Sonogram of Handclap and Chirped
plots frequency (vertical axis) against time (horizontal
axis). Loud sounds show in red; soft sounds show as yellow.
The vertical red
line is the spectrum of a handclap made by an observer
standing about 10 meters in front of the pyramid staircase.
A handclap, or any
other short, impulsive sound contains energy smeared
continuously over a wide range of frequencies. A handclap
contains noise rather than tonal energy because it is
distributed continuously over a wide range of frequencies.
The empty space to
the right of the handclap is the "echo latency" - the time
needed for the handclap echo to return to the observer from
the pyramid steps.
The chirped echo is
the set of three curved lines to the right of the handclap.
These curves are harmonics (integral multiples) of a fundamental
frequency. The fundamental frequency is not shown in the
sonogram because it is weak and lost in the noise. The
bottom curve is the second harmonic, and this is the
strongest component. The upper curves are the third and
Notice that low echo
frequencies are delayed
than high echo frequencies. This common feature of Bragg
diffraction gratings is responsible for the downward chirp.
The echo said to be "time dispersive" because it lasts
longer than the handclap. Time dispersion is another
familiar feature of inclined Bragg diffraction gratings.
What is the audible result? The continuous spectrum of a
brief handclap is transformed into a longer, melodious,
harmonic-rich quetzal-like chirp! It is remarkable that the
echo of a handclap should be a quetzal-like chirp! Where
else, outside of the world of
staircases, can this phenomenon be found?
But is this
art or artifact?
The most famous feature at Chichen Itza is the light and
shadow show that plays on the temple of Kukulkan around the
time of the spring and fall equinox. At that time, an
undulating shadow identified as the great plumed serpent
moves up or down the balustrade of the staircase. Cultural
connections identify the plumed serpent with the quetzal. Is
it a coincidence that the remarkable quetzal-echo emanates
near the location of the undulating shadow?
The signal-to-noise ratio is not very high in these
sonograms. I have plans to make better recordings!
The pyramid was
once covered with smooth finish plaster. The plaster has
been missing for many hundreds of years. You can see how
irregular the steps
are Despite this irregularity, the quetzal - like chirp
can still be heard in the echo. If smooth finish plaster
were reapplied, my acousticianís judgment is that the
echo would sound slightly less raspy and
Theoretical Calculation of Chirped Echo Second Harmonic
Frequency vs Time
This was calculated from a Mathcad
program from a simple 2 dimensional ray model.
The initial frequency, fi, depends only on
the tread length of the stairs, TL, and the speed of
fi = c/2TL
The second harmonic shown here is twice that, or
The chirp final frequency ff depends on
ones distance from the base of the pyramid. The lower
limiting frequency of the chirp declines as one moves
closer to the base. Then, precisely at the base, the
chirp disappears entirely! Just before the chirp
disappears, its lowest frequency is governed by the
hypotenuse of the triangle consisting of the tread
length and riser height
ff = c/2(TL2 +
OF THE QUETZAL/PYRAMID CONNECTION
magazine (SN) published a story about my
research in its January 16, 1999 issue titled "Singing
Stairs." In that story, my physics was unchallenged, but my
conjecture about the quetzal/pyramid connection was
criticized by archaeologists.
Criticism is good!
Every new scientific idea must be tested to see if it can
withstand even the most withering criticism. Let critics
tear it to pieces if they can! That's how science is done,
and so no offense is taken.
But for this system
to work, criticism needs the opportunity of rebuttal. This
may be a problem in the constricted forum of SN Letters to
the Editor. A wider forum is needed for pro and con
discussion of the exciting new ideas raised by
archaeological acoustics. In the future there will be a
listserver for archaeological acoustics. Those interested in
joining this discussion, please send me a brief e-mail
message requesting notification.
Below is my
response to SN. It is both too long and too short. Too long
to fit into the space normally reserved for SN Letters. Too
short to cover all of the important points I wanted to make,
just as the original article may have been too short for the
critics to make all the points they may have wanted to make.
I ask that readers of SN consider this response in forming
Feb 1, 1999
Letter to the
Editor of Science News magazine re the story "Singing
(Science news, Vol. 155, Jan 16 1999, pp 44-45)
by David Lubman
A. Taube would have me explain why the Maya would have
created the chirped echo at the temple of Kukulkan
(SN:1/16/99, p.44). He and art historian Samuel Y.
