Semantic gravity of music notation

Notation serves multiple purposes in musical practices and thus differences in how it is used can be observed according to those purposes. That is to say, more or less musical information with greater or lesser detail and precision may be provided depending on how the notation is intended to be used. I will start by characterising different notation in conjunction with the concept of semantic gravity to form a framework which will be applied to the specific use of notation in texts. It is worth specifying that the comparisons in this analysis are relative to the specific data set and the specific use in writing about performance: in other research contexts, what counts as stronger semantic gravity or weaker semantic gravity may have to be redefined.

Let us start with a particularly important notational text typeFootnote ¹ for jazz performance analysis, the transcription. The notation of a transcription attempts to mirror particular performances through a strong correlation between the rhythm and pitches written and those performed, whether representing an actual improvisation, or embellishments used in jazz performance. It therefore is characterised by relatively strong semantic gravity. Other information which conveys the stronger semantic gravity in the notational text itself occurs in the textual elements such as multiple headings, which specify performer, song title, album or performance, section of the music (e.g., first solo), and transcriber. This contextual information reinforces that the music describes a specific performance, by a specific performer, at a specific time, and often a specific place. While there are still various qualities which are not or cannot easily be transcribed, such as timbre or attack, the notation is strongly tied to its context, and thus exhibits stronger semantic gravity. Figure 2 displays a transcribed excerpt of an improvisation by Brad Mehldau (transcribed by student) of Bewitched (Rodgers & Hart, 1940/1981). It specifies the instrumentation and the exact pitch and rhythmic meanings are as faithful to the performance as the transcriber could make them.

Figure 2.

Transcription of Brad Mehldau improvisation of Bewitched (transcribed by student)

I take the transcription as the strongest point for semantic gravity of notation of the four types relevant in this study. I will now consider how other notational text types display weaker semantic gravity than the transcription.

The most common text type of Western staff notation in formal music education is the score. Whether for an orchestral arrangement or a piano study, a score specifies the notes to be played with accurate rhythm. Although the precise tempo may vary from piece to piece and performance to performance, the rhythm remains relatively internally consistent. Such notation therefore, while specifying piece or song, nonetheless covers a range of largely similar performances. While there can be some variation between performances, such as variations of duration (i.e., swing), or of performing media if not specified, these variations occur largely within the concepts not prescribed by music notation, such as timbre, and some instrumental methods, such as direction of bowing, attack and articulation. The primary meanings of notation, those of pitch and rhythm, melody and harmony, are relatively consistent across performances.

The aspects which strengthen the semantic gravity in regards to scores are those which ground its performance: identifying performance instrument (e.g., violin) and how it is to be played (e.g., pizzicato), providing time reference (e.g., 4/4), and specifying both notes and rhythms to be played (e.g., swing). Nonetheless the music notation does not specify particular performers, only instruments; thus one trombonist's performance may be substituted by another trombonist's performance. It also covers, and is intended to cover, a range of performances. Therefore the same pieces of music can be played relatively the same, at different times and in different locations by different people.

As an example, let us return to the song Bewitched. It was originally composed by Hart and Rodgers for the musical Pal Joey (1940/1981). The sheet music for the musical, in addition to labelling the title and composers, specifies instrumentation and the exact pitch and rhythm for each part to play. This enables instrumentalists to be changed, and different orchestras to play the piece at different times in different venues, in support of different casts. Such is the nature of music notation, and its strength. Therefore, scores will generally exhibit slightly weaker semantic gravity than a transcription, as they are less locked onto specific performances and specific performers.

Arguably the most common notational text type in jazz studies is the lead sheet. Lead sheets provide fewer details than a musical score: they specify the melody and the harmonic structure with chords symbols or tabs, and the labelling of sections (e.g., bridge, head) enables these to be sequenced in the typical patterns of the given genre. Thus Bewitched (Rodgers & Hart, Reference RODGERS, HART and Sher2000), represented as a lead sheet in Figure 3, includes only the melody, with potential harmonies indicated by chords which are in line with jazz harmonic conventions.

Figure 3.

Bewitched lead sheet (Rodgers & Hart, 1940/Reference RODGERS, HART and Sher2000)

The lead sheet therefore displays weaker semantic gravity than the score; it covers a range of possible performances but does not precisely represent any of them. The melody itself is changed from what is notated according to rhythmic variations of swing. The chords suggest a range of consonant notes that may be applied at any time, and by various instrumentation, according to the conventions of the field. Therefore there is greater variation between the possible performances of Bewitched which might use the lead sheet, and the notation on the lead sheet itself, than between the possible performances described by the musical score and the score itself. Thus scored music displays stronger semantic gravity than lead sheets, and lead sheets describe weaker semantic gravity than a score.

