Sonogram of Handclap and Chirped Echo 

The sonogram 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 fourth harmonics.

Notice that low echo frequencies are delayed more 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 Mayan staircases, can this phenomenon be found?

But is this Mayan 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!

Mayan Pyramid Steps 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 acoustician’s judgment is that the echo would sound slightly less raspy and more birdlike.

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 sound, c.  fi = c/2TL The second harmonic shown here is twice that, or c/TL. 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 + R2)1/2

CRITICISM OF THE QUETZAL/PYRAMID CONNECTION

Science News magazine (SN) published a story about my Mayan 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 their judgments.

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Feb 1, 1999

Letter to the Editor of Science News magazine re the story "Singing Stairs"
(Science news, Vol. 155, Jan 16 1999, pp 44-45)
by David Lubman

Archaeologist Karl 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 http://www.biohaven.com/bus/ratnavira/serpent.html.

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 plumed serpent.

The quetzal has even more 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 ceremony’s 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.)

Archaeologists Taube and Edgerton say they would be better convinced if other Mayan ruins produced such echoes. So be it!

I report from personal observation that Uxmal’s Pyramid of the Magicians also produces chirped echoes. (My Mayan tour guide didn’t know about the echoes until I demonstrated it with a handclap.)

Chirped echoes at Mayan pyramids are not just freak effects limited to these two sites. There are multiple reports of similar echoes at Mayan staircases and temples at other sites as well. Every Mayan 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 investigate them.

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 Mayan Ruins." http://www.eden.com/~tomzap/sounds.html.

Edgerton thought the question of how Mayan 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 Mesoamerican pyramids. What we have here is an effective form of theater architecture unknown in western and Mediterranean tradition. Maybe the Mayan 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 Mayan reverence for the quetzal.

Mayan mysteries may yield more 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."

David Lubman