acoustic analysis of the chavín pututus (strombus galeatus marine

Acoustical Society of America, Cancun, November 2010 Chavín Pututus 1

Acoustic Analysis of the Chavín Pututus (Strombus galeatus Marine Shell Trumpets)

Perry R. Cook

Princeton University Computer Science (also Music)

Jonathan S. Abel, Miriam A. Kolar, Patty Huang Stanford Center for Computer Research in Music and Acoustics (CCRMA)

Jyri Huopaniemi

Helsinki University of Technology and Nokia Research Center

John W. Rick Stanford Archeology Center and Department of Anthropology

Chris Chafe, John Chowning

Stanford CCRMA

Abstract: In 2001, twenty Strombus galeatus marine shell trumpets were excavated at the 3,000 year-old ceremonial center at Chavín de Huántar, Perú, marking the first documented contextual discovery of intact sound-producing instruments at this Formative Period site in the Andean highlands. These playable shells are decorated and crafted for musical use with well-formed mouthpieces created by cutting the small end (spine) off and grinding/polishing the resulting opening. The shells are use-polished, and additionally modified with a v-shaped cut to the outer apical lip. We present an acoustic analysis of the measured response of each instrument, to a variety of excitations, at microphones placed in the mouthpiece, player’s mouth, bore, bell, and surrounding near-field. From these measurements we characterize each instrument's sounding frequencies (fundamental and 1st overtone where possible), radiation pattern, and impedance, and we estimate the bore area function of each shell. Knowledge of the specific acoustic capabilities of these pututus allows us to understand and test their potential as sound sources in the ancient Chavín context, whose architectural acoustics are simultaneously studied by our research group.

PACS Numbers: 43.75.Fg Musical Instruments I. OVERVIEW

A study of the acoustics of ancient sound-producing instruments provides information about their use potential, and where architectural acoustics are also studied, illuminates interaction dynamics between the instruments and associated spaces. The 3,000 year-old ceremonial center at Chavín de Huántar, Perú, offers playable marine shell trumpets or "pututus", excavated as a group of 20 in 2001, and intact, relatively unmodified architecture that gives these instruments likely acoustic contexts (Rick 2008, VanValkenurgh 2002, Abel 2008).


Chavín de Huántar, a Formative Period site dating from about 1,500 B.C. and occupied until around 400 B.C., substantially prior to the Inca empire, is known for its massive stone architecture, ceramics, and carvings of stone, marine shell and bone. Archaeologists agree that in Chavín times, social stratification was an emerging factor, and such hierarchical distinctions appear to have been ceremonially integrated (Rick 2004). Despite the rich material evidence of culture, no written language or semantic interpretation of iconography exists to verify hypotheses about the nature of activities or ceremonial practice at the site, though stone carvings of figures presented in sequence suggest processional formations (Rick 2004). The importance and use of pututus to Chavín culture is demonstrated by graphic depictions of Strombus trumpets: played by a processing figure in the cornice fragment discovered in 1998 (Rick 2008), held by the so-called ”Smiling God‚” (Rowe 1962), depicted on the Tello Obelisk (Tello 1960), and figured in what has been interpreted as a live marine animal state in ceramics (Lumbreras 1993), among other instances. The wear patterns of hand and lip contact on the pututus unearthed at Chavín indicate that these specific instruments were frequently played; that most of the pututus remain playable in modern times allows the acoustic measurements of our study.

In previous work, Rick and Lubman (Rick 2002) presented an initial analysis and contextual interpretation of the Chavín Strombus trumpets, citing a rich overtone structure and measured sound pressure levels as high as 111 dBA at 1 meter (Rick 2002). In this new work, we present findings from measurements made by our research group of 19 of the 20 Chavín pututus now on display at the National Museum of Chavín. Here, we characterize each pututu in terms of its sounding frequency (fundamental, and 1st overtone where possible), natural bore resonance series, pitch range, bore impedance curve and area function, and radiation pattern.

While we are assuming that the bore shape across this group of pututus is isomorphic, that is, they share the exponential spiral form and thus can be considered a group of various-sized instruments of the same family, there are several conditions that require individual artifacts to be examined separately. Many of the pututus have so-called ”hanging holes‚” at the far lip end, and all were additionally modified with a v-shaped cut to the outer apical lip; these structural incisions have little acoustical impact. However, nine of the instruments have notable holes in the shell body that likely resulted from wear-through of decoration lines during use or earthen entombment (VanValkenburgh 2002). In our measurement sessions, we documented the pututu response both with and without covering these openings, to test hole effects on playability, radiation, and possible function as tone holes. II. MEASUREMENT SETUP AND METHODS IIa. MEASUREMENT SETUP

All shells were recorded, held by a player in the center of a room, dimensions 2.5m wide x 5m long x 3m high. Although one might desire more “pure” data about the pututu acoustics and radiation, we thought it appropriate that a player be present for two main reasons: 1) something has to excite the instrument, and 2) a human player would be present in all instances the shell would be played.

