In order to select a repertoire of established literature we drew upon recital programs from a database maintained by the Percussive Arts Society, compiling a list of solos written for the marimba (36) and xylophone (13) by 31 different composers. Analyzing the beginning and ending of each movement (i.e., structurally distinct sections) separately, our data included 152 examples (32 xylophone, 120 marimba). Rather than a fully randomized sample, this approach prioritized the most frequently performed pieces, reflecting the input of two musical groups—composers and performers. The resulting list of pieces represented some of the most commonly performed solos, and two of the paper's co-authors (myself and Kristopher Keeton) who are professional percussionists/educators had personally performed or taught over 70% of this repertoire.

Previous research has used modality as an a priori classifier (Huron, 2008; Turner and Huron, 2008; Ladinig and Huron, 2010) of emotion. Modality is a powerful cue for Western-acculturated listeners, with the major mode frequently regarded as “sounding happy” and the minor mode as “sounding sad.” Not only are major key melodies generally perceived as “more positive” by Western listeners (Gerardi and Gerken, 1995), minor key melodies tend to “sound happier” when altered to major (Gagnon and Peretz, 2003). Mode's importance has long been recognized (Hevner, 1935; Rigg, 1937), and often outweighs other cues such as pitch and timing (Eerola et al., 2013). This association is so pervasive that mode has even been used for psychological assessments of clinical deficits in music processing (Peretz et al., 1998), mood induction (Västfjäll, 2002; Houston and Haddock, 2007; Hunter et al., 2011), and assessing vision's influence on auditory judgments of interval affect (Thompson et al., 2008).

Admittedly, despite modality's power, its emotional control is not absolute. Much as master chefs mix ingredients to delight diners with desserts containing both salty and sweet components, composers can mix cues to provide nuance with respect to emotional messages (Hunter et al., 2008). Fast minor key themes such as the opening of Mozart's G minor Symphony (No. 40) do not strike most listeners as sad, as it moves quickly and uses relatively high pitches. However, these exceptions do not invalidate the broad recognition of modality's emotional power (Hevner, 1935; Rigg, 1937; Gerardi and Gerken, 1995; Gagnon and Peretz, 2003), reflecting the strong association between modality and emotion.

Previous explorations of musical corpora found mode a useful a priori classifier. For example, Huron (2008) compared the average pitch height for major and minor key themes (i.e., well known monophonic melodies without harmonic accompaniment), finding the major to be 1.1 semi-tones higher. Such comparisons have also shown major key pieces exhibit louder dynamic markings than minor (Turner and Huron, 2008; Ladinig and Huron, 2010). These comparisons of monophonic melodies (absent accompanying voices) and isolated dynamic markings provide a useful parallel to observations that happy speech is higher in pitch and louder than sad speech (Scherer, 2003). Yet they do not address the question raised by Martin's “sad banjo” sketch—how instrumental constraints on the use of pitch and timing shape compositional decisions.

Tabulating the relative proportion of modalities at the start and conclusion of our sample revealed that 60% of marimba pieces with clear tonal centers exhibited minor keys (Schutz et al., 2008). This provided a useful baseline for understanding composers' choices regarding modality when writing for a tuned, wood-bar percussion instrument offering a wide range of pitch heights and timings. In contrast, composers within this sample appear to avoid minor keys when writing for the xylophone, employing them in only 6% of the total analyzed repertoire (i.e., two compositions). See Figure 1 for a summary of these findings. As this sample included only pieces drawn from recital programs (rather than an exhaustive list), further research would help clarify questions about the repertoire as a whole. Nonetheless, this sample favored only those pieces favored by the performers themselves—reflecting the complex interaction between the choices of composers and performers in the evolution of an instrument's repertoire.

Both the percussionist-authors conducting that study immediately recognized that the only two examples of minor key xylophone pieces encountered shared something in common: they are rarely played on the xylophone. Subsequent inquiry with the percussionists listed in each surveyed program revealed that every performance had in fact occurred on the marimba. Performers offered straightforward explanations for their decisions such as “I personally don't like the sound of this piece on xylophone” (the piece in question is titled “Sonata for Xylophone”). When asked about “Fantasy on Japanese Woodprints”—a popular xylophone composition by Hovhaness (1965/1990) opening in minor—an accomplished percussionist replied “I've always thought this piece sounded better on marimba…in fact, I can't ever remember hearing a performance on the xylophone! I wish I had something more profound to tell you, but it's that simple” (Schutz et al., 2008). Personally, I found this unexpected outcome both intriguing and amusing. For despite many years of moving between the concert hall and research lab as a percussionist/researcher, I had never wondered why this xylophone repertoire seemed better suited for the marimba. This illustrates the symbiotic relationship between musical research and performance—performance related questions can lead to novel research discoveries, which can in turn inform both academic and artistic pursuits.

