Reconsidering Acoustical Design for Traditional Chinese Courtyard Theater in Taiwan

Abstract

Traditional Chinese courtyard theaters in Taiwan possess a unique architectural and performative identity, distinct from Western-style proscenium theaters that dominate contemporary performance venues. These Western configurations often impose spatial and acoustic constraints that hinder the authentic expression of traditional Chinese opera. In contrast, courtyard-style theaters—characterized by open-air layouts and architectural enclosures—offer inherent acoustic advantages rooted in structural coupling and boundary reflections. This study focuses on the Da-Hua Hall at the Wu-Feng Lin Family Mansion, employing on site acoustic measurements to characterize its sound environment not only distribute sound energy and calibrate a sound tracing and a wave-based simulation model. The finite element method framework enables precise modeling of low-frequency acoustic phenomena, including modal behavior and resonance, which were conducted to assess the impact of stage permeability, vessel geometry, and wall-mounted resonators on acoustic parameters. The results demonstrate that the interaction between sub-stage resonators and architectural elements, specifically the width of stage floorboard joints and the presence of embedded jars, significantly influences acoustic performance, notably affecting the distribution of sound waves. These findings underscore the acoustically responsive architectural design in preserving the sonic integrity of traditional Chinese opera and highlight the value of simulation-based approaches in heritage research.

1. Introduction

Taiwan’s cultural landscape is shaped by a dynamic blend of artistic expressions, with popular music and contemporary dance dominating mainstream appeal, particularly among younger audiences. Amid these trends, a dedicated group of young students continues to advocate for the preservation and revitalization of traditional Chinese opera. However, their efforts face a critical challenge: the lack of acoustically appropriate performance environments. Most modern venues are designed to meet the spatial and acoustic demands of Western music and theater, often overlooking the specific needs of traditional Chinese opera—especially its reliance on natural vocal projection and live instrumental accompaniment. This design mismatch has led to widespread dependence on electronic amplification, which compromises the authenticity and subtlety of traditional vocal techniques. Historically, traditional opera was performed in courtyard-style architectural settings—such as open-air plazas, enclosed compounds, and central halls—featuring elevated stages, domed canopies, peripheral galleries, and semi-enclosed halls that supported natural sound transmission and intimate audience engagement. In contemporary Taiwan, heritage sites like the Da-Hua Hall in Wu-Feng remain rare examples of venues that preserve the acoustic integrity required for traditional opera. Most performances now occur in spaces calibrated for Western acoustics, which often exhibit reverberation characteristics and spatial arrangements misaligned with the sonic demands of Chinese opera. This disconnect undermines both the performative authenticity and the sonic heritage of the art form, underscoring the urgent need for acoustically responsive environments tailored to traditional operatic practices. In contrast, Western stage typologies evolved from spaces originally intended for both public and private gatherings, undergoing continuous transformation in response to factors such as lifestyle shifts, social interaction needs, and the dissemination of technical and performative knowledge [1,2,3]. A notable example of Western theater evolution is Shakespeare’s Globe in London, constructed in 1599, which features a three-sided thrust stage extending into the audience area—an architectural strategy that enhances performer–spectator interaction. Expanding this inquiry, the ERATO project examined a broader typological spectrum, including ancient Greek and Roman theaters. One of its key findings challenged a long-standing architectural assumption: sounding vessels, historically believed to serve acoustical functions based on Vitruvian descriptions, were found to have negligible influence on the measured acoustic performance of Roman theaters. This result refutes a persistent belief in the functional role of these elements, highlighting the importance of empirical validation in architectural acoustics research [4]. In parallel, targeted research on the acoustics of ancient Western open-air theaters has yielded critical insights into how specific architectural geometries influence core acoustical parameters. Bo et al. conducted a targeted investigation of the open-air theatre in Syracuse, Italy, evaluating the predictive accuracy of key acoustic parameters, reverberation time (RT), and sound strength (G), through integrated on-site measurements and computational simulations. Their findings validated the applicability of simulation-based methods in evaluating the performance of heritage soundscapes [5]. Findings from investigations of traditional Western theaters, including ancient Roman and Greek venues, cannot be directly generalized to traditional Chinese theatrical spaces, owing to fundamental divergences in architectural typology, performance practices, and acoustic propagation characteristics. Chinese-style theaters, particularly courtyard-style configurations, are predominantly constructed using timber as the primary structural material. Their spatial layout typically includes a roofed stage, peripheral aisles, a central main hall, and an open courtyard, forming a semi-enclosed acoustic environment. This unique configuration supports natural sound transmission and vocal projection, aligning with the performative needs of traditional Chinese opera and distinguishing it acoustically from Western theater models [6]. Wang conducted a series of sequential studies that significantly advanced the understanding of traditional Chinese theater acoustics, contributing to a broader scholarly movement that has increasingly recognized the architectural and cultural significance of these theaters [7,8,9]. Kang and his research team conducted a series of sound field simulations to investigate the effects of spatial geometry, with particular emphasis on the width-to-depth ratio, on key acoustic parameters in traditional Chinese theatres. In subsequent work, the group further investigated the acoustic impact of caisson ceiling configurations, analyzing the differences between hemispherical and octagonal forms in shaping sound reflections and distributions affecting both performers and audiences [10,11]. With respect to the acoustic characterization of traditional Chinese theaters, Chiang’s investigation in situ measurements at six courtyard-style theaters and three additional theaters integrated within classical Chinese gardens. Key acoustic parameters—including early decay time (EDT), sound strength (G), and early support (ST_early)—were systematically recorded and analyzed to assess the acoustic performance of these historically significant performance environments [12,13]. This study investigates the acoustic performance of traditional courtyard theaters, with particular emphasis on the influence of reinforcement elements—specifically, vessel-like architectural features—on spatial acoustic parameters, including the Inter-aural Cross-Correlation Coefficients (IACC) and the Lateral Energy Fraction (LF).

