AAWM Journal 13/No. 2 (2025)

A Computational Analysis of Melodic Characteristics in Hebei Bangzi Opera: A Case Study of the “Sha Miao” Aria^[1]

Zhaoxin Yu, Yukun Li, and Wei Yue

Hebei Bangzi Opera, Computational Musicology, Music Information Retrieval (MIR), Scale, Mode, Interval, Meter, Vocal Music

Hebei Bangzi (Clapper) Opera, a prominent form of traditional Chinese opera from Northern China, embodies rich cultural and musical traditions. This paper employs computational techniques to analyze the vocal music of the aria “Sha Miao” from Hebei Bangzi to examine empirical musicology theories and enhance understanding through quantitative results provided by a systematic approach. Initially, the study highlights the benefits of computational methods, provides an overview of Hebei Bangzi Opera, and includes a brief introduction to its musical characteristics and empirical theories. The recordings and metadata are then introduced in detail. Using estimated and manually corrected pitch curves and annotated note segments, we obtained pitch and interval histograms to investigate the scale and mode of “Sha Miao”. We examine the usage of unstable pitches in certain steps of the scale, a distinctive characteristic documented in existing theories, by comparing it to the twelve-tone equal temperament. Furthermore, we analyze the melodic intervals across different bǎnshì sections (characterized by tempo and meter) to demonstrate the correlation between intervals and bǎnshì sections. The results indicate that the interval sizes contribute to the song’s structure and storytelling, consistent with empirical theories, while the distribution of interval directions contradicts our predictions based on these theories. Overall, our approach identifies the qualitative and quantitative characteristics of vocal music in “Sha Miao”, demonstrating the potential of computational methods in vocal music analysis.

Zhaoxin Yu is a Professor at Shandong University of Arts, and Head of the Music Technology Innovation Center.

Yukun Li is a Faculty Member at South China University of Technology.

Wei Yue is an Associate Professor at Shandong University of Arts.

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Introduction

By the Qing Dynasty, the “Four Great Vocal Systems” had taken shape in traditional Chinese opera, and the Bangzi system emerged as a key component. All opera styles rooted in this system are collectively called Bangzi opera—they stand out for their unique singing styles and rhythms, and over time, they developed into many regional variants that took root across different areas. Hebei Bangzi Opera, a quintessential form of traditional Chinese Bangzi opera, is particularly noted for its rich cultural and musical traditions, encompassing a vast repertoire of over five hundred plays, with more than twenty actively performed today (Chen and Yin 2023). Bangzi opera is particularly noted for its meter and tempo variation, which forms the structural backbone of the performances, presenting a fertile ground for musicological exploration. The artistic characteristics of Hebei Bangzi is evident in its vocal melodic, orchestral, and vocal expression elements. A notable feature is the use of larger melodic intervals, which serve to heighten dramatic impact (Lv, Ji, and Xiang 1995, 41). In addition, the orchestration of Hebei Bangzi may incorporate local instruments alongside the traditional clappers and stringed instruments, contributing to its unique sound (An 2023, 28). Bangzi opera particularly emphasizes the nuanced expression of emotions through pitch and loudness variations in singing.

[2] This study of Hebei Bangzi is motivated not solely by academic interest, but also by the need for cultural sustainability. Traditional Chinese opera, including genres like Hebei Bangzi, faces challenges in its preservation and transmission. Understanding its stylistic intricacies and features is important for its continued viability, scholarly analysis, and transmission to future generations. In this context, computational methods offer a systematic approach for objectively documenting and analyzing these complex, often orally transmitted traditions, aiding in the preservation of cultural heritage. This research is relevant not only for Chinese music scholars but also for a wider interdisciplinary audience. Ethnomusicologists, who use various methods to understand music’s role and expressive techniques across cultures, can gain quantitative insights from this work. Computational musicologists and Music Information Retrieval (MIR) researchers, developing methods for analyzing diverse musical traditions, including non-Western musics, will find this study addresses relevant challenges in such applications. Furthermore, music performers and teachers can utilize the analytical insights from traditional practices to inform their performance and teaching approaches.

