Notation is a pervasive practice in media whose instances are far reaching but whose dynamics are rarely studied separately from the media with which they interface. The Oxford English Dictionary defines notation as “the process or method of representing numbers, quantities, relations, etc., by a set or system of signs or symbols, for the purpose of record or analysis.”  The term “record” points to the anchoring and archiving quality of notation. Notated forms are captured within the relations between the elements of a relevant “set or system,” and this capturing creates a physical document that can be studied, analyzed, referenced, reproduced, and reinterpreted. Notation as a noun is inextricably linked to notational systems, the sets of signs and symbols that are created within and through incidences of notation.
Notational systems facilitate capture and documentation across a wide array of media. Systems such as Labanotation record motion, dance, and movement within a closed space; scores using fixed bass and treble clefs record works of music and the interplay of sounds [link]; select groups of graphic symbols form written languages capable of organizing and recording thoughts and spoken words. This latter category is by far the richest, and many subsystems exist within the scope of language-based notation. Phonetic and linguistic notation use symbols to define and identify the specific phonemes of oral speech. Shorthand notation employs particular markings to capture and abbreviate long words and phrases for future replication and elaboration. Proofreading and editing notation in the form of marks and symbols on the page direct the writer to modify and adapt his/her text. Finally, scientific notation employs the language of numbers to designate and manipulate quantities which are extraordinarily large or physically impossible. The scope of this article limits discussion of notational systems to those particularly relevant to the study of media. Here, we are guided by Aristotle’s classic tripartite categorization of opsis, melos, lexis —Image, Music, Text.  C.S. Peirce roughly adopts this structure within his own triad Icon, Index, Symbol, as does Nelson Goodman within his more recent work on Score, Sketch, and Script. 
The Oxford English Dictionary’s relating notation to a “process of representing” highlights the important dynamic within notation of substitution or reproduction. Notational systems serve to capture through physical means the instantiation of temporal forms. Thoughts, motions, and sounds are naturally ephemeral. Their flow and commerce in society and culture are thus entirely dependent on techniques which can both contain their information and ensure the reproducibility of that information under varying circumstances. Simultaneously, the distinct properties of that information must be preserved—individual works must be identified as such in both their initial capture and subsequent reproduction. Notation thus becomes a material substitution of a temporal performative event, with a distinct authorial function.  The spark of an original thought—the electrical impulses in the brain of the thinker—must fade, but the idea can be discovered and rediscovered as it is read printed in a book or scribbled in the margins of a text. The first performance of Beethoven’s third symphony in August 1804 is irretrievably gone, but each note can be dutifully and passionately restored if musicians work from the official score.
This notion of mediated reproduction is well articulated by Aristotle in Poetics. Aristotle cites mimesis (Greek: Imitation) as a natural inclination in humankind, and he justifies the craft and performance of poetry as an organic product of man’s improvisational and imitative play: “Imitation is natural to man from childhood, one of his advantages over the lower animals being this, that he is the most imitative creature in the world, and learns at first by imitation. And it is also natural for all to delight in works of imitation.”  Aristotle laid the theoretical groundwork for both the physical creation and emotional reception of performance. In defining mimesis as a natural tendency and poetry as its extension or consequence, Aristotle posits that man is inherently capable of manipulating and processing imitative forms. While poetry, tragedy, and comedy function for Aristotle as oral elements, it seems possible to extend his thesis to include written elements as well. This consideration simply asserts that other forms of media (music, text) operate by the same principles of imitating or re-presenting an initial action to achieve a desired effect.  This seems a useful and important way to frame the dynamics of notation. For Aristotle, the performance of tragedy is already a mimetic instantiation of an original event: “We maintain that Tragedy is primarily an imitation of action, and that it is mainly for the sake of the action that it imitates the personal agents.”  In our broader view of mimesis, the notated form takes the place of tragedy, and the live or generating event assumes the position of “action.” A particular work as captured through its notational system thus imitates an original phenomenon and attempts to reproduce its effects through the particular relationship between the observer, the notation, its information, and its materials. As in the Aristotelian model, the imitation itself evokes a particular sensation linked to the original. 