A total of ten Countryman E6 omnidirectional microphones were used for data collection. Four microphones were located at or within the player and the shell: inside the player’s mouth, inside the mouthpiece, inside the shell, or at the bell (see Figure 1). The other six microphones were located on the principle axes in the near-field around the shell (see Figure 2). The experimental measurement microphones locations and functions are summarized in Table 1.


Figure 1, Three microphones in Strombus shell. Figure 2, Six microphones in near-field.

Mic 1 Inside the player’s mouth, just behind the lips/teeth, windscreen in place Mic 2 Just inside the shell mouthpiece, as close to lips as possible, windscreen in place. Mic 3 Inside the shell, approximately 16-17cm from the “bell,” windscreen in place Mic 4 In center of “bell” opening, no windscreen. Mic 5 1 Meter to right of shell (direction that the shell bell faced), no windscreen. Mic 6 1 Meter to left of shell (opposite direction shell faced), no windscreen. Mic 7 1 Meter in front of player (90 degrees off axis of shell bell), no windscreen. Mic 8 1 Meter to back of player (270 degrees off axis of shell bell), no windscreen. Mic 9 1 Meter above shell and player (90 degrees from shell bell, up), no windscreen. Mic 10 1 Meter below shell and player (90 degrees from shell bell, down), no windscreen.

Table 1, Strombus data collection microphones and their positions.

Twice per day over the two-day data collection period, the mic-array and room were “calibrated” using sine sweeps through a Meyer MM-4XP reference/calibration loudspeaker. For the calibration runs, the shell player held the speaker in the same position as the shells would be when played, and sine-sweeps were recorded with the speaker pointing in all six of the principle directions toward Microphones 5-10 (right, left, front, back, up, down). Sine sweeps of this type have been used in the past to determine and counteract the effects of room acoustics for research recordings (Farina 2000). The transfer function between the source and each microphone can be determined, and any room effects can be de-convolved from each microphone’s signal. In practice, however, for the purposes of our studies, we were able to accomplish the signal processing needed without having to use the calibration recordings. IIb. AUDIO EXCITATION SIGNALS

To collect as much data as possible, and to facilitate different types of analysis, each shell was excited in a variety of ways. The data collection signals, which will be described shortly in more detail, included:

1) playing the shells at their natural frequencies and 1st overtone frequencies (where possible) 2) noise injected into bore by player blowing through constricted lips (similar to /f/s/ consonant)


3) lip “fry” signal, a non-periodic chain of near-impulses 4) isolated impulse excitations made by slapping an open palm onto the shell mouthpiece and

holding it firmly there to keep the shell end closed until the impulse response in the bore died away (a few hundred milliseconds maximum).

Each pututu was played by a skilled player of brass, digeridoos, and musical seashells. A

number of “toots” (called “blasts” in prior publications (Rick 2002)) were played at the natural sounding frequency, with the player probing to find the best “feeling,” and the most powerful, purest sounding tone. Via their haptic/tactile senses through the lips and face, and combined with their hearing, skilled brass-players have been shown to have high acuity in determining the most effective sounding pitches and harmonics of a given brass instrument. In fact, studies have shown that this haptic/tactile feedback alone is enough for experienced players to find the purest tone, even without hearing (Cook 1996). After a number of toots were recorded at the fundamental sounding pitch (F0), the 1st overtone (H2, not necessarily the 2nd harmonic due to misalignments in bore resonance peaks) was probed, played, and recorded, if possible. Microphone 1, just behind the player’s teeth/lips, was in place for these sounding pitch data recording runs, except in one case where the shell mouthpiece shape did not allow it.

Each shell was excited by a noise signal injected at the mouthpiece, formed by constricting the lips to near closed and forcing air through, creating turbulence noise similar to the speech fricative phonemes /f/ (as in fife) and /s/ (as in sister). Microphone 1 was not present for noise data collection runs.

All shells were excited with lip “fry‚” in essence a non-periodic chain of impulsive spikes. This type of signal (in the form of glottal fold fry) has been found to be effective for studies of human vocal tract shape in speech and singing. Microphone 1 was not present for lip fry data recording runs.

