Extreme interpretation?

Some Observations on S. Rachmaninoff’s Version of Chopin’s Third Ballade in A-flat major, op. 47

- by Lasse Thoresen


The following is a brief resumé of a major essay, written as part of the Reflective Musician Project at the Norwegian Academy of Music, and awaiting complete publication in  “Collected Writings of the Orpheus Institute”. [1]  Many published studies emphasise the importance of analysing musical scores in order for the performer to prepare a high quality musical performance. The present essay is a study of the opposite approach: It shows how musical structure emerges, embodied in sound and time, in a full-fledged interpretation, and as a result reveals metrical functions beyond those traditionally found in a score analysis. While music theory certainly can teach the performer many things, music theory has other points to learn from the musical conception of accomplished performers. 

In his interpretation of Chopin’s Third Ballade S. Rachmaninoff deviates from a literal rendering of the score in many instances.  Compared to today’s standards of interpretation, his choices are extreme.  But then his contemporary A. Schoenberg calls him the pianist builder, the puritan, somebody who never went to extremes, and states his interpretations appeared the same year in and year out.  Evidently the pianist-composer Rachmaninoff does not only yield to momentary whims of emotion, but also takes care that the rubati, accelerandi and the additions of dynamics and accents, make sense as form-building elements in an organic whole.

I have pursued his logic of interpretation through selecting a few case studies from his performance. I have insisted on using qualitative rather than quantitative means.  

Methods of analysis

In the above-mentioned essay the investigations of Rachmaninoff’s music have been made by using methods that are part of the Aural Sonology Project at the Norwegian Academy of Music. [2]

They are ordered in five categories: Form-building functions, Types of velocity, Pulse typology, Flux, and Heard Metre. Below these terms will be briefly defined; for more complete definitions the reader is referred to publications mentioned in footnote 2.

‘Metre as heard’ is a new development within the Aural Sonology Project. It is published and discussed for the first time in the present essay.

Meter as heard

Aural musical metre is a regular or quasi-regular hierarchically organised time unit in middle or slow gesture-time. Its most important feature is a real or imagined recurring accent (down-beat) that functions as a metrical determinant. The term ‘imagined’ means that the recurring accent may not be a sonically manifest accent, but one projected by the listener.

The aurally perceived bar will be called an H-bar (‘heard bar’). The H-bar consists of a relatively stable number of shorter pulses (regular or oblique), called H-beats (‘heard beats’). An H-bar of four H-beats will be written: 4-H-bar. The H-bars may be organised into aural hypermeters. The H-meter (‘heard meter’) may or may not coincide with notated meter. 

Since H-meter consists in a hierarchical organisation of regular or oblique pulses in three or more strata of velocities (occasionally only in two), change in tempo may alter the H-meter. [3] The rule is that the H-beats have to be in regular or oblique gesture time, slow or quick; the duration of the H-bar should be in slow gesture time, or at the utmost in quick ambient time; the subdivisions are by preference in ripple-time, mostly regular, sometimes oblique. When changes in tempo causes pulses to pass over from one velocity type to another, the aural perception of the meter may change radically since the H-beats always need to be within the range of gesture-time, and the H-bar itself should remain within the range of (slow) gesture time. [4]

Functions internal to the H-bar are mainly a product of whether other H-beats are perceived as leading up to the Main Accent (down-beat/thesis); these are then called arsis/upbeat; or if they come in the shadow of the preceding Main Accent, they are called (stasis or after-beat).

Qualitative versus Quantitative analysis


The H-metre provides an ideal structural context for describing rubato-figures in qualitative terms since it constitutes an aural gestalt to which the performer/composer relates when playing the music. In addition, the H-metre is a unit that has a number of structural or syntactic correlates: internally the metrical functions described above; externally as elements in a greater form-building context, particularly for the dynamic form. Instead of measuring the deviations of the metre in chronometric time, the present project depicts them graphically and adds to them a characteristic of Flux. [5]


Observations on Rachmaninoff’s recorded performance (Phillips 456 943-2) of Chopin’s Third Ballade, op. 47