[3] Although the cultural and artistic significance of Hebei Bangzi has been thoroughly examined through descriptive musicology studies (Chen and Yin 2023, Lv, Ji, and Xiang 1995), there remains a notable gap in research employing computational methods to analyze the musical characteristics of Hebei Bangzi Opera. Although the study by An (2023) investigated the acoustics characteristics of vocal performances in Hebei Bangzi, examining aspects such as formants, vibrato, and speech characteristics across different role types, a computational exploration of Hebei Bangzi’s musical content has yet to be realized.

[4] In this paper, we aim to address this research gap through a computational analysis of the melodic content in the vocal music of Hebei Bangzi Opera, thereby revealing the intrinsic connections between melodic patterns (such as interval progressions) and narrative contexts as well as character emotions.Our study draws upon the recordings and digital note annotations of Chinese traditional opera from the Vocalnotes project, which was conceived not merely to elucidate the intricacies and variations in expert transcription practices—it was more than that: it seeks to unpack a core question: “What is in a note?” Focusing on the aria “Sha Miao” from the opera “Qin Xianglian,” our analysis delves into the scale, interval, mode, meter, and tempo, offering a case study in the computational examination of a traditional Chinese art form.By applying computational methodologies to the aforementioned recordings and digital note annotations, we aim to provide insights into the melodic characteristics of Hebei Bangzi vocal music and to explore how these methods can support and enhance the existing descriptive musicological theory.

Background

Related Work in Computational Ethnomusicology

[5] Computational methods are powerful tools for analyzing musical traditions that can yield a level of detail and scale that was previously unattainable prior to their introduction into…starting in the [input approximate year]. By automating tasks like pitch extraction and data visualization, these techniques overcome the limitations of manual transcription, enabling large-scale, corpus-level analyses that capture microtonal details often lost in Western notation. For oral traditions rich in such subtle yet meaningful details, this data-driven approach offers an objective framework to systematically investigate performance practices that often lack standardized notation.

[6] Pitch and interval histograms have emerged as a particularly effective method for revealing a tradition’s implicit tuning and modal structure. Scherbaum et al., (2022), for instance, aggregated F0 data from Georgian multipart field recordings into smoothed, voice-separated pitch-class histograms. By clustering the resulting peak centroids, they recovered a stable, non-tempered tuning system, demonstrating how large-scale statistics can reveal emergent intonation patterns in polyphonic folk repertoires. This approach is most effective for relatively stable pitches that produce clear histogram peaks. However, the inherent flexibility of vocal F0, especially in highly expressive genres, can blur these distributions. Shafiei et al. (2025) addressed this ambiguity by using Dynamic Time Warping (DTW) to align F0 track with a reference MIDI transcription. Our study utilized pitch histogram but replaced the rigid MIDI reference with a non-discretized transcription derived from expert human perception. This measure was taken to ensure that our analysis was grounded in the tradition’s actual intonational practices rather than a pre-defined theoretical framework.

[7] Computational methods offer objective measures to verify and enrich qualitative musicological descriptions. Within the study of Chinese opera, however, such computational research remains relatively scarce. Caro Repetto et al. (2015) used MIR features to distinguish between two schools of Peking Opera, corroborating established musicological knowledge while also exposing new stylistic markers. Yu (2019) applied signal analysis to the “Ou” vocal style of Zhangqiu Bangzi to quantify the relationships between pitch, duration, and intensity in different melodic contexts. While these studies provide insights into vocal performance, they focus primarily on general stylistic characteristics. Our research fills a critical gap by applying computational analysis specifically to the foundational elements of Bangzi vocal music structure: its scale, modes, and intervals.