Edgerton say I have overstated the relevance of the quetzal
to the temple where the echo is heard. The echo, they say,
honors not the quetzal, but a serpent named Quetzalcoatl,
that was covered with quetzal feathers.
I remind these
experts that many ancient Mesoamericans saw the quetzal as a
transformation of the sacred plumed serpent, an
identification that carries to the present day. A perfect,
if ironic proof is the quetzal painting S.N. chose for this
story. Its title "Plumed Serpent: Lord of the Cloudforest"
and its mystical qualities beautifully illustrate my point.
This radiant work of artist Gamini Ratnavira can be seen at
A clue to the
reason for identifying the quetzal with the plumed serpent
is seen in the spectacular display of the male quetzal that
takes place in the cloud forests, ancestral home of the
Maya, around the time of the spring equinox. In it, the
male quetzal rises a great altitude, then folds its wings to
dive vertically through the forest canopy while crying
sharply "tak-teek, tak-teek." Its long tail feathers
undulate behind him like a flying serpent. Thus, natural
behavior surely seen by ancient Maya link the quetzal to the
The quetzal has even
relevance to the temple of Kukulkan - at least for
those willing to believe that its famous equinox light and
shadow show was an intended design feature (this, too, is in
dispute). The descending, undulating shadow is said to
represent the mystical plumed serpent. The shadow plays
against a balustrade of the temple staircase where it is
viewed even today by the thousands thronging the wide plaza
below (shown at
http://www.piramideinn.com/equinox.htm ). The staircase
is the very place from which the quetzal-like chirped echo
emerges. The call can be heard by all close enough to
observe the shadow. The quetzal sound could have been
evoked by a priestly handclap made at a critical moment in
the show. This would strongly reinforce the ceremonyís
dramatic impact and religious purpose. Thus, Mayans had
good reason to engineer the sound of the quetzal into that
location of that temple.
There are reports
that even modern Mexicans link the chirped echo with the
quetzal. It is independently reported that the echo is named
"la cola del quetzal" (the tail of the quetzal) at "Mayan
ceremonial centers and at Teotihuacan." (I am trying to get
this report confirmed.)
and Edgerton say they would be better convinced if other
ruins produced such echoes. So be it!
I report from
personal observation that Uxmalís Pyramid of the Magicians
also produces chirped echoes. (My
tour guide didnít know about the echoes until I demonstrated
it with a handclap.)
Chirped echoes at
not just freak effects limited to these two sites. There are
multiple reports of similar echoes at
staircases and temples at other sites as well. Every
temple having a long stone staircase that faces into an open
plaza may exhibit this effect. It is much easier to find
reports of these echoes than it is to get archaeologists to
Nor is acoustical
phenomenology limited to chirped echoes. Other fascinating
and odd acoustical
effects are reported. They need to be investigated and
explained. Wayne Van Kirk has collected a number of reports
under the title "Acoustics of
thought the question of how
Kings projected their voices to large crowds needed study. I
agree, and have made a start at the temple of Kukulkan. I
confirm earlier reports of sound reinforcement from the top
of the temple to the plaza below. Sound reinforcement may
explain how the ceremony could have been heard by thousands
at great pageants. I have defined an experiment to document
the magnitude and extent of the sound reinforcement. I
suggest that the same mechanism may have been used at other
What we have here is an effective form of theater
architecture unknown in western and Mediterranean tradition.
builders actually knew what they were doing.
I believe Edgerton
is mistaken when he states that the quetzal was admired by
the Maya "mainly so they could kill it to get its tail
feathers for their helmets." Historical sources describe the
method by which quetzals were captured, their feathers
harvested, and the birds released to grow new feathers. The
penalty for harming a quetzal was death! There is abundant
evidence even today of extraordinary
reverence for the quetzal.
mysteries may yield
quickly to archaeologists who open their ears and eyes to
other available forms of historical evidence, including
acoustics, animal behavior and modern remnants of ancient
legends. Not all worthwhile archaeological knowledge lends
itself to presentation in a museum display case or as a wall
hanging. It may not be acousticians, but historians who
limit their research scope narrowly to epigraphic
interpretation, whose stories are "off the wall."