INTRODUCTION

APPROXIMATELY half of the world’s languages are tone languages (Hyman, 2011) [1] [2], but music with lyrics in tone languages has not received proportional scholarly attention. Among the growing body of research on tone-language music, one of the topics that has received significant attention is “tone-melody correspondence” (Kirby & Ladd, 2016; Li et al., 2024; Zhang & Cross, 2021)—that is, how musical melodies correlate with linguistic tones in the lyrics.[3] Since the 1980s, many studies have examined tone-melody correspondence in Cantonese popular music, also known as Cantopop (M. K. M. Chan, 1987a, 1987b; Chow, 2012; Ho, 2010; Kirby, 2022; Ladd, 2022; Li, 2021; Li et al., 2024; Lo, 2013; P. C. M. Wong & Diehl, 2002). Although these studies provide valuable insights, they have been limited by methodological issues: First, their findings have been constrained by small sample sizes, ranging from 2 to 19 songs, or only including a few selected passages from a larger collection of songs (see Table 1). Second, the representativeness of the song samples has often not been sufficiently justified. Researchers might have selected songs or passages that illustrate specific musical or linguistic properties, but it remains unclear whether these observations apply to Cantopop at large. Consequently, conclusions drawn from these limited datasets invite reassessment. To address these methodological issues, I constructed a larger and more representative corpus of 105 Cantopop songs encoded in the Humdrum format. The corpus originated as part of a research project first presented as a master’s thesis (Lee, 2023) and facilitates further research on tone-melody correspondence in the genre. In this article, I introduce this corpus and discuss patterns of tone-melody correspondence arising from the corpus data.

Note. ^aLadd’s study combines the datasets from Kirby (2022) and Lo (2013).

INTRODUCTION TO CANTONESE TONES AND TONE-MELODY CORRESPONDENCE

Cantonese is a tone language, where “differences in pitch are used to distinguish lexical or grammatical meaning” (Kirby, 2021, p. 291). Cantonese has six tones, each with a distinct pitch profile.[4] Linguists use Chao’s (1930) five-level numbering system to describe pitch heights of these tones on a relative scale, where 5 represents the highest pitch and 1 the lowest. Each tone is thus represented by two numbers: the initial pitch height and the ending pitch height—known as “tonal onset” and “tonal target” respectively (Matthews & Yip, 2011, p. 475). For example, Tone 1 (T1) is represented as [5-5], with both onset and target at the highest pitch level, 5. Among the six tones, T2 and T5 are contour tones, which start and end on different pitch heights. Linguists have categorized these six tones into four registers—high, mid, low, and extra-low—based on their tonal target (Cheung, 2016). Figure 1 summarizes the pitch profiles of the six Cantonese tones.

Figure 1. Graphical illustration and table summary of the six Cantonese tones.

In tone languages such as Cantonese, words should be pronounced with the correct tone, as using a different tone may alter the word’s meaning. For example, in Cantonese, 問 (man in T6) means “to ask,” while 吻 (man in T5) means “to kiss.” By the same token, in songs written in a tone language, song melody and linguistic tones often correlate with each other to maintain the intelligibility of the lyrics. This correlation is known as tone-melody correspondence, a phenomenon studied across diverse musical traditions, including Cantopop.

To quantify the degree of tone-melody correspondence, researchers compare two elements of a song: “speech melody” and “song melody” (Schellenberg, 2012). Speech melody refers to pitch variations arising from the succession of tones as the words would be naturally spoken, while song melody refers to the definite pitches from the music to be sung. Using the concepts of speech and song melodies, researchers approach the issue of tone-melody correspondence in tone languages by observing “sequential pairs of musical notes and the accompanying syllables,” also known as “bigrams” (Ladd, 2022, pp. 138–139). These bigrams can be described with concepts borrowed from musical counterpoint—similar, oblique, and contrary motions—according to the directional relationship between speech and song melodies (Ladd & Kirby, 2020; Schellenberg, 2012). These types of contrapuntal motions are visualized in Figure 2. For example, Figure 3 presents a seven-note phrase comprising six bigrams. The first bigram consists of the oblique motion between the level speech melody T5–T3 and the ascending major second from D3 to E3.[5] The second bigram features a similar motion between the rising speech melody T3–T1 and the ascending major second from E3 to F♯3, and so forth. By tallying the instances of each type of contrapuntal motion, researchers can assess the degree of tone-melody correspondence in a given sample of music. In general, tone-language music demonstrates a “text-setting constraint,” manifested primarily through the preference for similar motion and the avoidance of contrary motion (Ladd & Kirby, 2020).

