PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

The CHORDatabase: a twenty-one concert hall sphericalmicrophone and loudspeaker array measurement database
Matthew T. NEAL1; Michelle C. VIGEANT1
1

Graduate Program in Acoustics, The Pennsylvania State University, University Park, PA USA

ABSTRACT
Repeatability and realism are both highly important goals in concert hall perceptual studies, but it is hard tosatisfy both simultaneously. Auralization from room impulse response (RIR) measurements allows for
repeatable listening conditions between halls, but typical measurement loudspeakers do not realistically
represent an orchestra. To support both goals, the Concert Hall Orchestral Research Database(CHORDatabase) has been generated. This database consists of 32-channel spherical microphone arraymeasurements in 15 North American and 6 European concert halls. First, measurements were made at 7 to
15 seats in each hall using a three-part omnidirectional loudspeaker, maintaining omnidirectionality up to 5
kHz. These measurements enable standard room acoustic parameter calculations and higher-order sphericalarray beamforming techniques, and the overall variety of the database will be demonstrated using bothobjective analyses. Also, a compact 20-element spherical loudspeaker array was used to provide realistic
source directivities for RIR measurements. This array can accurately represent the frequency-dependent
radiation patterns of different instruments up to 3-4 kHz. Measurements were made at 20 orchestral source
positions and one seat in each hall, 15 meters from stage. Full-orchestra auralization techniques will bepresented, and the future potential of this database will be discussed. [Work supported by NSF Award#1302741.]
Keywords: concert hall, spherical, microphone, array, beamforming, directivity, measurements, auralization

1. INTRODUCTION
The central goal of concert hall design is to generate a room that enhances the music, providing
the most pleasing listening experience to all individuals in the audience. This preference is a complex
function of the spectral, temporal, and spatial character of the room impulse response (RIR), let alone
the complex and unique distribution of sources across the stage. The study of this topic is not new,originating from Sabine’s early work on reverberation time (RT). 1 After that work, many believed that
RT alone did not fully explain preference in a concert hall, so studies were initiat ed to more fully
explain concert hall preference. These efforts have spanned from the 1950s to the present, includinginterview- and survey-based approaches, 2-3 live-listening surveys, 4-7 simplified laboratory studies, 8-9
measurement-based auralizations, 10-16 and simulation-based auralizations. 17 From all of this work,suggestions exist as to which might be important regarding preference in concert halls, but still muchdisagreement exists regarding which perceptions are most important. Some limitations could be linked
to differences between measurement setups, auralization techniques, or the use of simulated data. 18

2. THE CONCERT HALL ORCHESTRAL MEASUREMENT DATABASE
A new room impulse response (RIR) measurement database of 21 concert halls has been generatedusing a spherical microphone array, compact spherical loudspeaker array, and a three -part
omnidirectional sound source. The halls included in the database were selected from an online survey,
where researchers and consultants in concert hall acoustics provided suggestions of halls with both
excellent and lower reputations. The final database included 15 halls located in North America and 6
halls located in Europe, having a large variety in shape, size, and RT, as shown in Table 1. In the table,
1

mtn5048@gmail.com (or mtn5048@psu.edu)7863

a hall shape category of either historic shoebox (H.Sh.), modern shoebox (M.Sh.), fan, vineyard(Vnyd.), or other shapes outside these four categories (other) are provided along with the midfrequency average T30, EDT, and C80 across all measured seat location s in each hall. For halls withvariable acoustics, a letter is assigned to represent the variable acoustic setting (VAS) with “A” always
corresponding to the setting used for unamplified orchestral performance. To maintain anonymity, hallvolumes are provided in ranges for various size designations: extra small (XS: 15,000 – 17,500 m3 ),small (S: 17,500 – 20,000 m3 ), medium (M: 20,000 – 22,500 m3 ), large (L: 22,500 – 25,000 m3 ), or
extra-large (XL: 25,000 – 27,500 m3 ).
Table 1 – Summary data of the shape, size, variable acoustic setting (VAS), and mid-frequency averaged
T30, EDT, and C80 across all measured seats. The Orch. column indicates whether the full-orchestra source
measurements were made in each hall / setting, and the Rec. column specifies the number of seatsmeasured using the omnidirectional source. Hall sizes are given in broad categories of XXS to XXL.
Hall

Shape

Size

VAS

T30 (s)EDT (s)C80 (s)Rec.

Orch.?