Finally, each shell was excited with “impulses” made by the player rapidly slapping his open palm onto the shell mouthpiece, and continuing to hold the palm firmly there to keep the shell end closed until the impulse response in the bore died away (a few hundred milliseconds maximum).

All of these excitation signals were repeated multiple times, and for any shells with holes, data was collected for both open and closed conditions. IIc. MEASUREMENT PROCESS

The player, with the help of the recording engineers and photo/videographers present, endeavored to hold each shell as closely as possible to the same room and mic-array centered location (the same location as the calibration speaker for sine-sweeps). The shell was held as still as possible, and the player held as still as possible, during the extent of any “toot,” noise, or “fry” trial. Due to the player needing to move his arm/hand to perform the impulse excitation, however, there was some trial-to-trial movement for impulse responses, and during some trials.

A number of physical measurements have already been taken of the pututus by previous studies and researchers (Rick 2002, VanValkenburgh 2002). For our study, each shell was measured (coarse exterior dimensions), sketched, and photographed extensively. Notes as to holes, markings, mouthpiece condition, etc. were taken. The player made comments about the playability of the fundamental and 1st overtone of each shell. These were later transcribed into a scale between 0.0 (impossible to play a tone, no perceivable resonant impedance peak) to 10.0 (perfectly playable, highly resonant). These are summarized in Tables 2 and 3.


It would have been desirable to take more measurements, such as castings and details of the interior mouthpiece shape, castings of exact dimensions and shape of the bell, an estimate of the internal length from mouthpiece to bell (no easy way to measure this), total interior shell volume, and an (even more elusive) exact estimate of the entire interior bore shape. Indeed, Magnetic Resonance Imaging (MRI) or other 3D density scanning technologies could provide all of these measurements. However, the time available to measure all nineteen shells plus two modern reference shells, the remote location of Chavín (3150m in the Andes), and the sensitive nature of these 3000 year-old Peruvian national treasures, did not allow for additional measurements.

There was one shell which was completely blocked with dried mud, likely fill from prehistoric times (Rick 2008). Permission was granted for us to purge and flood this shell (Strombus 11) with water to wash it out. We took this opportunity to estimate the volume of the shell by the following procedure: the player placed his palm flat on the mouthpiece and we filled the shell with water, taking care to turn it a few times to make sure all chambers were flooded. This water was then poured out through the mouthpiece into a measuring beaker. The process was repeated multiple times, yielding an average volume measurement of 420ml. We will discuss this more in the Area Functions section. III. EDITING AND ANALYSES

All recorded files were edited to extract (sample-synchronous for all ten channels, using scripts) the “Toots,” “Noises,” “Frys,” and “Impulses.” Open/closed conditions for shells with holes were extracted separately. Signal processing routines written in MATLAB and the C language were used to perform various analysis, comparison, and graphing functions. IIIa. SOUNDING FREQUENCIES

The “toots” files were edited to include all attempts at playing the fundamental (F0), and 1st overtone (called H2, for harmonic 2, even though strictly in many cases the frequency was not a harmonic multiple of the fundamental). For stable and successful toots, autocorrelation fundamental frequency detection was performed in 50ms windows at 40 frames per second (each window overlapped the neighboring windows by 25 ms). Figure 3 shows graphically the frequency detection results of one set of shell toots. Power (sum of squares of samples within each 50ms window) and detected frequency is plotted vs. time.

Once the fundamental frequency estimates stabilized within a toot (running variance dropped below a threshold), a mean and standard deviation was calculated. A mean and standard deviation was calculated for all stable toots, and these are summarized for all shells without holes in Table 2, and all shells with holes in Table 3. Each sounding frequency F0 (Table 2/3 column 3) and H2 (Table 2/3 column 4) is expressed as a mean frequency and σ=Standard Deviation, and as a musical note +/- cents with a standard deviation in cents.


Figure 3. Plot of power and fundamental frequency for a typical “toots” trial.

IIIb. BORE IMPEDANCE FUNCTION AND PEAKS

Impulses generated by slapping the player’s open palm against the mouthpiece were used to calculate, analyze, and graph the shell bore frequency response. Each set of impulses for each shell, for holes open and closed conditions (for holey shells), was edited to remove silences between impulses (tightened). Then, 32768 point zero-padded Fast Fourier Transforms (FFTs) were calculated for 4096 sample (approx 0.1 seconds) sliding windows with 2048 samples overlap across the entire “tightened” impulses file. The power (magnitude squared) spectra of these FFTs were then averaged, and the result plotted to yield a smooth estimate of the frequency response of the shell bore. The first three spectral peaks (F1, F2, F3) were located and marked in each plot, and are entered in the last three columns of Tables 2 and 3. Spectral bore resonance peak location frequencies are noted in the table as frequencies in Hz. as well as musical note +/- cents. Figure 4 shows typical plots for a shell with holes, comparing all (two) holes open, one hole open, and all holes closed conditions.

