AS multiple authors have pointed out, many of the exciting early advances in computational musicology have been built on the foundation of a few important but stylistically limited corpora (London, 2022; Savage, 2022; London, 2013). While the number of new corpora coming online has dramatically increased recently, several of these new datasets extend the focus on common-practice tonal music (e.g., Neuwirth et al., 2018; Devaney et al., 2015) while several others focus on broadening corpora to include popular music (e.g., de Clercq, 2022; Moss et al., 2020). One important stylistic era that is still lacking in deep representation is the overlapping periods of late Romanticism and early post-tonality, approximately 1880–1920. The music of this era is both disparate and complex, often comprising blends of tonal and post-tonal harmonies and using methods of rhythmic and metric organization that are idiosyncratic to individual composers (Cohn, 2012; Samson, 1977). Nevertheless, this era continues the longstanding tradition of Western musical notation, making its music a natural candidate for inclusion into use for symbolic music corpora.

This article presents a new corpus that intends to fill this gap. The Mysterium corpus comprises the entirety of the solo piano music of Alexander Scriabin. It comprises 207 pieces composed from 1885–1914 and, apart from a few symphonic pieces and some juvenilia, comprises almost all of Scriabin's music. The name Mysterium comes from a large-scale, multi-sensory composition that Scriabin left unfinished upon his death, and alludes to the mystical qualities that people often associate with the enigmatic composer and his late music. The Mysterium corpus is one component of a larger research project, presented as a Master's thesis, An Inner Metric Analysis of Meter in the Music of Alexander Scriabin (Bell, 2022).

ENCODING PROCESS

Despite Scriabin's use of largely conventional musical notation, the process of encoding his solo piano music into a digital symbolic representation is not straightforward. For this project, we elected to encode the dataset in Humdrum's kern representation (Huron, 2002) due to the flexibility of its representation to overcome certain challenges within the corpus and the availability of analytical programs. The dataset is available at the following GitHub repository: https://github.com/bel28kent/Mysterium.

There were two inclusion criteria for the Mysterium corpus: (1) the piece must have had an opus number and have been published during Scriabin's lifetime, and (2) Scriabin must have composed the piece for solo piano. As a result of (1), juvenilia, sketches, and unfinished pieces are not present in the corpus. As a result of (2), there are a handful of symphonic pieces that are absent from the corpus. Specifically missing are the five symphonies (Opp. 26, 29, 43, 54, 60), the piano concerto (Op. 20), and the orchestral prelude Rêverie (Op. 24). Despite these missing works, the Mysterium corpus almost fully captures the composer's output in a single dataset, given Scriabin's status as primarily a virtuoso pianist-composer in the same vein as Chopin.

Scriabin's published output is listed as Opp. 1–74. (Note that Scriabin did not publish with the opus numbers 50 or 55.) Several of these works are multi-movement piano sonatas or collections of individual pieces, such as Prelude sets or Mazurka sets, resulting in a total of 207 individual works, movements, or pieces within larger sets. Works were encoded in random order to prevent introducing systematic errors into the corpus. The 207 pieces were randomized using random.org (Haahr, 2022), and encoded in that order.

Before encoding the music, high-quality editions were identified. The Petrucci Music Library (IMSLP) provides a convenient repository for various editions of Scriabin's output. However, there are sometimes editorial differences between different publishers, and these differences can have a significant impact on the music. Generally—based on our informal assessment—first editions by Scriabin's publishers P. Jurgenson and Mitrofan Belaieff were plagued with various printing and editing typos, including missing accidentals, ties, dots, and other minor issues. This is anecdotally supported by an examination of errata listed in the beginnings of scores reprinted by P. Jurgenson (see Yekimovsky, 1997). When possible, works were taken instead from Günter Philipp's Ausgewählte Klavierwerke, assembled between (1967–1972). Not only were these the most recent editions available on IMSLP, but they were more reliable than older editions. When IMSLP did not provide Philipp's edition for a piece, the edition by Igumnov and Milstein (1948) was used, also because this edition was more reliable than earlier options. When IMSLP provided neither of these editions, whatever available score was encoded. This was rare, but when it happened first editions were typically the only editions available. Table 1 below lists frequency distributions for each of the most recent editions of Scriabin's works available on IMSLP.

Table 1. Frequency distributions of most recent editions of Scriabin's works available on IMSLP.