1
2
3

H. Sh.
H. Sh.
H. Sh.

S
XS
S

4

H. Sh.

M

5

H. Sh.

XXS

6

M. Sh.

S

7

M. Sh.

L

8

M. Sh.

L

9

M. Sh.

S

10

M. Sh.

L

11
12
13
14
15
16
17
18
19
20

Fan
Fan
Fan
Fan
Vnyd.
Vnyd.
Vnyd.
Vnyd.
Other
Other

XL
S
XXL
S
M
XS
S
XXL
XL
M

21

Other

L

–
–
–
A
B
A
B
A
B
A
B
A
B
C
D
E
F
–
A
B
–
–
–
–
–
–
–
–
–
–
A
B
C

2.50
2.17
2.51
2.56
1.97
2.27
2.37
1.61
1.71
2.73
1.54
2.86
2.38
2.80
2.74
2.62
2.65
2.12
2.81
1.78
1.58
1.79
2.29
1.78
2.09
2.09
2.21
3.28
1.73
2.41
2.09
1.75
1.58

2.55
2.13
2.43
2.92
2.38
2.27
2.43
1.62
1.64
2.54
1.74
2.09
1.93
2.11
2.12
2.07
2.05
2.07
2.35
1.57
1.71
1.75
2.21
1.76
2.06
1.85
2.09
2.80
1.44
2.40
2.00
1.76
1.68

-2.76
-2.51
-3.25
-2.53
–
-3.21
–
0.41
–
-2.79
–
-1.33
-0.76
–
–
–
–
-3.15
-1.80
-0.28
-0.35
0.81
-2.76
-0.53
-0.59
-2.34
-0.40
-1.32
0.71
-3.84
-2.22
–
–

11
9
12
11
3
5
3
4
1
12
1
7
6
1
1
1
1
14
7
6
7
14
10
10
13
5
15
12
12
11
11
3
3

Yes
Yes
Yes
Yes
No
No
No
Yes
No
Yes
No
Yes
Yes
No
No
No
No
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No

33

–

–

–

242

21

Totals:7864

5m

2.1 Objectively-motivated omnidirectional source measurements
The first goal of the database was to provide repeatable, objective measurement s for sound field
analysis that could be reproduced by other research teams. A three-part omnidirectional sound source
was used for this objective measurement protocol to provide a wide -bandwidth omnidirectional
measurement up through 5 kHz, with adequate signal-to-noise at low frequencies. 19 Single
dodecahedron omnidirectional loudspeakers are common, since they provide adequate low-frequency
power, but deviations from omnidirectional radiation are quite significant above 1 kHz whenconstructed using 10 cm (4-inch) driver elements. RIRs were captured with a 32-channel sphericalmicrophone array, the Eigenmike em32, by mh Acoustics (4.2 cm radius). Measurements using thisarray can be processed using spatial beamforming techniques up to a high-frequency aliasing at 8 kHz.
From this measurement, omnidirectional and figure-of-eight RIRs can also be extracted for standard
metric calculation. 20
These measurements were made in a number of seats, with the purpose of obtaining a
representative sample of all seating areas in each hall. First, a standard grid of receiver locations wasdeveloped, to provide consistency between halls in terms of source-receiver distance, shown in Figure
1.21 Four central hall receivers, R1 – R4, were placed at 10, 15, 20, and 25 m from the ‘conductor’
location of an orchestra, placed 1 m from the front of the stage. These four receivers were measured
in each hall for setting A, and sometimes fully in other VAS. Three additional receivers were placed
5 m off-center, located in the same rows as R2 – R4. Once these receivers were completed, additional
receivers were placed around each hall, contributing to a mostly uniform sampling throughout the hall,time permitting. The total number of receivers in setting A varied from 5 to 15, largely a function of
the seating design and the measurement time limitations in each hall. In total, 242 individual seats
were measured, the largest database with this degree of accuracy and repeatability created to date.

