A Methodology for the Analysis of Ancient Aerophones.
Case: Four Mexica Tlapitzalzintli from Templo Mayor Museum.
(Working draft for international public consultation)
Roberto Velázquez Cabrera
A short version of this study was presented in the 142nd Acoustical Society of America (ASA) Meeting at Ft. Lauderdale, Florida, December 3-7, 2001.
Study using experimental replicas.
1. Objectives, introduction and available information.
2. Visual analysis of the aerophones and their dimensions.
3. Analysis in function of similar aerophones of the same culture.
4. Construction of the aerophones.
5. Analysis of the sounds using experimental replicas.
5.1 Ideal analysis.
5.2 Analysis using spectrograms.
5.3. Experiments in archaeological sites using replicas.
References from Internet.
Study using experimental replicas.
1. Objectives, introduction and available information.
The main objective of this study is to improve a methodology for the analysis of ancient aerophones and to test it with a relevant case of four Mexica (Aztec) Tlapitzalzintlis 1 from an Offering that was in exhibition in Ritual and Sacrifice Hall of Templo Mayor Museum of Mexico City (1), The basic methodology already was used in previous studies (2). It was wished to complement it with the recommendations and advise of some experts on aerophones and flutes as Alan Albright (3) and Professor Dr. Ray Dessy (4) and other acousticians as Dr. Rolando Menchaca and Sergio Beristain and musicians as Nancy Rumbel to generate a improved methodology opening the process to an international consultation with the experts and institutions that may be interested.
The improvement of a formal methodology is important because it was not found in the literature efforts to define and prove something useful and applicable. The methodology must be applied to clay aerophones, because they are the majority of the archaeological sonic artifacts found in playable conditions. There are some studies on ancient aerophones, but most of them are general or introductory. They show only descriptions, pictures or drawings and try to cover wide sets of cultures or periods. Some of them are specific but most of them have mistakes or are contradictory, mainly derived from the fact that they where studies from the point of view or references only of the actual music and organology or they did not used a formal method of analysis, metrology equipment and software for the analysis of the sounds and the dynamics of the flows. The methodology must be applied to specific cases and every relevant ancient aerophone must be studied as deep as it can be. However, there are important studies on ancient aerophones and some of them includes acoustical analysis. The best found studies are the following:
The best study of a Mexican flute is "La flauta triple de Tenenexpan" by Charles Lafallette Boiles, published in La Palabra y el Hombre, 2, Epoca 34, magazine of the Universidad Veracruzana, April-June of 1965. It was made from the point of view of a musicologist. The triple flute is in exibition at the Anthropology Museum of Xalapa.
Susan Rawcliffe (5) included two spectrums to show the influence of the voicing dimensions of two Mexican ocarinas in her paper "Complex Acoustics in Pre- Columbian Flute Systems". She included also several drawings of "dissected" ancient clay aerophones, some of them with several chambers and complex sounds.
The first formal study of a set of relevant ancient aerophones, is on "Peruvian Whistling Bottles", from Steve Garrett and Daniel Statnekov (6) published in JASA (Journal of the Acoustical Society of America) that included acoustical measurements and the use of Helmholtz's equation.
Flutes of Caral were analized by Sady Solis and other researchers from Peru (19) using archaeological and acoustical methods. The Aerophones of Caral were anlized by the author, because the original paper provides their organological structure and dimensions.
There is a Project on Antaras Nasquences by Anna Gruszczyñska (20) from the Warsaw University with musical and acoustical analysis.
Dr. James Cottingham analized acoustically several reed instruments from Asia (21) including the sheng.
Professor Neville Fletcher analysed acoustically the didjeridu or yidaki from Australia (22). Its methods and finds were used to study the Maya Trumpets of Bonampak.
It was found only one study on Mexican aerophones, on "Musical Artifacts of Pre-Hispanic West Mexico", by the musicologist Peter Crossley-Holland published by the Department of Ethnomusicology of UCLA in the Selected Reports in Ethnomusicology, Vol. I (out of print) (7) that includes a methodology for the analysis of the sounds, but it has not been applied.
The paper "Análisis Acústico de Artefactos Sonoros de Viento del México Antiguo" presented in The VII Mexican Congress on Acoustics by Dr. Rolando Menchaca and the author, in Veracruz City, Mexico, in October, 2000. It includes an acoustic methodology for the analysis of Mexican sonic artifacts.
The bests technical elements for analysis of those extraordinary papers will be considered and applied in the study (if it is possible).
I must mention that there are very few leaders in acoustics of wind musical instruments that are interested and made studies on ancient aerophones or globular resonators as Drs. John Coltman (8) Ray Dessy and Neville Fletcher. Also, there are many excellent acoustical and musical studies of modern aerophones, like those of the recorder, the Boehm flute, tubes of organs and whistles, but some of their ends may not be very useful to find secrets of those Tlapitzalzintlis, when they had the actual music as the only reference for the analysis. Those advanced method used to analyze wind musical instruments were not applied to ancient aerophones.