Figure 2. Types of “contrapuntal motion” between speech and song melodies.

Figure 3. Bigram types in a phrase from the Cantopop song “K歌之王 [King of Karaoke]”

CORPUS CONSTRUCTION AND ENCODING

Selection Criteria

To ensure broad representativeness of the Cantopop corpus, I adopt popularity as the criterion for selecting songs, focusing on the most widely recognized tracks. I assess the popularity of Cantopop songs based on the number of music awards they received at major award ceremonies in Hong Kong, where Cantonese is the first language of more than 80% of the population (Eberhard et al., 2024) and where Cantopop has held significant cultural influence since the 1970s (Chu, 2017). Four major media channels, including radio and TV stations, host annual award ceremonies for Cantopop (see Table 2). Criteria for these awards include airplay frequency, fan voting, and internal adjudication preferences specific to each channel (Chu, 2017, p. 102; Chung, 2001; K. J. Wang 2020, p. 374).

The Cantopop corpus consists of songs released between 2000 and 2020.[6] To create a preliminary set of songs for forming the corpus, I compiled a list of songs credited as top songs of the year by the four media channels, each of which gives out 10 to 20 awards annually. During this period, 728 distinct songs received such awards. Figure 4 shows the distribution of these songs across the channels. From this preliminary set of 728 songs, I selected five songs per year, prioritizing those that received awards across all four channels (represented by the central intersection of 38 songs in Figure 4), followed by those awarded by three channels, and so on. This method resulted in a corpus of 105 songs (5 songs per year × 21 years). Each song in the corpus was assigned a unique song ID, composed of the character “C,” the last two digits of the release year, and an arbitrary ordinal number indicating its sequence within the year (e.g., C0204 for one of the five songs from 2002).

Figure 4. Distribution of the 728 awarded songs across the four media channels for the period 2000–2020.

The corpus is significantly larger than those examined in previous studies of Cantopop and was selected from more clearly defined selection criteria. Moreover, the selection procedure aligns with scholarly suggestions that music corpora should not be drawn from a single chart but from multiple sources (Covach, 2022; London, 2013). Even though outcomes of the Cantopop awards have sparked criticism and controversy (K. Chan et al., 2022, pp. 77–87; Ng, 2024, p. 89), the multi-chart basis of the corpus helps neutralize critical biases and idiosyncratic preferences inherent in each award. Accordingly, the corpus offers a more balanced representation of the Cantopop genre than any single chart.

Data Transcription

I transcribed musical and textual data of the corpus in the Humdrum kern (.krn) format (Huron, 1997, 2002) with Verovio Humdrum Viewer (VHV) and its spreadsheet plugin (Sapp, 2017). Figure 5 illustrates a Humdrum transcription of the phrase excerpted in Figure 3. Lines 1–8 consist of metadata “reference records,” listing information such as song title, song ID, release year, and names of the singer, composer, lyricist, arranger, and producer.[7] As line 9 of the Humdrum representation indicates, each song’s data are stored in three vertical spines: **kern, **text, and **jyutping. These spines represent melodic, textual, and phonetic information respectively. Annotations regarding formal sections (e.g., verse, chorus, bridge; see line 15), which represent my preliminary interpretation, are also included in the transcription to facilitate further analysis of the corpus data.

Figure 5. The first 24 lines of Humdrum representation of “K歌之王 [King of Karaoke]” (song ID: C0001) on VHV.

The melodic transcription includes only the vocal melody and excludes instrumental parts. Each transcription begins with the singer’s first entry and ends with the final note of the vocal part. I transcribed the melodies by ear, with rhythms and note durations quantized aurally to a level that balances precision and practicality. While the level of quantization varies across songs, the shortest transcribed note value in the corpus is the thirty-second note. The metrical interpretation of melodies is guided by de Clercq’s (2016) heuristic that the determination of measure lengths should be guided by a two-second “ideal” duration, complemented by other musical considerations such as drum patterns and harmonic rhythm. Each transcription also includes an approximate tempo in terms of beats per minute (see line 14 in Figure 5), which I obtained by tapping the perceived tactus on a digital metronome application. This value is based on the initial tempo of each song, without regard to any subsequent tempo changes. Moreover, Cantopop singers often realize contour tones (i.e., T2 and T5) with an upward microtonal glide at the beginning of the syllable before settling on the principal pitch, which occupies most of the time in a syllable (Schellenberg & Gick, 2020). These glides serve not as a distinct musical pitch, but to differentiate contour tones from their level-tone counterparts that have the same tonal target (i.e., T2 vs. T1 and T5 vs. T3). In these instances, the melodic transcription only includes the principal pitch, disregarding the initial glide.