R5

R6

R7

R1 R2

R3

R4

10 m
15 m
20 m
25 m

Figure 1 – The standard receivers, R1 – R7, with a constant source-receiver distance in all halls.
2.2 Subjectively-motivated compact spherical loudspeaker array (CSLA) measurements
Although the measurements described in section 2.1 employed a more standard and accessible
technique, they are not directly related to the reality of a full orchestral performance. A full orchestra
is made of many sources distributed across the stage with unique radiation patterns, changing
significantly for the same instrument at different frequencies. 22 A compact spherical loudspeaker array(CSLA) was constructed to reconstruct the directional radiation patterns of different orchestral
instruments. 21 This array consisted of 20 compact 40-mm drivers with an extended 200 Hz lowfrequency resonance for drivers of this size, shown in Fig. 2. The array’s overall size was 15.2 cm indiameter, compact enough to limit high frequency aliasing to frequencies above 3000 Hz.
A measurement database of instrument directivities represented in the spherical harmonic domain
was used to reconstruct the frequency-dependent radiation patterns of each orchestral instrument. 23
Full-frequency filters were designed to build-in directional radiation patterns for specific orchestral
instruments into a measurement signal. The use of built-in radiation patterns allowed for time-efficientmeasurements of many orchestral positions across the stage. This single source was capable of flexibly
recreating any orchestral instrument, not requiring an extensive multi -loudspeaker setup. To validate
the directional control of the array, full-3D impulse response measurements were made using aturntable in an anechoic chamber. The radiation pattern targets for an oboe, shown in the upper half

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Figure 2 – The compact spherical loudspeaker array (CSLA) used for directional source radiation control.
of Fig. 3 (a), are compared against the reconstructed sound pressure levels as a function of direct ion
in the bottom half of Fig. 3 (a). By comparing the upper target and lower reconstructed plots, highagreement is found between the target and reconstructed directio nal radiation patterns. This
performance is maintained from low frequencies up to a spatial aliasing limit for the array around 3 –4 kHz. Above that limit, incoherence due to driver spacing causes accuracy to degrade.
To provide a consistent measurement between halls, a receiver gird of 20 source locations wasdeveloped where each location was placed at a specific radius and angle from a central ‘cond uctor’
location, shown in Fig. 3 (b). Each position was assigned to a particular instrument, as radiation
patterns were built-into each measurement. This layout provided a consistent source representation
between halls, allowing for repeatability, while still ensuring a realistic presentation of a full orchestra.
To achieve better low-frequency signal to noise for auralizations, an additional measurement was
taken at each instrument position with the subwoofer component of the omnidirectional sound source.
Full orchestral auralizations were generated using anechoic recording of Beethoven’s 8 th symphony,separately recorded for a 61-piece orchestra. 24 Full details on the 20-source measurement setup andthe extension to a 61-piece orchestral for the auralizations are provided chapters 4 and 5 of Ref. [21].
S17
S16

S13

S12

S7

S6

S11

S18

S4

S19
S14

S5

S8

S2
S10

S1 ߠ

S20

S9

S15
S

S3

(b)
(a)
Figure 3 – Directional radiation pattern reconstruction results of an oboe’s directivity using the CSLA.
Results are shown at discrete one-third octave band center frequencies. In general, frequencies below 3000
Hz demonstrate accurate reconstruction and accuracy is fully degraded above 4000 Hz.

3. RESULTS
3.1 Standard Metric Distributions and CorrelationsFirst, standard room acoustics metrics, as provided in ISO 3382, were calculated for all 242 seatpositions across the entire database. The full processing details can be found in chapter 5 of Ref. [21].
To calculate each metric, the following steps in the calculation procedure were used:
Step 1: Individual microphone capsule differences were removed, correcting for broadband
sensitivity differences across the thirty-two 12.7 mm (½”) microphone capsules.