The selected case is very important, because those aerophones were found in an Offering of the main Mexica Ceremonial Center Precinct (Recinto del Centro Ceremonial) at Tenotchtitlan . They belong to one of the main organological cultures that were alive before the Conquest. During the Conquest the best Mexican organology was killed and forbidden as their masters and players, because "they belong to the devil" and they wanted to impose their religion-culture, economy and technology (or their Colonization).
The music was fundamental in their everyday life. And the best music and organology were played in the main ceremonial center. They had big celebrations every month. The massacre in the Great Temple took place during the festival of Huitzilopochtli, when the dance was loveliest and when song was linked to song the watching Spaniards rushed into the courtyard and slaughtered the celebrants who carried nothing in their hands but flowers, feathers and their musical instruments (Panhuehuetl and Teponaztli), that can be seen in the drawing of the killing (The drawing of Armando Ramirez Nava was taken from Duran Codex and it was painted with Photoshop).
In addition to the Calmecac, the school for priests, there was a special house called Cuicacalli (house of singing). It was for teaching the music. In this school of music there were two main priests, one was Ometochtli, representing the God of "pulque" and the other was Tlapitzcalzin, Sir of the flutes´ house, to provide all the necessary for such so important cult. There was a house called Miscoacalli, where all the masters of singing and dancing from Tenotchtitlan and Tlaltelolco had their performances with all their musical instruments. In that situation it is impossible to imagine the ancient Ceremonial Center without singing and their sonic artifacts. Also, there was a Mecatan, where the priest-performers learned to play flutes.
The Conquest, the Inquisition, and the Colonization were so destructive and effective that the Cuicacali , the Mecatan and the Miscoacalli, that existed in the Ceremonial Centers of all the Mexican cultures remain "killed". Furthermore, the modern temples of the knowledge have not accepted the ancient music and organology in their educational and research programs. The colonization was institucionalized when the schools were created as copies of those from the colonizers. The Mexica culture is one of the most studied, mainly in relation to war, dead, visual arts, monumental constructions, sculptures and ancient artifacts, but other fine Mexica art and technology are not well known. The formal analysis of the discovered Mexica organology remains to be done.
As the information of the Mexica aerophones is unknown, other objective is to show that even in this case without any descriptive information and data, it is possible to make some analysis. It is important to be able to make studies even in this situation, because the lack of organological information is very common in museums and in the literature.
Many specialists related to the ancient organology (mainly archaeologists, anthropologists, ethnomusicologists and musicologists) think and say that it is impossible to get something interesting about the substantive function of ancient musical instruments or sonic artifacts and it is one of the main origin of the lack of studies on the Mexican organology. They say that if we do not have their recorded or written music it is impossible to know something about their music scales, fingering, etc. It is true that it is impossible to know the exact performance of the ancient music, but I will try to show that it is possible to get some secrets of the construction, properties and probable ancient use of those little aerophones, including their best sounds and fingering, even without any descriptive data and without having direct physical access to them. It is a work for specialized detectives, but it can be done in this difficult case. The only information available to the public of the Tlapitzalzintlis is a text that was included in the display cabinet:
"Offering 2 comes from the excavations in the Game of Ball located under the Chapel of Animas (souls), in the rear of the Metropolitan Cathedral. The offering is composed mainly of musical instruments, some of them are decorated with the face of Xochipilli, God of the flowers, music and the game."
The text is very short but its deep meaning is very significant. It means that they considered that the sonic artifacts were very important for them and to play their best "music", because they were offerings to their Gods and they live by and for their Gods. It may be that the objects included in the Offering are sacred or related with sacred ceremonies, relations, communications and experiences, as Alan Albright remarks seriously.
Their concept of "Music" was very important, wide and especial. The law created by Natzahualcoyotl (the king poet - philosopher from Texcoco) that was adopted later by the Mexicas, included four councils: War, Justice, Finances (the previous three were for the administration of their kingdom as in any nation) and Music. Music was also a matter of good government at the highest level but it included all their knowledge and culture: music, science, history, art, literature and poetry, dance, singing, theater, and everything that they had for their Gods.
Unfortunately, the powers of the new Nation are not interested in the study, the development or the use of that rich ancient Mexican culture-technology of organology. In practice and officially5 it is a forbidden matter (9) and no one is interested in their research and divulgation. The laws that order the study of the pre Columbian and indigenous cultures are "dead" words, in this field. Now, most of the best professional musical instruments and music are imported.
It was solicited to INAH (Instituto Nacional de Antropología e Historia), Museo del Templo Mayor and Museo Nacional de Antropología the regulations to get information and data of ancient aerophones to test the proposed methodology 5. A letter to the President of México was sent (10) including some details of the difficulties to study the rich ancient organology and to ask him for help to solve the problems to study and promote the Mexican organology and a letter to the Senate (11) to request and recommend that in the legislative works made to rescue and to promote the Mexican cultures and technologies they include regulations and programs to assure their suitable attention and compliance. The best answer was the silence.
One of the main archaeologists-researchers of Templo Mayor Museum, Leonardo López Lujan, in 1990 made a thesis on the Offerings, that were 110 at that time. In his study he mentions that several offerings have many object classified as "representation of musical instruments". Indeed it is possible to see several representations in the museum and in some publications, because they are solid miniatures of the real ones, but there are other artifacts that may sing like the subjects of this study. It was not found an official publication with the archaeological or organological information of any musical instrument found in that site, but there are other aerophones in exhibition in the Museum and photos in publications. The most extraordinary of them are the whistles and flutes on stone, that are also unique.
