[Aztlan] Plaster & Echoes

[David Lubman]

Thanks Sam, for your scholarly open-mindedness.

----- Original Message ----- 
From: "Sam Edgerton" <Samuel.Y.Edgerton at williams.edu>
To: <@williams.edu>
Sent: Tuesday, August 26, 2008 9:02 AM
Subject: [Aztlan] Plaster & Echoes


> Listeros: As a frequent critic of David Lubman's and Wayne van Kirk's
> acoustical theories because, given the fact that the ancient builders did
> not employ measured drawings to scale by which to anticipate such sacred
> bird-call echoes a priori, there is no way they could have erected such
> huge stone monuments shaped from the ground up to reflect sound waves in
> such precise imitations.
-------------------------
Do not rule out intentional acoustical design because the Maya (presumably) 
lacked scale drawings. Why? Because the building precision necessary to 
produce chirped echo effects is probably less than you imagine.

Consider the two restored staircases at the temple of Kukulkan. The chirped 
echo is present at both staircases despite the marked irregularity of stair 
tread lengths and riser heights.

How irregular? With ruler measurements, I estimated the standard deviation 
of tread length and riser heights as just under 1 cm. I hope you would agree 
that achieving this precision was no problem for ancient Maya builders. 
Actually, those staircases are pretty rough! And yet they chirp.

The construction tolerance for chirped echoes is apparantly larger than 1 
cm. (1At a frequency of 1 KHz, 1 cm is about 11 degrees of phase for 
airborne sound. Equivalently, 1 cm is about 3% of a free-space wavelength.)

Since the restored staircases are modern constructions, acoustical tests 
renovations may not seem compelling. But the chirp is also present at 
Kukulkan's two unrestored staircases. These are excavated, original 
constructions. The chirp is much weaker. But it is audible and its gliding 
harmonics are clearly visible in spectrograms of my sound recordings there. 
They unrestored staircases chirp at the same frequencies as the restored 
staircases.

 It remarkable that the unrestored staircases chirp, since they are in 
shambles. Hardly more than the suggestion of spatial periodicity of the 
staircases remain. (Spatial periodicity is a necessary condition for the 
chirp).

[Sidebar - the fact that unrestored Kukulkan staircases also chirp is 
absolute proof that the chirp is not an artifact of reconstruction. 
Evidently the chirp was originally present around the pyramid of Kukulkan.]

Why does the chirp work even there? It is because human ears are good 
detectors of periodic signals such as tones. Human ears can detect tonal 
signals well below the background noise.

(For this acoustic detection paradigm, acoustic scattering from nonperiodic 
portions of unrestored staircases is considered to be "noise". Actual site 
acoustical noise adds to the pseudonoise of scattering from the nonperiodic 
portions of staircases.)

The chirps of some older pyramid staircases are very weak. For example, The 
staircase at the temple of Inscriptions at Palenque is just barely 
discernable. The explanation is different here. The problem is low sonic 
scattering coefficients of the stone staircases because of high sound 
absorption. Porous stones can be poor reflectors / scatterers of sound 
waves.

Staircases smoothly plastered with dense and nonporous plaster have much 
higher scattering strength. The chirped echo of freshly plastered staircases 
must have been considerably louder. Not just at Kukulkan. Everywhere in the 
Mesoamerican world. Chirped echoes must have been a significant feature of 
the soundscape near Mesoamerican pyramids.  If you want to learn what their 
world sounded like, you must recognize this.
----------------------

However, given the possibility that some structure
> somewhere in the Mayab did just happen to produce such an echo by accident
> (and indeed it would have aroused quite a sensation!), it is also possible
> that by careful molding of plaster surfaces over the stonework, the
> mystical  sound might not only have been enhanced but the same 
> acoustically
> receptive sculpted shapes repeated in other structures.  We have still no
> proof that this was ever done, but can never be sure that it wasn't. So
> many Maya ruins exist today in only their ragged stone "underwear" as it
> were - the original plaster veneers with all there    intriguing forms -
> aesthetic if not also acoustical - have long since been weathered away.
> Sam Edgerton
>

Sam - I, too, am very comfortable assuming the discovery of the chirped echo 
phenomenon was accidental. But once noticed, a little experimentation would 
allow them to adjust tread length to match the pitch of the quetzal.

I imagine Mesoamericans venerated the quetzal long before they started 
temple building. Is that true?

I also imagine that the Mesos tried building temples of many sizes and 
shapes. Through that, they would have found that only temples with long 
outdoor staircases echoed back the approval of the gods. (At least one 
respected Mexican source claims the quetzal was the messenger of the gods.)

Best regards,

David Lubman, FASA
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