Edition	Number of opuses available for	Percentage of opuses available for
GP	39	60%
IM	15	23%
MB	5	8%
PJ	4	6%
OM	2	3%
Total:	65	100%

Encoding took place in four folds. First, notes and rhythms were entered into the notation software Finale (version 26.1.643). A second pass by the same encoder involved direct comparisons between the Finale score and the published PDF, checking for accuracy and fixing any found errors. Once checked, the score was exported to a MusicXML file and converted to kern using the musicxml2hum tool (Sapp, 2017b). As a last check, the kern file was imported into Verovio Humdrum Viewer (VHV; Sapp, 2017a) and comparisons between the kern file and the rendered score were examined for any conversion errors. If an error was found, the kern file was updated in VHV and then exported as a new kern file. Rarely, the musicxml2hum tool threw a segmentation fault error when used; when this happened, the MusicXML file was imported directly into VHV and then exported using the "Convert to Humdrum" option.

The process of encoding revealed some features of Scriabin's music, especially in regard to his use of rhythm and meter, that were either necessary or more efficient to encode directly into kern. For example, the Finale tremolo tool only encodes the pitch at the notated rhythmic value instead of dividing that value into the sounded rhythm, which is necessary for kern logic. (For example, two quarter notes with three tremolo marks between them signifies a heard thirty-second note alternation between the two notes. The actual thirty-second-note rhythm is requisite in kern.) Complex tuplets (especially when on one staff with other voices) and beaming across the bar are not necessary to encode in kern, but it is much easier to do so. While Finale is very powerful, the software does not automatically format the score in a way that engenders fast editing and error-checking. Complex tuplets and cross-bar beams are particularly messy in Finale. In less time than it takes to manually adjust the Finale score, the same information can be manually encoded directly into kern.

Other features of Scriabin's music require changes when being converted from the score to kern. Some of these changes are small. For instance, a note must be added to a voice in kern when, on the score, a tie is drawn between two noteheads in different voices. See Figure 1 for a simple example of this.

Some changes, however, are more substantive. The primary notation on Scriabin's scores that is problematic in kern is his use of two simultaneous time signatures. In one instance, Scriabin notated time signatures with measures that do not align in a 1:1 ratio. (Sonata No. 6, Op. 62, mm. 330–334 and 365–369; Scriabin notates two 2/8 measures per one 3/8 measure.) In most instances, though, when Scriabin used two competing time signatures, one bar line was drawn through the grand staff, suggesting that each measure lasts for the same duration, and therefore that the two measures are proportionately related. In all such instances, the proportions aligned with 3:2 cross-rhythms. There are no problems in kern when two time signatures' total rhythmic values are equivalent (e.g., 3/4 and 6/8), but when a measure uses two time signatures whose values are not equivalent the score will not render in VHV, as a reflection of the conflicting logic in kern.

There were no "one-size-fits-all" solutions to this type of problem, and so the musical context of each excerpt called for different solutions. Consider, for example, Scriabin's Sonata No. 10, Op. 70, shown in Figure 2. In this excerpt, Scriabin originally chose to simultaneously use 2/4 and 3/8 in mm. 21–22 (Figure 2a). Using these meters, it is necessary to consider the rhythmic values proportionally rather than in relative terms. Since the bar line is drawn through both staves, each 2/4 and 3/8 measure must last for the same length of time. We assign each measure a value of 1, and then work out the proportions to find a 3:2 cross-rhythm between the soprano and tenor voices, indicated by the dashed lines showing the alignment between the two voices. Unfortunately, the original notation is not compatible with the computational approach taken by the kern format. Therefore, in (2b), we have re-notated this polyrhythm in 6/8 (for 2/4) and 3/4 (for 3/8), a notation that both works in kern and is used by Scriabin himself in other works. This notation preserves the duple meter of the right hand and the triple meter of the left hand, but represents the compound subdivisions of the right hand as natural rather than borrowed subdivisions. For detailed notes about every modification made to Scriabin's original notation, along with a rationale, consult the README.md file included on the GitHub repository: https://github.com/bel28kent/Mysterium.

To assist in computational studies, each kern file in the Mysterium corpus includes metadata in the form of standard Humdrum reference records at the beginning, including: composer (!!!COM), title (!!!OTL), title of parent work (!!!OPR), opus number (!!!OPS), work number (!!!ONM), date of composition (!!!ODT), and genre (!!!AGN). See Figure 3 for a representative example of reference records.

Eleven pieces included in the corpus were already encoded and publicly available on the website of the Center for Computer Assisted Research in the Humanities (KernScores, n.d.). Nevertheless, reference records were added to these pre-existing files, consistent with the style for the corpus. We sourced all dates given in the !!!ODT reference records from Schloezer's (1987) memoir of Scriabin, which includes dates for each composition. At the end of each file, reference records are included regarding the encoder and encoding date (!!!ENC and !!!END, respectively) as well as the editor and edition title (!!!PED and !!!PTL, respectively). Additionally, a directory is included in the GitHub repository (called reference_editions) that contains PDF copies of all editions used for encoding.

