Music Theory Ontology
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Running Head: MUSIC THEORY ONTOLOGY
Formal Ontology of Music Theory and Music Information Artifacts:
Response to The OMRAS2 Chord Ontology†
Jordan Michael Feenstra
National Center for Ontological Research,
State University of New York at Buffalo
Correspondence concerning this article should be addressed to Jordan Feenstra or Yonatan
Schreiber, Department of Philosophy, 135 Park Hall, College of Arts and Sciences, State University
of New York at Buffalo, Buffalo, NY 14260-4150. Electronic mail may be sent via Internet to
jmfeenst@buffalo.edu or yonatans@buffalo.edu.
† Sutton, Christopher, et al. (2007)
Music Theory Ontology
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Abstract
We address aspects of the OMRAS2 Chord Ontology (Sutton, Raimond, and Mauch, 2007). A larger
objective, beyond intentions "to provide a common, versatile vocabulary for describing chords and
chord sequences in RDF," is defined. We provide an alternative ontology, which is a direct response
to the "several issues which must be addressed". We discuss the motivation for a broad formal
ontology of music theory and music information artifacts, and the benefits of building such an
ontology from the Basic Formal Ontology. The resulting ontology shows candidacy for an application (as opposed to merely a reference) ontology.
Music Theory Ontology
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Formal Ontology of Music Theory and Music Information Artifacts:
Response to The OMRAS2 Chord Ontology
In this paper, we address many aspects of the OMRAS2 Chord Ontology (Sutton, Raimond, and
Mauch, 2007). Beyond the intention "to provide a common, versatile vocabulary for describing
chords and chord sequences in RDF,"1 the Chord Ontology falls short of our larger objective, the
scope of which is briefly defined herein. Accordingly, we provide an alternative ontology, which
should be taken as a direct response to the "several issues which must be addressed in future
versions of the" 2 Chord Ontology. Additionally, we discuss the motivation for a broad formal
ontology of music theory and music information artifacts (e.g., Pitch, Tone, and ChordEvent, and
MusicNote, MusicNoteModifier, and Orchestra, i.o.), and the benefits of building such an ontology
from an upper level ontology, such as BFO2.0. The definitive difference of the resulting ontology is
its candidacy for use as an application ontology—as opposed to merely a reference ontology.
I. Introduction
In terms of use, there are two types of ontologies—reference and application. Although not
mutually exclusive, the former is typically limited in its static nature, while the latter is distinguished
by its ability to subsume values and individual instances of its classes and provide an overarching
architecture for its outputs. For example, while some upper level ontologies are capable of the latter,
they may be defined in terms of their general use cases; that is, many ontologists and database
engineers and specialists, for example, use the Basic Formal Ontology (BFO) 3 as a reference
ontology for structuring and building their ontologies, of which are typically application ontologies.
Identifying the intentions of the relevant ontologist(s) is another, and related, means of
categorizing an ontology, whereby, in terms of its structure, there is a noticeable difference in
whether the ontology was built from the "top-down" or "bottom-up". Regarding the above
1
http://motools.sourceforge.net/chord_draft_1/chord.html#introduction
Ibid.
3
cf. figure 1 - BFO 2.0 class hierarchy view
2
Music Theory Ontology
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reference/application distinction, a top-down approach is that which can be seen to be built with
some sort of upper-level notion(s) in mind such that the resulting hierarchy is noticeably structured
from class-to-subclass which results in the identification of instances, whereas a bottom-up
approach can be seen to be built by noticeable identification of some number of instances in some
particular domain which results in the identification of subclasses-to-classes. Similarly, these two
approaches are also not mutually exclusive; and, like reference ontologies, the top-down approach
tends to be the method used by philosophically oriented ontologists whereas the bottom-up
approach tends to be the method used by relevant domain experts. Consider an ontology of
furniture, for example. The ontologist might start by gathering a taxonomy of furniture and furniture
related terms and concepts and placing items of the taxonomy into an upper-level structure which
already has classes that will distinguish, say, furniture use as opposed to furniture material, whereas as,
say, an interior decorator might start by clustering instances of furniture based on which type of
setting it is typically in, its typical construction materials, etc., and thereby coming to distinguish an
upper-level structure.
Accordingly, we exploited a two-fold opportunity; being both philosophers and musicians,
we sought to both apply and expand both our knowledge of traditional Western diatonic music
theory and the philosophical and scientific aspects of ontology—moving from both "bottom" and
"top" to meet in the middle on both issues.