Background Knowledge of Hebei Bangzi Opera

One Main Type of Shengqiang: Bangzi Qiang

[8] Chinese traditional opera is a multifaceted art form with a rich history. One of its most defining properties is “Shengqiang,” a musical form that guides the mode, instrumental arrangements, and vocal style. Shengqiang varies significantly across different regional opera forms, and four main types are prevalent in China: Bangzi Qiang, Pihuang Qiang, Kun Qiang, and Yiyang Qiang (An 2023, 104).

[9] Bangzi Qiang, with its origins tracing back approximately 400 years, emerged in the Shaanxi and Shanxi regions of China. The spread of this operatic form to other regions is largely attributed to the movement of merchants from these areas (An 2023, 14). This form of opera, commonly referred to as Bangzi Opera, is characterized by the inclusion of percussion instruments (clappers), Bangzi, in conjunction with traditional Chinese string instruments.

[10] The spread of Bangzi Qiang gave rise to the development of nearly 100 distinct regional genres of Bangzi Opera, each shaped by the specific accents and cultural nuances of its area. Notable among these are Shandong Bangzi, Hebei Bangzi, and Henan Bangzi (also recognized as Yu Opera), distinguished by their unique regional attributes. A defining characteristic of Bangzi Opera is the employment of wooden clappers, known as “Bangzi,” which have two main roles. These clappers not only serve as musical instruments accompanying the singing and speech, they also act as metronomic devices that orchestrate the opera’s structure through various meters, known as “bǎnshì”. Each type of meter combined with a specific tempo level forms an individual bǎnshì section of the aria to convey specific emotions and to advance the opera’s plot. Predominantly in northern China, Bangzi Opera is renowned for its loud and resonant vocal style, distinguishing it as a vibrant component of the region’s cultural heritage.

A Regional Focus: Hebei Bangzi

[11] Hebei Bangzi, a regional variant of Bangziqiang, exhibits unique characteristics developed through its integration with the local dialogue and musical tones of Hebei province. The following section includes a brief introduction of the basic characteristics of vocal melodic content on whichthis paper focuses, based on the documented musicological literature on Hebei Bangzi Opera.

Meter or Bǎnshì

[12] Bǎnshì, is a fundamental element in music. In Hebei Bangzi opera, bǎnshì not only determines the structure but also helps shape the musical expression through its diverse metrical patterns. Hebei Bangzi employs four primary meter types, which can be interchanged or modified in tempo to suit the narrative and emotional context of the opera:

Two-Six Meter (Èrlù Bǎn): A foundational meter in Hebei Bangzi, its name reflects its two six-syllable phrases. It is typically noted as a 2/4 time signature in modern Western notation and has two subtypes differentiated by speed:
- Slow Two-Six Meter: Characterized by rich ornamentation, it conveys nuanced emotions.
- Fast Two-Six Meter: Brisk with less ornamentation, it is well-suited for direct narration.
Slow Meter: Commonly in 4/4 time, it emphasizes a strong first beat followed by three weaker beats.
Flowing Water Meter: Often using 1/4 or 1/8 time signatures, this meter is generally rapid. It has two variants:
- Fast Singing: Featuring short notes, it expresses agitation or urgency.
- Slow Singing: Characterized by long melismas, it achieves a sorrowful or passionate effect.
Free Rhythm: Lacking fixed beats, this offers fluidity within Hebei Bangzi. It allows rhythmic freedom and often functions as a transition between banshi sections that employ the other three types of meters.

Musical Scale and Mode

[13] The musical scale system in Hebei Bangzi Opera is fundamentally rooted in the Chinese pentatonic tradition, with the base pentatonic scale consisting of “Gong (宫), Shang (商), Jue (角), Zhi (徵), Yu (羽),” which corresponds to the Western “do, re, mi, so, la.” These five scale steps are systematically developed based on perfect fifth intervals in the generative order of “Gong (do), Zhi (so), Shang (re), Yu (la), Jue (mi).”