Figure 4. Plots of power averaged spectrum for impulses data. The three plots

compare all holes open, one hole open, and all holes closed. The first three significant peaks (natural bore resonances) for each condition are labeled.

Table 2 summarizes the analysis results discussed thus far for all shells having no holes. The

first column gives the Strombus name and/or number, and any significant comments or nicknames used by the original researchers or our team. The 2nd column summarizes the players estimate of the playability of the fundamental F0 and 1st overtone (H2), on a scale of 0.0 = “unplayable, unresonant” to 10.0 = “perfectly playable, highly resonant.” The next two columns show the sounding frequencies of F0 and H2, expressed in Hz and musical notation, with standard deviations (variation in detected frequency over the “toots”). The final three columns show the first three significant peaks of the power spectrum, expressed both in Hz and musical notation.


Note that each fundamental sounding frequency F0 in most cases closely matches the first power spectral peak F1 as would be expected if the player were playing the most natural and efficient fundamental tone. The slight misalignment between the two frequencies, with F0 being a little lower than F1, is exactly as expected due to the mass of the player’s lip, which causes the natural resonant frequency of a horn to shift downward during steady-state harmonic oscillation coupled with a lip-reed [Fletcher 1998]. Results are similar for H2 vs F2 frequencies, in most cases.

Also interesting to note is which shells exhibit nearly harmonic F1-F3 patterns (expected of a well-formed exponentially flaring horn, coupled to a properly fashioned Helmholtz resonator mouthpiece). Such shells should be expected to have high playability, and shells with poor F1-F3 harmonicity agreement should be more difficult to play.

Table 2. Analysis results for shells with no holes. Playability (0.0 – 10.0), sounding frequencies, and power spectrum peak frequencies are shown.

Table 3 summarizes the results for shells with holes. For most shells, each open/closed hole condition was recorded and analyzed. Some holes had little effect, while others greatly changed playability, sounding frequency, impedance functions, etc. Due to difficulties producing some tones, holding the shell, or other, some entries report “NOT POSSIBLE” or “NO ATTEMPT.”

Shell Name/# Playability (1-10)

Fundamental Sounding F0 Mean σ=StDev

2nd Harmonic Sounding Freq. Mean σ=StDev

Power Spectrum Peak F1



Strombus 9 Play F0 10.0 PlayH2 8.5

300.90 σ=3.35 D4+42c σ=19.17c

602.08 σ=8.28 D5+43c σ=23.65c

306.15 D#4-28c

610.84 D#5-32c

881.84 A5+4c

Strombus 18 Play F0 10.0 PlayH2 7.5

306.196 σ=2.46 D#4-28c σ=13.85

629.30 σ=5.88 D#5+20c σ=16.10c

309.08 D#4-11c

628.42 D#5+17c

940.43 A#5+15c

Strombus 6 "Cool Mouthpiece"

Play F0 10.0 PlayH2 7.0

332.43 σ=5.75 E4+15c σ=29.69c

648.63 σ=8.99 E5-28c σ=23.83c

336.91 E4+38c

667.97 E5+23c

971.19 B5-29c

Strombus 11 Unblocked Vol. = 420ml


339.97 σ=1.75 F4-47c σ=8.89c

671.86 σ=13.16 E5+33c σ=33.58c

341.31 F4-40c

700.20 F5+4c

1045.9 C6-1c

Textile 2 (Original #0)


303.90 σ=5.88 D#4-41c σ=33.17c

603.05 σ=9.48 D5+46c σ=27.0c

313.48 D#4+13c

631.35 D#5+25c

880.37 A5+1c

Strombus 7 PlayF0 8.0 PlayH2 7.0

304.86 σ=6.15 D#4-35c σ=34.85c

613.81 σ=6.79 D#5-24c σ=19.05c

301.76 D4+47c

619.63 D#5-7c

902.34 A5+43c

Strombus 4 "Deep in Size"

PlayF0 8.0 PlayH2 4.0

272.11 σ=3.15 C#4-32c σ=19.93c

565.52 σ=7.36 C#5+34c σ=22.39c

276.86 C#4-2c

575.68 D5-35c

826.17 G#5-9c

Strombus 2 "Cupisnique"