Naturally, the audience/observer (that person who is in direct contact with the mimetic instantiation of the notation) is aware that what he is experiencing is a material substitution for an original event. No one holding a musical score could confuse the notes on the page with an actual performance. But those notes could be played, and an actual performance would logically result. In this way, notation becomes a form of reference to past (or future) experiences and sensations.
C. S. Peirce discusses this type of referencing in his articles “Logic as Semiotic: The Theory of Signs” and “On the Algebra of Logic: A Contribution to the Philosophy of Notation.” Peirce defines referencing as the interplay of signs, and broadly defines signs as vessels for specific meanings agreed upon and shared between people: “A sign, or representamen, is something which stands to somebody for something in some respect or capacity. It addresses somebody, that is, creates in the mind of that person an equivalent sign, or perhaps a more developed sign.”  Peirce stresses that signs work through prior mental arrangements, that a sign’s rapport with its object is arbitrary and is “related…only in consequence of a mental association, and depends upon a habit.”  Notation, as a form of written language, relies on this dynamic to function effectively. Our recognition of numbers, letters, notes, and other markings as visual representations of quantities, words, and sounds is a powerful instance of this “mental association” depending on habit.  But Peirce carries this discussion further, dividing all signs into the forms of Icon, Index, and Symbol. Indices and symbols are of particular import in the workings of notation.
Peirce defines an index as a sign “which refers to the Object that it denotes by virtue of being really affected by that Object.”  The index is not an independent sign—for it is not self-evident—but is rather a marker of interaction or interrelation between other signs and processes. Indices connect one experience with another: “A rap on the door is an index. Anything which focuses the attention is an index. Anything which startles us is an index, in so far as it marks the junction between two portions of experience.”  Notations serve as indices in their capacity to relate prior temporal phenomena to current material signification: the musical score is an index whose Object is the sequence of sounds it designates; the shorthand letter is an index whose Object is the content of the letter’s initial dictation.
These relations per se are incomplete; they demand a third term, the Interpretant, which, with the sign) and the object (second), form another triadic relation of representation.  In the Peirceian triad of Representamen – Object – Interpretant, the third term provides the conceptual framework, the “mental association” depending on habit, that allows the first two terms to coexist. Within a notational index, then, the Representamen is the form of notation, the Object is its raw content of information, and the Interpretant is the nature of the original medium through which that information was delivered. Thus the awareness the observer feels of mediation, of the difference between the original and the notated forms of expression, can be localized within Peirce’s triadic relation. Our willingness to let score stand as music or text as idea is made possible by a prior accord to equate these things within our own conceptions of the original media: we allow our media to be organically flexible. The Interpretant (third) thus both permits and supports the relation of the first and second.
But none of this would be possible unless the notational index could be broken down into smaller units of signification. For that, we turn to Peirce’s treatment of the Symbol, “a sign naturally fit to declare that the set of objects which is denoted by whatever set of indices may be in certain ways attached to it is represented by an icon associated with it.”  The symbol [link] gives the notational system its units of meaning and simultaneously defines its function: “A Symbol is a Representamen whose Representative character consists precisely in its being a rule that will determine its Interpretant.” The symbol [link] graphically represents some element found within the original medium, and the totality of symbols [link] within the notation forms a language [link] that explicitly relates the notation back to that medium, as per an a priori agreement to honor the “rule that will determine…”  In other words, the notation rises from its symbols [link], which rise from the Interpretant.
Yet a viable notation is much more than a collection of symbols that have distinct object equivalents. Nelson Goodman in Languages of Art offers several conditions of acceptable notational systems: unambiguity, syntactic and semantic disjointness, and differentiation. In other words, each character in the notational language must have an unambiguous, exclusive, and singular relation to a unique element in the original medium.  These criteria lead Goodman to separate true notational systems such as music transcription from false ones such as drawing. In a somewhat debatable move, Goodman places modern language (spoken and written) on the side of false notation.  Yet Goodman’s main project is not a classification of notation but rather a theory of it: his strongest arguments center on the work of signs and compliance classes within notational dynamics. 