This study presents a comparative acoustic analysis of Eastern and Western courtyard theater typologies, focusing on the role of embedded resonator systems in shaping sound field characteristics. Comprehensive on-site measurements were conducted to document both geometric and acoustic parameters, followed by the development of a simulation model using specialized software. The model was calibrated and validated against empirical data to ensure predictive reliability. Parametric modifications were introduced to examine the acoustic effects of coupling configurations, including variations in parquet width, vessel geometry, and wall-mounted installations. These elements were systematically analyzed for their influence on sound energy distribution and resonance behavior. In Da-Hua Hall, ceramic jars installed beneath the stage function as acoustic resonators—an intentional design strategy rooted in Qing dynasty stagecraft. Similar practices are observed in the Li Zicheng Temporary Palace Theater in Mizhi County, Shaanxi Province, where porcelain jars were embedded beneath the stage. These configurations—ranging from sub-stage cavities and wall-mounted jars to backstage voids—collectively facilitated enhanced vocal projection, often described as “singing without exertion,” by amplifying sound energy and reinforcing resonance. The ceramic jar system in Da-Hua Hall, traceable to the Qing dynasty period (1851–1861), reflects a sophisticated understanding of acoustic design principles. The findings underscore the importance of architectural acoustics in traditional performance environments and highlight the need to preserve and adapt such design strategies in contemporary theater architecture. A notable example is the Longtian Temple ancient theater in Shita Village, Fenyang, Shanxi Province, China, which stands as a verified case of transitioning from sub-stage to wall-mounted jar installations, this exemplifies the evolution of stage acoustic practices during the Qing dynasty [14]. In this case, three types of ceramic jars with distinct volumes were employed to produce specific natural resonance frequencies, thereby enhancing both sound amplification and long-distance audibility. However, existing research primarily highlights the natural frequencies and associated pitch ranges of individual pottery jars, without addressing their integrated acoustic performance within architectural settings. The broader objective of integrating architectural form with performance acoustics, particularly through the combined application of on-site measurements and simulations, remains an underexplored dimension in the study of traditional theater design. Although numerous historical investigations have documented the architectural characteristics of traditional Chinese theaters, especially with respect to spatial typologies, material applications, and decorative symbolism, there is a marked scarcity of empirical research addressing the acoustic performance of embedded resonant devices within these spaces. This research not only provides physical evidence of such acoustical practices but also illustrates the evolutionary development of resonance strategies for natural sound, demonstrating the historical intentionality behind integrating architectural form with performance acoustics, an aspect that remains insufficiently examined through on-site measurement and simulation.

2. Methods

2.1. Introduction of Da-Hua Hall

This study explores the spatial and acoustic characteristics of traditional Chinese theater architecture through the framework of spatial coupling theory, which posits that interconnected volumes can enhance sound energy distribution and reverberation. Focusing on architectural features such as peripheral balconies, domed stage canopies, and semi-enclosed halls, which are common in late imperial residential design, the research investigates whether these historically unoptimized forms inherently support advantageous acoustic phenomena. The Da-Hua Hall, constructed between 1890 and 1894 within the Lower Mansion (Xiàcuò) of the Wu-Feng Lin Family estate in present-day Taichung, Taiwan, serves as the empirical case study. This three-hall structure, aligned along a central axis and integrating Minnan and Zhejiang stylistic influences, functioned as both a private theater and a formal reception hall, exemplifying elite Qing dynasty spatial logic. As part of Taiwan’s most expansive and well-preserved Qing-era residential complex—including the Upper Residence (Dǐngcuò), Lower Residence, and Lai-Yuan Garden—the Da-Hua Hall offers a compelling context for examining how architectural morphology intersects with acoustic behavior in culturally significant performance spaces. The hall features a five-bay façade measuring approximately 17.5 m in width and 14.5 m in depth, yielding a total floor area of 250 square meters. Its dual function as a reception hall and theatrical venue reflects the Wu-Feng Lin family’s socio-political stature and cultural patronage. The stage pavilion rises approximately 8.5 m from courtyard ground level to roof ridge, with the stage platform elevated 1.2 m to enhance visibility and acoustic projection. The 7.5 m frontal width aligns with the five-bay structural rhythm, and the pavilion is vertically stratified into three tiers: a raised platform, a central volume framed by columns and lattice screens, and a crowning roof with swallowtail ridges and upward-curving eaves—elements that serve both environmental and symbolic functions. Flanking corridors and upper-level viewing balconies, connected via semi-open passageways, create a coupled spatial cavity that likely augments low-frequency reverberation. Together, the stage pavilion, central courtyard, rear hall, lateral colonnades, and upper gallery (as outlined in

Table 1. Dimensional characteristics of architectural spaces within the Da-Hua Hall of the Wu-Feng Lin Family Mansion.

Architectural Space	Dimensions (Width × Length × Height) (m)	Remarks
Central courtyard	18.5 × 2 × 3.3–8.6	Variable height due to architectural form
Main stage (Front hall)	5.8 × 6.3 × 4.3	Performance platform
Colonnades (1st and 2nd floors)	3.8 × 16.6	Flanking corridors on two levels
Main Hall	12 × 5.6	Reception and gathering space

) form an acoustically responsive and culturally resonant spatial continuum.

This passage provides a detailed contextualization of the Da-Hua Hall’s spatial and acoustic characteristics, emphasizing the role of peripheral architectural elements—such as flanking corridors and upper-level balconies—in forming a coupled spatial system with the central stage. Through on-site documentation, including in situ photography (Figure 1) and sectional elevation drawings (Figure 2 and Figure 3), the architectural stratification and spatial interconnectivity are elucidated, offering empirical grounding for the acoustic simulation framework. The spatial placement of the sound source and receiver replicates realistic performance and listening conditions, thereby supporting the study’s broader inquiry into how volumetric coupling in traditional Chinese performance spaces may influence low-frequency reverberation and overall acoustic behavior.

2.2. Acoustical Parameters

To ensure consistency and comparability in the measurement of interior sound field properties, this study adopts the monaural acoustic performance parameters defined by ISO 3382-1:2009(E) [15]. This internationally recognized index system provides a comprehensive framework for evaluating multiple aspects of sound field performance. By applying this standardized Western acoustic index to the Da-Hua Hall, the study enables cross-comparison across different theater typologies, including traditional Chinese and Western spaces. This approach situates Da-Hua Hall within a broader analytical context while maintaining methodological rigor. Previous research has emphasized the distinct acoustic requirements of traditional Chinese theatrical performances, noting that while evaluative frameworks between Chinese and Western contexts are generally aligned, differences persist in the prioritization of specific acoustic parameters—particularly those related to vocal clarity and spatial intimacy. For instance, while sound strength (G), early decay time (EDT), early support (ST_early), inter-aural cross correlation coefficients (IACC) and the lateral energy fraction (LF) may be prioritized differently, the adoption of a unified evaluation framework ensures methodological comparability. In the preliminary phase of this study, acoustic measurements were conducted under the “theatre mode” spatial configuration, identified by venue administrators as the most frequently used setting. Field measurements were carried out across multiple sessions to capture representative acoustic responses under varying operational conditions. This approach ensures that the data reflect realistic usage scenarios and provide a robust foundation for simulation calibration. A subsequent phase of the research will undertake a comprehensive analysis of the functional roles and evaluative significance of discrete acoustic parameters, contributing to a deeper understanding of sound field characteristics in traditional Chinese theater spaces.

