The Case for Numerical Music Notation. Part 3: The Challenge of Chord Notation

How ever we choose to notate polyphonic music, whether it is with Standard Music Notation (SMN), one of the numerical notation variants, like JianPu and Rousseau, or any other available symbol system, we have more than one approach available to us.

We can choose to do it with a complete, specific and absolute approach, writing every musical event (note, rest, percussive hit) when and where it happens, thus creating a comprehensive musical score and leaving a minimum to individual interpretation or chance. This has been the classical approach, applicable to every kind of ensemble from symphony orchestras to marching bands to string quartets to choirs. In this type of musical environment, where works are often the sum of many individual skill contributions, this comprehensive approach makes perfect sense, since roles are specialised and the benefit of different perspectives comes into play. It is the composer’s role to dream the music up, the arranger’s, to shape it to the instruments that will play it in the contexts it is to be performed in. Theirs is a macro perspective. It is the musicians’ role to physically create the sounds envisaged in the composition/arrangement. Theirs is a micro perspective. Where there’s a conductor or bandmaster, his role is to form a link between these two perspectives. With specialisation, it is not the composer’s or arranger’s job to worry about how sounds are physically produced from hundreds of different types of instrument, as long as he knows what the instruments can theoretically do and what he can reasonably expect of the players. By the same token, it is not the individual musician’s job to worry about what harmonies or textures are being produced between instruments and instrument groups or how they fit together in harmonic theory or overall dynamics. It clearly serves the best interests of the finished work that no one is in any doubt about what to do, where and when. It also serves the work that creative and interpretational aspects are separated from mechanical, technical ones, i.e. that the player doesn’t have to figure out what to play, as someone else has already decided that.

Examples of this approach to notation are orchestral and band scores, as well as music for solo instruments, with or without accompaniment. Since a musician in this classical approach to music is in essence technical specialist, rather than one who is expected to know harmony, even solo works for polyphonic instruments like guitar and piano are notated this way.

We can also choose to notate with a much looser approach, depending on just how much looseness and interpretational freedom we’re writing for. We might, for example, be working with a composition with a certain level of definition, so it is recognisable, but which we don’t intend to sound the same every time it is played or in the hands of different players or groups. The challenge here is to find the fine line between what we want decided beforehand and what we want freely interpreted. This is characteristic of most jazz music, where a loose and often quite incomplete notation isn’t the product of laziness, but rather the appeal of music with some degree of novelty, freshness, unpredictability. The loose notation never stands completely alone, meeting a sea of unwritten, even unspoken conventions that guide the way jazz music of diverse styles unfolds in performance. The performances of some styles may be very free, allowing for a good deal of untidiness and dissonance. Others styles are much more regimented and orderly than they might appear on the surface, following strict rules for what kind of interpretation/improvisation should occur, where and when and to what extent.

A sub-category of this second approach we could characterise as notating in the interests of brevity. This would chiefly be because we are writing for a reader whose knowledge is comprehensive and who only needs a certain amount of information in order to fill in the blanks. We want to tell this person what our musical idea is, not specifically what to do with it. We don’t want to supply an arrangement, but inspire any number of different, unique and exciting interpretations of our idea.

Typical for this brief, looser approach to notation is “top line and chords,” familiar from commercial sheet music and song books.

Fig. 1. “Top line and chords” is the most flexible use of SMN, as it requires several levels of interpretation from notation to performance. While the melody is given in absolute, concrete terms (and in a specific key), the chord symbols constitute a more abstract, multi dimensional layer of information, requiring not only harmonic knowledge (relation to one another and back to the key), but also comprehensive strategies for representing them as a set of voices, moving in conjunction with each other in musical time. This latter skill is essentially the ability to see harmony as both cross sections in time and moving lines of pitch at once. This interpretation requires relational, analytical and practical knowledge not present in the notation and which gets neglected in teaching as a result. A literal reading of this notation would be musically quite uninteresting, lacking a world of nuances, implicit in the context, like counterpoint and rhythmic “feel.”
Fig. 2. Top line with chords notated in a literal reading, as rudimentary voicings and stationary blocks. The annotations represent just some of the many considerations that the musician undertakes as a craftsman and interpreter. The most obvious of several possible counterpoint lines is highlighted, showing how chords are not just blocks of notes, but cross sections in a flow of moving voices. The question of whether this line is a harmonic counterpoint over a static bass or a bass line leading to chord substitutions is not just an either/or question. It is part of a general speculation in equally valid possibilities, any of which can come into play in an extended version of the song. The voicing of the chords requires them to be understood with a high level of abstraction, freeing them from specific forms, specific pitches and octaves or specific distributions in time. This cognitive process is a craft that takes years to master, partly because a notation with an inherent exactitude must be read loosely. Top line and chords in SMN is undoubtedly the best medium for master use, but as an absolute notation it is too easily read as a literal instruction. Numerical notation has the potential to provide an excellent educational supplement to this.

