Leon 1 Encoding Non-Standard Forms of Music Notation Using MEI (May 2016) Matthew Leon, Music & Computer Science, University of Virginia Class of 2017 I. ABSTRACT II. MEI Since the 1950’s, computers have been utilized MEI is an open-source Extensible Markup heavily to further the study of music. Now, music is Language (XML) vocabulary for musical notation. conceived, recorded, produced, stored, and XML, a hierarchical encoding system, can be used consumed almost entirely with the assistance of to represent virtually any type of document in a computers. Though music and computers are deeply simple, machine-readable format. MEI utilizes intertwined in the modern age, there is still a XML to encode symbolic musical information in a disconnect between music notation and computer way that can be easily parsed and utilized by representation. As an avid lover of both music and computers. For example, the simple musical phrase computer science, I became intrigued with this void shown in Figure 1 can be represented as MEI code on the left. in computer music. What is the proper way to store and symbolize musical scores? Is there a way to encode scores that do not follow standardized rules of notation? Inspired by both the old and new methods of computer music composition and technology, this project seeks to overcome the boundaries between music notation and digital encoding. Though several established formats for standard digital music encoding exist, it becomes quite difficult to use these formats to encode graphic Figure 1 - A musical phrase represented as MEI markup. notation. Scores like György Ligeti’s ‘Artikulation,’ Each piece of information associated with the George Crumb’s ‘Spiral Galaxy,’ Baude Cordier’s musical phrase is encoded as MEI data. Though the ‘Belle, Bonne, Sage,’ Brian Eno’s ‘Music for musical notation and MEI code do not look very Airports,’ and Karlheinz Stockhausen’s similar, they both are equivalently representing the ‘Elektronische Studie II’ all contain unique forms of same musical phrase. Similarly, entire scores can be notation which are nearly impossible to represent translated and represented using MEI, as using standard means of encoding. How can an demonstrated in Appendix A. Encoding in this unusual shape be encoded in the same way that a format allows more functionality and interaction with the score, as I attempted to execute in this standard chord or note would be encoded? Using project. Stockhausen’s 1954 piece as a proof-of-concept, this paper explores the limitations and capabilities of MEI (Music Encoding Initiative) as a tool for III. MEI’S LIMITATIONS encoding non-standard graphic scores. One of the first issues I encountered with MEI was its inability to represent non-standard scores in a Using a combination of Python, MEI, and suitable format. The glaring issue that stood out to JavaScript, I detail below a method for the encoding me was the lack of a standard framework for and representation of graphic musical notation as encoding pieces with non-conventional notation, well as the creation of an interactive score utilizing like those found in Appendix B. Since MEI does not this encoding. currently allow for an easy encoding of this type of Leon 2 score, I attempted to devise a framework for implementing my plan much more difficult. First, encoding a non-standard score. the score was produced after the piece was written, and was not created by Ligeti himself, which means IV. PROJECT OVERVIEW the score is not a perfect representation of the piece. After understanding the limitations of MEI, I Without a straightforward and exact representation wanted to create a project that pushed the of the piece, an interactive and playable score boundaries in order to adapt to these limitations. would be virtually impossible. Furthermore, the First, after finding a suitable score, I planned to piece is laden with ambiguity, since there are many formulate a method for encoding each bit of images overlaid atop each other. Using computer information in the piece. Using this method, the graphics image tracing, isolating individual shapes entire score would be encoded using MEI. Once would be very difficult, and I found it to be a represented as MEI, a website would be created that fruitless task. Finding this piece too difficult to could interpret this data and display it as an encode, I decided to pursue another path. interactive visual score. Armed with a long-term plan, I set out to find a fitting score. V. LIGETI’S ‘ARTIKULATION’ The first piece I examined was György Ligeti’s 1958 piece ‘Artikulation.’ This piece is accompanied by Rainer Wehinger’s 1970 graphic notation which was created several years after the composition of the piece, and breaks the piece into several different symbols. The graphic score, shown in Figure 2, is vibrant and interesting to look at, and I attempted to use this piece as my sample encoding. Figure 2 - Rainer Wehinger's graphic score for György Ligeti's 1958 piece 'Artikulation.' Initially I intended to use scans of the graphic score that would be processed using Adobe Illustrator’s VI. STOCKHAUSEN’S ‘STUDIE II’ computer graphics to generate Scalable Vector Graphics (SVG) files which could then be linked to After much searching, I settled on Karlheinz MEI. Once encoded, I wanted to create a timeline Stockhausen’s 1954 piece, ‘Elektronische Studie view of the score which would link each SVG II,’ pictured in Figure 3. I chose this piece for object to a sound from the original piece. After the several reasons. Stockhausen is one of the most SVG objects were linked, the score could be influential and important electronic composers of th interactive and playable, displaying a description of the 20 Century, and several of his works have been each note event so that information would be critical in fueling my interest in electronic music. In available for every note. Each note could also be addition, Stockhausen’s piece was one of the first synthesized in order to hear the note individually. early electronic music compositions to utilize this type of graphic score. I began the task of analyzing each note of the score, using the visual programming language Max/MSP The piece was formulaically composed, with to process an image of the score and convert the relatively distinct and separate segments, allowing image using spectral analysis, but ultimately this me to write a framework for encoding the piece in a method generated too much noise and was unable to much easier way than Ligeti’s piece allowed. create a clean analysis of the piece. Furthermore, Stockhausen’s piece is confusing to understand simply by looking at it; a deep I attempted a few other methods to encode the understanding of the piece is necessary in order to Ligeti piece, but a few issues arose that made Leon 3 interpret the score, so encoding the piece would lowest and highest frequency of each note mixture, allow for easier interpretation. the rest of the component frequencies can be calculated. Initially, I attempted to calculate each frequency from the lowest and highest frequencies VII. ELEMENTS OF ‘STUDIE II’ listed on the vertical axis, but my results were not After choosing my piece, I confronted the initial consistent with Stockhausen’s results due to problem with this score: its underlying meaning is Stockhausen’s use of gratuitous rounding. Since obscured by the unique nature of the notation. The oscillators were not very advanced in 1954, score consists of rectangles denoting note mixtures, Stockhausen often rounded, resulting in varying and triangles denoting dynamics. Though the score effects. In order to alleviate this issue, I created an looks quite different than standard notation, both array containing each frequency in the score, and hold essentially the same information. Every used the index of the highest and lowest frequencies rectangle is essentially a chord containing five to reference the frequencies stored in the array. The notes, and each triangle details the attack or decay next element, volume, is indicated by the triangles of the chord. on the bottom of the score. Each shape correlates directly with the envelope of volume for each note, Each note mixture has three defining characteristics: and thus the increase or decrease in volume over pitch, volume, and duration. Pitch is indicated on time can be calculated by determining the side of the vertical axis, shown by the numbers on the left the triangle. Finally, the duration of each note is that correspond to frequencies in hertz. The scale of indicated by the numbers along the middle of the frequencies is based on an interval between each score. Each value is shown in centimeters, which step, which consists of the frequency proportion of corresponds to the length of tape played at 76.2 the 25th root of 5, as compared to the traditional centimeters per second. Since Stockhausen chose tempered tuning system with the proportion of the the duration of each note mixture by cutting strips 12th root of 2. Each rectangular note mixture of magnetic tape, each number indicates the length consists of five component frequencies, each of tape rather than the duration of the mixture in equally spaced using this scale. By determining the time. In order to calculate the duration of each note Figure 3 - Karlheinz Stockhausen's graphic score for the formulaically composed 1954 piece 'Elektronische Studie II'. Leon 4 mixture in seconds, the tape length value can be definitions are shown in Appendix E. Finally, the divided by 76.2. calculated note mixtures are appended to the XML tree, and exported as an MEI file. The code for XML appending is shown in Appendix F, and a VIII.