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Step 2: A spherical Fourier transform using the SoFIA Toolbox was used to translate from aspatially sampled microphone RIR (MicRIR) to a spherical harmonic RIR (ShRIR) in thecomplex-orthonormal normalization format. 25-26
Step 3: Steps 1 and 2 were repeated for each of the three parts of the omnidirectional source,
where each was filtered to correct for diffuse-field equalization and overall gain
differences from both driver sensitivity and power amplifier gain settings.
Step 4: A linear-phase three-band crossover filter was applied to combine all three separate
measured ShRIRs into a single, broadband source-omnidirectional ShRIR. This step also
included a small adjustment for time delays between the direct sound of the first channelof the ShRIR, due to changing computer latency between measurements.
Step 5: Radial filtering was used to correct for the effect of the size of the microphone array andscattered pressure term due to the presence of a rigid boundary condition in the soundfield. 25
Step 6: Diffuse-field equalization was used to correct for the non-flat response of the Eigenmike’s
measured omnidirectional RIR.
Step 7: The ShRIR was rotated in the spherical harmonic (SH) domain using a toolbox developed
by Archontis Politis, such that the microphone was oriented directly at the omnidirectionalsound source. 27
Step 8: The RIR was cleaned using a RIR slope-fitting technique based upon nonlinear leastsquares regression of the backwards integrated RIR. 21 Since SH functions are orthogonal,
cleaning was performed in the ShRIR, replacing the noise floor with uncorrelated
decaying noise in each SH channel. This fit was done separately in each octave band,using the same slope across all ShRIR channels for a given frequency band.
Step 9: The ShRIR was transformed from the complex-valued orthonormal SH format to the
ambiX format, based upon real-valued spherical harmonics. This representation allows
for the direct extraction of the omnidirectional (W) and laterally oriented dipole response(Y) from ShRIR channels 1 and 2, respectively. This conversion was also performed using
the toolbox develop by Politis, with modifications.27
Once the cleaned omnidirectional and figure-of-eight RIRs were extracted from the ShRIR,
parameters from ISO 3382 could be calculated for each octave band. 28 The metrics for reverberation
time (T30 and EDT) along with metrics for clarity (C80 and center time, Ts) were calculated from 63
Hz to 4000 Hz. Since the source maintained omnidirectionality over this range, the parameters were
found to be reproducible over this frequency range. The distribution of the parameters for low- (63 –250 Hz), mid- (500 – 1000 Hz), and high-frequency (2000 – 4000 Hz) averages are shown as
overlapping histograms in Fig. 4. ISO 3382 lists the typical ranges for each of these parameters as:
1.0 to 3.0 s for T30 / EDT, -5.0 to 5.0 dB for C80, and 60 to 260 ms for Ts. All of these ranges are
specifically given for mid-frequency average values, shown in green in Fig. 4.

Figure 4 – Histogram of low- (63 – 250 Hz), mid- (500 – 1000 Hz), and high-frequency (2000 – 4000 Hz)
distributions for T30, EDT, C80, and Ts as defined in ISO 3382.
The range is well covered for T30 and EDT, except for no metric results close to 1.0 s for T30.
This limited range is due to the requirement of stages that could accommodate a full orchestra, as
large rooms tend to have longer RTs. The range exceeds the upper 3.0 s limit, as two rooms had quite
high values of T30. For C80, the range is well sampled down to -5 dB, with slightly reduced coverage7867

at the upper limit, around 2 – 3 dB. This upper limitation is due to the same reason as the limited RT
range. Finally, Ts covered the expected range from 60 to 260 ms, having dis tribution ends right atthese end points. These distributions illustrate the large coverage of the CHORDatabase.
3.2 Visualizations using Spherical Array Beamforming
Once RIRs have been represented as a ShRIR, spherical array beamforming techniques can be use d
to decompose a RIR into individual spatial maps. These maps represent the energy given in a specifictime and frequency region of a RIR, plotted as a function of azimuth and elevation. An example ofone of these maps is shown in Fig. 5. For the ShRIR, plane-wave decomposition (PWD) was used togenerate a set of directional RIRs (DirRIRs), each representing the respon se of the microphone arrayhaving a beam-like directivity pattern in a particular direction. 25-26 This beam directivity pattern isthen rotated in full-3D space around the sphere, and each of these RIRs can be time-windowed, bandpass filtered, and then energy integrated. Specifically, these plots were generated using a -25 dB side
lobe level Dolph-Chebyshev beam pattern, designed to reduce side lobe artifacts. 25
Each point in the map below represents the energy integration for a DirRIR from a beam oriented
in the specific direction of the selected point, generating a spatial “heat map” of the RIR. The example
below is for a 1 ms time window of the RIR, isolating a single strong reflection arriving from 55 to
56 ms following the direct sound. The upper rectangular grid had artifacts that are similar to those
associated with unwrapping a 3D globe onto a 2D rectangular map. The top and bottom of the globe
are stretched across the top and bottom of the plots. The key directions are identified below as front(F), left (L), right (R), back (B), top (Up), and bottom (Down). The more natural representation ofthis data is shown as a balloon-style plot, with color and radius indicating energy amplitude, shownin the lower portion of Fig. 5. Both plots are normalized to the maximum spatial energy in the specifictime-frequency region.