(1)

Early reverberation time (EDT):

EDT (Early Decay Time) refers to the time required for the sound pressure level to decay from −10 dB to −60 dB after the sound source ceases, calculated based on the initial portion of the sound energy decay curve. Compared to the conventional reverberation time (RT), EDT is widely recognized as a more effective indicator of the subjective perception of reverberance by the human ear. EDT has also been shown to be more suitable for evaluating the reverberation characteristics of traditional Chinese courtyard theaters [16,17,18]. Given the rapid attenuation of sound energy in outdoor environments and the frequent presence of background noise, this study adopted EDT as the primary reverberation index during on-site measurements and curve fitting procedures, to ensure compliance with the signal-to-noise ratio requirements stipulated in ISO 3382-1.

(2)

Sound strength (G):

The sound strength parameter (G) is a standardized acoustic metric used to evaluate perceived loudness within enclosed spaces. It is defined as the difference in sound energy received at a specific audience location relative to a reference level measured at 10 m from an omnidirectional source in a free-field condition. This index effectively reflects the sound energy distribution within the listening area. Empirical data from global concert hall measurements indicate that the optimal mid-frequency G value—averaged across the 500 Hz and 1 kHz octave bands—typically ranges between 4.0 dB and 5.5 dB [19]. Prior research further indicates that audience preference for higher loudness is markedly greater in traditional Chinese performance spaces than in Western theaters. Consequently, G is regarded as a critical acoustic parameter in assessing sound field performance in traditional Chinese courtyard theaters, where amplified vocal clarity and spatial intimacy are acoustically prioritized [20].

(3)

Early support (ST_early):

Early support (ST_early) is an acoustic parameter proposed by Gade to evaluate the degree of sound support provided by theater spaces to performers on stage. This metric is defined as the ratio, expressed in decibels (dB), of the early reflected sound energy within the first 0.1 s to the direct sound energy (including floor reflections), measured at a distance of 1.0 m from the acoustic center of an omnidirectional sound source. The subscript “E” denotes “Early,” emphasizing its basis in early reflections. Based on cumulative measurement data from concert hall stages, the average ST_early value generally falls between –11 dB and –13 dB for solo performances and between –9 dB and –12 dB for ensemble performances, ranges that are considered acoustically satisfactory for effective onstage communication among performers [21,22].

(4)

Inter-aural Cross Correlation Coefficients (IACC):

The inter-aural cross correlation coefficients (IACC) is a psychoacoustic parameter proposed by Professor Yoichi Ando to evaluate the spatial impression and localization clarity in a sound field, particularly from the perspective of a seated listener. IACC is defined as the maximum value of the normalized cross-correlation function between the signals arriving at the left and right ears (or microphones simulating ear positions) within a specified time interval, typically 0 to 1 ms or 0 to 80 ms after the arrival of direct sound [23].

(5)

Lateral Energy Fraction (LF)

Lateral Energy Fraction (LF) is defined as the ratio of early lateral-reflected sound energy (from 5 ms to 80 ms) to the total early sound energy (also from 5 ms to 80 ms), measured at listener positions in the audience area. The calculation uses impulse response data and is typically frequency-dependent. LF is an important objective acoustic parameter introduced by Marshall to quantify the spatial impression in concert halls, particularly focusing on the apparent source width (ASW) perceived by listeners. It reflects how much sound energy arrives from the side directions as opposed to from the front, which is crucial for producing a sense of spaciousness in music performance environments [24].

2.3. On-Site Measurement

The in situ measurements conducted in this study, along with the corresponding experimental procedures, data analysis methods, calibrated omnidirectional sound source were performed in accordance with the international standard ISO 3382:2009. To ensure the accuracy and stability of the measurement results, a high signal-to-noise ratio (exceeding 45 dB across all frequency bands) and multiple sweep measurements were employed to obtain acoustical parameters that are representative of the selected measurement positions. Acoustic measurements were conducted on the evening of September 2, 2022, between 19:00 and 22:00, under stable meteorological conditions. During the measurement period, ambient weather in Taichung exhibited temperatures ranging from 24 °C to 25 °C with relative humidity between 76% and 79%. Preliminary assessments of the external sound environment recorded an average equivalent continuous A-weighted sound pressure level (LAeq) of approximately 35 dB(A), indicating a low background noise level with minimal transient interference. Field measurements were performed using a Brüel and Kjær Type 2250 real-time analyzer, compliant with IEC Type 1 precision standards, and operating across a frequency range of 6.3 Hz to 20 kHz. The monaural sound field evaluation system comprised the DIRAC Room Acoustics Software (version 6.0), coupled with a B&K 4296 dodecahedral omnidirectional loudspeaker and a B&K 4190 1/2-inch Free Field Microphone. To capture spatial acoustic parameters, binaural measurements were conducted using a Neumann KN100 dummy head for IACC, and lateral energy distribution was assessed through the LF parameter using a figure-eight directional microphone (Sennheiser MKH 80). All receivers were strategically positioned at representative listening areas within the courtyard, the main hall, the first-floor corridor, and the second-floor balcony to ensure consistent environmental exposure. The measured parameters included EDT, G, ST_early, IACC, and LF, in alignment with ISO 3382-1 standards for performance spaces. Results are presented in 1/1 octave bands, covering the frequency range from 125 Hz to 4000 Hz, as detailed in

Table 2. Summary of measurement instruments, acoustical parameters, and corresponding frequency bands used in field measurements.

Parameter	Measurement Instrument	Frequency Rage Band
EDT (s)	B&K, DIRAC Room Acoustics Software (version 6.0)	ISO 3382-1 is used as the relevant standard for the acoustical field measurement, 1/1 octave band of the 125 Hz to 4000 Hz
G (dB)	B&K model 4296, Omni Source Dodecahedral Loudspeaker
STearly (dB)	B&K model 4190, 1/2-inch Free Field Microphone
IACC (-)	B&K, DIRAC Room Acoustics Software (version 6.0)
	B&K model 4296, Omni Source Dodecahedral Loudspeaker
	Neumann model KN100, Dummy head
LF (-)	B&K model 4296, Omni Source Dodecahedral Loudspeaker
	Sennheiser model MKH 80, 1/2-inch Free Field Microphone
Leq (A)	B&K Type 2250, Hand-held Analyzer, 1/2-inch Free Field Microphone	1/3 octave band and for the 6.3 Hz to 20 kHz

.