PlayF0 6.0 PlayH2 3.0

317.5 σ=1.5 D#4+35c σ=8.16c

620.0 σ=11.7 D#5-6c σ=32.37c

317.87 D#4+37c

625.49 D#5+9c

842.29 G#5+24c

Strombus 8 PlayF0 4.0 PlayH2 6.5

302.83 σ=4.62 D#4-47c σ=26.21c

620.58 σ=19.32 D#5-5c σ=53.08c

300.29 D4+39c

622.56 D#5+1c

893.55 A5+26c

Strombus 16 Play F0 4.5 Play H2 4.0

311.60 σ=18.2 D#4+3c σ=98.28c

627.05 σ=27.52 D#5+13c σ=74.36

310.55 D#4-3c

626.95 D#5+13c

915.53 A#5-31c


Table 3. Analysis results for shells with holes. Multiple conditions of holes closed/open are compared. Playability (0.0 – 10.0), sounding

frequencies, and power spectrum peak frequencies are shown. IIIc. RADIATION PATTERN ANALYSIS

The edited noise recordings were used to estimate the radiation patterns of each shell using the following technique: the Microphone 4 (located at the bell lip) signal was cross-correlated

Shell Name/# and Condition

Playability (1-10)

Fundamental Sounding F0 Mean σ=StDev

2nd Harmonic Sounding Freq. Mean σ=StDev




Strombus 10* Play F0 9.0 Play H2 6.0

290.80 σ=3.16 D4-17c σ=18.71c

611.16 σ=11.54 D#5-31c σ=32.38c

295.9 D4+13c

625.49 D#5+9c

924.32 A#5-15c

S10 Open Play F0 6.0 Play H2 0.5

297.40 σ=4.54 D4+22c σ=26.23c NOT POSSIBLE 303.22

D#4-45c 637.21 D#5+41c

922.85 A#5-18c

Strombus 15* "The Valve" big hole

PlayF0 8.0 PlayH2 7.0 no open trial

293.48 σ=2.41 D4-1c σ=14.16

614.603 σ=44.9 D#5-21c σ=122.07c

295.90 D4+13c

626.95 D#5+13c

837.89 G#5+15c

Strombus 13* Play F0 9.0 PlayH2 1.0

304.46 σ=2.33 D#4-38c σ=13.2c

553.51 σ=24.17 C#5-3c σ=74.0c

314.94 D#4+21c

654.79 E5-12c

963.73 B5-43c

S 13 1/2Open No Toots Here NO ATTEMPT NO ATTEMPT 364.75

F#4-25c 660.64 E5+4c

974.12 B5-24c

S13 Open Play F0 2.0 No H2

377.56 σ=13.21 F#4+35c σ=59.54c NOT POSSIBLE 417.48

G#4+9c 654.79 E5-12c

1010.74 B5+40c

Strombus 5* Play F0 8.5 No H2

281.76 σ=3.37 C#4+28c σ=20.58c NO ATTEMPT 285.64

D4-48c 593.26 D5+17c

862.79 A5-34c

S5 Open Play F0 7.5 Play H2 3.0

280.35 σ=3.30 C#4+20c σ=20.26c

590.06 σ=12.38 D5+8c σ=35.95c

291.50 D4-13c

607.91 D#5-40c

889.16 A5+18c

Strombus 17* "Big Mouthpiece"