In The Program for the 2nd Symposium of the International Study Group on Music Archaeology at Michaelstein on Sept. 17-24, 2000 (12) was included a conference of Bertina Olmedo Vera "Miniatures of Musical Instruments in The Templo Mayor Mexico". Unfortunately, she informed me that she did not attended that conference and the paper was not made.
A Manuscript of 2001 on Aztec-Flower Flutes from the Ethnologisches Museum in Berlin was provided by Arnd Adje Both. It has acoustics, music iconology, ethnohitory and symbolism elements. His last paper on Flutes of Tlaloc from an Offering of Templo Mayor, that will be included in a doctoral thesis in progress, was presented in the First Sessions on Ancient Sounding Instruments at Cancun (23).
The display cabinet of Offering 2 shows other four whistles without tone holes with a tubular wind way and a globular resonator with the head of a little bird that seems cock or bully or perhaps parakeet, two miniature representations of Teponaztlis (the real ones are two-toned drum of hard wood) and drums of clay, and other small artifacts of stone and clay. This possibly means that the Tlapitzalzintlis may be played with other sets of relevant Mexica instruments.
Alvaro Barrera Rivera, the archaeologist that directed the exploration of Offering 2, in 2000, commented that the report of this exploration has not been elaborated. He is the first that commented that the instruments can generate sounds. Also, he informed that the aerophones really were found in Offerings 2 and 3 located in the West - South corner of the Game of Ball. There are three similar flutes in other Offerings from Templo Mayor like the 106.
2. Visual analysis of the aerophones and their dimensions.
In this case, the visual analysis of the Tlapizalzintlis is necessary, because it is the only way to get information and estimation of their dimensions.
They have all the organological requirements to produce sounds: wind way, voicing, edge, resonating tube and four pitch holes. The clay used is fine but sandy. The color is red without painting. Their making is very fine and it must be difficult and delicate due to their very small size, design and assembly.
Their structure and shape are typically Mexica. They have the resonating tube closed with the Xochipilli's face and they have a short wind way.
Organologicaly they are similar to the known Mexica flutes (like the modern recorder) as Muy agudas (high pitch), Texcatlipoca and other that are in museums or in studies. Some of them are five Mexica flutes classified by Leopoldo Batres in the beginning of the last century as 128, 129, 130, 131 y 132. They can be used as a reference because they were studied by several researchers. The author made an analysis of the 130 (13) (which it is the smallest). But there are differences in sizes, internal and external shapes and external adornments.
The best study of those Mexica flutes was made by the engineer Daniel Castañeda in 1930. It seems that the same flutes were studied also by José Montes de Oca, Miguel Galindo, Samuel Marti and Thomas Stanford. Unfortunately, the studies were realized also from the point of view of actual music and they did not have advanced metrology equipment (not invented at the time) to make the acoustical measurements. Their main purpose was to analyze the pitch of the sounds but they found different musical scales and notes for the same flutes.
It is interesting to know that Leopoldo Batres was the first archaeologist that found old musical instruments in the same site in his exploration on Escalerillas street realized in 1900, along the center of the Ball Game area. Alvaro Barrera informed that those aerophones are in the Museo Nacional de Antropología and in the same area other musical instruments were found during the construction of the tunnel for the Metro.
The small size of the four Mexican aerophones is their main distinction. They are in the limit between tubular and globular resonators. They are similar in size and shape, but total length is not equal. Using a trick from copyists (a ruler with millimeters and a square) I estimate the sizes of each one in 72, 73, 74 and 76 mm +/- 2 mm of maximum error, I hope. The differences in sizes may mean that they are not tuned to a musical scale, but they can be rich in beats if they are played together at the same time.
Using photos, their total length as a reference and a method of perspective from Leonardo da Vincy (trigonometric proportions and projections) it is possible to estimate the main organological dimensions of each one. For example, if we use the photo of the smallest, that is the nearest from this point of vision and parallel to the glass, the main data in millimeters may be: total length = 72; wind way length = 10; voicing length = 4; voicing width = 5; distance from the edge to the tone hole 1= 8; distance between centers of tone holes 1 - 2 is = 8, 2 - 3 = 7.5 and 3 - 4 = 7; and the diameter of the tone holes = 3.5. If the thickness of the wall is 3 mm and the thickness of Xochipilli face is nearly 15 mm the internal length of the tube may be nearly 45 mm and the minimum and maximum diameters 7 mm (near the face) and 9 mm (in the voicing). The real internal dimensions may be different because we do not had access to the artifacts and we do know the thickness of the head and the wall.
Using a computer and a program to process digital photos (like Photoshop) it is possible to print the photo at a wished scale to get the measures directly. This exercise was made to test the previous estimations. The exact dimensions can be obtained only with the direct analysis of the ancient aerophones and to their X-rays or other good method to know their structure.
The visual analysis and the digital photos of the Tlapitzalzintlis are also useful to see their organological structure in detail and as an input to know the procedure of their probable construction and the making of experimental replicas for the study.
