Balisage Paper: Musical Variants: Encoding, Analysis and Visualization

Introduction

The core tasks of a scholarly edition of music are the investigation, documentation, and explanation of the transmission of the work. In traditional textual criticism, this is done by examining all available sources, comparing the textual version(s) they contain, tracing the filiation of sources, selecting a main (or "base") source, and providing an edited text that resembles the main source as closely as is reasonably possible. The textual variation recorded in this process is traditionally documented in a separate list that identifies readings by movement, measure, and (sometimes) beat within the measure and voice. In contrast to traditional print publications, which restrict themselves to a single base text because of pragmatic and/or financial considerations, in the digital medium one may include all pertinent sources without regard to their relevance to filiation. In addition, the determination of a base source, and thus a listing of variants compared only to it, is not necessary. The edition can therefore document all readings, not just a single edited version of the text [Bohl et al. 2011]. In fact, it is now possible to provide all historically legitimate alternative versions of the text simultaneously.

Musical Variants

Based on earlier literature [Feder 1987], German musicologist Bernhard R. Appel proposed a systematic model for variants in his article Variatio delectat – Variatio perturbat [Appel 2005, pp. 7–24]. He identifies four main types of local variation between sources: additions (Ergänzung), deletions (Streichung), substitutions (Ersetzungen) and rearrangements (Umstellungen). An addition denotes the introduction of new material to the musical text, as compared with an older version (AB ⇒ AXB). In contrast, a deletion is characterized by leaving out parts of the text (ABC ⇒ AC). A variant where a portion of the musical text is replaced by another is identified as a substitution (ABC ⇒ AXC). In this case, the original portion and its replacement may differ in length. In the last species of variant, rearrangements, the musical text itself is not changed, but portions are reordered (ABC ⇒ ACB). With regard to their effect on the musical text, Appel points out that all variants can be assigned to one of these four types.

However, considering the fact that the actual filiation of sources is very often all but clear [Feder 1987, p. 64], additions and deletions may be consolidated into a larger category. That is, when it is not possible to establish the direction of dependency between two sources, the only possible observation in both cases is that one source holds text not present in the other. Therefore, considering both additions and deletions as the exchange of something with nothing, and thus special cases of substitution, the number of types may be reduced. A rearrangement may be thought of as two substitutions at different positions. What would be lost when taking this perspective, though, is the identity of the material omitted in one place and inserted at another, so that a rearrangement requires an additional pairing of two atomic substitutions. Therefore, the number of variant types may be reduced to only two—substitutions and rearrangements.

When comparing more than two sources, variants amongst them may also be classified by another taxonomy. German philology offers the terms Bindefehler and Trennfehler. A Bindefehler is a variant reading shared by two or more, but not all, sources. By sharing a particular variant, the sources are logically connected and therefore have a closer filial relationship than sources that do not share this material. A Trennfehler describes the opposite case. It denotes a variant that distinguishes two sources that have been subjected to either a substitution (in the broad sense mentioned above) or a rearrangement. A Trennfehler argues for a distant relationship between sources. A variant in the musical text transmitted in at least three sources is therefore always a Bindefehler for some of these sources, and a Trennfehler for others at the same time.^[1]

Textual variation may appear at various levels—from single notes with a different pitch to revised melody lines of almost any length and from the addition of measures and measure groups to the rearrangement of entire movements. It is also important to keep in mind that, while common music notation (CMN) features a very clear structure of measures and staves, the visual structure of music notation does not limit the musical content in any way and must not be confused with the semantics of the musical content. Composers and copyists alike have never restricted themselves to changes that do not cross this structure. When a melody line is replaced by another, changes to several measures may be required, without affecting the place of these measures in the context of the notation as a whole. Like the conventions of line, paragraph, and page breaks in literary text, the visual structures of CMN are simply conventions that facilitate reading and writing—no more, no less.

Encoding Variants in MEI

In the case of editorial markup, MEI implements the same concepts and mechanisms as TEI (Text Encoding Initiative). Those familiar with TEI can therefore safely assume the same concepts behind the elements of the same name in MEI. Thus, encoding variance in MEI is based on use of the <app> element, which is allowed at almost every level. It identifies a portion of the musical text that varies among different sources. Each distinct reading drawn from the available witnesses is held in a <rdg> element that identifies its source or sources using its @source attribute. This model matches the concept of Bindefehler and Trennfehler almost perfectly. For sources sharing a reading, an <app> element acts as a Bindefehler, while in the case of sources with different readings, it acts as a Trennfehler.

