong beats.
The result proofs that the methodology used is effective to help find and to disclose secrets of Mexican organology, that was developed during several millenniums and was destroyed, forbidden and forgotten for five centuries. Only after making similar analysis of each type of Mexican relevant aerophone, it induces to aspire to make comparisons and correlation between them. The difficulty to make them with good sounding shows that artisans and high priest makers were very skillful, and they must have been specialists.
It is necessary to analyze the original "Gamitadera" with better tools and to make replicas more near the original one. It is necessary to get pictures, x-ray pictures and the dimensions of the ancient artifact. It is to analyze its sounds with a recorder and microphone, to get digital files for processing.
1. Velázquez-Cabrera, Roberto, "Estudio de Aerófonos Mexicanos Usando Técnicas Artesanales y Computacionales. Polifonía Mexicana Virtual", MD thesis (in Spanish), CIC, IPN, May 2000.
2. Medellín-Zenil, Alfonzo, "Cerámicas de Totonacapan. Exploraciones Arqueológicas en el Centro de Veracruz". Universidad Veracruzana, Instituto de Antropología, Xalapa, Ver. México, 1960.
3 Boiles-Lafayette, Charles. "La fluta triple de Tenenexpan". La palabra y el Hombre, II, Epoca 34, Revista de la Universidad Veracruzana, Abril-junio de 1965.
4. Raucliff, Susan. "Complex Acoustics in Pre-Columbian Flute Systems", Experimental Musical Instruments, Organology, Vol. III, #2, 1986. Also publised in the book "Musical Repercussions of 1942: Encounters in Text and Performance", Smithsonian Institution Press, 1992.
5. Vacio, Minerva, "Brigido Lara, inventor del nuevo arte prehispánico", Arqueología Mexicana, Vol. IV, Núm. 21, Sepiembre-octubre de 1996.
6. Franco, José Luis, "Flautas de Muelle de aire", Excélsior, México, 14 de octubre de 1962.
7. 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.
8. Martí, Samuel. "Instrumentos Musicales Precortesianos." INAH. 1968.
9. Horne, Richard, Spectogram V 5.0.5, Freeware, Gram (http://www.monumental.com/rshore/gram.html).
10. Volkmer, D., "TUNE!IT", (http://www.zeta.org.au/~dvolkmer/tuneit.html) Shareware. Used in the time allowed for testing.
Fig. 1. Unburned replica made with Brigido Lara´s sandy clay
Burned replica made with "
Fig. 3. Sketch with lateral view of "Gamitadera" cutting.
Fig. 4. 5 clay experimental replicas.
Fig. 5. Signal levels (in dB)
Fig. 6. Spectrograms of 5 replicas
Fig. 7. Louder replica spectrogram.
Fig. 8. Louder replica spectrogram, in 3D.