3. Analysis in function of similar aerophones.
This analysis may be made in relation to the Tlapitzalzintly Mexica 130 (13), because it is from the same culture, it is very similar in size and it was studied before. If we use other kind of reference, as aerophones from different cultures and uses, it is possible to fall in big mistakes or to find nothing or few features in common, new or original findings. That is the detected main error of most of the very few studies on ancient aerophones.
It is probable that they can produce similar sounds, but the main difference is that the Tlapitzalzintlis can not function with the tube opened as the 130 and therefore they can not produce the two timbers of their two modes. The sound produced with the pitch holes and the tube closed can not be played in wind musical instruments, using the fingers. In the 130 the louder sound was obtained in his open mode.
There are other differences. The embouchure of the 130 is larger, it has a tube of constant section and a bell in his front end. This means that their sounds may be different in timber and harmonics.
By its smallest size the pitch of their sounds must be higher, but maybe more in the middle of the range of maximum hearing sensitivity of humans (1-4 kHz), which makes them good to transmit sounds at long distances or in wide areas, as those of any ancient ceremonial center.
Similar to the 130, because they have four holes, they can be played with one hand, freeing one hand to play other instrument or to handle other ancient artifact. If the flutes have more than four holes it is necessary to use the two hands to operate them. And we must remember that the number four was a sacred number for them.
Equal to the 130, by the previous advantage, it is possible to play two little aerophones at the same time by one performer.
As the 130, equal and by their smaller distance between the tone holes they are more likely to be played by kids with small fingers and/or to be operated by adults with two fingers, using each finger to close two adjacent tone holes. The last feature reduces their tonal range and the possibility to play melodies with a wide series of tones, but it facilitates the generation of sounds richest in special and continuous variations like "trinos", "glissandos", etc.
It may be equal to 130 but more difficult to find a good mathematical model adapted to them, due to their small size and the influence of the voicing geometry and relative dimension, specially in their highest notes. The sounds of 130 when was operated closed, were of low intensity. But the performance of the Tlapitazalzintlis will be seen in point 5.
The visual analysis of other similar Mexica flutes and whistles from museums and publications was very useful to see the structure and assembly of their main elements to find the probable process of their making. In this analysis the broken similar Mexica aerophones were the most useful, due to the lack of X-rays and drawings to see their internal structure.
4. Construction of the aerophones 4.
The objective of this work is to provide insight into a possible way that might have been originally used in the construction of the Tlapitzalzintlis. The Mexica flutes of small format are unique in archaeological finds and represented for the makers challenging processing, construction and playing, whose details are currently unknown.
I have made copies of the flutes using a very fine clay, without sand. It is commercially called "Oaxaca". (Oaxaca is a State of Mexico). It is good to make small pieces and it has a shrinking factor during drying and burning of ~ 8%. The yellow ochre of this clay is also good to take the photos of the construction. The clay of Mexica flutes seems to be sandier, but its analysis is not known.
Considering previous experiences in the construction of this type of Mexica flutes and the visual analysis of the Tlapitzalzintlis in the display cabinet and other broken flutes of the same structure, it is very probable that the original construction used several pieces and very delicate processes. The main manual work steps and tools may be the following:
Note. A click in the Photo number of each section leads to an illustrative image.
Photo 1. Several tools of wood and clay. Little sticks: a conical one to mold the resonator tube; flattened and sharpened ones to make the mouth, the edge and wind way; and a round one to drill the pitch holes. A clay mold may be used to make the Xochipolli face.
Photo 2. The resonator tube can be formed with a "tortilla" of clay. There are several ways to make a suitable "tortilla" (patty) or a plain piece of clay of predetermined thickness. One of them involves two little tables of the desired thickness. Two flattened sticks or thin trowels can be used (2 mm) and a round wood like roller employed in a manner similar to that used in forming a flat mass of wheat dough. The resulting thickness is between 2 and 3 mm. A second approach involves the more common process used in making "tortillas" of maize, using the hands and two tables.
Photo 3. The cut clay "tortilla" is coiled around a stick, which is a little conical and thinner in the far, or distal end and made of the desired thickness.
Photo 4. The tube is smoothed and cut at both ends (inclined a little) to the desired length (this is not known with precision) anticipating the reduction of the clay after drying and burning.
Photo 5. A round stick can be used to mark and create the four pitch holes.
Photo 6. With a sharpened and flattened stick it is possible to cut and to mold the mouth and its blade (bevel or edge).
Photo 7. A very delicate operation is the flattening of the bevel and shaping it into a wedge.
Photo 8. The pitch holes are sharpened and the internal flashes are eliminated. The pitch holes and the bevel can be done after covering the tube and putting in the wind way, but this makes it difficult to flatten the holes on the inside, to avoid turbulence which can interfere with the production of pure sounds.
Photo 9. The back of the tube is covered with a flattened piece of clay.
Photo 10. The back piece is flattened at the same level of the superior (upper) part of the sonorous hole or mouth and opposite the face of the bevel or edge.