[14] The theoretical framework underlying Hebei Bangzi Opera derives from China’s imperial court music system, making the use of traditional Chinese imperial court music terminologies both appropriate and necessary for rigorous academic analysis.

However, it is crucial to recognize the distinction between theoretical framework and performance practice: while we employ formal court music terminology for analytical purposes, Hebei Bangzi Opera remains fundamentally a vernacular folk tradition. Performers typically navigate modes through intuitive feel and interval relationships rather than formal theoretical designations, reflecting the orally-transmitted nature of this regional operatic form.

[15] The melodic structure of Hebei Bangzi Opera employs heptatonic scales created by adding two additional tones to the foundational pentatonic framework. From four available supplementary scale steps, different combinations are selected to create three distinct heptatonic scales used in traditional vocal performance. The singing parts primarily utilize the Qingyue scale (清乐音阶), supplemented by the Yayue scale (雅乐音阶), with the Yanyue scale (燕乐音阶) also employed in the traditional vocal style of Hebei Bangzi Opera (An 2023). The specific construction of each scale is as follows:

Yayue scale: The scale consists of Gong (do), Shang (re), Jue (mi), Bian Zhi (sharp fa), Zhi (so), Yu (la), Bian Gong (si).
Qingyue scale: This scale includes Gong (do), Shang (re), Jue (mi), Qing Jue (fa), Zhi (so), Yu (la), Bian Gong (si).
Yanyue scale: The notes are Gong (do), Shang (re), Jue (mi), Qing Jue (fa), Zhi (so), Yu (la), Run (flat si).

[16] In the scales above, notes are categorized into two types. The additional 4 notes Bian Zhi (sharp fa), Bian Gong (si), Qing Jue (fa), Run (flat si) are regarded as auxiliary steps, while the five steps in pentatonic scale are main notes in these heptatonic scales. It should be noted that the scales are not in twelve-tone equal temperament. In real Chinese traditional opera performance, these auxiliary steps are often sung at pitches that deviate from the twelve-tone equal temperament. Among the three heptatonic scales, Qingyue scale is mostly utilized in Hebei Bangzi Opera, while the other two are used to emphasize special color of the melody (Lv, Ji, and Xiang 1995, 28–29).

[17] Influenced by “QinQiang,” another regional genre of Bangzi Opera considered to be one of the original sources of Hebei Bangzi—Hebei Bangzi has inherited distinctive musical characteristics such as bold vocalization and rhythmic flexibility.The melodic system demonstrates systematic pitch alterations specifically in the 4th and 7th scale degrees to create distinct emotional colorations. These two scale degrees undergo deliberate pitch modifications while other degrees strive to maintain stable pitch. The formation of contrasting emotional modes—characterized as either “happy” or “bitter” sonic modalities—is primarily governed by the strategic alteration of these two scale degrees. Experts within the Bangzi Opera tradition possess sophisticated knowledge of these intentional pitch variations and their expressive functions. Empirical documentation of this traditional practice was established through systematic acoustic testing conducted at the 1986 National Conference on Folk Music Notation in Shanxi Province. The research revealed precise pitch relationships: in “happy” mode, the 4th scale degree is raised approximately 30 cents above its standard position while remaining below the semitone threshold of #4, with the 7th degree maintaining its natural position. Conversely, in “bitter” mode, the 4th degree remains unaltered while the 7th degree exhibits controlled pitch drift, positioning itself between the natural 7th and b7—specifically 25 cents above b7, representing not a lowered 7th but rather a raised b7. This systematic approach to microtonal inflection demonstrates how traditional knowledge translates into measurable acoustic phenomena that serve specific expressive purposes within the operatic tradition (Zhang 2015, 82–117).