The final notational text type to consider is the harmonic progression. A harmonic progression displays the harmonic structure of a piece and one of a number of consonant options. It does not relate to any performance, and in fact may not relate to a single song as many pieces in jazz share a harmonic structure (contrafacts) and differ in melody. To return to Question and Answer (Metheny, Reference METHENY1989), Figure 4 is a harmonic progression for the first four bars, displaying the structure largely with the chord symbols, and a consonant pitch for each chord. It therefore does not represent a particular performance but instead extracts essential information about the piece. There is therefore a relatively weak connection between this notational text type and performances; it exhibits relatively weak semantic gravity.

Figure 4.

Harmonic progression of Question and Answer by Pat Metheny (Reference METHENY1989)

This is a brief and somewhat crude overview of four notational text types; there are others which occur between and beyond these four, or there are times when one notational text type is not used for its typical purpose, e.g., a classical music score reinterpreted according to jazz principles. Nevertheless this provides a functional departure point and the four types can be placed along a cline as depicted in Figure 5, with the strongest semantic gravity, and thus the most embedded in performance, at the bottom, and the weakest semantic gravity, and thus the least embedded in performance, at the top. One reason for using this variety of notation, as shall be demonstrated below, is that while stronger semantic gravity allows for accurate and precise descriptions, weaker semantic gravity enables generalizable insights and analysis.

Figure 5.

Cline of semantic gravity of notational text types

I am necessarily simplifying the complexity of notation. My point is not to provide definitive categorisations of notational text types, otherwise we risk providing an endless typology which is continually fragmented into sub-types. Instead, my aim is to highlight how semantic gravity can reveal the principles by which notation text types are selected and utilised and thus how they contribute to representing musical knowledge.

This will therefore provide groundwork for considering actual instances within the data of research.

Semantic gravity profile of notational excerpts

Mapping the variations in semantic gravity through the use of different notational quotes over the course of a text produces a profile of the text (Maton, Reference MATON2014). I will compare how two performance students, in 5000-word research projects, used notational quotes in different ways to generate different semantic profiles and then consider the implications of these different profiles.

The first text to consider focused on a double bass player and his performance of bass lines rather than improvisations. The writer titled her research project ‘A discussion of Ron Carter's construction of bass lines’ and analysed the bass lines from three pieces which she had transcribed. In her text, she used short excerpts of the transcriptions of generally two to six bars, as shown in Figure 6.

Figure 6.

Bass line transcription example Beatrice bars 105–107 (transcribed by student)

The only variations were a single instance of the melody line for the relevant piece, and a pedagogical example from the bass musician's instructional book which demonstrated consonant note choices for certain chords but which were not related to a specific performance or song. This can be represented in semantic profile (see Figure 7) as a low semantic flat line with few variations.

Figure 7.

Semantic gravity profile of notation in text 1

Given the use of transcriptions, we can therefore characterise it as having relatively strong semantic gravity, as the knowledge represented is tied to a particular performance that was not pre-composed. This is further developed in the captions as each excerpt is specified by performer (Ron Carter), piece (e.g., Dolphin Dance) and section within the piece (e.g., bars 20–24). As was observed above, transcriptions establish strong correlations between the notes played and the notes depicted, therefore having stronger semantic gravity than the melody line which would be idiomatically performed with rhythmic and potentially pitch variations. As the pedagogical example represents several hypothetical options but no particular performance, it is represented as having weaker semantic gravity than the transcriptions.

The second text focused on a range of musicians and instruments to argue for a particular improvisation technique. The writer titled his research project ‘Improvising the song’ and wrote his own essay question to respond to:

In comparison to text 1, he used notational excerpts of varying lengths, from a one bar lick, to 16 bars of the lead sheet, and in the appendix an entire improvisation. The second student used transcriptions as well, but in addition included lead sheet excerpts and harmonic progressions as comparisons, as well as several bebop licks. Thus semantic gravity varied over the course of his writing as he provided different perspectives of the same piece, considered underlying structure through harmonic progressions (weaker semantic gravity) and specific performances through transcriptions (stronger semantic gravity). This is therefore depicted as a semantic gravity wave (see Figure 8).

Figure 8.

Semantic gravity profile of notation in text 2

The second student therefore exhibits what Maton (Reference MATON2014) calls greater semantic range, being able to move between abstraction and specificity, while the first student's reduced semantic range means that observations, at least notationally, remain embedded in specific performances.

The selection and sequencing of examples plays a role in the variation of the second text: not just in terms of relative semantic gravity but in terms of pieces of music. The first text used excerpts from the transcription of three pieces which were included interchangeably to demonstrate examples for all concepts; by contrast the second chose pieces from different musicians and thus delineated sections around each example, providing different perspectives of each example.