The sound sources (S1 and S2) were positioned within the stage area, while the receiver positions were strategically distributed across various architectural zones: the central courtyard (R1–R3, R5–R8), the arcade areas on both the first and second floors (R11–R18), three locations within the main hall (R4, R9, and R10), and two receiver points located on the stage (R19 and R20). The spatial configuration of the sound sources and receiver positions is illustrated in Figure 4. The on-site measurement setup is depicted in Figure 5. A monaural, non-directional sound source (S1) was positioned along the central axis of the stage, located 2 m from the front edge and elevated 125 cm above the floor level. This source emitted an exponential sweep (e-sweep) signal for acoustic measurements. The microphone receiver positions were placed at a height of 1.2 m above the ground, consistent with standard ear height for seated listeners. This configuration was designed to capture the spatial variation in acoustic parameters across the entire performance and audience area. The acquired signals were processed using a digital workstation (DIRAC), where the impulse responses were derived through deconvolution. These responses were subsequently filtered and subjected to backward integration to obtain energy decay curves. These measurements were conducted to characterize the hall’s current acoustical suitability for unamplified sound performances. Under strictly controlled conditions, tests were conducted with an unoccupied seating area, fully closed entrances, and consistent lighting operation throughout.

Acoustic measurements were conducted across multiple spatial zones, including the courtyard, main hall, first-floor corridor, and second-floor balcony. Early Decay Time (EDT), more sensitive to initial sound decay than T30, better represents perceived reverberance by capturing early reflections, while T30 characterizes late decay. Under source S1, EDT exhibited low variability in mid-to-high frequencies (500 Hz–4 kHz), indicating spatial uniformity, whereas greater variability at low frequencies (125–250 Hz) highlighted localized acoustic irregularities (Figure 6). The sound strength factor (G), quantifying perceived loudness as the gain of sound energy relative to a free-field reference, is crucial for evaluating sound projection efficiency in performance spaces. In Da-Hua Hall, G values decreased with source–receiver distance across zones (1F Courtyard, Main Hall, 1F Corridor, 2F Balcony), reflecting spatial attenuation, notably within the mid-frequency range (500 Hz and 1 kHz) where a strong linear correlation (R² = 0.8371) validates this trend (Figure 7). These findings emphasize the critical role of geometry in sound energy distribution; however, further analysis of the temporal domain is warranted.

In addition to temporal (EDT) and energy-based (G) parameters, a comprehensive sound field analysis was conducted.

Table 3. Mid-frequency (500 Hz and 1 kHz average) acoustic parameters and corresponding standard deviations at receiver positions within Da-Hua Hall.

Location/Receiver		EDT (s)	G (dB)	IACC (-)	LF (-)	STearly (dB)
Courtyard	Average of Mid-Frequency Band	0.96	4.1	0.54	0.13	S1 (Frontal stage): −15.9 dB S2 (Below octagonal ceiling): −3.7 dB
	Std. deviation	0.20	0.90	0.10	0.05
Main hall	Average of Mid-Frequency Band	1.13	1.5	0.42	0.23
	Std. deviation	0.13	0.65	0.07	0.03
1F Corridor	Average of Mid-Frequency Band	1.00	2.9	0.44	0.15
	Std. deviation	0.10	0.34	0.08	0.04
2F Balcony	Average of Mid-Frequency Band	0.92	2.5	0.46	0.13
	Std. deviation	0.12	0.66	0.06	0.03

presents an evaluation of interaural cross-correlation (IACC) and lateral fraction (LF), and early strength (ST_early) across measured locations. ST_early values at two key positions—S1 (near the front of the stage) and S2 (beneath the octagonal well)—are reported to highlight spatial variation in early reflected energy within the mid-frequency range. In addition to the temporal parameter EDT, the energy-based parameter G in the mid-frequency bands exhibited values ranging from +4.1 dB to +2.5 dB at various receiver positions within the courtyard. This gradual attenuation of sound energy with increasing distance indicates a sufficiently energized sound field characteristic of a semi-free acoustic environment. Under the sound source condition S2, the measured ST_early across octave bands yielded a value of −3.7 dB at the measurement position located beneath the coffered dome (Bagua caisson ceiling). This result indicates that sufficient acoustic energy is provided to the stage area, ensuring effective mutual audibility and communication among performers across different voice parts on stage. In the binaural measurements of the IACC and LF, the IACC values in the mid-frequency bands at various receiver positions were all below 0.55. This indicates that the sound field within the grand hall provides subjectively favorable spatial impression and auditory envelopment across the measured locations. As for the LF, the mid-frequency value measured at the main hall receiver which average was 0.23, indicating the presence of sufficient lateral energy, thereby contributing to a favorable subjective auditory experience. However, the LF values at other receiver positions were comparatively low, suggesting a deficiency in lateral energy. The standard deviation analysis reinforces the acoustic differentiation between enclosed and semi-open architectural zones. The Courtyard demonstrates the variability across key acoustic parameters, particularly in EDT and G, indicating pronounced spatial non-uniformity in its acoustic field. The Main Hall exhibits the acoustic stability across measured parameters, indicative of its enclosed geometry and consistent boundary conditions. Conversely, the Courtyard demonstrates pronounced variability, particularly in sound energy decay and spatial parameters, underscoring the need for targeted acoustic interventions should be further investigated through subsequent computational simulations and acoustic modeling analyses.

Based on monophonic sound energy measurements in the mid-frequency bands (500 Hz and 1 kHz), the acoustic performance under the stage-performance sound source configuration (S1) yielded the following average EDT values at the respective receiver locations: 0.96 s in the courtyard, 1.13 s in the main hall, 1.00 s in the 1F corridor, and 0.91 s on the 2F balcony (

Table 4. Measured results of Early Decay Time (EDT) in octave frequency bands from 125 Hz to 4 kHz at various receiver locations within Da-Hua Hall. The last column presents the average of mid-frequency bands (500 Hz and 1 kHz), while standard deviations, MAE and RMSE indicate the degree of spatial variability within each zone.