[18] The vocal music of Hebei Bangzi Opera predominantly employs the Zhi mode, with Zhi acting as the tonic in the scale (Lv, Ji, and Xiang 1995, 33–34). This mode forms the foundational framework for Hebei Bangzi Opera’s melodic structure. Typically, the scale utilized follows the Qing Yue scale, which comprises the notes: Zhi (do), Yu (re), Bian Gong (mi), Gong (fa), Shang (so), Jue (la), and Qing Jue (si). The Zhi, Shang, and Gong are pivotal in defining the mode’s tonality, playing the same roles as the tonic, dominant, and subdominant in Western music. These three core notes frequently appear at the beginning and end of sections, providing a cohesive link between segments of varying meters.

Melodic Intervals

[19] Hebei Bangzi Opera utilizes a variety of intervals in the vocal parts, which are categorized into multiple levels, based on the number of semitones, with specific musicological terms in Chinese (Lv, Ji, and Xiang 1995, 42–49). Different intervallic levels play different roles of emotion and are accompanied by different meter and tempo levels.

Level 0: unison, called “同音反复” (tóng yīn fǎn fù) in Chinese, serves as a connective device within the melodic framework, bridging musical phrases or sections.
Level 1: Small step intervals, which is called “级进” (jí jìn), includes semitones and whole tones, typically signify a narrative-driven delivery, with a slow tempo for storytelling sections.
Level 2: Intervals of thirds, including both of major thirds and minor thirds, are characterized by a medium tempo that imparts a sense of gentleness and approachability.
Level 3: Leaps, called “跳进” (tiào jìn), spanning from fourths “四度” (sì dù) to sixths “六度” (liù dù), correlate with strong emotions and are presented with a rapid tempo.
Level 4: Big jump, which is called “大跳” (dà tiào), exceeding sixths, are reserved for moments of intense emotional expression.

[20] Additionally, the directionality of intervals in the melody contributes to its expressive quality. Ascending intervals are often used to build tension, especially when increasing in volume. Conversely, descending intervals tend to alleviate tension, and are commonly accompanied by a decrease in volume.

A Brief Introduction of the Selected Aria

[21] This paper delves into the extensive repertoire of classic plays associated with Hebei Bangzi, with a particular focus on an aria of a representative work: “Sha Miao”. “Sha Miao” stands out as an exemplary act within the traditional narrative of “Qin Xianglian”, which explores themes of justice, morality, and betrayal—ideas conveyed through distinct folk aesthetic expressions and a populist perspective rooted in the experiences of ordinary people.This opera delineates the story of the upright judge Bao Zheng executing Chen Shimei, a figure marked by ingratitude and deceit for abandoning his wife, Qin Xianglian. “Sha Miao” specifically unfolds Chen Shimei’s confrontation with his attempts to erase his transgressions through the assassination of Xianglian and her children.

[22] The selected aria of this paper captures a poignant moment of moral reckoning, as Han Qi, a subordinate of Chen Shimei, sent to execute Qin Xianglian, faces a profound ethical dilemma upon hearing her story, ultimately leading to his suicide. This aria not only underscores the opera’s rich exploration of ethical complexities but also highlights the character of Han Qi as embodying integrity and chivalrous spirit, qualities which are enhanced by the high-pitched and vigorous melody.

Methodology

Table 1. Metadata of eight fragments of the Shao Miao aria included in the dataset

Recording

[23] This study focuses on the aria “Sha Miao”—a piece from the classic Hebei Bangzi repertoire. The recording is a commercially available CD and is held by the Chinese Ministry of Culture and Tourism Ethnic and Folk Art Development Center in the Hebei Bangzi opera collection.

[24] Because meter is the most fundamental characteristic of Bangzi opera that decides the structure of an aria and significantly influences the plot progression, the aria is segmented into 8 fragments based on differing meters. Showcasing the diversity, 8 fragments have a variety of meters and exhibit a range of tempo levels, including slow, moderate, fast, and rubato patterns. Each fragment is regarded as a section with a specific meter and tempo level and these consecutive sections form the structure of the aria. Table 1 shows the statistics on details of each fragment.