The interplay between symbol, notational system, and original medium as read through Peirce and Goodman suggests a rather symbiotic relationship between the uses, forms, and instances of symbolic language across media. This idea is extended in Marshall McLuhan’s seminal work Understanding Media: The Extensions of Man. McLuhan postulates that the electric light is the sole modern medium to fully lack a message, as its “pure information” is in no way mediated by or conscribed within another function: “This fact, characteristic of all media, means that the ‘content’ of any medium is always another medium. The content of writing is speech, just as the written word is the content of print, and print is the content of the telegraph.”  The containment of media within other media is highly evident in notation, as the physical process of notating involves a minimum of two forms of media. Notation’s efforts to anchor the ephemeral event or performance in stable materials—sketch, score, and script—engage mediums from across the divide of temporal/permanent. As soon as music is transcribed, for example, two forms of content, one sonic (melos) and the other scopic (opsis) are engaged across what is ostensibly a single medium. McLuhan sees this as a natural property of media, and this consideration directly connects with Poetics. Just as Aristotle viewed the invention of poetry as a natural development from man’s propensity to imitate, McLuhan views newer technologies of media (viz. the typewriter, the television, the printing press) as naturally developing from and constantly referring to more ancient forms.  The creation throughout history of notational systems as a technology in their own right can thus be seen as an organic phenomenon. Although Peirce’s emphasis on the determining quality of the Interpretant suggests a certain deliberate artificiality in the creation of notation (i.e. forcing the reading of one medium through another), the rationale behind notation—using visual forms to capture and clarify fleeting packets of information—seems an entirely natural progression from the ancient to the modern.
Chronologically, the earliest form of abecedary written language notation emerged in Mesopotamia around 3200 BCE,  while notches in bones and sticks dating to more than 20,000 years ago have recently been considered as the first incidences of numerical notation.  Research on the origin of writing systems has done much to support the argument that written and oral communication evolved independently out of separate needs. Daniels and Bright note: “The earliest uses of writing systems seems to be to communicate things that really don’t have oral equivalents. In Mesopotamia, the earliest documents are business records… In China, the oldest writing is found in oracles addressing queries to the gods…”  These early instances of notation broach the issue of medium specificity. While McLuhan posits that all media contain other media, that “the content of writing is speech,” it is essential to recognize the distinct characteristics of each medium within any nested relation. The idea that written language emerged from business transactions connects the archiving quality of the notational process to the material conditions of its mediums. The need for a permanent and trustworthy physical medium for the conducting of business necessarily motivated the development of notation’s earliest forms. Similarly, the technological innovation of shorthand emerged from Greek civilization’s fascination with efficiency maximization. Inscriptions from the Athenian Acropolis from the 4th century BC already suggest experimentation with shorthand notation. The invention of the official form of Greek Tachygraphy, however, is credited to Cicero’s secretary, M. Tullius Tiro, who used a system of signs to abbreviate prepositions and small words as he recorded orations. His innovation would grow into a larger system adopted by the imperial administration and later by the Church.  The history of musical notation is likewise rich with technological advancements and progressions from rudimentary to more complex forms. The general evolution towards the contemporary system—established in France in the late 16th century—was motivated by concerns for specific properties of sound, most notably volume and duration, at the expense of others such as timbre. In this regard, the extant notation is considered the most flexible, but not necessarily the best system. 
Inherent in these technological developments is a sense of tension that should not be overlooked. As new forms of media develop, notational systems emerge to record and analyze new types of information. Yet this evolution is continually plagued by problems of authenticity and legitimacy. Since notation works across media, the question can always be raised whether the content of one medium can be reproduced with absolute fidelity from or within another. Goodman considered this at length in his discussion of the interpretation of music within Languages of Art,  while Laban, Hutchinson, and other theorists of dance notation take this inquiry as their practical and theoretical point of departure.  As we move towards a greater understanding of notation, we should keep this critical view in mind. It is perhaps best articulated in Plato’s dialogue “Phaedrus”, where the great philosopher warns that the new technology of writing could undermine the power of memory and the art of oration.  In our digital age of Instant Messages and e-mail, these prophetic words most certainly still ring true.
1. “Notation.” Oxford English Dictionary, Second Edition. 11 February 2007.
2. The triad is addressed throughout Poetics, but for an authoritative critical discussion of the terms, Vanessa Chang’s Keywords article, http://csmt.uchicago.edu/glossary2004 /melosopsislexis.htm, is an excellent resource.
