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Some thoughts on trying to improve understanding of pitch function in tonal music in undergraduate performers.
Dr Christopher Atkinson
Aural Skills Coordinator
Royal Academy of Music, Marylebone Road, London NW1 5HT, UK
7 April 2017
Part of my job as Coordinator for Aural Skills training at the Royal Academy of Music is curriculum design, particularly for the 200 or so first and second-year undergraduates for whom Aural Skills is a compulsory module, the vast majority of whom are classical performers. It’s therefore the relevance to performance which I need to keep in mind in curriculum design and this paper will address an area which, for me, is at the heart of musical performance.
I believe, in an ideal world, that a performer performs a piece of music that is retained as sound in their head – their musical inner ear – rather than simply, and unmusically, converting symbols on a score into muscle movements. This provides a possible definition of Aural Skills for this purpose as:
Skills necessary to receive, process, organise, understand, and hence fully apprehend, as conceived musical sound, the music we wish to perform.
The bit I want to focus on is understanding, but, as I think we’ll see, all those verbs may end up being more integrated than it may at first appear.
I hear a lot of student performances at the Academy and on the whole the standard is great; they’re technically very polished and could frequently pass as professional. But without wanting to put our students down, as an educator, I should always be looking for ways in which things could be better, and I sometimes feel performances lack some expressive conviction. The underlying feeling is that the performer doesn’t quite know what it is that they’re trying to express – in other words there is a bit of understanding missing.
This chimes very much with my own experience as a performer. I remember, as a clarinet student, performing the Brahms Eb sonata Op.120/2 and, on a particularly long slow phrase, thinking, ‘I don’t know what the purpose or function of this note is; what am I trying to do with it? Should it be growing; or fading? What role does it play within its surroundings?’ And so on.
Functions of notes could mean a variety of things, but in this paper I want to focus on pitch function in tonal music, and propose the probably much debated notion that greater analytical understanding, of the various pitch functions of the various elements of a phrase of tonal music, results in a better idea of how to express that phrase.
Why should this concern us as Aural trainers? (We teach lots of analytical skills to our students here in a strand that runs roughly parallel to our Aural Skills training). Well, it’s because music is of course sound – not a score – and so you might work out a lot of quasi-mathematical relationships between elements on a score, but if you can’t hear it, you can’t fully understand it. It’s a bit like watching a foreign language film but only understanding it by reading the subtitles.
So what evidence do I have that our students don’t hear the music they play with sufficient analytical understanding?
Well, I have talked to many of them about how they determine pitch in sight-singing and melody dictation exercises, but one can also tell from the points where they make mistakes and the kinds of those mistakes, that they are finding pitches overwhelmingly by interval from the previous or possibly other very recent note, rather than by what is often called scale degree, or by relation to tonal and harmonic context. It is of course this latter which would indicate a more sophisticated understanding of pitch function.
Here, for example, is a sight-singing exercise which all the first-year undergraduates (n = 106) did as part of an assessment last year.
Fig. 1 Aural Skills Level 1 Practical Exam March 2016, Q.2
This, by the way, was marked holistically and therefore probably quite unscientifically but the average score was 60.1%. Looking at it, you can see it was deliberately written to start easy and then get gradually harder (while remaining strictly tonal). Using the interval-from-previous-note method, it starts to get tricky in bar 5 and is pretty challenging from 7 to the end. Obviously concerning for me is the observation that, although the final bars are strictly limited to the harmonic pitches of a simple V7-I, these were probably the least well-performed notes.
I am not arguing for thinking about Roman-numeral analysis during performance;
I believe we should just think the sound, but it should be a sound that is conceived after thorough training, practice and preparation that involves understanding, and there is some evidence that the understanding can be there at a deeper level beneath conscious awareness.
This is going to sound a bit esoteric and Zen, but I’ll tell you anyway. I was lucky enough to go and study in Hannover with a clarinet professor called Hans Deinzer, who taught me to conceive the sound I wished to play, in response to which, my body and instrument automatically (after a few thousand hours of practice) produced that sound in all its conceived details – pitch, attack, tuning, dynamic gradation, colour – and with an understanding of its function. It might sound far-fetched, but that is how I experienced it (when I got it right, which was a minority of the time).
A performance is of course a sequence of such conceived sounds or notes, retrieved from memory which includes a greater or lesser understanding of how they all relate to each other. Looking into the psychology, retrieval of any musical component from long-term memory is enabled by finding the right cue. Context is also encoded in the complex web of memory traces, so recognition of melodic or harmonic context of a note may be part of the cuing process. We also process music in ‘chunks’ (Miller 1956) of notes, which may further be grouped into larger chunks, in order not to overload our working memory, which is thought to be able to deal with only around seven items at once (Miller 1956, Baddeley 1986). Also involved are ‘schemas’ (Snyder, in Hallam et al (eds.) 2009) or previously stored melodic configurations or harmonic combinations or progressions, cadences etc. Correlation of groups of notes to schemas facilitates processing them as a chunk (Levitin 2006).
Fig. 2 A Simplified Model of Music Information Processing
(adapted from the Atkinson-Shiffrin model, 1968)
Thus it seems memory encoding and retrieval skills are integrated with recognition skills: interval recognition and recognition by scale-degree or tonal/harmonic function, ie. our understanding. So when we conceive a sound for performance, there can be a great deal of understanding bound up with it.
I’ve already stated a preference for tonal/harmonic function over interval recognition because of what I believe it may contribute to performance, but there are studies which suggest that the sheer process of recognition alone works better where relation to tonal/harmonic context is more developed (Brattico et al, 2001; Potter, 1990; Sloboda et al 1985).