However, the <app> element is not capable of adequately dealing with all of the species of variance described earlier. MEI does offer a mechanism for additions, deletions, and substitutions; that is, <add>, <del> and <subst> elements. However, these elements are intended to describe scribal processes within a given witness, not variation across multiple sources. The more generic <app> element could be used, which is designated to describe variance of this kind as shown in the following encoding:

            <app>
	           <rdg xml:id="rdgA" source="#A"/>
	           <rdg xml:id="rdgB" source="#B">
		       <!-- additional content -->
	           </rdg>
            </app>
        

A complete example of an additional measure in source B including musical content might look like this:

            <section>
                <measure n="26">...</measure>
                <app>
                    <rdg xml:id="rdgA" source="#A"/>
                    <rdg xml:id="rdgB" source="#B">
                        <measure n="26b">
                            <staff>
                                <layer n="1">
                                    <note pname="c" oct="5" dur="4" dots="1"/>
                                    <note pname="b" oct="4" dur="8"/>
                                    <note pname="d" oct="5" dur="4"/>
                                    <rest dur="4"/>
                                </layer>
                            </staff>
                        </measure>
                    </rdg>
                </app>
                <measure n="27"/>
            </section>
        

This approach works for substitutions but it falls short on rearrangements. Here, it can only capture two seemingly separate operations (deletion and subsequent addition) in separate <app> elements. To circumvent this restriction, additional markup is necessary.

Because the identification of a rearrangement requires an additional step of interpretation, which may be made by the editor at any time in the editorial process, the encoding can begin with the use of two separate <app> elements, but allow for enrichment of the basic markup later. The simplest, and thus most useful, solution is to employ the @corresp attribute to cross-link the corresponding <rdg> elements:

            <app>
	           <rdg xml:id="oldPos" source="#A #B" corresp="#newPos">
	           <!-- content at old position -->
	           </rdg>
	           <rdg source="#C"/>
            </app>
            ...
            <app>
	           <rdg source="#A #B"/>
	           <rdg xml:id="newPos" source="#C" corresp="#oldPos">
	           <!-- content at new position -->
	           </rdg>
            </app>
            

Using these mechanisms clearly shows that the parallel segmentation method of <app> and <rdg> suffices to address musical variants occurring inside musical structures.

Example 1: Substitution over two measures

However, as mentioned earlier, substitutions (of melodies, for example) often ignore the structural features of music notation like measures and staves (see Example 1). In the given scenario, the musical notation, as encoded in MEI, requires splitting the description of variance into two separate <app> elements. This separation does not resemble a Befund, which obviously permits only one difference between the two sources. The fact that the change crosses the bar line results in a typical example of overlapping hierarchy issues confronted by any XML-based encoding system. For the encoding of the musical text, MEI is well prepared to handle such overlaps. For instance, slurs, one of the most common features of CMN that interfere with measure and staff structures, can be captured using various markup possibilities, including attribute-based milestone techniques and standoff markup.

For overlapping variants that interfere with the notational structure by crossing barlines, staves or similar boundaries, a mechanism like that proposed for rearrangements may be used. The difference here is that instead of relating the descendant <rdg> elements, the <app> elements themselves should be connected. Capturing cross references with @xml:id and @corresp attributes is less than ideal, however, as double-ended references can result in largely redundant pointers requiring careful maintenance. For example, consider that even a small change in a measure may affect a large number of staves.

A milestone approach, using elements such as TEI’s span elements (<addSpan>, <delSpan>, etc.) is of no help here, as CMN is a two-dimensional notation, making it impossible to describe an affected region of the text with just one start and one end point. Instead, a standoff approach allowing only single-direction pointers is more appropriate. The obvious solution would be to use the <annot> element (the MEI equivalent to TEI’s <note>), which offers a @plist (participant list) attribute. The <annot> element could be used to point to all related <app> elements, and its @type attribute could be used to identify its purpose. However, this solution also falls short with regard to explicitness. A standoff methodology explicitly identifying all relevant components is clearly the best strategy. But using generic <annot> elements, distinguished only by simple typing, for all these specific cases, overloads its semantics.

As an alternative, the authors propose adding specific grouping elements to MEI that identify isolated members of a feature group. In the case of multiple <app> elements, an <appGrp> element would be appropriate. The <appGrp> element could use its own @plist attribute to refer to a number of logically connected <app> elements that, taken together, represent a specific variant:

            <app xml:id="app1">
	           <rdg xml:id="rdgA1" source="#A"/>
	           <rdg xml:id="rdgB1" source="#B"/>
            </app>
            ...
            <app xml:id="app2">
	           <rdg xml:id="rdgA2" source="#A"/>
	           <rdg xml:id="rdgB2" source="#B"/>
            </app>
            ...
            <appGrp plist="#app1 #app2"/>
        

On a related topic, MEI currently lacks grouping mechanisms for the elements intended for capturing simple editorial changes, such as additions (<add>) and deletions (<del>). Like the variation in source material represented by <app>, these elements are also not bound to notational structures. They too require a grouping mechanism that helps encoders to overcome the hierarchical conflicts arising from a strict XML structure.

