AEROPHONE OF BLACK STONE
Roberto Velázquez Cabrera
First version
May 2000. Last update March 2002
The
Spanish version of this paper was presented in the Computing International
Congress CIC-2000, IPN,
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
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, althougt 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 photographer.
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 dobled (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
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 artifacs,
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
General Analysis
Beverido family permitted me to make the first direct study
of a Mexican ancient aerophone, 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 causing 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 and lower part)
and the resonating cavity viewed from the top. This section is used to show the
playing technique (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 neither was 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:
In the beginning, the sounding mechanism
might works as follows:
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 the 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
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
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
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 & Rosssing,
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 the
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
During research at the Brothahaven
National laboratory, (which is supported by the US Department of Energy), it
was found that important archaeological information and material (dated with
C14 technique), and cultures originated the aerophones. For the anlysis of the sounds they used a "stroboconn"
to measure the pitch of the sound of the best preserved instrument (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 museum’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 two musical tones
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
References.
* The English translation of this paper was
made especially for Dr. John W. Coltman, because he
had curiosity in the black stone aerophone. I was glad to send him several
replicas of this type for his collection of flutes and for his experiments,
because he is the first international expert that showed interest in the
matter. The last update of the English text has corrections provided by Baz Jennings, an expert in ocarinas (http://www.ocarina.demon.co.uk/).
Figures
Figure 1. Wind aerophone from Florentine Codex (Book VII. Miscoacalli instruments, Lam. 70)
Figure 2.
Bone "ocarina" from Araró (picture by Dájer)
Figure 3.
Picture of the black stone aerophone
Figure 4.
Sketch with two views and two cuttings
Figure 5.
Replicas of rigid materials (including a metallic cup of beer bottle)
Figure 6.
Schema of functioning (operation)
Figure 7.
Spectrogram in 2D of the same stone aerophone sound
Figure 8.
Spectrogram in 3D of the same sound
Figure 9.
Power spectrum of the same sound.
Figure 10. Other power spectrum of the same sound
Figure 11. Skordos´s computer simulation of a recorder
Figure 12. Spectrogram of a 9,000 years flute musical phrase