3. There is an important difference between the dynamics of notation and the dynamics of pictorial representation. The visual arts, whose modes and means of depiction do not fully qualify as notations, should not necessarily be compressed under the blanket term of “opsis” as it is used here. Hence, fine arts such as painting and sculpture have been deliberately removed from this discussion. A further qualification for this choice is advanced in Goodman, Nelson. Languages of Art. Hackett Publishing Company: Indianapolis, IN, 1976. Pages 194-198.
4. Goodman, Nelson. Languages of Art. Hackett Publishing Company: Indianapolis, IN, 1976. Page 128: “A score, whether or not ever used as a guide for a performance, has as a primary function the authoritative identification of a work from performance to performance. […] First, a score must define a work, marking off the performances that belong to the work from those that do not… What is required is that all and only performances that comply with the score be performances of the work.”
5. “Poetics.” Introduction to Aristotle. McKeon, Richard, Ed. The Modern Library: New York. Page 627.
6. Ibid., page 631: “A tragedy, then, is the imitation of an action that is serious, and also, as having magnitude, complete in itself; in language with pleasurable accessories, each kind brought in separately in the parts of the work; in a dramatic, nor in a narrative form; with incidents arousing pity and fear, wherewith to accomplish its catharsis of such emotions.”
7. Ibid., page 633.
8. If viewed in terms of performance, since the initial performative event (i.e. a line spoken or a note played) is always lost in its own creation, we willingly accept the substitute—a mimetic instantiation of the original, like a script or score—to deliver the same information, with strikingly similar effects. C.S. Peirce roughly described this process in slightly different terms: “I call a sign which stands for something merely because it resembles it, an icon. Icons are so completely substituted for their objects as hardly to be distinguished from them. Such are the diagrams of geometry. A diagram, indeed, so far as it has a general signification, is not a pure icon; but in the middle part of our reasonings we forget that abstractness in great measure, and the diagram is for us the very thing. So in contemplating a painting, there is a moment when we lose the consciousness that it is not the thing, the distinction between the real and the copy disappears, and it is for the moment a pure dream—not any particular existence, and yet not general. At that moment we are contemplating an icon.” “On the Algebra of Logic: A Contribution to the Philosophy of Notation.” Peirce, C. S. American Journal of Mathematics, Vol. 7, No. 2. (Jan. 1885) Page 181.
9. “Logic as Semiotic: The Theory of Signs.” Philosophical Writings of Peirce. Buchler, Justus, Ed. Dover Publications: New York. Page 99.
10. “On the Algebra of Logic: A Contribution to the Philosophy of Notation.” Peirce, C. S. American Journal of Mathematics, Vol. 7, No. 2. (Jan. 1885) Page 180: “A sign is a conjoint relation to the thing denoted and to the mind. If this triple relation is not of a degenerate species, the sign is related to its object only in consequence of a mental association, and depends upon a habit. Such signs are always abstract and general, because habits are general rules to which the organism has become subjected.”
11. A further discussion of the arbitrary nature of the sign, and of the overarching dynamics of signification, is readily available within Saussure, Ferdinand de; Bally, Charles (ed.); Sechehaye, Albert (ed.); Baskin, Wade (tr.). Course in general linguistics, New York: McGraw-Hill.
12. “Logic as Semiotic: The Theory of Signs.” Philosophical Writings of Peirce. Buchler, Justus, Ed. Dover Publications: New York. Page 102.
13. Ibid., pages 108-109.
14. Ibid., pages 99-100.
15. Ibid., pages 112-113.
16. The entire concept of establishing this rule is useful in that it will bring fluency and clarity to ideas and concepts which are not necessarily portable. Adopting a system of symbols will explicitly help with the visualization and comprehension of abstract things. In his “On the Algebra of Logic,” Peirce refines this notion with the useful example of mathematics: “The letters of applied algebra are usually tokens, but the x, y, z, etc. of a general formula, such as (x + y)z = xz + yz, are blanks to be filled up with tokens, they are indices of tokens. Such a formula might, it is true, be replaced by an abstractly stated rule (say that multiplication is distributive); but no application could be made of such an abstract statement without translating it into a sensible image.” (Pages 182-183)
17. Goodman, Nelson. Languages of Art. Hackett Publishing Company: Indianapolis, IN, 1976. Page 156: “A system is notational, then, if and only if all objects complying with inscriptions of a given character belong to the same compliance class and we can, theoretically, determine that each mark belongs to, and each object complies with inscriptions of, at most one particular character.”