This survey of percussion repertoire is consistent with the idea that the xylophone's acoustic restrictions constrain its ability to convey sadness. Not only does this sample contain few instances of minor key pieces, performers demonstrate passive (albeit subliminal) resistance by regularly choosing to perform minor key xylophone solos on the marimba. The xylophone's pitch and timing constraints render it an inherently happy instrument. As illustrated by Steve Martin's performance and Willie Nelson's “You Just Can't Play a Sad Song on a Banjo” (Buskirk and Jackson, 1994), this challenge is not unique to the xylophone. The finding that composers shy away from using the minor modality when writing for instruments ill-suited to playing low and slow leads naturally to another question: Would composers also choose to write higher and faster passages when writing in major keys vs. minor keys?

Our first challenge came in identifying repertoire with equal numbers of major and minor key pieces. We initially hoped to use sets of well-known themes, either from catalogs such as Barlow and Morgenstern (1983), symphonic themes from particular composer(s), or a fixed set of pieces (e.g., Haydn string quartets). However, balancing modality in those contexts quickly proved intractable, as Western music is overwhelmingly major. For example, only two of Mozart's 40+ symphonies are minor (Tan et al., 2010, p. 251), as are only 10 of Haydn's 100+ symphonies (Smith, 2002, p. 29). This same major-bias can be found in rock music (Temperley and de Clercq, 2013) as well as jazz¹. Because modality plays a crucial role in emotional communication within music (Hevner, 1935; Gerardi and Gerken, 1995; Gagnon and Peretz, 2003; Eerola and Vuoskoski, 2013), this imbalance poses significant challenges to undertaking corpus analyses of natural music paralleling those of natural speech (Banse and Scherer, 1996; Sobin and Alpert, 1999). Fortunately, Johann Sebastian Bach (1685–1750) inadvertently provided a beautiful solution to this vexing problem—albeit in response to a different challenge.

Prior to Bach, Western instruments commonly used “just intonation”—a tuning system with roots extending back to ancient Greece (Wild and Schubert, 2008). Just intonation offers the most pleasing tuning of certain intervals; however, it is highly restrictive with respect to modulation (i.e., movement between keys). Although singers, violinists, and wind players can dynamically adjust tunings to alter problematic intervals, fixed pitch instruments such as the harpsichord and organ lack this capability. Just intonation limits fixed pitch instruments' ability to modulate, constraining composers' creative options. The “well tempered” approach gaining popularity during Bach's time loosened this constraint, affording new musical possibilities for fixed pitch instruments.

In order to take advantage of the compositional flexibility afforded by well temperament, Bach wrote 24 preludes and 24 fugues balanced in both musical key and musical mode². Studied and performed widely by musicians ever since, this landmark collection of pieces inspired musical successors such as Frederic Chopin (1810–1849), whose 24 Preludes use a similar organizational approach. We analyzed both sets to gain a broader and more generalized perspective, contributing to a growing body of research documenting systematic differences in low-level cues across musical eras and between geographic regions (Daniele and Patel, 2013, 2015).

This corpus analysis of modality-balanced music widely recognized for its artistic and pedagogical value provides a useful counterpart to existing corpus analyses of natural speech. For although such analyses have proven insightful in linguistics (Banse and Scherer, 1996; Sobin and Alpert, 1999), efforts to conduct parallel musical corpus analyses have been complicated by two factors. First, although many adults are capable of generating sentences with different emotional connotations, few are capable of generating similarly effective musical passages. Second, those able to create effective musical compositions have historically chosen a disproportionate focus on major vs. minor keys. As modality plays a powerful role in conveying emotion, this imbalance across a range of musical styles presents significant challenges for identifying proper musical corpora (speech does not use modality, freeing linguists from this problematic challenge). Therefore, analysis of two 24 piece sets by renowned composers working in distinct musical eras offers a robust exploration of cues used for emotion in music, providing a useful musical counterpart to previous corpus analyses of speech.