Location/Receiver		125 Hz	250 Hz	500 Hz	1 k Hz	2 k Hz	4 k Hz	Average of Mid-Frequency Band (500 Hz and 1000 Hz)
Courtyard	R1	0.51	0.85	1.07	0.75	0.75	0.91	0.91
	R2	0.58	1.03	0.87	0.98	0.86	0.93	0.93
	R3	0.82	1.01	0.93	0.95	0.72	0.94	0.94
	R5	0.35	0.91	0.54	1.01	0.82	0.78	0.78
	R6	0.48	1.32	0.98	0.77	0.84	0.88	0.88
	R7	0.91	0.44	1.12	0.93	0.82	1.03	1.03
	R8	0.94	0.96	1.32	1.2	1.15	1.26	1.26
	Average	0.66	0.93	0.98	0.94	0.85	0.96	0.96
	Std. deviation	0.23	0.26	0.24	0.15	0.14	0.15	-
	MAE	0.23	0.18	0.10	0.07	0.06	0.09	-
	RMSE	0.27	0.21	0.13	0.08	0.08	0.11	-
Main hall	R4	1.4	1.16	0.99	0.97	0.86	1.18	0.98
	R9	1.26	1.23	1.18	1.31	0.95	1.08	1.25
	R10	0.71	1.31	1.2	1.15	0.88	1.07	1.18
	Average	1.12	1.23	1.12	1.14	0.90	1.11	1.13
	Std. deviation	0.36	0.08	0.12	0.17	0.05	0.06	-
	MAE	0.36	0.25	0.11	0.18	0.07	0.14	-
	RMSE	0.41	0.28	0.13	0.20	0.09	0.17	-
1F Corridor	R11	0.92	1.01	1.05	1.11	0.6	0.8	1.08
	R12	0.91	0.74	1.12	1.01	0.83	0.85	1.07
	R13	0.97	0.64	1.03	0.88	0.98	0.92	0.96
	R14	0.91	0.8	0.95	0.86	0.97	1.08	0.91
	Average	0.93	0.80	1.04	0.97	0.85	0.91	1.00
	Std. deviation	0.03	0.16	0.07	0.12	0.18	0.12	-
	MAE	0.10	0.19	0.09	0.12	0.13	0.09	-
	RMSE	0.12	0.21	0.10	0.13	0.14	0.10	-
2F Balcony	R15	1	0.91	0.84	0.76	0.69	0.91	0.80
	R16	0.76	1.1	0.86	0.84	0.67	0.93	0.85
	R17	1.05	0.91	0.94	0.91	0.9	0.94	0.93
	R18	0.64	1.52	1.06	1.11	0.94	0.78	1.09
	Average	0.86	1.11	0.93	0.91	0.80	0.89	0.92
	Std. deviation	0.20	0.29	0.10	0.15	0.14	0.07	-
	MAE	0.16	0.23	0.13	0.12	0.12	0.09	-
	RMSE	0.20	0.27	0.15	0.14	0.14	0.10	-
Overall average		0.84	0.99	1.00	0.97	0.85	0.96	0.92
Overall Std. deviation		0.27	0.26	0.17	0.16	0.13	0.13	-

). Minor numerical variations across architectural zones and frequency bands are now contextualized through the inclusion of standard deviations, facilitating more accurate interpretation of their significance relative to experimental uncertainty. Greater variability is observed in the courtyard and 2F balcony, particularly in the low-frequency bands, reflecting the influence of open or semi-enclosed spatial configurations. The comparative analysis of Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) across six octave bands (125 Hz to 4 kHz). Courtyard exhibits moderate deviation from the overall average, with relatively low MAE and RMSE values, particularly in the mid- to high-frequency range (500 Hz to 4 kHz). These distinctions enhance the reliability of the acoustic characterization between open-air and enclosed volumes within the hall. Following the elevation of the grand hall stage, the decay of reflected sound energy with sufficient temporal extent, coupled with the enclosure formed by lateral and rear reflective surfaces, may enhance the reverberant sensation. The influence of coupled spaces and the presence of wall-mounted jars installations on the acoustic field will be further investigated through computational acoustic simulations.

2.4. Simulation with Jars Underneath Stage and Wall-Mounted Jars

Odeon was used to simulate the sound fields of ancient open-air theaters, the sound field simulation was extended to include the architectural substructure beneath the stage, specifically a coupled vessel cavity and its enclosing vessel wall. This subterranean volume, structurally integrated with the stage platform, was modeled as an acoustically connected secondary volume. The inclusion of this sub-stage cavity effectively increases the total acoustic volume of the hall and introduces a low-frequency resonant characteristic that significantly contributes to the late energy decay profile. Through geometric and material-based modeling, the vessel was treated as a reverberant subsystem with acoustically reflective boundaries, allowing energy to be temporarily stored and gradually returned to the primary sound field. This architectural and acoustic integration illustrates the deliberate use of volumetric coupling as a design strategy to enhance reverberant perception, particularly in large-volume halls intended for musical performance. The three-dimensional geometric model of Da-Hua Hall was developed using Sketch Up and subsequently imported into Odeon Room Acoustics Software (version 16.09) for acoustic simulation (Figure 8).

The sound field model incorporated detailed definitions of all enclosed surface materials, wherein the sound absorption coefficients were informed by scaled model testing [25], while the scattering coefficients were assigned based on established simulation references [26]. These coefficients were determined based on manufacturer data, particularly drawing upon findings from previous research conducted by ancient traditional Chinese timber structures and brick wall plastering structure. Prior to initiating the simulations, all model parameters were calibrated in accordance with the specific computational and algorithmic requirements of the Odeon platform. This ensured that the simulation accurately represented both the material behavior and the spatial acoustics of the hall, thereby enabling reliable analysis of reverberation, energy decay, and spatial impression. Considering that the on-site acoustic measurements were conducted in a semi-open environment, the resulting relative errors were notably larger; however, the overall trends remained consistent. The subsequent phase of this study involved an in-depth analysis of the simulation results, with particular focus on the medium- and high-frequency ranges. The relative variations among acoustic parameters were examined, notably the distribution consistency of physical indices not only mono sound energy but binaural energy which impose the IACC; As shown in Figure 9, the minor discrepancies between simulated and measured data remain within acceptable limits, validating the reliability of the sound field simulation model and its configuration. This affirms its suitability as a robust foundation for subsequent sound field analyses using computational simulation.

Empirical results obtained from on-site acoustic measurements were further validated through computational numerical analysis, revealing consistent correlations. Building upon prior sound field measurements conducted in Da-Hua Hall, the study specifically examined the sound source position within the stage area to investigate its impact on the distribution of sound energy, particularly as it propagates beneath the stage. Particular attention was given to the four large ceramic jars embedded beneath the stage and the jar-integrated wall structure. By examining various stage floor openings situated above these subsurface resonators, the study investigated the potential of the jar system to enhance early decay time (EDT), thereby reinforcing the perception of reverberation under semi-free field conditions. The subsequent installation of the jar wall was evaluated for its contribution to the overall sound field. Based on the principle of resonance within enclosed jar chambers, these architectural elements were conceptualized as acoustic amplification systems, contributing to both sound energy reinforcement and spatial acoustic modulation. To systematically assess these effects, three experimental configurations were established: Schematic A retained the original stage setup with tightly joined wooden planks and four embedded ceramic jars (each 60 cm in diameter and height, positioned 81 cm below the stage floor, see in Figure 10; Schematic B introduced surface perforations with gap widths of 1 cm, 8 cm, and 15 cm to evaluate the impact of joint spacing on acoustic energy transmission; and Schematic C incorporated wall-mounted jar prototypes modeled as inverted frustums (upper diameter: 22 cm; base diameter: 34 cm; height: 43 cm; volume: ~26.88 L), as detailed in

Table 5. Geometric dimensions and volumetric characteristics of wall-mounted jar models compared with historical references.