Vocal Separation

[25] To isolate the vocal components from the instrumental accompaniments for analytical purposes, a two-stage approach was employed:

Initial Separation: A signal-processing-based vocal separation method was used to extract vocal part from the original mixed audio, dividing one channel containing a mixture of vocal and instrumental sounds from another channel dedicated solely to instrumental sounds.
Refinement with Residual UNet: While the initial separation removed the instrumentation, some residual instrumental sounds still remained. To achieve a higher level of vocal isolation, a pre-trained residual UNet neural network (Kong et al. 2021) was applied. This advanced technique focuses on identifying and removing the subtle instrumental frequencies that remain within the extracted vocal track.

[26] The separation results yielded clean vocals without noise, facilitating accurate annotation as confirmed by annotators’ feedback via subjective listening

Pitch Extraction and Note Annotation Method

[27] For a detailed analysis of Hebei Bangzi’s vocal music fundamentals, advanced computational methods were employed to extract features from the vocal recordings. The initial step involved the use of pYIN (Matthias and Dixon 2014), embedded in the Tony Software (Mauch et al. 2015), a sophisticated tool in Music Information Retrieval (MIR), to extract a continuous pitch track from the vocals. This pitch track serves as the foundation for subsequent analysis.

[28] Following the extraction of the pitch track, two annotators were tasked with independently transcribing the vocal parts into VocalNotes. This process entailed segmenting the audio into discrete notes, requiring meticulous attention to the nuances of the vocal performance.

[29] The annotators then utilized Sonic Visualiser (Cannam et al. 2006), a powerful tool for sound visualization and analysis, to import the audio, pitch track, and note segments. In this environment, they conducted a thorough review and correction of the pitch for each note, ensuring alignment with their auditory perception (source removed for anonymity).

[30] It is noteworthy that there was no interaction or communication between the annotators during this phase of the study. This approach was deliberate, aimed at preserving the objectivity and independence of their transcriptions. Upon completion, a comparative analysis of the annotations revealed distinct focus areas for each annotator—one concentrated on the detailed variations in pitch, while the other emphasized the overall melodic structure.

[31] For the purposes of this study, the latter annotation that provided a more descriptive overview of the melody was selected for further analysis. This version was deemed more suitable for the subsequent examination of musical elements such as scale, mode, and intervals. The decision to use the descriptive version was based on its alignment with the study’s objectives of exploring the broader musical characteristics of Hebei Bangzi opera.

Pitch and Interval Histogram

[32] To analyze the scale in those fragments in Hebei Bangzi Opera, our methodology encompasses the acquisition of pitch histograms through two distinct pitch data. The first pitch data is the frame-level pitch values of annotated notes. The second is the frame-level pitch values of the extracted pitch track. The pitch histogram is acquired by using Matlab^[2] histogram function with 10-cent bins and smoothing is applied by utilizing a moving average.

[33] To analyze interval distribution, we generated an interval histogram from the annotated notes. First, we calculated the pitch differences between consecutive notes to determine the intervals in each section. Next, we established bin centers and widths to represent the main musical intervals. Unison uses a center of 0 cents with a width of 20 cents. Other main intervals use multiples of 100 cents as their centers and a width of 100 cents (with the exception of the minor 1st, which has a width of 140 cents). Finally, we counted the occurrences of intervals within each main interval and visualize the results in the histogram.

Analysis of Results

Musical Scale and Mode Analysis

[34] To analyze the musical scale and mode of the aria “Sha Miao,” the smoothed pitch histograms were acquired using the method mentioned in Section 3.3. Two kinds of pitch data are presented in Figure 1. The upper subplot is the smoothed normalized pitch histogram of note segments, while the lower one depicts the pitch values of extracted continuous pitch track. Comparing the two subplots with different pitch data reveals that although they have very similar overall contours, the pitch of the annotated note is shown to yield a clearer distribution of pitches (see peaks with pitch around –600, –200, –100 cents). This is owing to the discreteness afforded by the note annotations. Therefore, we focused on the upper subplot to carry out the analysis.

