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Proceedings of the Institute of Acoustics
Vol. 37. Pt.3 2015
Willem Boning Arup Acoustics, New York, NY, USA
Alban Bassuet Tippet Rise Art Center, Fishtail, MT, USA
In spring 2014, the Tippet Rise Art Center commissioned Arup Acoustics to design an acoustical
shell, nicknamed the “Tiara,” for hosting outdoor chamber music concerts for an audience of 50-60
people. The shell was intended to be temporary, demountable and transportable to different
locations across the art center’s site, spread across 11,000 acres of rugged, rolling ranchland in
south central Montana (fig. 1). The clients wanted to allow audience members and performers to
engage visually with the site’s natural surroundings while enjoying the acoustical intimacy of a small
room. To balance the dual requirements of exposure and enclosure, we developed a concept for a
“room without walls,” beginning with a simple box, cutting out surfaces to open views of the
surrounding valleys and mountains and optimizing the remaining corners to provide an enveloping
array of reflections to the performers and audience.
Most outdoor sound-enhancing structures follow one of two models, as identified by Jaffe.1 First are
shells that surround the performers on stage, capturing sound energy and projecting it to an
audience sitting in an amphitheater or on a lawn. Examples include the Hollywood Bowl; the Minnie
Guggenheimer Shell, an adjustable, demountable stage enclosure designed by Jaffe for the New
York Philharmonic’s summer concerts in Central Park; and the Soundforms mobile performance
stage, a collaboration between BFLS Architects and Arup Acoustics.2 This type of shell improves
acoustic conditions for performers by providing early reflections from multiple directions so they can
hear themselves and each other, and improves the acoustics for audience members by amplifying
and enlarging the source image. The second type of structure is a “shed,” open at the back and
sides and covered by a roof, which protects audience members from the elements and allows
reverberation to build up. Sheds often include a stage enclosure and overhead reflector to give
Proceedings of the Institute of Acoustics
Vol. 37. Pt.3 2015
Figure 1: The initial Tippet Rise Tiara site before construction.
musicians stage support and to increase the level of clarity and early sound energy for audience
members. The Koussevitzky Music Shed, which features a tessellated stage wall and semi-open
canopy of triangular panels designed by Beranek, is a pioneering example.3
In designing the Tiara, we wanted to achieve the same degree of amplification, source enlargement
and stage support as in the best existing outdoor venues but with a less frontal, more enveloping
sound impression and a unified acoustical environment for performers and audience members to
share. To this end we looked to two indoor spaces as benchmarks, the Schloss Schwetzingen
Rokokotheater, a 450-seat baroque opera house, and the Esterházy Palace (Fertőd) Music Room,
which seats about 60 people. The Rokokotheater’s acoustics are noteworthy for being intimate and
enveloping despite a short reverberation time compared to other opera theaters of the period. 3D
impulse responses recorded by Bassuet reveal that the room owes its surrounding acoustical
qualities to strong early reflections off the proscenium, side walls, ceiling and curved balcony
undersides, which compensate for the lack of reverberant energy (fig. 2).4 Because the reflections
arrive from multiple directions and in quick succession after the direct sound, they do not result in
image shift but rather blend with the direct sound, giving listeners the impression that the opera
singer’s voice fills the entire space. The Music Room at Esterházy, on the other hand, is remarkable
for an immersive, enveloping sound impression that is consistent throughout the entire space.
Bassuet found that the uniform spatial distribution of sound energy is largely due to an array of
reflections arriving from the upper front and rear corners of the room.4
Figure 2: Principle early reflections in the Schloss Schwetzingen Rokokotheater and Esterházy
Music Room. (Photographs courtesy Florian Merdes and Esterházy Palace)
Proceedings of the Institute of Acoustics
Vol. 37. Pt.3 2015
Our initial design concept consisted of a fan-shaped room 22 ft (6.7 m) wide at the front and 32 ft
(9.8 m) wide at the back, 25 ft (7.6 m) deep, and 15’ (1.5 m) tall, with the middle of each surface
removed so that only the corners remained (fig. 3). We intended the corners to function like those of
the Esterházy Music Room, reflecting sound to the performers and audience from all directions to
create an immersive and unifying sound environment. We also hoped to emulate the beneficial
focusing effect of the Rokokotheater’s curved balcony undersides by optimizing our corners to
return as much energy as possible to the listeners, supporting a psychoacoustical impression of
being in a room despite a lack of reverberation.