(a)(b)
Figure 5 – Examples of a rectangular spatial energy “heat map” for a reflection occurring between 35 and35 ms following the direct sound (a). A more visually-intuitive balloon-style plot is also provided in (b).
3.2.1 Spatial Beamforming Maps
The spatial energy in a RIR can be analyzed over different time regions. To demonstrate this styleof analysis, the early energy (10 – 100 ms) has been isolated in a single RIR from eight different halls
in the CHORDatabase, shown in Fig. 6. For each hall, a time domain RIR is provided, highlighting
the current energy window in red, and both the 2D map and 3D balloon plot of the spatial energy are
visualized. Halls shown consist of fan-shaped halls (a & b), vineyard halls (c & d), historic shoebox
halls (e & f), a modern shoebox hall (g), and a theatrically-inspired hall geometry, categorized asother-shaped (h).
First, certain halls emerge as having a narrow early reflection character, including the fan-shaped
halls (a & b) and the other-shaped hall (h). The historic shoebox halls (e & f) both have strong,laterally-focused early energy, and a similar property is found in the second vineyard hall (d). Thisobservation matches with the general wisdom that shoebox halls are more enveloping than fan shaped
halls. The first vineyard hall, shown in (b), appears to have less lateral energy (c), but this conclusion
is mostly due to the very strong rear-upward reflection arriving quickly following the direct sound. It
is clear from the time-domain RIRs that this single reflection was stronger than any other single
reflection in any of the halls. If normalized to the same absolute reference, and not the maximum

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Figure 6 – Spatial energy maps of the early reflections (10 – 100 ms) for eight different halls in the
CHORDatabase from the 1 – 4 kHz bands. Plots are normalized to the maximum energy in each map.
value, the plots would highlight such differences. These visualizations are intuitive when inspecting
each hall, knowing their geometric properties. Such analysis methods provide clear advantages forassessing the spatial character of a RIR, difficult to assess with other techniques.

4. CONCLUSIONS
A concert hall RIR measurement database, the CHORDatabase, has been created using state -of-theart spherical array processing techniques. Objectively-motivated measurements with a widebandwidth omnidirectional sound source was used to allow for the repeatable calculation of standard
room acoustic metrics. These spherical microphone array measurements also allow for high -resolution
beamforming of the RIR. Beamforming techniques were applied to the early portion of the RIR foreight different rooms. Clear and intuitive comparisons were made between halls, highlighting theclassical lack of lateral, enveloping energy in fan-shaped halls as compared to shoebox-style halls.
Measurements using the compact spherical loudspeaker array (CSLA) and the subwoofer componentof the omnidirectional sound source were made at 20 source locations on stage. These RIRs wereauralized and superimposed to generate a full-orchestral concert hall auralization, comparable acrossall halls. These measurements can form the basis of future subjective testing, providing highly realistic
auralizations to study perception in a wide variety of halls. This testing can be rendered from thespherical harmonics domain to dedicated surrounding loudspeaker arrays or to headphones using
average or individually tailored binaural techniques.

ACKNOWLEDGEMENTS
The authors would like to acknowledge the students in Penn State’s Graduate Program in Acoustics
for measurement assistance. Special thanks to the many researchers and consultants who assisted incontacting many of the halls and all the hall employees who helped arrange and facilitate themeasurements. Special thanks in Ingo Witew, Marco Berzborn, and Prof. Michael Vorländer from ITA
at RWTH Aachen for equipment assistance prior to the European measurements. This work was
supported by the National Science Foundation (NSF) Award #130274.