Model Type	Mouth Diameter (cm)	Base Diameter (cm)	Height (cm)	Shape	Volume (L)
Wall-mounted jars	22	34	43	Inverted frustum	26.88
Historical References *	20–25	30–35	40–50	Inverted frustum	Approx. 20–30

* Compiled from documented Longtian Temple ancient theater in Shanxi Province, China.

and illustrated in Figure 11. These configurations enabled a comprehensive investigation into the acoustic role of embedded resonators and architectural detailing in traditional stage environments.

Schematic C draws upon historical documentation of the Longtian Temple ancient theater, where wall-mounted acoustical jar systems were traditionally employed. Archival records from the Shanxi region describe ceramic vessels with inverted frustum geometries—typically 40–50 cm in height, 30–35 cm in base diameter, and 20–25 cm in mouth diameter—installed in evenly spaced horizontal arrays approximately 1.5 m above floor level along interior walls. Informed by these precedents, the experimental simulation was designed to evaluate the interaction between stage floor apertures and the combined sub-stage and wall-mounted resonator systems. Particular emphasis was placed on identifying cavity resonance phenomena and assessing the acoustic contribution of these architectural elements to sound energy reinforcement and spatial modulation.

3. Result

Assumption underpins the comparative simulation among representing a seamless wooden floor condition (Schematic A), comprising three alternative joint-width models (Schematic B _1 cm, 8 cm, and 15 cm) and in conjunction with embedded wall-mounted jars (Schematic C). The analytical aim is to investigate how variations in joint configuration influence the spatial distribution and propagation of sound energy, particularly in relation to the interaction between surface geometry and embedded architectural acoustic elements. In traditional courtyard-style theater spaces, earthenware jar structures are often installed beneath the wooden stage floor. This study investigates whether such configurations exhibit characteristics of sound energy gain. Accordingly, the research evaluates not only monaural acoustic energy parameters G, EDT, IACC, LF, ST_early. Acoustic assessments were primarily conducted at five measurement points (R1–R5) within the central courtyard, as sound propagation in open-air environments typically exhibits reduced reverberation and a more rapid decay of sound energy compared to enclosed architectural spaces. The sound source was simulated at the stage position (S1) to investigate the acoustic effects of varying stage floorboard joint widths and the incorporation of wall-mounted jars on the overall sound field performance (see Figure 12). This experimental configuration was designed to validate the resonance effects induced by the cavity structures and to assess their efficacy in enhancing energy distribution and overall acoustic gain across mid- and low-frequency bands.

3.1. Acoustic Influence of Stage Floorboard Joint Configurations on Sub-Stage Ceramic Jar Resonance Response

It is assumed that variations in the spacing and permeability of stage floorboard joints influence the transmission and acoustic coupling of sound energy between the performance space and the sub-stage volume. These interstitial gaps are posited to function as acoustic apertures that modulate the degree to which resonant energy from embedded sub-stage elements is activated or attenuated. Accordingly, the structural detailing of the stage flooring becomes a significant parameter in evaluating the acoustic performance of traditional theatrical spaces. This assumption underpins the comparative simulation between Schematic A representing a seamless wooden floor condition and Schematic B—comprising three alternative joint-width models 1 cm, 8 cm, and 15 cm. Result is shown in

Table 6. Effects of floorboard joint widths on simulated acoustical parameters at mid-frequency bands (500 Hz).

Floorboard Joint Widths/Acoustical Parameters		EDT (s)	G (dB)	IACC (-)	LF (-)	STearly (dB)
Schematic A (Seamless)	R1	1.96	3.4	0.41	0.34	−11.53
	R2	1.62	10.1	0.56	0.23
	R3	1.89	7.2	0.48	0.37
	R4	1.74	8.7	0.58	0.34
	R5	1.95	8.3	0.55	0.36
	Ave. *	1.80	8.6	0.54	0.33
Schematic B (1 cm gap)	R1	1.68	13.1	0.43	0.2	−10.78
	R2	1.77	10.2	0.501	0.5
	R3	1.95	7.8	0.61	0.35
	R4	1.94	8.8	0.59	0.37
	R5	1.98	8.6	0.56	0.16
	Ave.	1.91	8.9	0.57	0.35
Schematic B (8 cm gap)	R1	1.31	17	0.35	0.16	−11.14
	R2	1.68	10.3	0.49	0.25
	R3	1.95	7.9	0.51	0.49
	R4	1.89	8.8	0.6	0.36
	R5	2.00	8.5	0.58	0.38
	Ave.	1.88	8.9	0.55	0.37
Schematic B (15 cm gap)	R1	1.16	14.3	0.34	0.27	−10.88
	R2	1.67	10.3	0.59	0.27
	R3	1.97	8.0	0.53	0.45
	R4	1.88	8.7	0.54	0.36
	R5	2.02	8.4	0.6	0.38
	Ave.	1.89	8.9	0.57	0.37

* The average values were calculated exclusively from points R2 to R5, located within the courtyard, excluding R1 due to its proximity to the stage.

. The calculated average values based on positions R2 to R5 more accurately reflect the acoustic conditions experienced at audience-relevant listening locations within the courtyard, thereby minimizing the potential bias introduced by proximity effects at the stage-adjacent measurement point (R1). EDT increases from 1.80 s (seamless) to a maximum of 1.92 s (1 cm joints), with slightly lower values observed at 8 cm (1.88 s) and 15 cm (1.89 s). The Strength parameter increases significantly with joint introduction, from 8.58 dB (seamless) to a peak of 8.88 dB at 8 cm, followed by a slight reduction to 8.85 dB at 15 cm. This indicates that floor openings allow more sound energy to interact with and be reinforced by the resonant system below. Other parameters, including IACC, LF, and ST_early, demonstrate consistent uniformity across measurement points, indicating that the simulated results reliably correspond to actual on-site acoustic field measurements (Compare with Table 2). A 5.56% increase in EDT following the introduction of narrow floorboard gaps (1 cm gap) suggests enhanced reverberation, likely attributable to improved acoustic coupling with the sub-stage cavity. The gain (G) value exhibited a marginal increase of 1.37%, suggesting limited sensitivity to variations in joint width (1 cm and 8 cm gap). While this may indicate a modest enhancement in sound energy distribution—potentially attributable to sub-stage cavity effects—the minimal change suggests that the energy amplification effect remains inconclusive and warrants further verification.

3.2. Comparative Analysis of Three Stage Floorboard Joint Configurations—Seamless, 1 cm, and 8 cm—Combined with Embedded Wall-Mounted Resonating Jars

A comparative simulation was conducted to assess the impact of floorboard joint configurations on perceived resonance and reverberation, with Early Decay Time (EDT) serving as the primary metric. Results from Schematic A (seamless floorboards) and Schematic B (1 cm and 8 cm gaps) indicated minimal variation in EDT, suggesting limited acoustic enhancement from joint width alone. To further explore potential resonance effects, Schematic C (wall mounted jars) incorporated wall-mounted ceramic jars, aiming to assess whether the inclusion of such historical resonant elements could intensify energy retention and improve overall reverberation behavior. This hypothesis-driven simulation targets the potential synergistic effect between structural openings and coupled cavity resonators in optimizing sound field distribution within traditional architectural frameworks.