Figure 3: Initial design concept.
We assessed the efficacy of each corner in the concept diagram by carrying out an image-source
method (ISM) analysis5,6 of the geometry. We found that while reflections off the upper corners
covered a substantial part of the audience, reflections off the lower vertical corners covered only a
narrow band of audience members. We therefore removed the lower corners from the concept
diagram, further opening the view. Reducing the diagram to surfaces exclusively above the heads
of musicians and audience members presented some risk of image shift, but we estimated that the
risk could be minimized by ensuring that each musician and audience member receive reflections
from multiple directions. Following the model of the Rokokotheater, a broad spread of early energy
could enlarge rather than displace the source. An ISM analysis for a single, central listening position
in our revised concept diagram indicated that a broad spread of incidence angles was possible, with
second and third-order reflections arriving from the front, back and sides (fig. 4).
Extending our ISM analysis to the entire audience and stage areas in the revised concept diagram,
we found that right-angled corners were not optimally reflecting sound back to the audience. To
maximize the quantity and directional spread of reflections arriving at each musician and audience
member, we optimized the corner angles of our concept diagram by pairing our ISM analysis
algorithm with the Galapagos genetic algorithm plugin for Grasshopper. Our optimization exercise
builds off a growing body of research on room acoustic optimization. Sato et al. were the first to
apply genetic algorithms to room acoustic geometry optimization, finding an ideal concert hall shape
by weighting four orthogonal parameters—strength (G), initial time delay gap (ITDG), reverberation
time (RT) and inter-aural cross-correlation coefficient (IACC).7 Six papers on room acoustic
Proceedings of the Institute of Acoustics
Vol. 37. Pt.3 2015
Figure 4: Revised concept diagram showing seven ideal reflection paths.
optimization were presented at the International Symposium on Room Acoustics (ISRA) 2013
alone. Among them, Palma et al. used stochastic raytracing and a genetic algorithm to optimize an
outdoor acoustical shell with the aim of maximizing energy distribution over an audience plane.8
We parametrized the geometry of our concept diagram to undergo six transformations (fig 5):
1. The bottom edge of the side walls moved in and out in the xy plane.
2. The bottom edge of the stage wall moved in and out on the xy plane.
3. The inner edge of the stage and side ceilings moved up and down along the z axis.
4. The upper back corners moved in and out parallel to the inner edges of the ceiling.
5. The lower back corners moved in and out parallel to the lower edges of the side walls.
6. The inside back corners moved in and out parallel to the upper edges of the side walls.
We imposed limits on the transformation ranges to prevent the geometry from obstructing views of
the mountain horizon and to keep within the dimensional limits allowable by a structural diagram
developed by the multidisciplinary design team.
Figure 5: Optimization parameters.
Proceedings of the Institute of Acoustics
Vol. 37. Pt.3 2015
The six independent transformations created a solution space too large to exhaust by brute force,
so we deployed the Galapagos evolutionary solver to seek out optimal combinations of parameter
values.9 Each geometric iteration was analyzed by ISM to identify specular second and third-order
reflections from a source to the 50 receiver positions (fig. 6) and the success or failure of each
iteration was evaluated by a fitness function. We developed two different fitness functions, the first a
count of the second and third-order reflections reaching all receivers, and the second a count of
second and third-order reflections limited to the 12 “poorest” receivers, ie. those receiving the
fewest reflections. We found that the first fitness function tended to maximize the total number of
reflections at the expense of the poorest receivers, whereas the second fitness function resulted in
a more even distribution with the total number of reflections comparable to (or in some cases even
exceeding) those generated by the first fitness function. We did not incorporate the spread of
reflection incidence angles into the fitness functions as we observed a consistently positive
correlation between the quantity and directional variety of incident reflections.