After choosing a domain, the second step in ontological engineering is to research existing
ontologies (if any) thereof, create an exhaustive taxonomy of the domain (by consulting relevant
texts or domain experts), and create a rough hierarchy estimating the general class-subclass structure.
As far as we know, there is only one relevant project (i.e., the OMRAS2 Chord Ontology, Music
Ontology, and Audio Features Ontology) that existed at the beginning of our research, and, to date,
our ontology—the Music Theory Ontology (MTO)—is the only additional formal ontology of
concepts relevant to music theory and music related concepts.
Music Theory Ontology
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The Chord Ontology is described as a first draft, with the motivation being "to provide a
common, versatile vocabulary for describing chords and chord sequences in RDF."4 It is part of a
larger project called OMRAS2, which—supplemented by the Music Ontology and Audio Features
Ontology, and Time Line, Event, and Vamp Plug-in (upper-level) ontologies—has the goal of
"linking a wide range [of] music-related information" by constructing "three levels of expressiveness—from the simplest . . . [to] most complex", supplemented by a structured vocabulary for
expressing 1) "editorial information (tracks, artists, releases, etc.)," 2) "music creation workflow (composition, arrangement, performance, recording, etc.)," and 3) "complex event decomposition, to express, for example, what happened during a particular performance, . . . the melody line of a particular work, etc."5
We provide a single, rigid, interoperable ontology that provides the structure needed to eventually
combine all three goals. However, we primarily focus on developing a completely human readable
and domain interoperable ontology of music theory and related terms and properties that is both an
exhaustively queryable educational reference tool as well as a rough estimation toward an application-ready source structure.
Figure 1: BFO 2.0
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5
Ibid.
http://www.omras2.org/MusicOntology
Music Theory Ontology
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II. Scope and Problems6
II.1. The Music Ontology
The Music Ontology largely corresponds to (1). Noted to be used by over 14 billion RDF triples, it
clearly merits much respect. However, what it lacks in terms of our goal of specifically representing
music theory in addition to music information artifacts is, plainly, music theory. In its favor, it has the
transparency of being completely human-readable (i.e., a novice to the domain may clearly understand the terms inherent in the hierarchy).
II.2. The Audio Features Ontology7
The Audio Features Ontology largely corresponds to (2). We saw many problems with its structure
in terms of interoperability with an upper-level ontology and other ontologies. For example, the
class "Interval" is encountered in the Chord-, Time Line-, Event-, and Audio Features Ontology.
While it clearly must have a separate URI for each ontology, firstly, it most noticeably lacks human
readability in terms of the possibility to result in confusion, and, secondly, it will face problems if
and when each or any of these four ontologies are merged. Thirdly, its structure heavily relies on the
Time Line Ontology and Event Ontology, which are both suspect in terms of lacking rigid axioms
and clear definitions. This is important as regards not just human readability but specifically
computer readability; that is, while it is clear that these underlying structures, or "upper-level"
ontologies, are used specifically for the Audio Features Ontology, they nonetheless present challenges to at least one tenant of the core methodology of ontology—reusability, the ability for a specific
ontology or specific terms and properties therein to be reused in future research in distal domains.
It is here we stress the invaluable resources afforded by BFO or BFO 2.0. Not only does
BFO provide the most basic components for eventually realizing a complete four-dimensional
ontology (which includes, among other things, "a non-extensional temporal mereology with
collections, sums, and universals"—the primitive relations and properties sufficient for completing
6
7
Space limits the depth to which we elaborate our criticisms, but hopefully such is intuitable from our .owl file.
A detailed assessment of the Time Line Ontology and Event Ontology is forthcoming, available May, 2014.
Music Theory Ontology
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an exhaustive ontology for the notions found in the Time Line and Event ontology), but it does so
in a way that is rigorously axiomatized and formalized (using such tools as Isabelle).8
II.3. The Chord Ontology
The Chord Ontology largely corresponds to (3). Since our primary objective, before encountering
OMRAS2, was to represent the fundamental structure of musical harmony and melody by way of
traditional Western music theory, the largest impetus for "starting from scratch" on such an
ontology came by way of our disappointment with the Chord Ontology . Our criticisms here are
largely able to be categorized into four groups: human readability, philosophical and ontological,
music theoretical, and scope.
Concerning scope, the name and aforementioned definition of the Chord Ontology
suggested to us that we might simply expand upon it to include what we desired. However, it is
counterproductive to expanding an ontology if its classes and properties are defined in such a way as
to be vague or ambiguous. For instance, nowhere in the ontology does it actually define what a chord
is. The suggestion of <rdfs:comment>Two or more notes played together</rdfs:comment>, lead us to our largest group of criticisms in terms of music theory,
human readability, and ontology. To give a general structure of our methodology and breadth of
criticisms, while trying remain succinct, we dissect this but only this description.