While lyrics of all songs included in the corpus are available from music-streaming platforms, I verified their accuracy before populating the **text spine with this information. Phonetic information for the lyrics—including tones—is transcribed in Jyutping, a Cantonese romanization scheme standardized by the Linguistic Society of Hong Kong. The Jyutping transcription follows standard pronunciations listed in the Multi-function Chinese Character Database (Research Centre for Humanities Computing, 2014).

Data Preprocessing

PHRASING

Previous research has shown that tone-related text-setting constraints in Cantopop do not apply across phrase boundaries (Ho, 2010; Lo, 2013). Therefore, I encoded the beginning and end of song phrases to exclude bigrams across phrase boundaries from the subsequent analysis. Phrase boundaries were determined by spaces and line breaks in the lyrics, based on subtitles from official music videos or lyric texts posted on Spotify. In cases of long phrases, the singer’s breaths within the phrase would indicate further segmentation of the phrase. This approach stems from practices in popular-music analysis, where singers’ breaths sometimes serve as markers of phrase boundaries (Duinker, 2021; Moore, 2001; Stephenson, 2002). Phrase boundaries were marked in the Humdrum files with curly brackets in the **kern spine, as shown in lines 16 and 23 in Figure 5.

MELISMATIC TEXT-SETTING

While Cantopop text-setting is predominantly syllabic, melismatic syllables do appear in a small but notable quantity. In the 105 songs of the corpus, 2.80% of all syllables—1,062 out of 37,877—are set melismatically. Since the computational analysis of tone-melody correspondence requires a one-pitch-per-syllable mapping (e.g., see Figure 3), researchers need to select a “mapping locus” for each melismatic syllable in the melody (Ho, 2010, p. 50)—that is, the most relevant musical pitch to be mapped onto the tone of the syllable. Despite growing research on tone-melody correspondence in Cantopop, scholars diverge on how to identify the mapping locus (e.g., see the different approaches by Chow, 2012; Ho, 2010; and P. C. M. Wong & Diehl, 2002).

In this study, I identified the mapping locus of melismatic syllables based on the pitches’ melodic functionality. As Malawey (2020, pp. 79–80) explains, melismas in popular music serve to embellish the vocal melody and showcase the singer’s virtuosity. According to Lerdahl and Jackendoff’s (1983, p. 106) framework of perceptual hierarchy, pitches within a melisma can be ranked by their structural importance; some pitches are structural, whereas some are embellishing in function. Therefore, I selected the most structurally important pitch within a melisma as the mapping locus, while non-chord tones and virtuosic end-of-syllable elaborations were treated as embellishing pitches and omitted in the tone-melody mapping.[8] For example, in the excerpt shown in Figure 6, I identified the mapping locus of the final syllable to be the chord tone C♯. The initial D♯ functions as an appoggiatura, whereas the B and the G♯ constitute the singer’s virtuosic display. In the Humdrum encoding, non-mapping-locus pitches were marked with “q” (for appoggiaturas or other non-chord tones preceding the mapping locus) or “P” (for end-of-syllable melismas) and were excluded from the bigram analysis.

Figure 6. An excerpt from the second chorus of “重新長大 [Growing Up Again]” (song ID: C1205) showing the mapping locus of the melismatic syllable.

Data Availability

To facilitate open research and collaboration, I have made the corpus publicly available on the project website (http://cantopop.humdrum.org/), which offers information such as the complete list of the 105 songs, the demographic profile of the corpus, and data on tone-melody correspondence. The website links to resources related to the corpus, including the GitHub repository that hosts the Humdrum files of the song transcriptions (https://github.com/jasonleeubc/Cantopop-corpus).