For genre, we distinguished between "sonata movement" and "sonata" to reflect, respectively, whether a work is one movement of a larger composition (as is the case with the first four sonatas) or is a single-movement work (as is the case with the last six sonatas). We have treated each sonata movement separately in this corpus, meaning that the first and third sonatas each contributed four movements to the "sonata movement" category and the second and fourth sonatas each contributed two movements.

All key signatures notated in the score were encoded as interpretation records in the kern files, notated using the Humdrum standard *k[], with sharped or flatted notes added within brackets in the order of appearance. This information was consistent with that which appeared in most printed editions. Notated key signature changes were added into the kern file at the proper location.

Somewhat more controversially, we elected to encode key interpretations for only the first key in each work. These keys were assigned by the lead author in the process of encoding through careful observation of the score. These key labels were then matched with key designations provided within the Naxos Music Library database. For example, the Four Preludes, Op. 33 were listed as being in the keys of E major, F-sharp major, C major, and A-flat major, respectively, for the Naxos album Scriabin, Preludes, Vol. 2, with Evgeny Zarafiants as pianist (2000). If the key assigned by the encoder did not match the Naxos album key assignment, then the encoder re-examined the score and confirmed the Naxos album's designation. Key designations were provided for works until around Op. 53, after which Scriabin moved away from a clearly tonal language. For later pieces beyond Op. 53, key designations become increasingly rare. This is because Scriabin's later music progressively embraces an atonal language, and the absence of accidentals reflects no key, not C major or A minor.

DESCRIPTIVE STATISTICS

The main contribution of this article is the encoding of the Mysterium corpus and public access being made available to interested researchers. However, it is also appropriate to offer discussion of some of the basic musical features of the corpus. The following sections provide descriptive statistics regarding the contents of the corpus and include genre distributions, features of Scriabin's meter, and elements of harmony. Below, we outline population distributions, but we also further explore the ways in which Scriabin's music evolved over time.

James Baker (1986) divided Scriabin's compositional output into three periods: tonal (1885–1903), transitional (1903–1913), and atonal (1913–1915). To some extent, any boundaries between periods are by nature arbitrary. Regardless, there are marked shifts in Scriabin's style throughout his career, and there are benefits to observing how his compositional choices evolved in different eras. Though Scriabin's music developed continuously over his career, there are still strong associations between compositional choices and other elements of his philosophy and aesthetics at specific points in his output. For a more comprehensive discussion of the relationship between Scriabin's philosophical ideas and their significance on his music, see Smith (2013). In keeping with the spirit of Baker's designations, we decided to also examine differences between Scriabin's periods, keeping Baker's main temporal cutoffs as approximate boundaries. However, to keep the compositional periods discrete, the year boundaries have been modified: tonal (1885–1902), transitional (1903–1912), and atonal (1913–1915). For a further discussion of the logic underlying period boundaries, see Bell (2022, 12–14). The tonal period, which is marked by highly chromatic and polyrhythmic late Romantic pieces, starts with his earliest pieces in the 1880s and ends with the Fantasie in B minor, Op. 28 in 1902. The transitional period begins with the Sonata No. 4, Op. 30 and ends with Sonata No. 9, Op. 68, a period in which Scriabin increasingly combines tonal harmony with dissonant octatonic and whole-tone collections. The final period, consisting of only his last two years, comprises works from the Deux Poèmes, Op. 69 to the Five Preludes, Op. 74, works that truly lack any pitch center. Pieces in the Mysterium corpus from the transitional and atonal periods abound with quartal harmony, aligning with Scriabin's progressive abandonment of tertian harmony. The music of these last two periods also increasingly involves complex rhythmic and metric constructs including polyrhythm, mixed meter, notation using smaller rhythmic values, and the simultaneous use of different time signatures.

FUTURE RESEARCH

The Mysterium corpus is a rich source of data for research into advanced rhythmic and metric phenomena and difficult tonal and atonal music, as well as music that does not obviously belong to one or the other of those two categories. It is a source of piano music, Russian music, and is a single body of repertoire that spans both common practice tonality and early post-tonality, as well as the transition between those periods. Possible applications of the corpus are boundless (though some specific pointers in the direction of metric analysis are given in the fifth chapter of Bell (2022)). Regarding the Mysterium corpus itself, plans for future work on the corpus are twofold. The first plan is to complete the encodings that already exist by adding the musical information not already encoded—tempo markings, dynamics, articulations, etc. The second plan is to complete the corpus by expanding it to include all of Scriabin published compositions, that is, to encode the symphonies, piano concerto, and Rêverie.

ACCESSING THE CORPUS

The Mysterium corpus is available at the following GitHub repository: https://github.com/bel28kent/Mysterium. We grouped the kern files into directories by opus number. The CCARH files are in a directory labeled ccarh_kern. We have also included a README.md file that lists changes made from Scriabin's original notation; it is highly recommended that this documentation be consulted before using the kern files.