Photo 11. With another strip of flattened clay the wind way (or air channel) is molded placing it around a stick with the internal form of the wind way. The making of the wind way in a separate form, and its patching to the flute body, is a common practice in many ancient Mexica aerophones (whistles, ocarinas and flutes). This can be verified by observing some broken aerophones in Museums, like the one of Xochimilco or in a whistle from Texcoco that I could see.
Photo 12. The molded wind way is placed upon the previously prepared mouth and edge. The direction of the wind way must be adjusted so that the instrument generates clear and strong sounds as the jet stream is split by the edge. It may be necessary to sharpen the bevel. This is an operation of great refinement and gentleness. One tenth of millimeter can make the difference between good sounds and silence
Photo 13. The molded wind way is patched to the tube using two small pieces of flattened clay with the form of a virgule (that also is an ancient symbol related to speaking and singing) in the two sides of the voicing. They also serve as guide for the exit air. The sonorous mechanism must be proved and if it is required it is possible to make new adjustments. The external and inner form of the mouth is sharpened and aligned.
Photo 14. The face is molded using a piece of clay and the mold. The use of one mold to make the face of the four aerophones may mean that they were made by the same Tlapitzcalzin.
Photo 15. The back part of the face in the mold is flattened and it is placed and beaten to the front of the little flute.
Photo 16. The patch is reinforced, with little pieces of clay, taking the opportunity to make lateral and superior adjustments to the hair and adornments.
Photo 17. This is the finished flute before firing. It is good to let it dry slowly in the shade. After several days it is put into the sun several hours, and then it can be fired with wood or charcoal. Because of its small format and thickness it can be burned in a brazier used for barbecue. Usually, the burning temperature must be incresed gradualy up to 800 – 1050 C, depending of the final hardness. The cooling must be also slowly. It seems that the original flutes did not have painted decorations.
Photo 18. This is the flute after firing.
a. The main relevance of this work of a modern Tlapitzcalzin is that it provides the first known detailed description of the possible steps used in the making of a relevant ancient clay aerophone. It was not easy. I had to practice nearly three years to make clay aerophones of good quality.Other very good result of this exercise was that I learned how to make the required experimental replicas for the following works of the study.
b. Similar procedures, with small changes, can be applied to other relevant known Mexica flutes.
c. Those Mexican flutes can be very similar to the modern recorder, but they were constructed and used many centuries before the perfection of the recorder in other geographical areas.
d. This work was posted in the network for public consultation and to ask for opinions in several specialized forums like Musical Instruments Maker Forum (14) and Ocarinaclub from Yahoo (15). I did not get opinion to improve the construction. The only opinion was from the Cortes brothers from Texcoco (16) the best Mexican makers of clay singers that I could find. Usually, they make the tone holes and the edge after the assembly of the aerophone, to be able to make them very fast. If this procedure was used in the past, the ancient aerophones must have internal flashes. I made other copies using clay provided by Cortes brothers, witch is very similar to the clay of the Mexica flutes.
5. Analysis of the sounds using experimental replicas.
5.1 Ideal analysis.
This ideal schema was made in base of a recommendation of Peter Crossley-Holland 2. It was not possible to be applied that method because the museums did not lend the ancient instruments to make the required analysis and the experts and laboratories were not available. With experimental replicas the method to analyze the sounds from Crossley-Holland can be applied and tested. The acoustical method can be complemented with the recommendations of other experts, if they are interested and available.
5.1.1 Recordings and measurements.
If I can find a laboratory to make measurements under controlled conditions and calibrated equipment I will try to do better and additional measurements. It is recommendable to obtain measurements of frequency, power, Q, impedance, etc., to have quantified levels as references for future studies.
5.1.2 Acoustical analysis.
This is the formal analysis of the sounds and the theoretical calculation or modeling of the flute(s). It is necessary to provide a replica to the expert and to make the supposition that it is an ancient one. In other words, the exercise is to define and prove a method, that can be used in the second part of the study. Other possibility is to make the works of point 5.1.1 and 5.1.2 with the aerophones from the Museum.
5.1.3 Native analysis.
To give a replica to a native musician to see if he/she can find something. Also it may be interesting to provide a replica to a kid from a rural area and other to a folk musician.
5.1.4 Musical analysis.
To ask an experienced flautist and ethnomusicologist to get to know the instrument and to overcome his/her ethnocentricity (if he/her is from other culture, as all musicians because the ancient Mexica performers are in the other life) to see what he/she can produce with systematic exploration in mind.
As I did not find a professional flautist and ethnomusicologist available or interested in researches of ancient aerophones, I provided a replica to a student of ethnomusicology and recorder from the National School of Music to make this exercise, Gonzalo Sanchez. He is native from Oaxaca State and he already made some exercises on Zapotec whistles (17). I wish to show that even a student can get something relevant or useful. His findings were included in my analysis of point 5.2.
5.2 Analysis using spectrograms.
If the previous analysis of point 5.1 are not possible, I can and I will follow the method and tools used in previous studies: experimentation, common sense, carefully observation and spectrograms. The exercise in this conditions is very interesting, because we will see that it is possible to get some findings without any information and data of the ancient aerophones and without the use of advanced laboratories and support of experts.
5.2.1 General analysis.
The aerophones are not equal in size. It means that the exact tuning between them was not a wish.