18. Ibid., page 178: “None of our usual natural languages is a notational system. Such discursive languages meet the two syntactic requirements but are exempt from the three semantic requirements. Accordingly, a definition or set of coextensive definitions is seldom uniquely determined by a member of the class defined. And as we have seen, ambiguity is not always to blame; a wheelbarrow belongs to many different compliance-classes of object-English…”
19. Goodman advances a similar triadic relation to Peirce, although some of the terms have shifted. Where Peirce presented Sign-Object-Interpretant, Goodman introduces the value of the compliant: “For a score, as I conceive it, is a character in a notational language, the compliants of a score are typically performances, and the compliance-class is a work.” (Ibid., page 173) Here, the score takes the place of the Sign, the compliant performance is roughly the content of the notation qua Object, and the compliance-class is a work within the medium and thus resembled the Peirceian Interpretant.
20. McLuhan, Marshall. Understanding Media: The Extensions of Man. The MIT Press: Cambridge, MA, 1994. Page 8.
21. For further thought, consider McLuhan’s discourse on human extension. From Understanding Media, page 45: “The development of writing and the visual organization of life made possible the discovery of individualism, introspection and so on. Any invention or technology is an extension or self-amputation of our physical bodies, and such extension also demands new ratios or new equilibriums among the other organs and extensions of the body…”
22. The World’s Writing Systems. Daniels, P. T. and Bright, W., Eds. Oxford University Press: Oxford, 1996. Page 19.
23. Ibid., page 795.
24. Ibid., page 5.
25. Tachygraphy” in The Oxford Classical Dictionary. Hornblower, S. and Spawforth, A., Eds. Oxford University Press, 1999. Page 1468.
26. Bosseur, Jean-Yves. Du son au signe: Histoire de la notation musicale. Éditions Alternatives : Paris, 2005. Pages 7-11.
27. Goodman, Nelson. Languages of Art. Hackett Publishing Company: Indianapolis, IN, 1976. Pages 184-188.
28. The first several chapters of Hutchinson, Ann. Labanotation. Theatre Arts Books: New York, 1977 and Laban, Rudolf. The Language of Movement. Plays, Inc.: Boston, MA, 1976 discuss these issues explicitly.
29. “Phaedrus.” The Dialogues of Plato. Jowett, B., Ed. Random House: New York. Page 278: “O most ingenious Theuth, the parent or inventor of an art is not always the best judge of the utility or inutility of his own inventions to the users of them. And in this instance, you who are the father of letters, from a paternal love of your own children have been led to attribute to them a quality which they cannot have; for this discovery of yours will create forgetfulness in the learners’ souls, because they will not use their memories; they will trust to the external written characters and not remember of themselves. The specific which you have discovered is an aid not to memory, but to reminiscence, and you give your disciples not truth, but only the semblance of truth…”
Bosseur, Jean-Yves. Du son au signe: Histoire de la notation musicale. Éditions Alternatives : Paris, 2005.
Goodman, Nelson. Languages of Art. Hackett Publishing Company: Indianapolis, IN, 1976.
Hutchinson, Ann. Labanotation. Theatre Arts Books: New York, 1977.
Laban, Rudolf. The Language of Movement. Plays, Inc.: Boston, MA, 1976.
McLuhan, Marshall. Understanding Media: The Extensions of Man. The MIT Press: Cambridge, MA, 1994.
The World’s Writing Systems. Daniels, P. T. and Bright, W., Eds. Oxford University Press: Oxford, 1996.
“Notation.” Oxford English Dictionary, Second Edition.
“On the Algebra of Logic: A Contribution to the Philosophy of Notation.” Peirce, C. S. American Journal of Mathematics, Vol. 7, No. 2. (Jan. 1885)
“Tachygraphy” in The Oxford Classical Dictionary. Hornblower, S. and Spawforth, A., Eds. Oxford University Press, 1999.
Philosophical Writings of Peirce. Buchler, Justus, Ed. Dover Publications: New York.
The Dialogues of Plato. Jowett, B., Ed. Random House: New York.
Introduction to Aristotle. McKeon, Richard, Ed. The Modern Library: New York.