[35] Multiple prominent peaks—including those near 0, 400, and 700 cents—exhibit deviations from Chinese traditional music tuning system of up to about 40 cents. This systematic pitch variance has not been thoroughly investigated in prior scholarship. The observed intonational flexibility in vocal performance may be attributed to several factors, including the influence of accompanying instruments that drift from standard pitch due to environmental temperature fluctuations. As traditional Chinese musical instruments are particularly sensitive to temperature variations, such deviations could affect the singer’s pitch reference, leading to corresponding adjustments in vocal intonation. This phenomenon raises important questions about the relationship between instrumental accompaniment and vocal pitch stability in traditional Chinese opera, warranting further systematic investigation.

[36] We systematically assigned each prominent peak in the smoothed pitch histogram to its corresponding scale degree, with solfège syllables shown in Figure 1. This analysis reveals the scale and mode of the aria. In Chinese music theory, the identification of mode requires determining both the tonic and the first degree (Gong), which serve distinct functions. The tonic is typically indicated by the final pitch of a piece, while the first degree, which establishes the modal foundation, is defined as the lower note of the major-third interval in the pitch histogram. Within the 0–400-cent range shown in the upper subplot, the first and third dominant peaks outline a compressed major-third interval. The peak at around 0 cents represents the first degree, Gong (宫). While this interval should theoretically span 407 cents, the observed measurement of approximately 350 cents—50 cents narrower than equal temperament—demonstrates a characteristic departure from twelve-tone equal temperament. The aria’s final note, measured at 383.6 Hz, falls slightly below equal-tempered g1 and corresponds to the peak at approximately –500 cents, which we identify as Zhi (徵) degree. Based on traditional nomenclature, this modal configuration places the piece in the G-Zhi mode of the C-Gong system (C宫系统的G徵调).

[37] With these two reference points established, the remaining peaks were mapped accordingly, showing that all five principal degrees—Gong, Shang, Jue, Zhi, and Yu—emerge clearly in the histogram. In addition, minor peaks at roughly –600 and –200 cents correspond to the auxiliary degrees Bian Zhi and Run, which show the characteristic of the seven-note scale system in Hebei Bangzi. Their presence suggests that the Yayue and Yanyue scales are interwoven within this aria. Furthermore, there are several small peaks occurring between si♭ and si as well as between fa and fa♯. This implies that the scale is slightly influenced by the “happy” and “bitter” mode identified in Section 2.2.2.

Figure 1. Two smoothed normalized pitch Histogram of “Sha Miao”. The upper one is estimated by using frame-level pitch values of the annotated notes. The lower is the frame-level pitch values of the extracted pitch track. The x-axis shows the pitch in cents, with C1 set as 0 cents as reference, while the y-axis represents normalized occurrences. Dash lines based on twelve-tone equal temperament are displayed on the plot to show the relative pitch scale as a reference.

Musical Interval Analysis

[38] Figure 2 presents interval histograms for each section, enabling an analysis of interval distribution. The interval histograms illustrate the dominant intervals within each section. Table 3 summarizes the dominant interval types (ordered by frequency), and the directionality, meter, and tempo for each section. This aria displays a strong directional predominance of downward intervals. This contrasts with the narrative goal of building tension, as Section 2.2.3 mentioned that descending intervals alleviate tension, underscoring the profound ethical dilemma faced by Han Qi upon hearing Qin Xianglian’s tragic story. However, the interval distribution in the 8 sections complies with the general rule mentioned in Section 2.2.3, with faster bǎnshì sections displaying larger intervals.

[39] While the occurrence of the unison intervals is not limited to a specific tempo, their role is to connect musical phrases and sections in some cases. Figure 3 depicts the distribution of notes with unison intervals throughout sections 1–7. Section 8 does not have unison intervals.