The tonal or pitch analysis can not be exact by the uncertainties on the internal size of the replicas.
If the pitch of the sounds are not exact, also the analysis of the scales and relations between sounds can not be exact.
If we follow the road of actual musical and organological analysis we find the those flutes can not play tuned melodic music in a wide range of musical notes and scales. Then, we have some questions. Must we accept previous opinions on this kind of ancient aerophones with four pitch holes? Are they only representations of musical instruments? Are they toys or playing things? Are they underdeveloped aerophones?. Are not they serious? If we think that it may be other possibilities, the main questions are: Why they offered those instruments to their Goods? and How was their music or their sounds?.
In this context, to find something relevant it is recommendable that the analyst and the performer play to be God, or try to act and to play like him, because the artifacts from the Offerings are for him. If that is nor possible we must try to think as a Tlapitzcalzin and to play like Tlamacazcateutl (master on music, singing and dancing) or Cuicanime (singers or musicians), because they created and used those aerophones. And if that is not possible we must forget our knowledge and open our mind and perception to some thing different to actual music and organology, if we wish to get findings of value. We must be centered to find the main and best sounds and the easiest fingering, blowing, breathing, etc., trying to open our mind to a very wide unknown concept of music.
5.2.2 First analysis, using experimental replicas and spectrograms.
I made the recordings in a PC with a microphone and a sound card in the room used for my studies at home. I used the Visualization Software 3 Spectrogram (18) by Richard H. Horne, to make the Audio Spectrum Analysis (spectrograms) of the sounds that were obtained with the same parameters, signal levels and frequency calibration.
Finding 1. Considering the difficult for the individual fingering of each pitch hole it seems that the main and best feature of these little aerophones is the "double or paired fingering" (closing two pitch holes at the same time). In this case it is very easy, because it is necessary only one finger to close two pitch holes. It is not only the best way of playing them by adults, it seems that it is the only way to do it, in the traditional way of playing and fingering. If this way of fingering is used there are five basic easy possibilities: 1) all holes closed, 2) the distal pair closed, 3) the proximal pair closed and 4) all holes open and 5) it is possible to close the pair of the middle, but to do it is necessary to move the operating hand, to change the position of a finger. This last operation is not used in any modern flute or recorder.
Finding 2. The spectrograms show those five very short plain musical notes from replica number 2. The fundamental is loud and there are only the two first harmonics of very low intensities. This feature implies that the replica 2 is not a classic "ocarina", because they say that "ocarinas" have the fundamental only. The five notes can be played very easily and clear. It means that replica 2 can be used to produce those five basic notes very easily, even with one hand to operate the mouse with the other hand at the same time. The main surprise was the perceived intensity of the sounds, because usually the small closed tubes generate low dBs levels.
Finding 3. The spectrograms show the frequency components of the sounds of three very similar replicas operated with their tone holes closed. The sound are very similar. The main differences are related with their harmonics, originated by the small differences in the internal shape of the resonating tubes and the voicing. But the magnitude of the harmonics are very low, as it is shown in the power spectrum of the sound from the replica 2.
I made additional recordings with other ways of fingering, phrasing and blowing to see "what happen if".
Finding 4. The spectrogram shows a short "glissandos" sound obtained by opening first the two distal pitch holes and then the proximal two pair holes with two fingers. The sound is strong, continuous and beautiful, in the range of three basic tones.
Finding 5. The spectrogram shows a "trino" sound obtained by opening and closing the two distal pitch holes with one finger while the other two holes are closed to generate a phrase with two tones. The sound is strong and clear. The fundamental in the spectrogram looks like a "little snake" or an ancient symbol used to designate all kinds of weaving beings and phenomenon, like music and sounds.
Finding 6. The spectrogram shows a "vibrato" sound obtained by moving fast the tongue inside the mouth during the blowing. The sound is loud and impressive.
Finding 7. The spectrogram shows a "Mexica" sound obtained in a very different way of fingering, moving very fast a finger on the pitch holes from distal to the proximal pitch hole and vise versa. It is the only way of playing all the single pitch holes but in a almost continuous way. The sound is loud and beautiful. This may be other main distinction of this little Mexica aerophones and must be considered for the analysis of modified models. No one modern wind musical instrument can be played in this way and produce similar sounds.
5.2.3 Analysis of hypothesis with modified models.
The main hypothesis must be analyzed in the extremes (the size of the flutes is already in an extreme) and other situations and possibilities. For example, following the relevant Finding 7 what happen if the pitch holes are closer? or if the flutes are of different sizes? What happen if the flutes are played in groups? Do they produce beats? And the most important is: what happen if their way of playing was very different?
Finding 8. The spectrogram shows a "Mexican" sound produced by a model in the extreme, with only one very special pitch hole made of a long channel. The spectrogram shows the fundamental as a wave of a wave, even in the harmonics. Similar but bigger flutes were found in other ancient cultures as those from the coast zone of Gulf of Mexico. Some drawings of these type of flutes were published by Jose Luis Franco and Guillermo Contreras. They are unique and can produce variations of very continuous pitches or "free intonations". The big pitch holes also were used in whistles to produce sounds of animals, mainly from birds. I think that to produce these kind of sounds was one of the main purpose of several wind ancient artifacts.