Firstly, a note can neither be played nor heard; a note can only be seen. A note is a MusicSymbol, an information artifact of music theory. It can be read in the form of the placement of a
"whole, "half, "quarter, "eighth, …, note" on the bar line of a staff or in the form of an alphabetical
character {A, B, C, D, E, F, G}. Moreover, the largest part of our hierarchy deals with the fact that
in the abstract and in real-time, an instance of a note may either correspond to a process (i.e.,
something that spans time, something that more persists rather than exists) in the abstract form of a
pitch or the real-time form of a tone, respectively. Hence, a note is going to be an 'information
content entity' (a subclass of 'generically independent continuant', which is a subclass of 'continu8
http://www.ifomis.org/bfo/fol
Music Theory Ontology
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ant'9), whereas a pitch or tone appear on the 'occurent' side of the BFO hierarchy. A pitch will
always instantiate a tone; that is, a tone is the instantiation of a pitch.
Secondly, by the offered definition—and assuming our distinction between note, pitch, and
tone are accepted, the simultaneous occurrence of two or more tones may be the simultaneous
occurrence of several hundred tones. Hence, the applicability of the notion shows no limits.
Thirdly, while obviously important to the overall project of both MTO and OMRAS2, the
act of playing a chord is different from the sound of playing a chord, the sound of a recording of the
playing of a chord, and simply the sound of a recording of a chord (e.g., consider the act of hearing a
MIDI sample which has, as proper occurent parts, the instantiation of a pitch which has a diatonic
interval of a major third to an instantiation of some other pitch, and has a diatonic interval of a
perfect fifth to an instantiation of some other pitch, respectively—or, simply, the sound of a
recording of a major chord). Accordingly, we forego this confusion by simply ignoring (for now) the
intentional acts in music and instead focusing on the concepts necessary for elaborating the basics of
music theory by speaking only in terms of process and the structures found therein.
We stress the importance of the distinction between the purely formal processual structure
of music—that would, granted, not exist (except as a purely mathematical structure void of any
significant relations) without the human dimension of discovery, creativity, and genius—and the
purely cognitive dimensions of both the phenomenology of creating and experiencing music and the
cultural artifacts of the music-related information content that result as a product of the former.
That is, we began the project wondering if describing music in the way that music theorists and
musicians tend to describe the theory (e.g., using terms like "note" almost interchangeably with
"pitch") would be sufficient for our project. Strictly speaking, this would result in a literally false
ontology, as already noted. However, regardless of being philosophically vacuous, our goal was to
ontologize traditional Western music theory, and do so in such a way that would leave room to
include various other traditions (e.g., we wonder as of yet whether our ontology could properly
9
cf. the Information Artifact Ontology: http://purl.obolibrary.org/obo/iao/iao-main.owl
Music Theory Ontology
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represent, with, of course, the relevant additions, something as complex as Shruti or certain Arabic
traditions), and, hence, we roughly laid out an ontology of just that. Not surprisingly, this failed
almost all trivial logical tests and thought experiments. Hence, we simply felt it was not only
impossible, but, more so, completely counterintuitive to the entire notion of ontology proper to
misrepresent a domain of reality for the simple purpose of having some novel reference tool. The
discipline's roots are over 2,000 years old, and to build an ontology which does is not, strictly, an
ontology of such and such is, quite seriously, anathema. Thus, we were compelled to do as much tedious
music theory and philosophy as our goal required. The result is a basic structure of traditional
Western diatonic music theory that while requiring much axiomatizing, formalizing, exhausting, and
revising nonetheless captures—at least to our best efforts—the core of what music really is.
III. Concluding Remarks
I note here simply that the .owl file of our Music Theory Ontology (MTO) does the work of
explaining the exact properties, relations, and class-subclass structure that we set out to provide. I
take this paper to be a statement of motivation and genesis, and, primarily, an introduction for, as
previously noted, our ontology as a response to the specific issues and questions that Sutton, et al.
(2007) addressed at the end of their description of the Chord Ontology.10
10
For an elaborate description of core notions in MTO, see my colleague's description here:
http://ncor.buffalo.edu/2013/IE500/Reports/MusTO-Documentation.docx
Music Theory Ontology
Figures
Figure 1. BFO 2.0
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Music Theory Ontology
Figure 2.
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