Table 7. Comparison of Early Decay Time (EDT) and percentage increase across octave bands for seamless floorboards versus joint openings and wall-mounted jar configurations.

1/1 Octave Band/Configuration of Stage and Wall	Seamless	Seamless + Wall Mounted Jars	1 cm Gap	1 cm Gap + Wall Mounted Jars	8 cm Gap	8 cm Gap + Wall Mounted Jars
63 Hz	1.40 (-)	1.45 (+3.57)	1.53 (+9.29)	1.54 (+10.00)	1.50 (+7.14)	1.53 (+9.29)
125 Hz	1.39 (-)	1.45 (+4.32)	1.52 (+9.35)	1.52 (+9.35)	1.49 (+7.19)	1.51 (+8.63)
250 Hz	1.70 (-)	1.75 (+2.94)	1.80 (+5.88)	1.81 (+6.47)	1.77 (+4.12)	1.80 (+5.88)
500 Hz	1.80 (-)	1.80 (+0)	1.91 (+6.11)	1.91 (+6.11)	1.88 (+4.44)	1.91 (+6.11)
1000 Hz	1.74 (-)	1.81 (+4.02)	1.85 (+6.32)	1.89 (+8.62)	1.82 (+4.60)	1.85 (+6.32)
2000 Hz	1.60 (-)	1.66 (+3.75)	1.70 (+6.25)	1.73 (+8.12)	1.68 (+5.00)	1.70 (+6.25)
4000 Hz	1.26 (-)	1.32 (+4.76)	1.35 (+7.14)	1.35 (+7.14)	1.34 (+6.35)	1.33 (+5.56)
8000 Hz	0.81 (-)	0.82 (+1.23)	0.85 (+4.94)	0.85 (+4.94)	0.84 (+3.70)	0.83 (+2.47)

Values enclosed in parentheses represent the percentage increase in Early Decay Time (EDT) relative to the baseline condition of the seamless floorboard configuration.

presents simulated Early Decay Time (EDT) values across 1/1 octave frequency bands (63 Hz–8000 Hz) for six stage floor configurations: (1) Seamless, (2) Seamless with wall-mounted jars, (3) 1 cm joint width, (4) 1 cm joint width with wall-mounted jars, (5) 8 cm joint width, and (6) 8 cm joint width with wall-mounted jars. The inclusion of floorboard joint gaps, particularly in conjunction with wall-mounted jars, consistently demonstrates positive increments in Early Decay Time (EDT) across all frequency bands when compared with the seamless baseline. For instance, the transition from a seamless configuration to a 1 cm or 8 cm gap yields a relative increase in EDT, typically ranging from +3% to +10%, highlighting enhanced sub-stage volumetric resonance. The presence of wall-mounted jars further reinforces this trend, particularly in the mid-frequency bands (500–1000 Hz), where EDT values increase modestly but consistently across all joint scenarios.

The most pronounced increases in Early Decay Time (EDT) were observed within the low-frequency spectrum (63–125 Hz), where enhancements reached up to +10% relative to the seamless baseline. These improvements are particularly evident in configurations incorporating wall-mounted jars, which appear to activate additional resonant modes within the spatial volume. The integration of such embedded resonators not only extends the reverberation duration but also contributes to modal density in low-frequency bands, thereby reinforcing the richness of the sound field. This suggests that volumetric cavity interactions—especially the combined effects of floorboard apertures and jar wall systems—play a pivotal role in augmenting low-frequency reverberation through enhanced modal coupling. However, it must be acknowledged that the precision of low-frequency simulation outputs, particularly below 125 Hz, may be constrained by the inherent limitations of the ODEON simulation algorithm. These include difficulties in accurately modeling complex resonance phenomena and wave interactions at low frequencies due to mesh resolution and boundary condition approximations. Consequently, while the results strongly imply beneficial modal contributions from the jars, further empirical validation via advanced modeling is necessary to substantiate these frequency acoustic effects in traditional stage configurations.

3.3. Finite Element Numerical Analysis (FEM) of Vessel–Stage Coupling

The application of COMSOL (version 6.3) multi-physics simulation offers distinct advantages for modeling complex acoustic-structural interactions, particularly in low-frequency domains where geometric acoustics tools such as Odeon are limited. Utilizing a finite element method framework, COMSOL enables precise resolution of wave-based phenomena—including modal behavior, resonance, and diffraction—critical for evaluating the acoustic performance of sub-stage cavities and embedded resonators. Its multi-physics coupling capabilities further allow integration of structural and acoustic boundary conditions, facilitating analysis of how architectural features such as floorboard joint configurations and ceramic vessels influence sound energy propagation, confinement, and radiation. This study employed a simplified two-dimensional cross-sectional model of the Da-Hua Hall stage, incorporating the sub-stage cavity and a single embedded ceramic vessel to isolate the effects of joint width variation on acoustic coupling. Results from Figure 13 indicate that narrower floorboard joints enhance cavity resonance and reverberation, consistent with improved sound energy coupling across other acoustic parameters. Spectral analysis reveals distinct resonance behaviors: at low frequencies (50–100 Hz), all configurations show pronounced peaks, with the 1 cm gap yielding the highest amplitude near 50 Hz. Between 100–300 Hz, the 1 cm gap consistently produces stronger peaks than the 8 cm and 15 cm gaps, indicating more effective energy coupling. Above 300 Hz, while resonance peaks become more frequent and less intense, the 1 cm gap maintains relatively elevated magnitudes, notably around 344 Hz. The 8 cm and 15 cm gaps exhibit similar patterns, with the 15 cm gap occasionally showing reduced amplitudes, suggesting a diminishing effect of increased joint width beyond 8 cm. Overall, the findings confirm that narrower joints—particularly the 1 cm configuration—are more effective in activating sub-stage cavity resonance and enhancing acoustic performance.

All model boundaries were assumed to be acoustically rigid (hard-wall conditions) to eliminate absorption and boundary losses, thereby focusing exclusively on structural transmission characteristics. Although this idealized condition may overestimate low frequency energy retention, particularly due to the exclusion of the semi open wooden lattice sidewalls of the actual Da Hua Hall stage, it facilitates clearer analysis of how varying joint widths affect energy transmission dynamics. Acoustic power flow was visualized using vector field representations, with the X and Y components (acpr.lx and acpr.ly, in W/m²) and their magnitude (acpr.l.mag) rendered via directional arrows and a scalar color map, enabling direct observation of whether energy remains entrapped within the vessel cavity or is radiated into the performance space. The simulation results at 68 Hz demonstrate that floorboard joint widths significantly modulate energy coupling between the sub-stage ceramic resonators and the stage environment. In the 1 cm gap condition [Figure 14a], acoustic energy is largely confined within the vessel, indicating strong internal resonance and limited upward transmission. In contrast, the 8 cm gap configuration [Figure 14b] produces more pronounced vertical energy flow and improved radiative efficiency into the stage volume. These findings suggest that wider floorboard gaps enhance low frequency energy release, and that an 8 cm joint width may be more favorable for supporting low frequency sound field amplification in traditional performance architecture.