Figure 6: ISM analyses of a small sample of iterations tested by the Galapagos evolutionary solver.
The selected scheme is highlighted.
After the first round of optimiziation, transformation parameter values converged on two solution
regions with similar quantities and distributions of reflections. The first solution region resulted in a
ceiling angled downwards towards the audience, a function of second-order side-wall-to-ceiling
reflections. The second solution region resulted in a ceiling angled downwards away from the
audience, a product of the inverse reflection path, ie. ceiling-to-side-wall. Despite the acoustical
similarity between the two solution regions, the design team proceeded with the second outcome as
the geometry it produced was easier to support structurally and would give audience members a
stronger visual sense of enclosure.
The final geometry we chose to serve as the basis for constructing the Tiara was found to return an
average of 5.7 second and third-order reflections to each receiver. We fell short of our goal to
provide each receiver the same 7 reflections but managed to provide each a minimum of one
reflection from the front, one from the left side and one from the right side.
Proceedings of the Institute of Acoustics
Vol. 37. Pt.3 2015
The Tippet Rise Tiara was constructed in July, 2014 and the first concerts were held over the
course of the summer (fig. 7). Due to unexpected wind gusts, the inaugural concert began indoors
and moved outside once the wind had died down, giving audience members the opportunity to
compare the two listening environments. (They expressed a strong preference for the sound in the
Tiara.) One member of the Billings Youth Orchestra string quartet remarked, “It helped to be
outside, with the wind blowing through your hair … to understand what Dvořak meant, to play this
like the bird, and you can feel like a bird flying in the wind.”10 Other performers have described
playing in the Tiara as a “liberating experience.”
Figure 7: The completed Tiara, July 2014.
During the first concerts, we experienced a high degree of consistency in sound strength and
envelopment throughout the audience area, indicating that our optimization exercise had been
successful. The reflected energy arriving from above was balanced and well-integrated with the
direct sound, creating a pleasant enlargement of the source dimensions. Optimizing the structure’s
geometry from a single point source risked that some instruments in an ensemble would be “picked
up” better than others by the structure’s geometry—indeed, during the first concert, the first violinist
and cellist seated downstage were louder and their source images were larger than the second
violinist and violist seated upstage. For the second concert, we moved the stage closer to the
audience, exposing the upstage musicians to a greater solid angle of the stage wall. This improved
the balance considerably for audience members, and musicians reported being able to hear
themselves and each other better. Optimization based on ISM analysis, which only identifies
specular reflections, also risked an uneven timbral response privileging high frequencies. While
reflections did appear to have more high frequency content than low, we heard some
responsiveness at bass and mid-frequencies, possibly due to comb filtering caused by reflections
arriving within a short time window of each other.
Proceedings of the Institute of Acoustics
Vol. 37. Pt.3 2015
Figure 8: Predicted and measured impulse responses for four receiver positions
Proceedings of the Institute of Acoustics
Vol. 37. Pt.3 2015
We carried out a validation of our acoustical predictions by comparing predicted impulse responses
to impulse responses recorded on site. To create a predicted impulse response, we identified
reflections from different receiver positions by ISM analysis and recorded their delay time and
attenuation due to distance. We recorded impulse responses at the same receiver positions on site
by recording balloon pops on a B-Format SoundField microphone and extracting the omnidirectional
W channel. Figure 8 shows a comparison of predicted to measured impulse responses, normalized
to the direct sound, for four receiver positions. The graphs show good correlation in time between
the arrival of reflections in predicted and measured impulse responses. The relative arrival time of
reflections from position to position also matches our predictions, with receivers closer to the source
receiving reflections later than those further from the source. Measured reflections are more spread
out in time than predicted reflections, which may be due in part to diffraction at the panel edges.
