Popular version of paper
Presented Tuesday afternoon, October 13, 1998
136th ASA Meeting, Norfolk, VA
The Pyramid of Kukulkan at Chichen Itza is recognized around the world as an icon of Mexico. As such, even small details around it merit scholarly interest. One small detail ignored by archaeologists until now is the odd chirped echo that resounds from the pyramid's staircases in response to hand claps of people standing near its base.
A physical explanation for the chirped echo is proposed: The staircase constitutes an acoustical diffraction grating. Two forms of analytical data are offered in support of this explanation. First, a mathematical simulation of the chirp fundamental frequency vs. time is calculated. Then a sonogram of the recorded echo is shown to be in reasonable agreement with these calculations .
Moving to archaeological issues, it is considered whether the echo was intended by its Mayan builders; is merely an artifact of reconstruction; or simply an ancient acoustical design defect. We speculate that the echo is intentional. That the steps were designed and constructed to echo the voice of the Mayan sacred bird, the resplendent quetzal (pharomachrus mocinno), viewed by ancient Maya as the "messenger of the gods."
The echo is not believed to be an artifact of reconstruction. Other Mayan pyramids also chirp, as do other Mayan staircases, though their acoustic parameters are different.
The echo is not believed to be an original design defect. Sound is very important to forest peoples whose livelihood or very lives may depend on accurate listening. In the cloud forest where their Mayan cultures were formed, one may hear over a much greater distance than one can see.
The Maya would have noticed such a profound acoustical anomaly (chirped echo) at their sacred site just as modern people react to alleged defects around their "holy" sites. (Think about the fuss over alleged acoustical defects at Lincoln Center in 1962. Eventually, the hall was gutted and rebuilt at great expense.)
Arguably, the Maya had the technological capability to correct such acoustical defects. This is implied by other evidence of subtle Maya manipulation of architectural acoustics suggesting that they were masterful practitioners of acoustical arts who created whispering galleries and other acoustical wonders.)
Sound recordings and sonograms of the chirped echo and quetzal were compared. A striking similarity is observed in sound quality, frequency, length and harmonic structure. However, they are not identical.
The Quetzal as the "Spirit of the Maya" and the Spirit of Kukulkan
Archaeological proposals are made to justify design intent by arguing the central importance of quetzal mythology to both ancient and modern Maya. The quetzal, is asserted to represent the "spirit of the Maya". It is shown that the Temple's very name is connected with the quetzal. The pyramid's Mayan name is "Temple of Kukulkan" The prefix K'uk has roots in the Mayan name for the quetzal. Also, the glyph of Kukulkan is represented in human form with a huge quetzal behind him, hovering like a spirit. There is much evidence that the Maya made use of quetzal feathers in their ceremonies at Chichen Itza and elsewhere. It is argued that for ancient man, echoes were voices from a spirit world. It seems appropriate that the Temple of Kukulkan should echo with the spirit voice of the quetzal.
Additional Benefit of Acoustical Hypothesis of Staircase Design
There is an unexpected benefit of the acoustical hypothesis for staircase design. It offers a more plausible explanation for the narrow treads and high risers on the pyramid steps. According to the acoustical hypothesis, these parameters were chosen to "tune" the echo to the pitch of the quetzal. The standard archaeological explanation for short treads is that the Maya, being short in stature, have small feet. This does not account for the higher-than-normal risers. Indeed, the "small stature" explanation predicts shorter risers. Nor does it account for the longer treads found at other Maya buildings at this and other sites.
If the hypothesis of intentional design has merit, we are led to two striking conjectures. The Maya are the only people known to have "coded" a sound into stone. The chirped echo at this 1300-year-old pyramid may be the world's oldest known sound recording!
Archaeologists seek features that persist through time. Understandably, archaeologists have until now ignored sound. It seems ironic that an entity as ephemeral as sound could serve their quest to understand ancient civilizations. But the human uses for sound, no less than the other perceptual modalities must surely have shaped human habitations in many ways not yet considered. Perhaps the fledgling field of acoustical archaeology will add to archaeologist's impressive accomplishments in rediscovering our human past.
It is fascinating to imagine the ancient Maya as the true inventors of playful soundscape ideas. Such ideas have only recently begun to be used by modern urban artists. Modern artists are creating such sonic architecture as sound parks. (See, e.g., www.users.interport.net/sonarc/maintext.html)
Appendix: The acoustics of outdoor staircases
Although staircases are surely a common element in design, and can contribute odd acoustical effects, the subject does not seem to have received extensive treatment in the scientific acoustical literature.
