in Articles

Seeking the shape of music

by Jarkko Hartikainen

"Although music analysis research, measured as a percentage of Finnish musicological studies, may have declined in the past decades due to changes in paedagogics, performing arts and culture, it has also become more diverse and attained a very high level of quality, to the point of being at the cutting edge."

Of the principal trends in music analysis, Schenker analysis in particular has proved popular in Finland, being employed with an open mind in a variety of applications from master’s theses to doctoral dissertations.

Timo Virtanen, who has been the editor-in-chief of the critical edition of the complete works of Sibelius since 2006, used Schenker analysis to uncover interesting features of modern principles of organisation and form in Sibelius’s Third Symphony, generally regarded as ‘Classical’, in his dissertation Jean Sibelius, Symphony No. 3 – Manuscript Study and Analysis (2005).

Esa Lilja, who completed a dissertation at the University of Helsinki, applied Schenker analysis alongside modal scale-degree analysis and spectral analysis to heavy metal music from the 1960s to the 1980s in his book Theory and Analysis of Classic Heavy Metal Harmony (2009). Ilkka Ferm, also an alumnus of the University of Helsinki, explored the applicability of the method to jazz in his master’s thesis (in Finnish) Schenker-analyysi jazzmusiikissa (Schenker analysis in jazz music, 2013).

The early music boom of recent years has been slow to show up in dissertations in the field of music analysis, but studies such as the one completed by Hilkka-Liisa Vuori (in Finnish), Neitsyt Marian yrttitarhassa – Birgittalaissisarten matutinumin suuret responsoriot (In the herbal garden of the Virgin Mary – The great Matins responsories of the Birgittine sisters, 2011), place the bar very high. Completed at the Sibelius Academy, this dissertation analyses the origins, tunes, modes and texts of the Medieval Cantus sororum responsories used at Birgittine convents. The author has a profound expertise in the subject, as she has been singing Medieval liturgical chants with her own ensemble, Vox Silentii, for two decades. The study offers an interesting perspective on music analysis in that it aims to illustrate the organisation of pitches in the chants not only through contemporary analysis but also through an analysis of overtone harmonies. This is also the first study in which this material has been studied at all.

Jaana Utriainen, who completed her doctorate at the University of Jyväskylä, created an analysis method for musical shapes in her dissertation A Gestalt Music Analysis (2008), which focuses on a comparative study of the symbolic, acoustic and sub-symbolic representations in the vocal works of French composer Iegor Reznikoff, exploring the formation of musical shapes (Gestalt) in the listener’s consciousness. Utriainen’s method combines Gestalt philosophy, sound analysis, performance analysis, observation analysis, philosophy of mind, analysis of the composition process (through an interview with the composer) and philosophical and aesthetic contemplation. The dissertation has a theoretical, a methodical and an analytic section.

The dissertation On Conceptualization of Music (2004) by Yrjö Mikkonen, also completed at the University of Jyväskylä, takes a systemic approach to concepts of the theory and analysis of music, aiming to erode the opposition of theoretical studies and practical music-making. In the systemic approach, concepts are linked on various levels: for instance, ‘chord’ is a textural concept that is linked to the pitch system through tonal colour, temperament, form, expression and narrative. His multi-discipline approach enables the application of general theoretical results in several fields, such as communication management, training, art therapy, cognitive sciences, informatics and artificial intelligence. The study presents practical models devised by the author for the theory and analysis of music within the scope of a discipline developed by the author, the ‘systematic basics of music’.

Another new departure may be found in the dissertation on orchestration research by Ville Komppa, a work in progress at the Sibelius Academy. He compares structural analytic results obtained through Schenker analysis to their manifestations in the composer’s orchestration choices. His research framework and first results (on Beethoven’s Eroica) may be seen in the article Discussing Orchestration as an Art published in Trio I/2013, the magazine of post-graduate students at the Sibelius Academy.

Following the above brief introduction illustrating the diversity of the field, I will explore two Finnish music analysis studies in more detail. These I feel are of particular significance.