Figure 2. Pitch interval histograms of note segments of 8 sections of “Sha Miao”. The x-axis displays the main intervals (abbreviations denote quality: P for perfect, M for major, m for minor, A for augmented; numbers represent the interval number; minus signs indicate downward intervals). The y-axis shows the frequency. The numbered vertical lines correspond to the range of five interval levels described in Section 2.2.3 and listed in Table 2.

Table 2. Interval levels descriptions.

Table 3. Relation between interval level and tempo of each section in “Sha Miao.”

Figure 3. Unison interval distribution in section 1-7 of “Sha Miao”. The x-axis represents time in seconds. Red blocks correspond to notes that utilize unison intervals, while blue blocks represent notes with other intervals. The arrows serve to illustratethe function of distinguishing the structural role of unison intervals: an arrow with thicker tail indicates unison intervals that connect two distinct sections, and arrows with thinner tails indicate unison bridging two phrases within a section.

Conclusion

[40] This study successfully demonstrates the significant value of computational techniques for the in-depth analysis of vocal music. By leveraging a digital interface for accurate pitch tracing and expert-driven note annotations, we enabled the precise histogram display of estimated scale steps and accurate melodic intervals. Through analyses based on visualization techniques and quantitative results, we gained a deeper understanding of the musical characteristics documented in the Hebei Bangzi Opera tradition, highlighted in our case study of the aria “Sha Miao”. In so doing, our study assists with the preservation and transmission of this intangible cultural heritage.

Our analysis reveals several key musical characteristics. We found that the scale employed in this aria exhibits an interweaving of elements from both the traditional Yayue and Yanque scales. Furthermore, our findings confirm a notable relationship between tempo, meter, and interval levels, where larger intervals become more prevalent as the tempo increases. While not directly correlated with tempo, unison intervals were shown to play a unique role in bridging musical phrases within and between sections, with the repetition of unison pitches particularly enhancing the dramatic tension. A statistical analysis of intervals across different sections of the aria also revealed a dominant presence of descending intervals, a finding that powerfully resonates with the ethical dilemma faced by the character Han Qi upon hearing Qin Xianglian’s tragic story. The observed interplay between musical features and narrative settings underscores the inherent connection among intervals, tempo, and emotion, offering novel perspectives on the dramatic expression in Hebei Bangzi Opera.

[41] This study therefore makes two primary contributions. First, we present a systematic methodology for modal identification directly from pitch histograms, grounding the interpretation of statistical peaks in the principles of traditional Chinese music theory. Secondly, we move beyond static analysis by computing interval histograms and correlating them with the tradition’s rhythmic-metric structures (bǎnshì), revealing how melodic patterns are linked to rhythmic function. Together, these contributions demonstrate how computational ethnomusicology can be adapted to respect a tradition’s internal theoretical logic, yielding replicable methodologies that not only describe but also explain musical practice.

[42] A significant insight from our work is that utilizing pitch histograms derived from expert-perceived note annotations, rather than solely from raw F0 traces, can provide a clearer distribution of peaks, offering a more refined understanding of pitch organization. Future research could build upon these methodologies by incorporating automated methods for scale and mode detection, enabling the analysis of a larger corpus of musical works. Ultimately, expanding the scope of such analyses could lead to more generalizable conclusions about the vocal music characteristics of Hebei Bangzi Opera, and potentially other regional opera traditions in China. Furthermore, observations of subtle pitch deviations during performance suggest a need for future systematic investigation of this phenomenon, utilizing larger sample sizes and interviews with performers to provide comprehensive insights.

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_[1]_. This study is a phased achievement of the 2021 National Social Science Fund of China (Art Science) General Project “Computational-Assisted Research on the Vocal Music of Bangzi Opera” (Project No.: 21BD061).

_[2]. https://ww2.mathworks.cn/products/matlab.html

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