CORPUS STATISTICS AND DISCUSSION

Distribution of Artists in the Corpus

Table 3 lists the top 10 singers, composers, and lyricists represented in the 105-song corpus of Cantopop, showing the predominance of some singers and lyricists. For example, the two most represented singers in the corpus are Joey Yung (容祖兒) and Eason Chan (陳奕迅), together accounting for one fifth of the total song count. The two most represented lyricists—Lin Xi (林夕, also known as Albert Leung) and Wyman Wong (黃偉文)—have 34 and 28 works included in the corpus respectively, contributing more than half of the 105 songs. These patterns echo findings from historical studies of Cantopop, which have indicated that the singers and lyricists in question have enjoyed remarkable commercial success and exerted significant influence on the genre during the decades covered by this study (Chu, 2017, pp. 158–162; Chu & Leung, 2015, p. 15). Accordingly, unlike some other popular-music corpus studies (e.g., Shea et al., 2024), I allowed this apparent overrepresentation of certain artists. This composition of the corpus, albeit uneven, accurately represents trends in Cantopop—captured by and averaged across the song awards—during the two decades considered.

Patterns of Tone-Melody Correspondence: Directionality

Using commands from the Humdrum Toolkit (Huron, 2002), I extracted all bigrams from the corpus data, excluding those straddling a phrase boundary and focusing on the mapping locus for melismatic syllables. The 105 songs in the corpus yield a total of 31,482 bigrams. Figure 7 illustrates the distribution of bigram types, categorized by the type of contrapuntal motion between speech and song melodies. The data show that speech and song melodies proceed mostly in similar motion (83.44%). This observation corroborates previous findings on tone-melody correspondence in Cantopop (see Table 4), where similar motion emerges as the most common bigram type. At the same time, contrary motion between speech and song melodies accounts for less than 1% of all bigrams, demonstrating a strong avoidance of contrary motion in Cantopop text-setting. A chi-square analysis of the distribution shown in Figure 7 reveals a statistically significant association between the direction of speech melody and that of song melody (χ²₍₄₎ = 37,836.64, p < .001). The resulting Cramér’s V value of .78 indicates a strong correlation between the direction of the two melodies. These findings reinforce the argument that the text-setting constraint in Cantopop manifests through a strong preference for similar motion and a strong avoidance of contrary motion.

Figure 7. Distribution of bigram types (n = 31,482) in the Cantopop corpus.

Table 4. Proportion of contrapuntal motions reported in previous quantitative studies on Cantopop.

Additionally, the corpus data support Ladd’s (2022) argument for the need to differentiate between oblique I and oblique II motions—the former category denotes instances where the speech melody moves upward or downward while the song melody remains level, whereas the latter refers to the reverse. The corpus data show that oblique II motion is the second most common bigram type in the corpus (14.92%), whereas oblique I motion accounts for only 0.66% of all the bigrams, a proportion even lower than that of contrary-motion bigrams. These statistics on oblique bigrams carry two implications. First, oblique II motion functions as a commonplace alternative to similar motion in satisfying the text-setting constraint in Cantopop, a practice that is also observed in several other tone languages, such as Duna (Sollis, 2010), Kalam Kohistani (Baart, 2004), and Vietnamese (Kirby & Ladd, 2016). Second, the rarity of oblique I motion in my corpus data warrants a categorical distinction between the two types of oblique motion. Some prior studies on tone-melody correspondence have collapsed similar motion and both types of oblique motion into a collective category, sometimes called “non-opposing” or “non-contrary” motion (Ho, 2010; McPherson & Ryan, 2018; Schellenberg, 2012). However, my corpus data suggests that oblique I motion should not be grouped with similar or oblique II motions, supporting Ladd’s (2022) claim that “the category ‘oblique’ may be somewhat incoherent” (p. 146).[9] By revealing the rarity of oblique I motion and the prevalence of oblique II motion, the corpus data reinforce the importance of treating these two motion types as analytically distinct—an approach that future studies of tone-melody correspondence in Cantopop and other tone languages should adopt to improve descriptive precision.

Note. Chow’s table only lists ascending speech melodies (i.e., bigrams where the second syllable has a higher tonal target than the first). It omits the optimal mapping for descending speech melodies, assuming that optimal intervals for descending intervals would be the inverse of their ascending counterpart.

Table 5. Chow’s (2012) table of optimal pairing between speech melody and melodic interval sizes.