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REFERENCES
1. Sabine W. Collected Papers on Acoustics, Cambridge: Harvard University Press, 1922.
2. Somerville T. "An Empirical Acoustic Criterion," Acustica 1953; 3(6): 365-369.
3. Beranek L. Concert Halls and Opera Houses, New York: Springer-Verlag, 2003.
4. Hawkes RJ, Douglas H. Subjective Acoustic Experience in Concert Auditoria. Acustica 1971; 2: 235-250.
5. Barron M. Subjective Study of British Symphony Concert Halls. Acustica 1988; 66(1): 1-14.
6. Sotiropoulou A, Fleming D. Concert Hall Acoustic Evaluations by Ordinary Concert-Goers: I, Multidimensional Description of Evaluations. Acustica 1995; 81: 1-9.
7. Kahle E, Bruneau M. Validation of an Objective Model of the Perception of Room Acoustical Quality in
an Ensemble of Concert Halls and Operas (Validation d'un modèle objectif de la perception de la qualité
acoustique dans un ensemble de salles de concerts et d' opéras). Dissertation, Le Mans, 1995.
8. Reichardt W, Lehmann, U. Definition of the room impression index R by determining the room
impression of the basis of subjective examination of musical performance (German). Appl. Acoust. 1978;
11(2): 99-127.
9. Lavandier, C. Perceptive validation of an objective model for characterization of room acoustic quality[French: Validation perceptive d'un modèle objectif de caractérisation de la qualité acoustique des salles].
Dissertation, Université du Maine, 1989.
10.Schroeder MR, Gottlob D and Siebrasse KF. Comparative study of European concert halls: correlation ofsubjective preference with geometric and acoustic parameters. J Acoust Soc Am. 1974; 56(4): 1195-1201.
11. Wilkens H. A Multidimensional Description of Subjective Judgement of Concert-Hall Acoustics[German: Mehrdimensionale Beschreibung subjektiver Beurteilungen der Akustik von Konzertstilen].
Acustica 1977; 38(1): 10-23.
12. Soulodre G, Bradley J. Subjective evaluation of new room acoustic measures. J Acoust Soc Am. 1995;
98(1): 294-301.
13. Kimura S. Study on criteria for acoustical design of rooms by subjective evaluation of room acoustics. J
Acoust Soc Jpn. 1976; 606-614.
14. Lokki T, Pätynen J, Kuusinen A, Vertanen H, Tervo S. Concert hall acoustics with individually elicited
attributes. J Acoust Soc Am. 2011; 130(2): 835-849.
15. Lokki T, Pätynen J, Kuusinen A, Tervo S. Disentangling preference ratings of concert hall acoustics using
subjective sensory profiles. J Acoust Soc Am. 2012; 132(5): 3148-3161.
16. Kuusinen A, Pätynen J, Tervo S, Lokki T. Relationships between preference ratings, sensory profiles, andacoustical measurements in concert halls. J Acoust Soc Am. 2014; 135(1): 239-250.
17. Weinzierl S, Lepa S, Ackermann D. A measuring instrument for the auditory perception of rooms: The
Room Acoustical Quality Inventory (RAQI). J Acoust Soc Am. 2018; 144(3): 1245-1257.
18. Brinkmann F, Aspöck L, Ackermann D, Lepa S, Vorländer M, Weinzierl S. A round robin on room
acoustical simulation and auralization. J Acoust Soc Am. 2019; 145(4): 2746-2760.
19. Dick D. A New Metric to Predict Listener Envelopment Based on Spherical Microphone Array
Measurements and Higher Order Ambisonic Reproductions. Dissertation, The Pennsylvania State
University, 2017.
20. Dick D, Vigeant M. A comparison of late lateral energy (GLL) and lateral energy fraction (LF)measurements using a spherical microphone array and conventional methods. Proc. of EAA Auralization& Ambisonics Symposium, Berlin, 2014.
21. Neal M. A spherical microphone and compact loudspeaker array measurement database for the study ofconcert hall preference. Dissertation, The Pennsylvania State University, August 2019.
22. Vigeant M, Wang L, Rindel JH. Investigations of Orchestra Auralizations Using the Multi-Channel MultiSource Auralization Technique. Acta Acust united Ac. 2008; 94: 866-882.
23. Shabtai N, Behler G, Vorländer M, Weinzierl S. Generation and analysis of an acoustic radiation patterndatabase for forty-one musical instruments. J Acoust Soc Am. 2017; 141(2): 1246-56.
24. Böhm C, Ackermann D, Weinzierl S. Eine mehrkanalige und nachhallfreie Aufnahme von Beethovens 8.
Sinfonie. DAGA, 2018.
25. Rafaely B. Fundamentals of Spherical Array Processing. Berlin: Springer-Verlag, 2015.
26. Bernschütz B, Porschman C, Spors S, Weinzierl S. SOFiA Sound Field Analysis Toolbox. Int. Conf. on
Spatial Audio, December 2010.
27. Politis A. Real/Complex Spherical Harmonic Transform, Gaunt Coefficients, and Rotations [Online].
Available:
https://www.mathworks.com/matlabcentral/fileexchange/43856-real-complex-sphericalharmonic-transform-gaunt-coefficients-and-rotations?s_tid=prof_contriblnk. [Accessed 3 May 2019].
28. ISO 3382: 2009, Acoustics – Measurements of room acoustics parameters – Part 1: Performance spaces.

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