Schenker analysis goes post-tonal

In 2004, music theoretician Olli Väisälä completed a compilation dissertation entitled Prolongation in Early Post-Tonal Music – Analytical Examples and Theoretical Principles. This was a ground-breaking work, exploring early post-tonal works through Schenker analysis. The dissertation explores the theoretical foundation of a field of study that is still in the process of emerging – post-tonal prolongation – taking into account psycho-acoustic phenomena such as critical band, the proximity principle and rootedness.

Whereas traditional Schenker analysis is based on tonal conventions, Väisälä takes as his starting point the non-triadic referential harmonies found in works by Debussy, Scriabin, Schönberg, Berg and Webern. Unlike earlier analysts, Väisälä also incorporates elements from beyond set theory, such as registerial features and the overtone series. The writer evaluates his research findings from two perspectives: how well they illustrate the works studied and how well they compare to perception and psycho-acoustic principles. He also manages to tie in the well-known definition of prolongation formulated by American theorist Joseph N. Straus – separating arpeggio from voice-leading – even though Straus himself considered this impossible to do outside the framework of conventional major-minor tonality.

Väisälä’s dissertation consists of an introductory essay of about 100 pages, describing the concepts used, and three articles previously published in the distinguished musicological periodicals Music Theory Spectrum and Journal of Music Theory, and by Pendragon Press.

The first article discusses the basics of post-tonal prolongation using Schoenberg’s Piano Piece op. 19/2 as a case study. The key issue here is defining structural consonance and dissonance, and Väisälä manages this by expanding the typical set theory approach with the concept of the ‘registrally ordered interval’ and by taking into account the critical band and the psycho-acoustic properties of the overtone series in identifying the reference harmony.

In the second article, Väisälä focuses on the overtone series, concluding that the overtone series can explain the harmonic organisation of works as diverse as Scriabin’s Vers la flamme, Berg’s song op. 2/2, Debussy’s Voiles and Webern’s song op. 3/1 (all written in or around 1910) on both the surface and the deep level. This insight is a strong argument in favour of the potential of applying the triad-based Schenkerian prolongation to these works, as demonstrated by Väisälä in graphic form.

The third article discusses late works by Debussy, following the principles of reference harmony, register placement, prolongation and psycho-acoustic principles. The conclusion is that Debussy’s harmonies (especially the maj9 chord) emerge as being filtered from one or two simultaneous overtone series. In coming to this conclusion, Väisälä sheds light on features in Debussy’s music that have previously not been covered by analysis: the relationships between the harmonies and motifs on the surface level on the one hand and deep structures on the other.

Sensory perception and temporality

Composer and musicologist Timo Laiho (b. 1957) ambitiously created a completely new perceptory analysis tool in his dissertation Perception, Time and Music Analysis (2013) at the University of Helsinki. His analytic-generative methodology (AGM) aims to serve as a tool for both composition and interpretation, because it can be easily inverted from a descriptive to a creative method.

Because the study is based on perception, the temporality of music emerges as an important factor. This is a dimension that music analysis – such as set theory or Schenker analysis – usually ignores as a subjective factor. This is paradoxal, because perceptory verification is generally considered an indicator of the feasibility of analytical results. Accordingly, Laiho highlights the interesting point that while music analysis considers observation to be subjective, music psychology considers it to be involuntary, reflex-like and unconscious.

In his review of the relationship between music analysis and sensory perception, the author also discusses Schenker analysis. He considers that its structure is based on an abstract hierarchy ultimately derived from linguistics that alienates the analysis from the concrete experience. He also poses the question of what actually prolongs what, noting that the method reduces events happening at different times to concurrent events, relying on axiomatic tonal rules in a manner strongly resembling circular reasoning. He considers Olli Väisälä’s idea of a work-specific referential harmony, referred to above, to be a paradigm shift, because it starts from the concrete details of an individual work and is thus a bottom-up approach; this emphasises the temporal dimension. Still, even Väisälä’s work is geared towards identifying a stable underlying harmonic structure.