Music for keyboard instruments³ such as the piano, harpsichord, or clavichord is ideally suited for our score-based corpus analysis. In contrast to the banjo and xylophone, the piano offers a wide range of pitches, giving composers numerous melodic and harmonic options—all of which can be precisely notated. Similarly, the instrument's range of note lengths affords fast-moving gestures as well as slow, evocative passages. Timing on such instruments is similarly amenable to precise quantification. In contrast to this wide range of pitch and timing possibilities, keyboard instruments are relatively constrained with respect to timbre variations for individual notes—at least relative to wind and string instruments. For example, Hugo Cole noted that “the timbre of a single oboe note may be varied in 98 ways by the use of different fingerings and methods of blowing” when discussing the challenges of notation (Cole, 1974, p. 128). These myriad timbral nuances are both difficult to discern from a notated musical score and variable between performers. As keyboard instruments produce sound from hammers striking (or plucking) strings whose movement trajectories are not readily altered, their timbre is less easily varied. Consequently keyboard literature is ideally suited for score-based corpus analyses as difficult-to-notate cues such as timbre are relatively constant, while composers have great latitude in selecting pitches and timings—cues that can be precisely notated.

Although quantifying pitch and timing in complex polyphonic music presents challenges, it offers four important benefits. First, musical scores clearly distinguish intention independent of production (which in speech might be influenced by other factors such as physiological constraints). Second, musical instruments' wide range of affordances provides a useful extension of speech utterances constrained by the vocal tract's physiology. Third, the notation of information from time periods prior to the advent of recording technology offers the possibility of exploring changes in cue use over centuries predating recorded sound. Finally, the structural approach of using all 24 keys within a single set of pieces offers a rare opportunity to explore the “top down” effects of modality. Bach and Chopin set out with the a priori intention to write a set of pieces balanced in modality—selecting pitch and timing cues fitting within each piece's pre-defined mode. Consequently, these sets offer a rare glimpse into how modality restrictions affect composers' selections of pitches and rhythms, complementing the first experiment examining how restrictions in pitches and rhythms shaped composers' selections of modality (Schutz et al., 2008). Basing this exploration on natural music means its outcomes will offer a useful counterpart to previous explorations of emotional cues in natural speech (Banse and Scherer, 1996; Sobin and Alpert, 1999).

Our approach established the “center of gravity” of pitch height in each measure by weighting the pitch height of each note in accordance with its duration. Faithfully reflecting the nuances so important to these compositions led to challenges regarding treatment of grace notes, ornaments, double stemmed notes, and other such details common in music composed for artistic fulfillment, rather than scientific study. Although the proper way of treating such cases might garner some debate, they appeared in similar proportions amongst major and minor key pieces. Therefore, different decisions on their treatment did not affect the relative differences between major and minor pieces crucial to our analysis (further details can be found in Poon and Schutz, 2015).

We operationalized timing using attack rate—essentially the number of notes per second⁴—which offers several advantages over tempo. Primarily, it more closely parallels speech researchers' use of articulation rate, which is generally measured in the number of attacks⁵ per second (Johnstone and Scherer, 2000; Scherer, 2003). Occasionally called attack density (Pigeon and Verlinde, 2009; Mailman, 2012) or event density (Madison et al., 2011; Schaefer et al., 2011), this measure differentiates between passages with different rhythms played at identical tempi. For example, although the assessed segment of Bach's F# minor Prelude (No. 14) is marked at the same tempo of ♩ = 108 as the Ab Major Prelude (No. 17), its attack rate is considerably faster due to its denser rhythmic structure. However, despite a tempo marking of 108, its attack rate is considerably slower than Bach's Bb Major Prelude (No. 21), with a tempo of ♩ = 76.

We counted the number of note attacks per measure, treating simultaneous onsets such as chords as a single attack. We considered ornamentations to “decorate” individual notes, and did not alter the attack rate of measures with trills from the literal note durations specified in the score (although we counted grace notes marked explicitly). Using the tempo markings provided by Hans Bischoff Bach (1883), we then translated our tabulation of note-attacks-per-measure into note-attacks-per-second, allowing for differentiation between attack rate and tempo.

Bach did not give explicit tempi because the metronome did not achieve widespread use until after his death (Samama, 2016, p. 61). Therefore, our timing analysis used tempi suggestions provided by the respected editor and interpreter Hans Bischoff (Bach, 1883). As scholars often disagree about the correct tempi for these pieces, we assessed the stability of our findings using renowned musicologist Willard Palmer's (Bach, 2004) helpful table of seven different sets of tempi. Re-running our analysis, we found major pieces faster than minor in each of these seven cases (Figure 4). Therefore, we conclude that within this corpus Bach's major key pieces are faster than minor—regardless of which set of editorial tempi are consulted. As Palmer's data provide useful insight into an issue of broad relevance, we have created an interactive online tool for researchers, pianists, and music lovers to explore this landmark composition at www.maplelab.net/bachtempi.

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.