Patterns of Tone-Melody Correspondence: Interval Size

Although some studies have examined the relationship between tone-melody correspondence in Cantopop and the size of melodic intervals (Chow, 2012; Ho, 2010; C. W. Wong, 2020), they lack statistical support from a sizable and representative sample. Table 5 reproduces Chow’s (2012) catalog of “optimal mapping” (p. 60) between speech melodies and melodic interval sizes, which also covers pairings suggested by Ho (2010) and C. W. Wong (2020). In addition, results of K.-Y. Chan’s (2021) experiments suggest a list of “intelligible intervals” for all possible successions of tones (not reproduced here). Chan’s results indicate a more flexible mapping between speech melodies and melodic intervals than Chow’s. For example, while Chow identifies the ascending melodic intervals of 3, 5, or 8 semitones as “optimal” for bigrams with a T4–T3 speech melody, Chan’s findings show that this tone pattern remains intelligible also with the intervals of 6, 7, 10, 12, or 13 semitones.

In Tables 6–8, I report the corpus data on the most common melodic intervals for ascending, descending, and level speech melodies. These data reveal that K.-Y. Chan’s (2021) findings on intelligible intervals and Chow’s (2012) catalog of optimal pairings only partly describe text-setting practices in Cantopop; some intervals not identified as “intelligible” or “optimal” are nonetheless commonly observed in the corpus. For example, as shown in Table 6, the ascending minor second (+1 semitone) is the second most common melodic interval for T6–T1 bigrams and the third most common for T6–T2, outnumbering intervals deemed “optimal” or “intelligible.” However, neither of the earlier studies identifies the ascending minor second as a viable interval for these speech melodies. Similar discrepancies are observed in the corpus for bigram types T3–T2 and T6–T3, for which other melodic intervals occur more frequently than those reported in previous studies.

Table 6. Most common melodic intervals for ascending speech melodies.

In Table 7, I present the corpus data on bigrams with descending speech melodies, which also diverge from Chan’s and Chow’s findings. For instance, Chan reports the descending octave (‑12 semitones) as an intelligible melodic interval for all descending speech melodies starting from T1. However, my corpus data show that it is common only for T1–T4, but not T1–T3, T1–T5, and T1–T6. For speech melodies T3–T4 and T5–T4, both Chow and Chan report the descending minor sixth (-8 semitones) as a viable interval. Yet, this interval occurs less frequently in the corpus than some other intervals not identified by either author, including the ascending major second (+2 semitones). These instances of setting an ascending major second to T3–T4 and T5–T4 speech melodies are among the few types of contrary motion that occur in significant numbers in the corpus.

Table 7. Most common melodic intervals for descending speech melodies.

For level speech melodies, similar motion (a level melody set to the melodic interval of zero semitones, i.e., unison or repeated note) is indeed the most common occurrence in the corpus. Nonetheless, the melodic interval of two semitones (either ascending or descending) ranks as the second most common interval for all bigram types with level speech melodies. This observation offers new insights that are not revealed by Chan and Chow, whose studies have obscured the role of oblique motion in the text-setting for level speech melodies. Interestingly, level speech melodies with consecutive T1, T2, or T6 tend to feature a descending major second, whereas those with T3, T4, or T5 tend to feature an ascending major second. These patterns can help evaluate previous claims concerning the opposite directionalities of oblique II motion for different tones (Chow, 2012; Ho, 2010; Ladd, 2022; Lo, 2013).

Table 8. Most common melodic intervals for level speech melodies.

Patterns observed in the Cantopop corpus reveal that the mapping between linguistic tones and melodic intervals is more flexible than previously reported. Some interval settings deemed unintelligible in isolation occur frequently in practice. One possible reason for this discrepancy is that my analysis considers all bigrams within a phrase, whereas earlier studies focus primarily on bigrams within a syntactic/semantic unit. For instance, K.-Y. Chan (2021) uses only isolated two-syllable word compounds as stimuli in his experiment. As a result, my data include bigrams that cross syntactic boundaries, revealing patterns disregarded by previous studies. For example, as reported in Table 7, 9.94% of T3–T4 speech melodies are set to an ascending major second (+2 semitones) in contrary motion, which outnumbers the “intelligible” interval of a descending perfect fifth (-7 semitones). One such instance is shown in Figure 8, excerpted from the song “任我行 [The Wanderer]” (song ID: C1303). The bigram in question comprises the syllables “怕paa3” and “遙 jiu4,” set to F3–G3. The former syllable of the bigram constitutes the first verb complement in the sentence (“to fear”), whereas the latter is part of the second verb complement (“to gaze”). Previous studies treat such cases of contrary motion across syntactic boundaries as exceptions to the text-setting constraint (Ho, 2010; C. W. Wong, 2020). However, my corpus data suggest the contrary: Some of these so-called exceptions prove to be more prevalent than the presumed norms (e.g., the interval of a descending fifth for T3–T4). In other words, my findings from the Cantopop corpus offer evidence for recentering analytical attention on marginalized patterns and redefining the standard text-setting practice in Cantopop.