Perception, Time and Music Analysis admirably steps outside the box and anchors itself into contemporary findings in various fields of science. The first part of the work is an extensive review of the prerequisites of musical cognition and analysis, drawing on cognitive science, linguistics, semiotics and modern physics, touching also on artificial intelligence research. The treatment of the subject is post-structuralist in the spirit of Deleuze, Guattari and Derrida.

Analysis and perception are here dealt with at a very general and fundamental level, which enables the leveraging of multiple disciplines. Laiho discusses contextuality, the difference between perception and sensation, high-level and low-level processing in observation mechanisms, computer modelling of cognition (and its criticisms), structural features of formal languages, top-down and bottom-up processing, visual grouping, conceptuality and non-contextuality, and signs and sign systems. Pitch perception in relation to the overtone series is also structurally analysed.

AGM is based on the registral distance between pitches (interval) combined with their temporal distance (rhythm) – in other words, movement. The relationships plotted on the pitch and time axes are analysed using custom-developed tools.

The first of these, the musical vector (muV), is a straight line between the given pitches on the time axes; it depicts movement, or more specifically the velocity and directionality of movement. By analysing vectors beginning from the various notes in a musical phrase, one can discover connections (lines) between notes when several notes fall on the same vector, i.e. form part of the same temporal-registral movement. This distillation of structural lines is roughly equivalent to what Schenkerian analysis does with the harmonic structure, but it proceeds in a ‘bottom-down’ fashion, starting from the concrete details of the music, particularly as related to time and perception (ignoring register shifts). In an illustrative example, Laiho analyses an extract from Mahler’s Symphony no. 4 where the vectors derived from the internal structure of the theme reflect the temporal-registral shape of the entire extract.

Another key concept in AGM is the Interval–Time Complex (intiC), which from the mathematical perspective is differential calculus performed on the musical vectors (dividing the pitch interval with the temporal distance between the notes, p1–p2 / t1–t2). This tool is used for comparing musical vectors: the larger its value, the greater the movement. The Interval–Time Complex facilitates the identification of variations and also their easy generation in graphic form. The author illustrates this with variations created from a row by Schoenberg, with steadily increasing (faster movement) or decreasing (slower movement) values of intiC. He also speculates that the tool might be useful for comparing the complexity of phrases. Laiho further successfully compares the functioning of his method to the research findings of Nicola Dibben, who in 1999 examined musical stability as perceived by test subjects in this same musical extract.

The third analytical concept introduced in AGM has to do with the sectional analysis and differentiation of music. In the listener’s experience, similarities tend to be perceived as belonging to the same milieu however far apart they may be temporally. In Laiho’s Schoenberg example, the thirds-based material contrasts against the passages based on seconds that form part of the same phrase, while the entire phrase represents a territorial assemblage. The role of memory in the perception of music is highlighted, as this method is based on a ‘both-and’ concept of perception rather than an ‘either-or’ concept.

The fourth and final analytical concept in AGM, harmonic deconstruction, is left for future research to explore. Its aim is to consider the relationship of the harmonic structure to the overtone series, to analyse repeated interval structures in the harmony in relation to the bass note and to bring out the milieu and territorial structures in the harmonic framework. The dissertation also offers other interesting ideas for further development in the use of the method, even extending as far as Einstein’s theory of relativity. In discussing cognition, Laiho also constructs a wholly applicable subsemiotic (arts) analysis model of his own. Professor Alastair Borthwick from the University of Hull in the UK has noted that the dissertation has much to offer to disciplines beyond the realm of music, mentioning biology (!) as an example.


Jarkko Hartikainen is a composer and music writer and also editor-in-chief of Amfion, an online classical music magazine. His master’s thesis at the Sibelius Academy was an analysis of the playing techniques and structures of the String Quartets of Helmut Lachenmann. He has also been a peer reviewer for the Ruukku periodical of the University of Arts Helsinki.

Translation: Jaakko Mäntyjärvi
Featured photo: Eva mater, Cantus sororum