An Automatic Translator for Semantically Encoded Musical Languages

Since the 1950s, scientists have attempted to codify human language and to write automatic translators from one language to another (Locke and Booth 1955). This translation problem is strikingly difficult, caused not only by syntax, but by the meaning or semantics of the languages themselves. In this article, we present a translation problem of a different nature: the translation between musical languages.

A musical language comprises both the symbols that represent sound or music and the underlying meaning of those symbols. Musical languages show striking similarities to natural languages. Just as in natural language, similar symbols can imply the same, or similar, underlying meanings. Musical languages present different levels of information, ranging from very exacting to rough approximations of what the performer should do. Trying to reconcile approximations with the exact is musically analogous to the colloquial phrase "lost in translation."

A musical language translator may be beneficial in studying historical music, unusually notated music, or for simplifying the notation of a complicated score. Just as there are a variety of spoken languages, there is a vast and growing number of musical languages. It is unreasonable to expect composers or performers to understand all musical languages. Translations may require expertise in two or more notation systems, and translating musical languages by hand—even with the required knowledge—is both tedious and time-consuming.

Thus, we present Ammmp, a general-purpose musical language translator and music-notation editor. Ammmp has several musical languages and translators implemented. Currently, we have implemented Ben Johnston's microtonal notation, a form of microtonal performance notation, standard non-microtonal Western notation, and a form of chromatic staff notation invented by Grace Frix. All of these musical languages can be automatically translated to any others in Ammmp.

As we will demonstrate, not all translators are created equal. Some translators require an alteration of a musical language's semantics, others require changes to the graphics, and still others require both. We see Ammmp as a system that translates musical languages in the general sense, and present a framework for doing so. We chose microtonal notations to demonstrate languages that are extremely difficult to translate, and we chose a chromatic staff and standard Western notation as examples of relatively straightforward, non-microtonal, translations.

Since 2002, we have been using Ammmp technology, or pieces of it, to provide the Kepler Quartet with synthesized recordings of several of Ben Johnston's string quartets (Johnston 2006). This technology, as it evolved, was an invaluable tool for the quartet in hearing and understanding Ben Johnston's musical language.

In the course of this article, we first present related work and the Ammmp music-notation framework, including the translation framework. Next, we discuss both the basic concepts in microtonal music theory and several music notations for which we present translators. Lastly, we discuss our methods for automatic musical language translation, focusing on the most difficult translation, back and forth from Johnston to performance notation.

Background

Designing and implementing a music-notation editor is a serious undertaking. Algorithms as seemingly simple as spacing a line of music have a rich history (Gourlay 1987; Haken and Blostein 1995; Bellini and Nesi 2004), and determining a proper design for the system is equally challenging (Brandorff, Lindholm, and Christensen 2005). In this section, we present work relevant to translating between languages, both musical and otherwise.

Brown, in a 1958 talk at Georgetown University, said, "I must begin by admitting, as is scarcely necessary, that I am at least several months away from being able to feed a new piece of French text into a computer and have an English translation come out at the other end" (Brown 1958). The translation problem at this early stage was far from solved. What is enlightening about this text, however, is that Brown said he was several months away in 1958, perhaps showing how deceptively difficult this kind of work can be.

One element of particular difficulty in language translation is the meaning of words, or semantics. Early work considered only the syntax of language, which was soon shown to...