With the proposed models in place, it will be possible to encode all the types of variants identified by Appel and their scope. The intention is to allow representation of textual variation in stages or layers, from no interpretation to the capture of complex relationships, in way that permits the editor to make informed decisions about the filiation of the sources of the text.

Qualitative Analysis based on Encoding

The Functional Requirements for Bibliographical Records (FRBR) conceptual model was proposed by the International Federation of Library Associations and Institutions (IFLA) in 1998. It does not offer a ready-to-use data format, but rather generic concepts that help to create cataloging formats that address advanced user needs. As the FRBR terminology is also applicable to music philology, especially with regard to the filiation of sources, it has been adopted by MEI for its 2013 release.

FRBR is organized into three separate but related entity groups. Only the first group, which provides work, expression, manifestation and item entities, has been adopted by MEI so far. These four so-called Group 1 entities provide a clear terminology for dealing with the transmission of a work in manuscripts and prints alike. While a work entity represents only the conceptual idea of a musical piece, independent from the details of its composition, such as its instrumentation, an expression identifies a slightly less abstract entity that does include these details. In other words, it also denotes a specific version of the text, even though this requires a manifestation (MEI uses its pre-existing <source> element for this entity) for its materialization. An item is a distinct physical instantiation of a manifestation, for example, a copy of a certain print.

FRBR also allows specification of the relationships between the basic entities. In MEI, some of the hierarchical relations are implicitly encoded using inheritance (an expression for example is a child element of a work) while others, such as those between expressions and manifestations, are dealt with using pointers. This change in approach is necessitated by the many-to-many relationships that can exist between expressions and sources. For example, a single expression of a work may be transmitted by many sources or a single source may contain multiple expressions of one or more works. FRBR offers a number of relation types, which establish an entity-relationship-model for bibliographic and editorial needs. For example, an expression may be described as a translation or rearrangement of another and a print may be identified as a copy of a manuscript source. These relations, however, clearly denote the overall relation between two affected entities—they are not operating at the level of individual variants, but on the global level of complete objects.

We believe the recommended types for relationships identified and provided by FRBR are also useful to describe processes behind textual variation at more granular levels. For example, isSupplementOf may be used for additions, isAbridgementOf for deletions, isRevisionOf for substitions and isReconfigurationOf for rearrangements. Adding such relations to individual textual variants is required to give a better overview of the arguments for a specific filiation of sources. The suggested implementation mostly relies on existing MEI models. The only important change is to allow the @rel attribute, which is currently only available on the <relation> element to describe full-entity relations stored in the header, to be used on <rdg> elements. In this implementation, material added in a later and derived version of the text would be encoded so:

            <app>
	           <rdg xml:id="rdgA" source="#A"/>
	           <rdg xml:id="rdgB" source="#B" rel="isSupplementOf" target="#rdgA">
		       <!-- additional content -->
	           </rdg>
            </app>
        

The example shows how one reading is identified as an addition to another. The empty reading serves as a placeholder for the base text. By adding @cert and @evidence attributes to <rdg>, the editor may also state the reliability of his assessment. While at some point in the future it may be necessary to allow an alternate encoding method that employs dedicated elements in order to capture divergent interpretation from multiple editors, the simple approach described here will suffice.

The purpose of filiation is to identify the relations (and their directionalities) between sources and to create a stemma that illustrates these relations. The results may be expressed with FRBR, but they are based on the evaluation of individual variants as described above. This evaluation, stored in a FRBR-compliant way, can be used to provide a better overview of all arguments and to inform the editor's interpretation of the overall connection. It may also help to better explore the filiation of sources with multiple intermingled ancestors and other complex situations often overlooked in traditional filiation [Feder 1987]. However, a fully automated analysis of those variants seems impossible; simply quantifying the number of variants indicating a filiation from A to B vs. arguments for B to A is not particularly helpful, as some arguments are more convincing than others [Feder 1987, p. 58]. The swapping of two pitches has nearly no persuasiveness with regard to the derivation, whereas a missing note in a manuscript is an almost unquestionable argument that it was copied from the source to which it is compared. To make full use of the encoding, it is therefore important to assess the impact of a particular variant based on the content of the readings it holds. Following this reasoning, a variant holding an additional staff in one source and no corresponding material in another should be given more weight than a variant where the sources differ only on the pitch of a single note. Likewise, a variant affecting substantial information of the text is more compelling than a variation in the accidental layer of the text [Greg 1950]. Accurately judging the impact of a variant by an automated examination is clearly a large-scale project of its own, but it is fairly easy to get a first suggestion from less ambitious algorithms. When considering the fact that the final evaluation must be based on the editor's experience and judgment, it seems unnecessary to get a perfect analysis—it just needs to be good enough to be a helpful starting point. Under these circumstances, it seems logical not to hard-wire the weight given to each category of argument, but instead to let the editor balance them according to his expertise.