It is this category, the need for looseness and brevity, that has the greatest relevance for numerical notation and vice versa. The knowledge required to read and interpret this notation is a craft that takes years to learn, and I fear that many with potential fail to acquire it for lack of teaching aids that can provide the kind of insights that are absent from the notation. Part of this knowledge is harmonic theory, which is all about weightings and relationships between notes, information which numerical notation hinges on, but SMN doesn’t show. As I have shown with examples previously, numerical notation is no competitor to SMN as a tool for the expert, but as a way to map musical relationships, it is potentially better suited to this loose and brief musical “sketching” than SMN is.

SMN is built to be specific and can only be loose by virtue of a loose interpretation (the realm of the expert). Numerical notation, by contrast, is built to be general and loose and by its very nature requires interpretation. So whilst SMN can be used neutrally and mechanically, without harmonic insight, numerical notation has to be read and understood at an abstract level, pushing the development of this kind of interpretational thinking.

But what form should a numerical chord notation take? The absolute chord notation shown in the above example (figs. 1. and 2.) had its origin around the turn of the 20th century, bringing brevity and interpretational freedom, but as an absolute system, still emphasizing the description of what’s there, rather than what it means in any contextual sense. A harmonic notation system with quite a different emphasis was developed at approximately the same time by Hugo Riemann in his theory of harmonic function.

Fig. 3. Compare scale degree notation in Roman numerals (a) with functional harmonic analysis (b) of the same excerpt of “Look for The Silver Lining” (Kern, DeSylva). Both are relative (abstract) symbol systems for describing harmonic patterns, but whereas the first is a shorthand for communicating equivalent content, the latter is an academic, analytical tool, designed to unearth deep seated movements in harmony, rather than to communicate usable information in real time. These symbols are abbreviations of names given to chords on degrees of the scale reflecting their role in harmonic theory (where they are called functions). T stands for “tonic,” S for “subdominant,” D for “dominant,” Sp for “subdominant parallel.” There are very many variations on this terminology and the symbols used, depending on the academic school of thought, country of origin, etc. A look at the last bar of the excerpt should illustrate the difference between notation for communicative purposes (a) and analytical purposes(b), where the same content (a dominant seventh on scale degree 6) requires a complex expression consisting of many more symbols in harmonic analysis.

Riemann’s symbol system (fig. 3. b), like many similar and related systems, emphasizes contextual analysis rather than description, but it is much too “long haired” to be useful as notation, and neither is this its purpose.

We could, in a sense, regard numerical notation as analytical, since it depicts relationships rather than just plotting what happens. But analysis must also be approached with caution in a notation system whose purpose is to communicate as well as educate. So, whilst a numerical chord notation will in the nature of things be analytical, having its origin in scale degrees, we should ideally seek the right balance between analysis and blind description, a sweet spot between imparting relational context and disappearing down philosophical wormholes.

The musicians’ scale degree chord notation (fig. 3. a) is a step towards this balance, yet some problems arise from certain characteristics it borrows from the absolute chord notation. The use of Roman numerals for the scale degrees arises to avoid confusion with the another set of numerals, used to describe the details of chords, their character and embellishments. This is seen for example in the last bar of a), where “VI7” means a dominant seventh chord on scale degree 6. This is a type of chord, defined (among other things) by the minor seventh interval, where the number 7 refers to an interval of seven steps from the chord root, i.e. describing a relationship local to the chord, rather than the key. A few examples of quite common modern (and slightly jazzy) chords like “IIIm7b5”, “VI7#9” or “bIII9b5” are enough to show how this system will get confusing fast, when numerals are used simultaneously for different things.

My instinct is to discard this local numeral set from the notation and, consistent with the overall principle of numerical notation, describe only from the root of the key or tonal centre. Then I would ditch the cumbersome Roman numerals in favour of the familiar Arabic ones, but with some alteration to indicate that harmonies, not just single notes, are meant. We could, for example, bracket them, as I will do in this text, or, as I have chosen to do in my modified notation, circle them.

Fig. 4. A basic harmonisation of the children’s tune “ABC” with scale degree chord notation, using only the three major functions. Notice that the (5) chord in the third bar becomes a dominant seventh, not by embellishment of the chord notation, but by context, i.e. the presence of scale degree 4 in the melody at that point.

