The Case for Numerical Music Notation. Part 1: Introduction and History
This article is a presentation of the concept and history of notating diatonic music with the use of numerals, of which several systems exist. This concept has enormous potential, particularly in the field of music education, borne out by my own experiences teaching with it. However, I feel that existing systems of numerical notation lack some important developments in order to bring them up to date and optimize them to the task of notating modern music and teaching the skills required for playing it. I will therefore outline the potential I see in the concept, as well as tackle some problems that existing systems come up against. Finally, I will propose an optimized, modernized system for notating music numerically with suggestions on how it can be put to beneficial use.
In 1742, philosopher, writer, composer and music copyist Jean Jacques Rousseau presented a system of numerical music notation to the French Academy of Sciences, later published in his Dissertation on Modern Music (1743). He is by no means the only person to have thought of representing the notes of the diatonic scale with numerals, and it seems that many variations of this idea have cropped up more or less independently of each other since Rousseau (and possibly even before). Despite usage in Germany, France, and the Netherlands, numerical notation has never become widespread in the West, even though its central idea— numbers for degrees of the scale- is used as a sort of shorthand among jazz and country musicians to describe harmonic sequences as relative patterns, rather than absolute values.
The concept of describing and notating musical notes relatively, rather than in absolute terms, has a long history. Chinese Gongche notation, in which syllables and their characters stand for degrees of the scale, dates back to the Tang Dynasty (AD 618 to 907). In Europe, the Aretinian syllables ut, re, mi, fa, sol, la, si denoting the seven steps of the diatonic scale (named after their inventor, music theorist Guido d’Arrezzo), date back to eleventh century Italy. This system has undergone development at various times and in various places and evolved into the system known variously as solfege, sol-fa, solfeo etc., in which do, re, mi, fa, sol, la and ti denote the degrees of the diatonic scale. There are two schools of thought regarding its use. In fixed-do, particularly in use in Latin speaking countries, these syllables are the names given to the absolute notes, known to us as C, D, E, F, G, A, and B respectively. It is of course the use of solfege as moveable-do, independent of absolute pitches, that is of interest here. It has particular relevance for singers — whose instrument is in its nature unconnected to absolute pitch- who can use it in conjunction with or without Standard Music Notation to pitch notes relative to a root note (do at a particular pitch) in order to read notation, sing, conceptualise and remember complex vocal parts. The use of solfege in this fashion owes much to the work of English music teachers Sarah Glover and John Curwen in the 19th century, as well as that of a French school consisting of Pierre Galin, Aimé Paris and Emile Chevé, whose Galin-Paris-Chevé method was arguably based on Rousseau’s ideas from 1742. A set of hand signs developed by Curwen, corresponding to the seven degrees of the diatonic scale (and popularised in Stephen Spielberg’s film Close Encounters of The Third Kind), was later adopted by Zoltán Kodály in the method he developed in the 20th century in Hungary.
Whilst intoned syllables and hand signs have communication value monophonically (a single voice of music at a time), the recording, communication and development of complex harmony (polyphony) requires written symbol systems. Standard Music Notation (SMN) is one such system, whose capacity for notating pretty much anything within music is unparalleled. However, in music education, SMN can be enormously misleading as a depiction of music, as well as requiring considerable skills and experience if one is to write in it. As an absolute pitch notation system and essentially a graph, SMN simply plots what happens where and when in music. As seen in fig. 1 above, it is not immediately apparent to the untrained eye that the three examples are equivalent (the same thing at different pitches), because neither SMN or the absolute chord notation says anything about the roles of the chords or their relationship to each other and back to the key they’re in. It is only in the numerical version that these relationships are described, because this version is an abstraction, based on movable symbols, variables. So whilst this neutrality makes SMN versatile in the hands of an expert, the abstract version provides a pattern recognition tool in conjunction with it, a supplement that can help the uninitiated reader to understand what’s going on musically.
Despite never really catching on in the West, numerical musical notation is in widespread use in Asia, particularly in China. JianPu, a notation system closely related to Rousseau’s (and possibly indirectly derived from it via the Galin-Paris-Chevé method) was adopted around 1900 and is more entrenched in Chinese music culture than SMN. This is perhaps hardly surprising given the long legacy of Gongche,i.e. relative (as opposed to absolute) pitch, and symbol based (as opposed to graphic), notation.
Whilst I in no way claim that numerical notation is better than SMN overall, it has certain advantages in various contexts. As symbols rather than note heads denote pitch, they are not only easy to write as sequences (rather than having to plot them on a graph) but can also be notated first, before rhythm notation is considered. This is ideal for a beginner, using his ear to pick out the notes of a tune and jotting them down for future reference. This kind of task, directly engaging the musical ear as a source of musical knowledge, is invaluable for musical development, but often neglected at beginner and even intermediate levels, precisely because it’s not supported by a user friendly notation, i.e. one for writing in, rather than just reading and blindly following. For a beginner, SMN can’t be anything other than an instruction manual, giving a misleading sense of where music comes from and “lives.”
For many pupils, such an assignment is greatly aided by the use of lyrics as a guide to work by, not least because lyrics can help to “frame” the rhythm, while identifying the syllables where note events occur. As numerical symbols, the notes can simply be assigned to syllables without the strict necessity of rhythmic markers, a task that SMN is quite unsuited to performing.
Whilst I see numerical music notation as a valuable, but neglected, resource, I also feel that its own potential for further development has been neglected. My own work with the system as an educational aid has led to a preference for JianPu over Rousseau as a wholly symbol based system, free of the constraints of graphic notation. The rhythmic markers of JianPu mirror to a large extent those of SMN, a distinct advantage when using numerical notation as a learning aid and supplement to SMN. I do however find Rousseau’s octave change method (of defaulting to the present octave) superior and have adopted it in my own system of numerical notation.
In direct conjunction with SMN, numerical notation has various uses. One of these is close to the way solfege has been used to “translate” SMN into the diatonic language of the musical ear. As with the musicians’ harmonic (Roman numeral) shorthand, the relative notation shows equivalence between keys and common patterns in different examples and can be used as an aid to deciphering, learning and transposing SMN.
This use of numerical notation, in direct conjunction with SMN, has been of considerable benefit to my own students, who have often written in the numerals as a help to reading and transposing SMN. It has also inspired me to make a number of modifications to numerical notation, which I will cover along the way.
It is, of course, not my intention to plead a case for numerical notation as anything more than a supplement to SMN, as for all its strengths as an educational aid, it is by its nature inherently limited to diatonic music. Also within this realm it has some problems that need addressing. These concern chromaticism, notation of tunes in minor mode and the quite substantial question of how polyphony (multiple simultaneous voices) can and should be tackled. I will take these questions up in the next article.
Quiz, fig.3: a) “Itsy Bitsy Spider.” b) “Frere Jacques”