After a number of successful concerts in the Tiara, the art center decided to expand the Tiara to
accommodate up to 80 audience members. An ISM analysis revealed that simply extending the
arms of the structure would not provide adequate coverage to listeners in the middle of the
audience area. To ensure coverage in this area, we added a kink to the structure’s arms and re-
optimized the structure along the same lines as the optimization described above. The final form
returns an average of 5.6 reflections to each receiver inside the structure, about the same as in the
initial construction but with a broader distribution of third-order reflections (fig. 9). The expanded
shell was constructed in the spring of 2015 and three concerts have been held to date. It is likely
that the Tiara could continue to be scaled up to a certain extent. We note, however, that as a
growing number of audience members pushes the structure further from the source, the larger the
corners will need to become to reflect sound back to the majority of the stage and audience area
(and the weaker those reflections will become).
Figure 9: Image source analysis of original and expanded shells with the same receiver layout in
Proceedings of the Institute of Acoustics
Vol. 37. Pt.3 2015
Figure 10: Expanded Tiara, August 2015.
At its current scale, the Tippet Rise Tiara creates an open yet intimate performance space where
musicians and audience members share the same enveloping acoustical environment. The Tiara
heightens engagement between performers and listeners while at the same time inviting
contemplation of the relationship between music and the natural environment. Because the Tiara is
demountable and transportable, it can be reconstructed in different locations across the Tippet Rise
site, and in each location, new relationships will become visible and audible.
The authors would like to extend special thanks to Léonard Roussel of Arup for assisting in the
acoustical optimization and validation of the Tiara. Brian Markham and Guilherme Cadaval of Arup
developed the initial structural concepts for the Tiara and Ed Arenius and Chris Darland of Arup
assisted in venue planning. The Tiara was constructed by Gunnstock Timber Frames with
Firetower Engineering as structural engineer of record.
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Hollywood Bowl. New York: W.W. Norton & Company. (2010).
2. A. Bassuet, D. Rife and L. Dellatorre. 'Computational and Optimization Design in Geometric
Acoustics', Proc. International Symposium on Room Acoustics. Toronto (2013).
3. L. Beranek. Concert Halls and Opera Houses. New York: Springer. (2004), p. 85.
Proceedings of the Institute of Acoustics
Vol. 37. Pt.3 2015
4. A. Bassuet. 'Acoustics of a selection of famous 18th century opera houses: Versailles,
Markgrafliches, Drottningholm, Schweitzingen', Proc. Acoustics ’08. Paris (2008).
5. J.B. Allen and D.A. Berkley. 'Image method for efficiently simulating small-room acoustics',
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Society of America 75(6), 1827-1836. (1984).
7. S. Sato et al. 'Applying Genetic Algorithms to the Optimum Design of a Concert Hall', J.
Sound and Vibration 258 (3), 517-526. (2002).
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field environment', Proc. International Symposium on Room Acoustics. Toronto (2013).
9. D. Rutten. 'Evolutionary Principles applied to Problem Solving'. Online article. (2010).
10. “Kids Video.”
... In 2015, the initial design solution was further expanded in order to accommodate up to 80 people, by the addition of two kinks to the structure, which were optimized with a procedure similar to that used for the initial solution. The final configuration of the shell provides on average 5.6 s-and third-order reflections to each receiver, with a minimum of one from the front, one from the right side and one from the left side [94]. The temporary acoustic pavilion was developed within a research framework. ...
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The Acoustics of Performance Halls: Spaces for Music from Carnegie Hall to the Hollywood Bowl
  • J C Jaffe
J. C. Jaffe. The Acoustics of Performance Halls: Spaces for Music from Carnegie Hall to the Hollywood Bowl. New York: W.W. Norton & Company. (2010).
Acoustics of a selection of famous 18th century opera houses
  • A Bassuet
A. Bassuet. 'Acoustics of a selection of famous 18th century opera houses: Versailles, Markgrafliches, Drottningholm, Schweitzingen', Proc. Acoustics '08. Paris (2008).