Play F0 7.0 Play H2 3.0

295.93 σ=6.08 D4+13c σ=35.21c

613.65 σ=22.86 D#5-24c σ=63.32c

325.20 E4-23c

629.88 D#5+21c

922.85 A#5-18c

S 17 Open Play F0 5.0 331.90 σ=5.78 E4+12c σ=29.89c NO ATTEMPT 373.54

F#4+17c 675.29 E5+42c

928.71 A#5-7c


309.23 σ=9.85 D4-11c σ=54.29c

634.40 σ=27.67 D#5+33c σ=73.91c

300.29 D4+39c

607.91 D#5-40c

889.16 A5+18c

S 14 1/2Open Play F0 5.0 Play H2 4.0

338.92 σ=7.80 E4+48c σ=39.39c

666.05 σ=18.19 E5+18c σ=46.65c

347.17 F4-10c

691.41 F5-18c

930.18 A#5-4c

S 14 Open Play F0 3.0 416.87 σ=21.94 G#4+7c σ=88.8c NO ATTEMPT 421.88

G#4+27c 708.98 F5+26c

963.73 B5-43c

Strombus 12* Play F0 7.0 Play H2 0

302.80 σ=4.70 D#4-47c σ=26.67c NOT POSSIBLE 323.73

E4-31c 657.71 E5-4c

927.25 A#5-9c

ST 12 Open Play F0 5.0 308.81 σ=7.28 D#4-13c σ=40.34c NOT POSSIBLE NA NA NA


305.71 σ=2.72 D#4-30c σ=15.33c

631.98 σ=22.34 D#5+27c σ=60.14c

309.09 D#4-11c

646.00 E5-35c

971.19 B5-29c

S20 Open Play F0 3.0 386.73 σ=58.87 G4-23c σ=245.31c NOT POSSIBLE 389.65

G4-10c 641.60 E5-47c

999.02 B5+20c

JuacaPrieta* "Huaca Prieta"

Play F0 6.0 Play H2 2.0

326.44 σ=3.73 E4-17c σ=19.67

675.99 σ=18.97 E5+43c σ=47.91

344.24 F4-25c

706.05 F5+19c

993.16 B5+9c

JP Open Play F0 7.0 Play H2 1.0

341.25 σ=1.95 F4-40c σ=9.86

696.12 σ=7.52 F5-6c σ=18.60 NA NA NA


with each of the near-field 1-meter distant microphone signals, and normalized by the signal formed from the autocorrelation of Microphone 4 with itself:

Hm(n) = |X4 (n) * Xm(n)| / |X4 (n) * X4(n)| , where m = 5, 6, … 10 (near field microphones)

Figure 5 shows a family of six such normalized cross-correlation signals for one shell. Note the significant first peak, the point at which the cross-correlation is greatest, which represents the direct shell sound incident on each microphone.

Figure 5. Normalized cross-correlation of microphone 4 (bell) with each near-field array microphone. First peak is direct sound, other peaks are reflections from walls, player, etc.

To estimate the signals radiated in each direction, the area around the first significant peak was isolated by windowing as shown in Figure 6.

Figure 6. The 1st peak of each normalized cross-correlation signal is windowed for further analysis.

The log magnitude of the Fourier transform of each windowed normalized cross correlation signal can be plotted, giving an idea of both the radiated magnitude and frequency response of each direction, as shown in Figure 7. As expected, the most (and most broadband) energy is radiated to the right (the direction the shell bell was facing), and the least in the direction behind the player (shadowing). The next most significant energy is radiated upward. The total energy across the entire frequency spectrum (or in subbands) can be calculated to derive a 3D polar plot of the energy radiated from a given shell, as shown in Figure 8.


Figure 7. Power spectra of normalized cross-correlation signals at each near field mic.

Figure 8. Radiated energy in each of three planes: right/front (upper left), right/up (lower left), and front/up (upper and lower right).

This type of polar plot is useful in comparing the radiation patterns of two particular shells,

or of an individual shell with holes open and closed. Figure 9 compares hole-open (blue) to hole-closed radiation (black) patterns of one shell.


Figure 8. Radiated energy in each of three planes for one shell with hole open (blue) compared to hole closed (black). The shell with hole itself is also shown.

IIId. AREA FUNCTION ESTIMATION

As a final type of analysis, the fry signals were used to compute estimates of the area functions of each hole-free (and closed) shell. Using Linear Predictive Coding (LPC) and related techniques commonly used in speech analysis (Makhoul 1975), the assumption is that of a linear source-filter model. The source itself can be non-linear as is the case in the vocal folds or lip-reed of a brass/shell player, but the model assumes that the bore is linear and the signal from the lips is linearly filtered by the bore transfer function/frequency response. A further assumption is that the bore is a single closed waveguide tube of varying area (no side chains or holes). A final assumption or parameter is the length of the bore, which in our case is not known, but the effective length of an assumed exponentially flaring horn can be derived from the fundamental sounding frequency. We computed area functions assuming 96, 72, and 64 sections, to correspond to lengths of 0.65, 0.49, and 0.43 meters (at 48k sample rate and assuming a speed of sound of 324 m/s at 3150 meters altitude).

LPC decomposes the signal into a linear all-pole resonant filter that models the bore, and a residue representing the source signal. The Microphone 4 fry signals were used, because they represent a non-periodic, spectrally rich, low signal-to-noise system identification signal. The coefficients of the computed all-pole resonant filter can be directly transformed into partial correlation (PARCOR) coefficients of a ladder filter with spatial interpretation. Finally, the reflection coefficients of this ladder filter can be used to derive relative cross-sectional areas for an acoustic tube. Options for plotting this data include areas (assuming one area at one end or the


other), log areas (which should show a linear flare for an exponential bore), area ratios, or log area ratios (which should show a straight line at zero for an exponential bore). Figure 10 shows log area functions for a typical “well-behaved” (playable, no holes) shell for 96 and 72 sections (assumed length). The figures only differ in the slope of the log-linear flare. Note the region near the mouthpiece end is the only place deviations from an ideal flare appear, corresponding well with the fashioning and shape of the mouthpieces of well-behaved shells (and brass instrument mouthpieces as well).