Before considering the implications of these differing profiles, I will explore how the text that directly referred to the notational excerpts affected the semantic gravity.

Semantic gravity of writing about music

No matter the differences in the semantic gravity profiles of the two students’ use of music notation, accompanying text can provide greater or lesser connection to the specific performance, or greater or lesser generalisation across performances; it can strengthen or weaken the semantic gravity, or do both, or neither. I will first define how this can occur in texts; this is based on linguistic analysis described elsewhere (Martin Reference MARTIN2012, Reference MARTIN2013, Reference MARTIN2014).

Semantic gravity is strengthened in accompanying text by providing contextual information of the performance which may be lacking in the notation such as when and where the performance took place, and who was involved in the performance. It is also strengthened by increasing the embodiment of the notation, by specifying instrumental technique, such as picking versus strumming, or pivoting off strings between notes. For example, in regards to one notational excerpt, additional precision in rhythm, timbre and technique are provided by the subsequent text: ‘The bottom voice of the double stop speaks just before the upper voice, which along with the tone colour of the two notes indicates that Carter is striking the strings with his right thumb instead of using his fingers.’ It therefore connects the notation to concrete instances and observations.

Semantic gravity is weakened in accompanying text by taking the information beyond its particular context of a performance, and by providing observation independent of the realisation of the music through embodiment – such as across instruments, performers or pieces. Semantic gravity may be slightly weakened with interpretations of notation relating to musical concepts such as intervals and rhythmic patterns, (e.g., ‘there is a strong intervallic identity within this excerpt’) or weakened more substantially with reference to abstract generalisations such as the effect of musical choices (e.g., ‘Carter uses these “kicks” quite regularly because they create momentum and added rhythmic interest.’) or more aesthetic interpretations (e.g., ‘the fact that Mehldau has returned to simplistically reflect on the melody having developed ideas, which were not necessarily reminiscent of the song's original melody, in the previous four bars displays a heightened awareness of musicality’; ‘This chromatic sound is exceptionally strong, and creates an elegant melodic line.’)

It is worth noting that the use of notational excerpts necessarily strengthens semantic gravity of text by grounding concepts in examples; consequently text about notational excerpts does not greatly weaken the semantic gravity until the knowledge becomes disconnected from the specific piece. Nevertheless it provides insight into the flow of musical knowledge between concrete examples and observations and general and abstract concepts. Again a semantic gravity profile can be drawn of these two concepts, and again a sharp contrast between the two students' texts is demonstrated by the semantic profile.

Semantic gravity profile of notation and writing

In the first text, the semantic gravity profile of the language echoes that of the notation, with observations about the notation remaining strongly embedded in performance (Figure 9). It is not so much a flat line as a ripple as she does unpack details from each notational quote, embodying the performance and strengthening semantic gravity, for example,

Figure 9.

Semantic gravity profile of text and notation excerpt from text 1

She also weakens semantic gravity occasionally as she focuses on how specific techniques produce an effect for the band such as ‘This four bars creates a sudden and dramatic change in the direction of the band and almost functions as comic relief’, or for the audience such as building tension and release, e.g., ‘In this excerpt Carter has used multiple large leaps bringing a strong feeling of contrast to the line.’ Overall the effects of the performance remain relatively embedded in the physical experience of the audience and other band members, as opposed to being connected to musical theoretical concepts. Therefore the semantic gravity remains relatively strong, with disconnects as each notational example is given and then described and interpreted.

By contrast, the second text again generates a semantic gravity wave (Figure 10). The student strengthens semantic gravity by unpacking the notation, spelling out both the notes and the performance, for example, ‘Similarly the left hand in bar adds chromatic movement from B Flat – A Natural – A Flat finishing with G in the right hand's chord in bar 3’. Significantly, though, he frequently finishes discussion of a notational excerpt by weakening semantic gravity, providing general observations no longer tied to the specific performance, or performative context, but moving to the compositional trends and effects: ‘It is primarily through the rhythmic “weight” (the longer the rhythm, the more powerful and noticeable it is) that the melody is recognised.’

Figure 10.

Semantic gravity profile of text and notation excerpt from text 2

As the student is not focusing on a specific instrument, the ‘dips’ on the semantic profile are not as low as the first student as he does not emphasise the embodied performance or specific instrumentation, thus semantic gravity is not as strong as in the first student's text. When he does generalise, he reaches greater abstraction by looking at overarching theoretical concepts and their effect across performers and performances, thus conveying weaker semantic gravity than much more than the first student's text.