To illustrate the energy flow dynamics and acoustic intensity distribution at the dominant peak frequencies for each joint width condition, specifically, Figure 15a displays the energy flow and intensity map for the 1 cm gap at 344 Hz, while Figure 15b illustrates the same for the 8 cm gap at 115 Hz. The 1 cm gap condition demonstrates pronounced energy localization within the vessel cavity, indicative of strong modal confinement and limited outward propagation. In contrast, the 8 cm gap exhibits enhanced vertical energy transmission, suggesting more effective acoustic coupling between the sub-stage cavity and the performance space. These comparative results underscore the influence of floorboard joint width on frequency-dependent acoustic transmission. Narrower gaps tend to promote internal resonance retention, while wider gaps facilitate the release of low-frequency energy into the surrounding environment. This finding highlights the critical role of architectural detailing in shaping the acoustic behavior of traditional stage structures.

The cavity pressure response of the wall-mounted vessel model, as illustrated in Figure 16a, reveals a pronounced low-frequency resonance behavior, with a dominant pressure peak occurring at approximately 127 Hz. This peak corresponds to the vessel’s fundamental resonance mode and reflects strong acoustic coupling within the enclosed cavity volume. Secondary peaks observed at higher frequencies suggest the presence of higher-order modal responses, indicating the vessel’s capacity to function as a frequency-selective resonator. Complementary to this, Figure 16b presents the acoustic energy flow lines and intensity map (W/m²) at the dominant resonance frequency of 127 Hz. The visualization demonstrates concentrated energy retention within the vessel cavity and the directional flow of acoustic power, further verifying the presence of localized resonance. Together, these findings substantiate the theoretical rationale for integrating embedded ceramic resonators within traditional performance architecture, as they effectively reinforce low-frequency sound energy through modal confinement and cavity resonance, thus contributing to the enhancement of spatial acoustic richness.

4. Conclusions

This study reveals that traditional Chinese courtyard theaters, exemplified by Da-Hua Hall, deliberately integrate ceramic resonator jars and sub-stage cavities to enhance unamplified vocal and instrumental acoustics. Narrow stage floorboard joints improve mid- to high-frequency resonance and reverberation, while wider joints facilitate low-frequency amplification, highlighting frequency-dependent acoustic coupling shaped by architectural detailing. By demonstrating how the incorporation of acoustic jars beneath the stage and within wall structures serves not only to amplify sound energy but also to enhance vocal clarity and projection. Such effects are particularly beneficial for unamplified traditional operatic or theatrical performances, where the natural voice must carry across a space without electronic reinforcement. From the audience’s perspective, these resonant systems contribute to improved speech intelligibility and aid in preserving the tonal richness of acoustic instruments and vocal timbre, thereby reinforcing the immersive quality of the auditory experience in natural sound environments. The findings provide empirical evidence of historical acoustic design intentionality, demonstrating how architectural structure and resonance strategies evolved to optimize natural sound projection and reverberation in performance spaces. The analysis yielded the following key findings:

• On-site acoustic measurements at Da-Hua Hall, conducted in accordance with ISO 3382-1:2009, revealed an average Early Decay Time (EDT) of 0.96 s across listener zones, with higher values in the Main Hall (1.13 s), confirming its suitability for unamplified performance. Sound Strength (G) ranged from +2.5 to +4.1 dB, while ST_early measured–3.7 dB at the stage, indicating sufficient acoustic support for performers. Spatial qualities were favorable, with Inter-aural Cross Correlation (IACC) values below 0.55 and a Lateral Energy Fraction (LF) of 0.23 in the main hall. These results demonstrate balanced reverberation, effective spatial impression, and validate the historically embedded architectural-acoustic strategies, providing a calibrated reference for simulation analysis.
• Utilizing Odeon, acoustic simulations demonstrated that introducing a 1 cm floorboard gap increased Early Decay Time (EDT) by 6.1%, suggesting improved reverberation through enhanced sub-stage acoustic coupling. Sound Strength (G) exhibited a 1.37% rise at the 8 cm gap, indicating a modest gain in sound energy distribution. The addition of wall-mounted ceramic jars further increased EDT by up to 10% in the 63–125 Hz range, while mid-frequency bands (500 Hz to 1 kHz) showed a moderate EDT increase of approximately 4%, reflecting enhanced reverberation and modal interactions across the spectrum. Nonetheless, owing to Odeon’s limitations in modeling wave-based phenomena below 125 Hz, further validation through Finite Element Method (FEM) simulation using COMSOL was deemed necessary.
• These limitations encompass challenges in precisely simulating complex resonance phenomena and wave interactions at low frequencies, primarily due to constraints in mesh resolution and the approximations inherent in boundary condition modeling. Consequently, although Odeon simulations strongly suggest advantageous modal contributions from the wall-mounted jars, the literature emphasizes the necessity of further empirical validation. Advanced numerical methods, such as Finite Element Method (FEM) simulations implemented via COMSOL are recommended to robustly substantiate these low-frequency acoustic effects within traditional stage configurations.
• This study employed COMSOL FEM simulations to overcome Odeon’s limitations in modeling low-frequency acoustics (<125 Hz) in traditional stage architecture. Results showed that narrow floorboard joints (1 cm) enhance internal resonance, while wider joints (8 cm) favor low-frequency energy radiation. Wall-mounted ceramic jars exhibited strong resonance near 127 Hz, confirming their role as passive acoustic resonators. Together, these findings validate historical design strategies that intentionally integrated architectural form and acoustic performance to enrich the sound field in traditional courtyard theaters.
• The traditional acoustical design of Chinese courtyard theaters, exemplified by Da-Hua Hall, enhances both performers’ vocal projection and audience listening experience through architectural integration of resonant elements like sub-stage and wall-mounted ceramic jars. These features enable performers to project clearly without amplification and facilitate effective onstage communication. The design of stage floorboard joints further influences sound transmission and resonance, balancing energy retention and radiation to enrich the performance environment. For audiences, this results in improved speech intelligibility, tonal richness, and sufficient loudness, creating a balanced and immersive auditory experience. Spatial design elements promote a sense of envelopment and spaciousness, reflecting a historically intentional integration of architectural form with performance acoustics to optimize both performer and listener engagement.