Figure 10. Log area function for a well-playable shell assuming 96 sections (0.68m, left), and 72 sections (0.51m, right) effective length.

Since all well-formed and well-behaved shells are assumed to exhibit a simple exponential flare, and characteristic deviations at the mouthpiece end, one potentially useful function for area functions is to compare well-behaved vs. “pathological” shells (low playability, clear deviation from harmonicity of the impulse spectral peaks). Figure 11 compares the two most playable shells (top) with two of the least playable shells (lower). The deviations at the mouthpiece seem to be qualitatively different, (especially for Strombus16), but our analyses so far are inconclusive. This does, however, indicate that this type of analysis could be useful in the future.

VI. CONCLUSIONS

We have presented our data collection methods, analyses, and findings in investigating nineteen of the twenty Strombus galeatus marine shell trumpets excavated from the 3000 year-old ceremonial center at Chavín de Huántar, Perú. Our team performed acoustic analyses of the measured response of each instrument, to a variety of excitations, at microphones placed in the mouthpiece, player’s mouth, bore, bell, and surrounding near-field. From these measurements we characterized each instrument's sounding frequencies (fundamental and 1st overtone where possible), radiation pattern, impedance, and estimated its bore area function.

Many questions still remain, as summarized in the next section. To facilitate further studies, all project data and analyses are publicly available for the research (and artistic) communities.


Figure 11. Log area functions(left) and log area ratios (right) for two well-behaved

playable shells (top), contrasted to two of the least playable shells (lower). V. FURTHER QUESTIONS AND FUTURE WORK

Although our team collected as much information and data as we could in our time with the Chavín pututus, there is much that could be gleaned from more data. As mentioned before, it would have been desirable to take more measurements, such as castings and measurements of the interior mouthpiece shape, castings for exact dimensions and shape of the bell, an estimate of internal length from mouthpiece to bell, total interior shell volume, and exact details of the interior bore shape. Indeed, Magnetic Resonance Imaging (MRI) or other 3D density scanning technologies could provide all of these measurements.

These instruments were most likely played in ancient times as modern seashells are played across many cultures today: with the right hand moving in and out to modulate the pitch and tone. But in fact it is not known for certain how the shells were held and played. Some believe that the shells were held with the bell facing upward (VanValkenburgh 2002), while graphic artifacts such as the exterior cornice fragment (Rick 2008) depict the shells being held as they were in our experiments (bell rightward). One possible reason for the “Chavín Cut” (cutout in the apical lip of the shell bell, see Figure 12) might have been to allow the player to see more easily, to enable walking with the shell in a procession, for example. However, from a player’s perspective, a likely reason for the cutout is to allow the player to insert a hand farther into the bell, to affect sound production. There could be an even more functional/practical reason for the “Chavin Cut” having to do with the morphology of galeatus shells, in that many Strombus lips tend to extend far up the spine (mouthpiece area), making it impossible to place the mouth on a fashioned mouthpiece without some part of the pututu lip being cut away.


If the shells were modulated with the hand while played, the continuum of hand positions in and out of the bell changed not only pitch, but radiation pattern as well. For completeness, these aspects should be investigated in the future.

The question of holes in the shells remains open as well. Many of the holes were obviously caused by failure of the shell wall due to etching of artwork in the shell surface (see Figure 13). Other holes seem to have been due to natural wear and breakdown in the shell materials (Figure 14). Could others, however, have been intentionally fashioned into the shells to serve as “tone holes”? We know of little evidence to indicate that such holes have been crafted into the musical seashells of Peruvian, South American, or any other conch-playing cultures ranging from India to Polynesia. We also saw no holes that seemed to modulate the pitch in good ways while still leaving the shell playable in both open/closed conditions, but the question merits more study.

Figure 12“Chavin Cut”

Figure 13. Shell hole clearly due to failure of etched artwork pattern.

Figure 14. Holes likely due to

shell wear and breakdown.

