In this paper, Johann Sebastian Bach’s Goldberg Variations (BWV 988) will be analyzed from a voice-leading perspective based on David Huron’s book, Voice Leading: The Science Behind a Musical Art (2016). The reason to select this work is the complexity of the variations that made them well-known across centuries and schools. This stylishness brings the question of: “How does J. S. Bach’s writing style line up with the top-down processing mechanism (voice leading) as well as the bottom-up approach (4 part-writing rules) in the context of predictability?”. This paper will be focusing on the first 16-measures of Variation 5, which was written for two keyboards and requires extensive virtuosity to play duly. I believe that the extremity that this piece offers will be valuable to align the piece with the set of principles that Huron has provided.
A broad look at the piece can be established by deciding the tessitura of the piece. Usually ranging from E2 to G5, tessitura is the most commonly used range for pitches that also offers the most distinctive pitch information as human hearing is not linear throughout the hearing range. The range of this piece is G2 to B5, which nearly fits exactly into the preferred range due to both ends of the spectrum do not occur often. For tessitura, B3 to G5 range can be accepted as the most time spent for the first 16-measures.
Another important aspect of this variation is that hand-crossing is happening multiple times throughout the piece since it was written for two keyboards. The hand-crossing concept can be evaluated from many directions as it is fundamental to the perception of voice leading and timbre for this specific piece. At this point, it is better to mention trill and yodel boundaries for further discussion. Smaller interval sizes and slower tempos will lead to hearing one stream, defined as trill boundary, which is almost a flat curve along the tempo plane. Contrarily, larger interval sizes and faster tempos will lead to hearing two streams, defined as yodel boundary, which is almost a vertical arc along the interval size plane. In the region between these boundaries, it is possible to hear one or two auditory streams depending on the context or listener’s perception. We can observe momentary or note-specific hand-crossing on the left hand at the start of the piece, as seen in Fig. 1. This vast leap from G3 to B4, then coming back to G3, and the repetition of this pattern for almost 8-measures creates a contrasting melody competing with the right-hand melody, which is a stream of notes. However, as these successive melodic intervals of these leaps on left hand fall into the yodel boundary (+16 semitone difference in very short duration), it is possible to hear two static beeping tones with no sense of movement between the pitches (Huron, 70). Right-hand movement on the 3rd beat of m. 5 is the first time we can hear two streams for the first time as the interval between successive notes is larger than 5 semitones. Again, there is a similar separation on the 2nd and 3rd beat of m. 6 and 1st beat of m. 7. These moments point out a deviation from the trill boundary that was maintained for the first 4-measures.
The continuity is maintained very well for the first 8-measures with significant predictability elements that were already ensured at m. 2 as the ascending and descending movement on the right hand is presented. Nevertheless, the transition in m. 4 is the ending of the first phrase, as shown in Fig. 2. This time, we are introduced to successive intervals larger than two steps that break our expectations on left hand, yet also building up another tension as the successive intervals increase and then decrease during mm. 6-7..
With the highest note B5 occurring on the downbeat of m. 9 as stated in Fig. 2, we start to hear a shift in overall timbre. This moment of change is emphasized using the evocation of a high pitched noted as a timbral distinction. The rapid motion of extending and reverting the interval size starting at m. 6 on the left-hand leads to a transition in m. 8. The movement on the left hand starting at m. 9 is inversely related to movement on the right hand, going down on the second beat then up on the third beat versus going up on the second beat then down on the third beat. In one way, it is only a permutation, but it is good enough to overcome the pattern that was established earlier. The previous pattern on the right hand maintained until the 2nd beat of m. 8 is reverted in the pitch direction, which is the new pattern on the left hand. Narrowed down interval size for the upcoming sections creates a new texture with less contrast than earlier sections.
The auditory stream segregation becomes more of an issue at m. 11, where differing from the earlier sections, although sixteenth notes are still played in one hand, in the other one rests have been removed and replaced with eighths. This split second is a striking moment in the piece as the importance of the rests is now more distinguishable. This moment also can be perceived as more of a flood or as a feeling of crowdedness. The reason for the overpopulation could be related to the leap lengthening rule, as Huron (p. 92) suggests that “when a large leap is unavoidable, long durations are preferred for either one or both of the tones forming the leap”. This is partially related to a narrow register being used. But more importantly, as the rests are removed, the duration between each successive notes are shorter which contributes to overall crowdedness. General crowdedness is sustained throughout the first part until the end of m. 16 as can be seen from Fig. 3; there are no rests before the half cadence.
It is also important to mention the importance of the performer when it comes to notated music. Although Glenn Gould’s recording from 1981 (Columbia Records) gives an appropriate feeling for the tempo and style, a different approach from another player might change the whole feeling: especially for such a rapid piece, a slight change in tempo will have a significant impact on how we perceive the trill and yodel boundaries.
David Huron’s Voice Leading book lays out the psychological aspects of successful part-writing and explains the predictability or expectation element to convert successful part-writing into successful voice leading. As it is possible to notice from the tempo and melodic rhythm, this piece eventually suffers slightly from both trill and yodel boundary limitations and leap lengthening rule as they are both causing significant auditory stream issues overall. However, these sufferation are not hard violations; they are clever use of creating two textures that are happening at the same time yet perceptually distinctive.
Huron, D. (2016). Voice Leading: The Science behind a Musical Art. The MIT Press.
Thanks for the supervision of Dr. Jane Ellen Harrison at İstanbul Technical University, Center for Advanced Studies in Music. I wrote this paper for MYL 5032E Psychology and Neuroscience of Music course during the 2021 Spring semester.
Other music analysis papers I wrote: Form Analysis of Haydn, Piano Sonata in F major, Hob. XVI:23, 1st movement, Computational Modeling of Music Perception.