Finding 9. The spectrogram shows a "Mexica" sound produced by a smaller replica, moving the finger as in Findings 5 and 6. The sound is loud and clear. It proves that the design in very good, because bigger similar flutes work very fine also. The question is why they selected a particular range of size? The bigger are more pleasant but not very laud and the smaller are very laud (and high pitch) but are not pleasant for many listeners.
Finding 10. The spectrogram shows a "double plain" note produced by two very similar replicas played at the same time (replicas 2 and 4). They produce beats and the signal is complex. The harmonics are paired and one is stronger than the fundamental!
Finding 11. The spectrogram shows a "double complex" sound produced by replicas 2 and 4 played at the same time, but in a "paired bird" way. They produce beats and the signal in more complex. Also, the harmonic is strong.
Finding 12. The spectrogram shows a "double complex sound" produced by two similar replicas with a pitch hole in channel played at the same time. They produce complex beats and the signal also is more complex, but their pitch varies more continuously.
Finding 13. The spectrogram shows the frequency components of a complex "nature" sound produced by the mixing of some previous ways of playing. This is one of the best possible way of playing these little aerophones, very near of the way to produce sounds from nature or something for their Gods. If they are played in groups they produce "chorus or symphonies of birds" but with beats by the small differences in their tubes size.
Finding 14. All the replicas produce sounds with fundamentals in the range of maximum hearing sensitivity of humans. This feature may be one of the reasons of the selected size.
5.2.4. Experiments in archaeological sites using replicas.
It is impossible to make an acoustical experiment in the original site, because it was devastated. It is very difficult to make an exercise in a similar space, because the exact location of the possible place for the making of the Tlapítzalzintlis and for the celebration of the Offering is unknown as the exact original location and structure of all the buildings and open spaces from the Sacred Precinct. It is relevant to mention that the scale model of the site is not exact, because they are finding new localization of some buildings.
We do not know the location of the Cuicacalli and Mixcoacalli. One possibility is that they were Halls of the Calmecac or other building. If the Tlapitzalzintlis were played and tested in a Hall, in a building or in the Game of Ball it is very sure that they could be heard very well, because that happens in similar situations.
If the ceremony for the Offering was in an open space, the spatial situation can not be repeated exactly. However, it is possible to make experiments in other existing archaeological sites with pyramids and open spaces, as Teotihuacan. As we could not find metrology equipment to make acoustical measurements Angel Mendoza (19) and Gonzalo Sánchez helped me to test in that site some replicas of Tlapitzalzintlis, with a fine ancient instrument: the ear. The experiments were made in Saturday July 21, with many tourists walking and talking.
Finding 15. The sounds could be heard very well in all main plazas from the top of the pyramids (and vise versa) to a distance of nearly 250 m. The map of Teotihuacan site shows with yellow the ceremonial areas where the sound could be heard: Sun pyramid (left), Moon pyramid (center) and Quetzacoatl pyramid or Adosado plaza (right). In the experiment on Moon pyramid we found that the sounds can be heard from that top of the pyramid to the Jaguar mural (and vise versa), a distance of ~ 500 m.
Finding 16. The previous Finding 14 means that the sounds of this little aerophones could be heard in any open space of the ancient Mexica Ceremonial Center Precinct, because their internal dimensions were estimated (by Alvaro Barrera and Raul Garcia ) in ~ 350 m (North-South) and 290 m (East-West) .
Finding 17. The Mexica and Teotihuacan archaeological sites are different but they had some similarities in the distances from the top of their pyramids to the distal end of their Ceremonial Centers or plazas. For example, the distance from the top of the Templo Mayor pyramid to the west door of the Ceremonial Center (estimated in ~ 240 m) is almost equal than the estimated distance from the top of the Sun pyramid to the West side of the Plaza and similar to the distance from the top of the Moon pyramid to the South side of his plaza and from the top of the Adosado of Quetzacoatl pyramid to the west side of Citadel plaza ~ 230m - 250 m.
Finding 18. In previous experiments we found that the bests similar Mexican aerophones can be heard very well in those and other ancient ceremonial spaces, as those from Tepozteco, Xochicalco and Monte Alban. One experiment was made in Monte Alban site using a replica of the little Mexica aerophone. It could be heard from the North to the South constructions of the plaza al a distance of more than 300 m.
a. The main result in relation to the used methodology, despite its apparent simplicity, is that it is good to get findings in this very common situation of lack of information and without the use of other advanced tools and techniques. Other great advantage is its low cost, because we need only clay and a PC to make similar experiments.
b. The main result of the analysis is that the ancient organological design is very fine and can produce very special sounds that are in harmony with the best Mexica soul, music and philosophy. The design may be a toy and a representation, but it was very special to be played for their Gods. They are some of the best sacred artifacts for a Mexica Offering.
c. Their best sounds (from Findings 5, 7, 8, 9, 12 y 13) can not be produced by modern wind musical instruments, by their size and location of their pitch holes. Some probable ancient fingering is not used by modern flutists and it can not be played with longer tubes at a similar speed and with the same "continuity".