Figure 8. An excerpt from the third chorus of “任我行 [The Wanderer]” (song ID: C1303) showing a T3–T4 speech melody set to an ascending major second.

The more flexible mapping between speech melodies and interval sizes in the Cantopop corpus may also have arisen from the fact that—while tones do distinguish word meanings—Cantonese sentences often remain intelligible and unambiguous even without the correct tones, such as in monotone speech (H. Wang et al., 2011). Vowels and consonants of the words, as well as the semantic context, usually offer sufficient cues for understanding the sentence’s meaning. In other words, the text-setting constraint in Cantopop is an aesthetic preference—one that seeks a closer resemblance between speech and music—rather than a practical requirement for intelligibility, since a suboptimal match or mismatch between speech and song melodies does not necessarily lead to unintelligibility or confusion. Music in some other tone languages, such as Mandarin Chinese, does not exhibit a strong text-setting constraint, with speech and song melodies only loosely correlated and contrary-motion settings abounding (Kirby, 2022). More generally, the intelligibility of lyrics varies greatly across vocal genres along the speech-song continuum, in both tone and non-tone languages (Condit-Schultz & Huron, 2015; List, 1963; Schellenberg, 2012), and other aesthetic priorities may override the preference for intelligible text (Fine & Ginsborg, 2014). For example, in both Mandarin and Cantonese pop music, tone-melody correspondence is sometimes intentionally disregarded or violated for expressive purposes, while the text’s overall meaning remains intact (Liu et al., 2023; Mak, 2025). In sum, while my corpus data suggest a generally strong manifestation of the text-setting constraint in Cantopop, the tone-interval mappings reflect the flexible nature of tone-melody correspondence, whereby the intelligibility of lyrics constitutes but one of many aesthetic priorities.

CONCLUSION

While scholarly interest in Cantopop and its linguistic aspects has grown in recent years, key questions regarding this topic are yet to be answered in a quantitative way. This article introduces the first Cantopop corpus constructed with clearly defined criteria so that these research questions can be answered with evidence from a large and representative sample. Using the corpus data, I have reported findings regarding patterns of tone-melody correspondence in relation to the aspects of directionality and interval size. The dataset’s public availability in the Humdrum kern format ensures its adaptability and accessibility, allowing future research to utilize this dataset for expanding the research on Cantopop and the intercultural study of song melodies.

Data from this corpus may also be further analyzed in future studies to illuminate other aspects of tone-melody correspondence in Cantopop, such as the role of scale degrees.[10] Another example of a potential use of this corpus is the study of how different Cantopop lyricists set their lyrics differently, as the corpus includes a substantial amount of works by the two prominent lyricists Lin Xi and Wyman Wong (see Table 3). Beyond the study of tone-melody correspondence, my Cantopop corpus can also be a starting point for investigations related to other aspects of Cantopop, such as rhythmic features and formal design. Beyond musical inquiries, the corpus may be used to study the lyrical content of Cantopop, supplementing related studies on the linguistic and cultural aspects of the genre (Chu, 2019; So, 2025). The range of questions that can be answered with the support of the corpus is enormous, and the corpus data will constitute substantial quantitative evidence.

ACKNOWLEDGMENTS

I am deeply grateful to Leigh VanHandel and Hedy Law for their advice and inspiration throughout the development of this project. I would also like to thank Nicole Biamonte and Jonathan Wild for their suggestions in editing this manuscript. Special thanks go to Craig Sapp for his technical assistance with Humdrum and VHV. This article was copyedited by Jonathan Tang and layout-edited by Niels Chr. Hansen.

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