So how do we improve this? Clearly, familiarity with schemas is important, and unfortunately, at the bottom end of the ability range of our students, we do simply have to do a bit of systematic familiarisation, even by rote. Two of my colleagues Thomas Oehler, and Colin Huehns, have devised sets of singing exercises, possibly from slightly different pedagogical standpoints but, learning schemas is essentially the aim.
But how do we specifically promote the processing of elements in melodies etc. in terms of their function within the tonal/harmonic context? We can do dictation-type exercises in which we ask them to write down the functions of what they hear, rather than just the notes. In other words, write down Roman-numeral chord labels in exercises such as this:
Fig. 3 Worksheet used in Aural Skills Level 1 classroom training
There are lots of variations on this principle of course and many are widely used and in various Aural training text-books, workbooks, and more recently computer software (eg. Karpinski, 2007; Auralia software). The use of a skeleton score like this one is one of my trademarks and helps locate the harmonies we’re talking about in the class situation with minimal confusion. I think it’s important if possible to use a real performance of real music because it immediately relates the exercise to the performing context.
One could do it alongside dictation elements (write down the melody and or the bass line) but that can still encourage thinking of notes in absolute pitch terms rather than their function and they could still end up doing an interval-by-interval transcription prior to working out functions. Even so, it’s probably still useful.
Just parenthetically at this point, I should mention those students with absolute pitch, of whom we have a good number. I find they are just as guilty on the whole of neglecting the tonal/harmonic context of the music (I know this from having talked to them), as they simply recognise pitch in sight-singing or dictation exercises in relation to their internal absolute pitch set. Even if I make them transpose (which they hate) they tend to recognise each note and transpose it individually rather than relate to context.
And in the chord-labelling exercise above, these students too will tend to think ‘that’s a C, an E and a G, therefore it’s a major triad on the tonic root’ rather than simply hearing a tonic major triad which, it might be fair to speculate, is the neurologically more streamlined route towards the potential expressive content of the notes involved. The situation can get worse if there’s dissonance involved which isn’t recognised as such.
But I have recently tried a new (for me) exercise which is a kind of vocal figured-bass realisation but made more explicitly or exclusively functional on the various levels by replacing the pitch-specific bass-line with chord labels. In other words, it’s a kind of inverse of chord labelling, in which one sings, for example, the following, using any pitch as I1:
I5 1 3 1 IV4 3 3 ii1 3 1 V4 3 I1 23
which translates as:
Fig. 4 Mozart, Clarinet Quintet K.581, ii) Larghetto (opening)
Or, at a more advanced level:
I1 2 3 5 3 5 6 5 3 V5 IV3 4 vi3 4 5 ii(i3 viio5) II5
ii(V1 1 1 7 6 5 1 i3 2 1 ) V1 1 1 7 6 iii(V3 5 i1)
which translates as:
Fig. 5 Berlioz, Les Nuits d’Été, i) Villanelle (opening)
Again, this extends from various fairly widely used ideas (singing Roman-numerals – Karpinski, 2007), and notation systems (such as movable-‘do’ solfege) although I personally haven’t seen it done precisely like this with figuring, effectively to notate a full melody in functional terms. We have to make slight adaptations to normal chord labelling and figured bass, but it’s hopefully self-evident why we need to use, for example, I1.
I’m in the early days of doing these exercises in class and so I’m afraid I can’t yet report as to its efficacy. But the classroom pilot has worked in the sense that students quickly get used to reading and understanding the code and some are already more fluent than I am. You can start by just singing the Roman numerals, then maybe select out the quicker ones in the class to sing the figures while the others sing the numerals; then swap. You can add rhythm by traditional notation once they’ve got the pitch. You could conceivably add a second line or a bass line with another set of parallel figures.
But crucially we are now forcing them (even, by their own admission, those with absolute-pitch) to use tonal/harmonic context at the very first hurdle to determine pitch. They have to understand it before they can even hear or sing it.
Taking the fifth note of the Mozart melody, they must first relate it from chord IV. Already it starts to acquire some gravity – even the relatively common chord IV in Mozart is a relatively expressive harmony. Then they must work out that this is the dissonant augmented 4th degree above the root of IV, falling and resolving to the 3rd, and the expressive potential of this note is revealed by the time they can actually get to sing it.
One might often hear this phrase performed beautifully, with a hushed and burnished, rich sound, perfectly in tune, and yet, for all that, I would also like in an ideal world to hear some apparent awareness or communication of the significance of that fifth note. I’m not saying there’s a ‘right’ way to play it – it doesn’t need to be unsubtly accented – but if we were waltzing to this music, we would take a bigger step on that downbeat and Mozart has chosen to add a gesture to that step which somehow I think a performer needs to make.
I’m aware there is perhaps an as yet under-discussed gap between recognition of tonal/harmonic function of a note and a possible understanding of how to express it in performance. But intuitively and from experience, I feel that once I’ve put an analytical label on a note or group of notes I have got ninety percent of the way there. That final step to interpretation and performance is, for now, beyond the scope of this discussion.
References
Richard Atkinson and Richard Shiffrin, ‘Human memory: A proposed system and its control processes’ in Spence, K. W., & Spence, J. T. The psychology of learning and motivation (Volume 2) (New York: Academic Press 1968) pp. 89–195. As a model of memory processes, this has been criticised and superseded by other models, particularly concerning Working Memory (originally ‘Short-Term Memory’ in the Atkinson-Shiffrin model) and the separation of the Sensory Register. Working Memory and Long Term Memory are now thought to consist of a number of components. The diagram presented above as Fig. 2, however, is an attempt to present a simplified illustration of the principal processes discussed.