A design element that is repeated at regular intervals in a region of space can be termed "spatially periodic". Staircases are examples of spatially "periodic" elements. (Theater seating is another example of a spatially periodic feature.) The visual impact of spatially periodic features can be desirable, for they introduce an ordered, unifying element into the design.
The German poet Goethe aptly described architecture as "frozen music". Spatial periodicities are the analogs of "rhythm" in music. As we will see, spatial periodicities can be more than analogues of musical sounds. They can introduce audible, tonal elements of their own!
When periodic design elements are composed of sound reflective materials (such as stone), and if certain other conditions are met, odd echoes or other strange acoustical effects may result.
So far as I know, in all cases where they do occur in the "Western" or "Mediterranean" world, these effects are "accidents" unintended by architects. They are a result of the architect's ignorance of, or indifference to, acoustics. They are always considered undesirable elements in a "built environment". The Mayan echo, if it is indeed deliberate, would be the only exception to this "rule".
An example of an unintended tonal echo is found in the ancient ampitheater at Epidauros in the Peloponnesus (now Turkey). The reflecting feature are concrete seating banks that are periodically spaced about 1 meter apart. An impulsive sound made in the stage area gives rise to periodic reflections from the seating banks that are heard in the "orchestra". The result is an odd but clearly heard low tone (about 340 Hz, according to my calculation). It is very brief, lasting less than 50 milliseconds, (5 hundredths of a second).
Such unintended tonal echoes are not uncommon in open spaces in front of wide staircases, such as libraries and other public buildings. The phenomenon is termed "picket-fence effect", a name evocative of the kind of spatially periodic feature that is responsible for the tonal echo.
At least two steps are needed to produce a perceptible tone. With more steps, say 5-10, the sensation of tone is stronger. With a short staircase of only 10 steps, a tone will persists for not more than one or two hundredths of a second. Unless the stimulating noise is very short, such as a single handclap, the picket-fence tone may be imperceptible because it is "masked" by the long stimulus. Moreover, if the space is not open, echoes from other structures can mask the tone. Ideally, an open space and a very long staircase is needed to perceive this effect.
The Temple of Kukulkan exhibits the most remarkable picket-fence echo I have encountered. The Temple, situated in an open field and possessing wide, long staircases, seems ideal for an exhibit of this phenomenon. Picket fence echoes are heard from each of the two restored, wide staircases of 92 steps each. Equally remarkable, the tones are audible, if somewhat weaker, on the two unrestored sides. These are ruins with little more than the suggestion of the grand staircases existing when the site was mysteriously abandoned around 1200 C.E. Also, the smooth finish plaster on the steps is long gone.
Because the staircase is very long, the staircase echo is correspondingly longer, persisting for more than 100 milliseconds (1/10 second), more than twice as long as the tonal echo in the theater at Epidauros. (The quetzal chirp is even longer, about 200 milliseconds long, or 1/5 second.)
Because of the Pyramid's high staircase, the echo exhibits an additional auditory feature. More than a tone, the echo possesses a birdlike "chirp" that moves downward in frequency. I do not remember having heard such a long chirped echo elsewhere. (But an acquaintance reports having heard a long chirped echo arising the from periodic features on metal roofs of a long row of periodically spaced mining shacks in South Africa.)
Staircase as a Diffraction Grating
An explanation for the downward chirp is easily obtained by a simple extension of the picket fence effect. This essentially amounts to a diffraction grating, familiar to physicists. Echoes arrive first from the lower stepfaces near the observer's head level. The time between succesive echoes is proportional to the length of the step tread length, T, and the frequency is roughly f = c/T, where c = the speed of sound, about 343 m/sec. Later echoes arrive from the upper steps. The time between successive echoes gradually lengthens for the upper steps because the ray path becomes nearly parallel to the angle of staircase's rise. In the limit the time between successive echoes is proportional to the hypotenuse of the triangle consisting of the tread length and rise height. Because the hypotenuse is longer than either side of a triangle, the period of the tone is greater and the frequency is lower.
The average tread length T was measured as 26.2 cm (10.3 inches) This gives a maximum chirp starting frequency of about 1310 Hz
The average riser height was measured at 26.4 cm. This gives a hypotenuse length of 37.3 cm (14.68 inches) and a minimum chirp ending frequency of 922 Hz.
The actual frequency range also depends on one's distance from the pyramid. The farther away one stands, the smaller the frequency range.
The measured frequencies
agree reasonably well with these simple predictions.