An automated analysis of the variation across multiple sources must start with a listing of all Trennfehler and Bindefehler for every combination of two sources. At this stage, the variants do not require further argumentation and stand on their own. An initial graph grouping the sources by their level of conformance with each other is already possible. However, in order to assess the edges of this graph, the content of these variants must be evaluated. Simple pitch changes (which may be nothing more than mere copying errors), will be treated differently than larger groups of non-corresponding measures. After measuring the strength of these arguments, the next step is to identify their directions. This process is also based on an evaluation of the content—is it more likely that the textual difference is a later addition to a formerly shorter text, or is it more likely that something has been canceled from a formerly richer text? Again, these arguments will differ in their persuasiveness, but here the situation is much better, as additional information can be used to inform the determination of direction. For example, if both sources can be precisely dated, the direction is already clear. Likewise, the identification of scribal hands may help to determine filiation when more information about the scribe, such as birth and death dates or work locations, is available.

Even when the general relationship between two sources seems to be clear, based on a number of arguments regarded as indisputable, it is important that all contradictory variants remain available to the editor, as they may hint at a possible contamination of sources. Accordingly, the graphical interface for this analysis needs to differentiate between parts of these sources and provide hints if there is a significant variation in the likely directionality of filiation amongst them. Very often, editors will be able to identify the filiation of sources very quickly. The purpose of an automated analysis like this is to ensure that editors do not overlook possible alternatives or mixed relationships, resulting in oversimplification of the filiations. Having the editor's judgment explicitly recorded in @rel attributes on <rdg> and a determination of a level of certainty for the assertion in @cert attributes, permits better decision-making, ultimately making the edition more transparent for the user.

Visualization and Analysis of Variants

As the purpose of the proposed encoding and analysis methodology is both to support the editor and to better illustrate the editorial process to the user, an adequate visualization is very important. Even though the encoding itself is designed to be as legible as possible, the vast amount of data requires provision of a condensed view—without which the resulting information would likely be unusable.

Following the order of steps given above, a first visualization will provide an overview of the variance of two or more sources under comparison.

Example 2: Visualization of Variance with a kind of piano roll notation

Example 3: Visualization of Variance in multiple voices

This visualization draws on the concept of piano roll notation (see Example 2 and Example 3), but compared to regular piano roll notation, it is scaled down to a barely legible size, similar to Edward Tufte's sparklines concept [Tufte 2008]. The idea is to provide an overview of large segments of the source. Every source is assigned a distinct color. Everything shown in black is shared amongst all sources, whereas the colored parts show the differences between them. Piano roll notation represents only the substantial parts of the score, ignoring accidental components like articulation, dynamics, etc. In a proper visualization, this kind of information is provided in a separate stream for every staff. This stream could also be reduced, showing only a dot for each accidental sign (not visible in the examples). Separation into multiple streams helps to distinguish the kind of variance even at this high-level overview stage. In the future, scaling may also be provided in this view, allowing the user to zoom into more and more detail, terminating in the actual notation. Until then, this visualization provides an excellent overview of the level of variance between the compared sources. It is also possible to highlight variants acting as Bindefehler between two sources by putting them on a differently colored background.^[2]

The next step is to make use of the FRBR-compatible classification of individual variants. This is possible by making the interface customizable, allowing the user to highlight specific types of variants. The project intends to provide yet another perspective on the data that resembles traditional stemmata more closely.

In the projected interface, there will be a stemma-like graph on the left side of the screen, paired with a list of all variants on the right side. These variants can be ordered by their type, ascribed FRBR-relations, the editor's certainty, the estimated relevance (following customizable categories), and the affected sources and their position in the document. Manipulating this list will influence the stemma on the left. If, for instance, the editor (or user) decides to focus on a single movement of the work, it will reflect only relations in that movement.

Conclusion

The system described in this paper can only operate on fully encoded sources. The Freischütz Digital project will provide data of the required verbosity for the first time. The amount of data contained in encodings of music notation is already large and providing the additional details described in this paper will increase their complexity even further. However, the end result of doing so—detailed insight into the transmission and transformation of musical works—is highly desirable. While it has not been possible before, by leveraging the potentials of both MEI and FRBR it is possible to create intuitive tools that permit the exploration and communication of relations among sources containing notated music.