Of course, of critical importance is how these shells were used in ceremony, and how they interacted with the architecture of Chavín de Huántar. Many members of our team are simultaneously studying the architecture and acoustics of the Chavín galleries (Kolar 2010), with an eye toward modeling, simulating, and better understanding the “whole picture” of life and ritual at Chavín de Huántar.

VI. DATA AND DOCUMENTATION

All recorded/edited data, figures as shown in this paper, notes, and characteristics for each marine shell trumpet, are presented on our project website:

http://ccrma.stanford.edu/groups/chavin/pututus VII. ACKNOWLEDGEMENTS

On site measurement of the Chavín pututus was funded by a grant from the Stanford Institute for Creativity and the Arts (SiCa), with additional support from the Princeton University David A. Gardner ’69 Magic Foundation Grant. We thank Dr. Christian Mesía and the staff of the Instituto Nacional de Cultura at the Museo Nacional Chavín for logistical assistance. Stacie Brink served as photographer and physical measurement coordinator, and provided other invaluable support and assistance. Many thanks to José Luis Cruzado and Cobi Van Tonder for videography, additional photography and assistance. Meyer Sound Labs contributed high-performance loudspeakers, and Countryman Associates, Inc. supplied precision microphones.


VIII. BIBLIOGRAPHY Abel, Jonathan S., John W. Rick, Patty Huang, Miriam A. Kolar, Julius O. Smith, and John M. (2008), Chowning. On the Acoustics of the Underground Galleries of Ancient Chavín de Huántar, Perú. Invited paper presented at Acoustics '08, Paris, France.

Kolar, Miriam A., Jonathan S. Abel, Ritesh Y. Kolte, Patty Huang, John W. Rick, Julius O. Smith III, and Chris Chafe (2010), A Modular Computational Model of Ancient Chavín de Huántar, Perú. Invited paper presented at the 2nd PanAmerican/Iberian Meeting on Acoustics, Cancún, Mexico.

Berthou, P., J. M. Poutiers, P. Goulletquer, and J. C. Dao (2010), SHELLED MOLLUSCS, in FISHERIES AND AQUACULTURE. Encyclopedia of Life Support Systems (EOLSS). Developed under the Auspices of the UNESCO, Eolss Publishers, Oxford, UK. Retrieved from http://www.eolss.net.

Cook, Perry R. (1996), Hearing, Feeling, and Performing: Masking Studies with Trombone Players, International Conference on Music Perception and Cognition, Montreal.

Fletcher, Neville H. and Thomas D. Rossing (1998), The Physics of Musical Instruments, New York: Springer-Verlag.

Lumbreras, Luis G. (1993), Chavín de Huántar: excavaciones en la Galeria de las Ofrendas. Materialien zur Allgemeinen und Vergleichenden Archaologie bd. 51. Mainz am Rhein: P. von Zabern.

Makhoul, John (1975), Linear Prediction: A Tutorial Review, Proc. of the IEEE, 63:4.

Rick, John W. and David Lubman (2002), Characteristics and speculations on the uses of Strombus trumpets found at the ancient Peruvian center Chavín de Huántar. (Abstract), Journal of the Acoustical Society of America. Volume 112, Issue 5, pp. 2366-2366.

Rick, John W. (2004), The Evolution of Authority and Power at Chavín de Huántar, Perú. In: Kevin Vaughn, Dennis Ogburn, and Christina A. Conlee, eds., The Foundations of Power in the Prehispanic Andes, pp. 71-89. Archaeological Papers of the American Anthropological Association 14.

Rick, John W. (2008), Context, Construction, and Ritual in the Development of Authority at Chavín de Huántar. In Chavín Art, Architecture and Culture. Monograph 61. Conklin, William J. and Jeffrey Quilter, Editors. Cotsen Institute of Archaeology, University of California, Los Angeles, pp. 3-34.

Rowe, John H. (1962), Chavín Art, An Inquiry Into Its Form and Meaning. New York, University Publishers.

Tello, Julio C. (1960), Chavín: Cultura Matriz de la Civilización Andina. Primera parte, con revisión de Toribio Mejía Xesspe. Imprenta de la Universidad de San Marcos. Lima, Peru 1960.

VanValkenburgh, Parker (2002), Style and Interregionalism in the Early Horizon: Twenty Strombus galeatus trumpets from Chavín de Huántar, Perú. Stanford University Undergraduate Honors Thesis, Department of Anthropological Sciences. Stanford, CA.

Farina, Angelo (2000), Simultaneous measurement of impulse response and distortion with a swept- sine technique, Paper 5093, 108th Audio Engineering Society Convention, Paris.

acoustic analysis of the chavín pututus (strombus galeatus marine

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