d. It seems that the operation of the more complex way of playing them can not be simulated mathematically or with the available technology and it is very difficult to be written it in the musical staff.
e. The ancient designer and maker of these Mexica Tlapitzalzintlis, the ancient master Tlapitacalzin, had secrets and he was a better maker than the modern masters of the same geographical zone and many other, as those where the modern musical wind musical instruments are imported.
f. The use of replicas is very important, because the experiments of points 5.2.3 and 5.2.4 can not be made with the ancient instruments. The learning to make experimental replicas permitted us to recover, study and divulgate that fine art-technology.
g. The Findings 15, 16, 17 and 18 shows the maximum distance for the transmission of their sounds in ancient ceremonies zones of those sites. The analyzed sonic artifacts are good to be played in ceremonial sites and the ceremonial spaces are good to transmit that type of sounds. In other words, it means that the design and construction of archaeological sites and wind sonic artifacts were acoustically adequate to develop their main and common sonorous function.
To study of the Tlapitzalzintlis from Templo Mayor Museum. The study may include the following main works:
1. Analysis of the archaeological information of their Offerings.
The main information is from the formats "Hoja de Libro de Registro de Ofrendas del Proyecto Templo Mayor" and the "Cedulas" requires by INAH of any found archaeological object. But usually these formats do not include any organologycal data. This information may be good to know it there are other musical instruments or related objects. It may not change the previous findings, because the best of it is the exact localization of the offering and the list of their artifacts and their original position in x, y an z and the dimensions of the aerophones (total length, wide and high). But it is very relevant to see if there are associated objects and information to make and support the analysis.
For example, if the other whistles, Teponaztlis and drums were found in the same Offering the situation is very complex, because they could (or wanted to) be played together with the Tlapitzalzintlis.
2. Direct analysis of Mexica Tlapitzalzintlis.
It is recommendable to make the works from
point 2, 5.1.1, 5.1.2 and 5.2.2 to refine the measurements, recordings and the
acoustical analysis. The main questions are if it will be possible to obtain
X-rays to eliminate the uncertainty of the internal sizes of the resonating
tube to see the differences in the findings. I think and I hope that the
results may be very similar to those obtained previously with replicas, but we
must be open to any result. The main interest in this point is to test the
validity of the method used and see if the replicas can or can not generate
sounds with the same quality that those made by the ancient Tlapitazcalzin
master. It seems that these works can not be made by the author, according with
a letter from INAH5. The independent studies of ancient organology is officially
The studies and their publication were continued. Some acoustic measurements of dB levels and recordings of some experimental replicas were made with the support of Sergio Beristain, President of the Instituto Mexicano de Acústica AC (IMA). The results of those analysis were presented in the 142nd ASA (Acoustical Society of America) Meeting, Ft. Lauderdale, Florida, 3 -- 7 December 2001..
1. Tlapitzalzintli means little flute in Nahuatl, the Mexica language. Tlapitzalli = flute and tzintli = little = ito, ita, in Spanish. This diminutive is very used by many Mexicans, but more than smallness its ancient meaning is reverence. I am using the word Tlapitzalzintli because the original designation of ancient aerophones were lost and the actual words used to designate wind musical instruments like whistle, ocarina, recorder and flute do not adjust well to them. Neither the words used by the Spanish writers to mention the Mexica aerophones are well adjusted like "pitos", "silbos", "bocinas", "chirimias", "pífanos" or "flautas", that were used in their country at the time of the Conquest. There are other few words in Nahuatl that can be used, as uilacaptiztli, but it seems that they may be applied to other type of globular aerophones in form of birds.
2. It is not known why the method to analyze the sound was not applied by Peter Crossley-Holland, if we know that he collected during ten years and have 150 Pre-Hispanic musical artifacts from West Mexico and he could use the best experts and laboratories, as those from UCLA. He recommended also to use a multidisciplinary approach, but an application of it to any specific ancient aerophone was not found. Unfortunately, he died on April 27, 2001, aged 85. It is interesting that the UCLA (Professor Isador Rudnik leader of the Acoustic Group) have supported also the other relevant study by Garret and Statnekov and (Roger Kendall, Dept of Ethnomusicology) by Susan Rawcliffe.
3. Richard Horn authorized me to use his excellent program Gram (freeware version 5.7) in my studies. Now, there is a new $25 shareware version 6.2.1.
4. I wish to thank Professor Dr. Ray Dessy, because he kindly made corrections of the English text from point 4 and he is interested in the study and in ancient aerophones.
5. It was sent a letter to la General Director of INAH informing about this study and the recommendation. The National Coordinator of Legal Subjects (Coordinación Nacional de Asuntos Jurídicos) of INAH sent an official letter informing that they are not in possibility to give a permit to make the tests, because the analysis on the aerophones are realized by the responsible archaeologist. The legal or regulatory elements to support that decision were not provided and and the technical reason is not valid because the aerophones from Ancient Mexico have not been analyzed formally and systematically, considering the official opinion of the National Coordinator of Archaeology (Coordinador Nacional de Arqueología). It was not found in the literature any official and formal study on them. It was sent a new letter to the National Coordinator of Legal Subjects and the final result is that the old flutes were not analized directly..
References from Internet.