When we describe chords from the key root, a number of details and embellishments that are required in absolute chord notation fall away. By virtue of the diatonic basis, the triads (three note chords) (1), (4) and (5) are major, whilst (2), (3) and (6) are minor. (7) is a tritone, i.e. neither major nor minor but a stack of two minor thirds. Unless otherwise indicated, these single scale degree integers, given as chord symbols, will default to their natural (diatonic) chord types. It will be noted that (5) is very often embellished to a four note chord (a dominant seventh), whilst (1) and (4) can be embellished to major sevenths, though in fewer appropriate contexts. As seen above (fig. 4.), a dominant seventh arises because of the melodic context in bar three, an embellishment that would also be quite appropriate in all instances of (5) in this harmonisation. Before I look at how we could indicate this, I would first ask how necessary it is to do so. After all, the purpose of this notation is not tell the musician (even a beginner) what to do, but to give him an idea to interpret (yes, even a beginner). Perhaps it’s sufficient for the player to know that (5), embellished to a four note chord is a viable (and testable) option everywhere. With this basic knowledge, his ear — and aesthetic judgement- can do the rest.

Fig. 5. The relevance of (5) as a dominant seventh, extrapolated to all instances of (5) by the student himself, and noted above the chord notation as a reminder. As (5) is nominally a major triad, the addition of scale degree 4 makes it a dominant seventh.

The addition of scale degree 4 over the instances of (5) indicates the embellishment of a minor third stacked on the nominal major triad, making it a dominant seventh. This is not strictly necessary, as no embellishment is ruled out just because it isn’t added. But note that adding it tends to make it appear as a requirement. In this case, it is the student’s own reminder of a desired embellishment.

Fig. 6. A more advanced harmony uses some alternative voicings and, in bar ten, chromaticism. Here, the scale degree annotations over the chords are not just optional embellishments but specific details that define the intended chords.

My inclination is to argue for a minimal approach to chord annotation. Whilst diverse embellishments are optional and not strictly necessary to notate, priority should be given to details that for one reason or another actually define (in lieu of clear contextual markers) how a chord is to be understood. In this case (fig. 6.), none of the (3) chords are intended to be the nominal minor function on step 3, but actually (1) chords on the root/bass note 3. This is indicated by the integer 1 over the chord, which raises the 7 in the (3) chord to 1. In bar eight, the first (5), in combination with melody note 3 and annotation 1 above the chord is actually a (1) chord on root 5. In bar ten, (#4) in conjunction with b3 and melody 6 should be enough to indicate a diminished seventh on (#4). It is followed by another (1) chord on 5 (annotations 1 and 3), then (6) as a dominant seventh, leading functionally towards the following (2) chord.

This way of indicating harmonic structure favours key contextual transparency over uniformity of chord structure notation. By this, I mean that any individual chord type (dominant seventh, major, minor, diminished) is notated differently from one functional context to another, giving priority to the perception of harmony as linear movements in time, rather than just stacks of notes.

This type of harmony notation harks in some ways back to basso continuo, a chord notation in use from around 1600 until the mid 1700s. It is interesting to note that the classical and romantic periods saw harmony written out in full, which made sense with the advent of large ensembles and specialisation, but also says something about perceptions of art music as a composed rather than improvised medium. Basso continuo was a notation form in which only the bass voice was scored and where harmony and melody were improvised with the help of numeral annotations. Thus, the English name for this system, “figured bass.” It was, in modern terms, a “bottom line and chords.” Unlike mine, these annotations were local as in absolute chord notation, i.e. intervals to the chord root. By contrast, we could accurately describe my system of chord notation, consisting of scale degrees with modifiers relating back to the tonal centre, as “relative figured bass.”

This tonal centre based numerical chord notation will seem foreign to readers of absolute chord notation, but if it’s used wisely and moderately, I see no inherent problems that would make it harder to learn or execute. The greatest challenge is surely a different perspective, supplanting a habitual one. But as in all questions of notation, any system must be used to its strengths rather than just for its own sake in a compromising role. Again, it would be missing a vital point to push this notation into the realm of absolute chord notation by using it to denote specific, complex chords, when its forte is clearly a more advisory role, where the minimum is stated and the player/student is left to his own judgement as far as possible. It is desirable to avoid copious, superfluous annotations over every chord symbol. If the player/student needs reminders of his own choices of chord embellishments, the notation gives the freedom to add these.

In the next article, I will examine Relative Figured Bass in greater detail, outlining some harmonic theory behind it as well as some potential uses, with and without numerical melody notation.