Example 1 shows an example of a photo exported from the Acousmograph. [6] At the bottom one sees the analysis of Dynamic Forms. [7] The vertical lines are exactly aligned with the beats of the H-metre in Rachmaninoff’s performance. Long vertical lines mark the 4-H-bar, and even longer vertical lines mark the 8-H-bar (aural hypermeter). The reader will notice that the distances between the H-beats are unequal. Here the Acousmograph is of help in representing the rubato exactly, because it shows the musical sound as a spectrogram, and so it is easy to see exactly where a beat should be marked. The representation of longer and shorter durations of the beats in quantitative terms (chronometric time) are then transferred to the realm of qualitative, musical meaning (endo-semantics): the variations in length and tempo are given a flux-interpretation on the top of the vertical line, so that the longer gesture-time durations create an impression of arresting the flux of the music, the shorter ones of increasing the flow. 

Salient accents (thus generally, accents where the performer seems to place his emphases) are marked with circles placed on the vertical lines representing the H-beats. To the extent these accents have the functions of articulating the Dynamic Forms they are marked above the latter by an indication of accent function. [8] It should be noted that this analysis integrates and interprets the structural tendencies of harmony, dynamics, and rhythm, and suggests in addition the segmentation into phrases and sentences.


In addition, the total duration of the 4-H-bar is given in two ways: in chronometric time as seconds (at the bottom), reinterpreted as metronome numbers (BPM, at the top); then, in the middle, the durations indicated by a metronome numbers are stated as a note values (here dotted whole-notes). The opening bars are taken as the reference for all tempo alterations in the rest of the piece. The middle line, perhaps more ornamental than functional, shows a reduced physical imprint of the performers dynamics.

Observations of Rachmaninoff’s interpretation of the Theme Presentation 

As the H-meter of the Ballade we opt for a group of four H-beats. Comparing with the score (example 2), one will find that one H-beat corresponds to a dotted fourth-note; one H-bar corresponds to two notated bars. Thus the H-metre is in fact a hypermeter.

The form of the theme-presentation is a ‘Period’ in A. Schoenberg’s terminology [9] consisting of two phrases (antecedent and consequent) the beginning of each containing the core idea. The theme presentation as a whole is perceived to be presence-oriented. A closer look into the four constituent phrases can then be made; the dynamic form of the first and the third are similar, the last one (fourth) is different from the third in being entirely symmetric. [10] The analysis takes into account the dynamics that Rachmaninoff imposes on the time-directions that are already implicit in the composed texture: the secondary time-directions result from that fact that Rachmaninoff starts the phrases stronger and play them in a diminuendo, and supports this by instances of ritardandi. Particularly noteworthy is the accent he places on the third H-bar.

Closer scrutiny of the performance shows that the H-beats are really irregular (Ex. 1). A theme presentation would need a degree of stasis and self-containment in order to communicate its axiomatic status in the musical form to the listener. The presence-orientation we pointed out in the analysis is essential in this regard. However, the strong rubati that we observe in Rachmaninoff’s performance could easily obstruct this character. The challenge for a performer that – for expressive reasons – would like to play molto rubato, would then be how to counterbalance these irregularities with a sufficient symmetry and balance. Rachmaninoff’s solution is striking, although not immediately evident to the untrained ear: The duration of all four H-bars is exactly equal despite their internal irregularities! Thus a strong reference for the time feeling of the music is set. This is further enhanced by the last phrase of the theme-presentation: The H-beats present exactly equal subdivisions of the 4-H-bar that previously had been played molto rubato. One may marvel at the aural time-consciousness that Rachmaninoff as a performer must have possessed in managing to balance the variable H-beats up against the longer values of the H-bars; and then of course contextualising these within a tempo-plan that pertains to the overall form.

Another original feature of Rachmaninoff’s interpretation is that he imposes a declining dynamic tendency on most of the phrases. Traces of the physical amplitude of his dynamics can be seen on the wavy middle line. This influences the dynamic form of the phrase, thus a backward-oriented secondary time-direction is drawn along the whole phrase, one that to a certain extent contradicts the tendencies that are already implicit and the metrical, rhythmical and tonal forces that provide the composed structural anatomy of the music.


…The full essay goes on to analyse a number of sections of Rachmaninoff’s performance in a similar way. The play with a regular metre is summed up in terms of endosemantic isotopies, i.e. meanings arising in a specific musical context and describable as conceptual opposites describing the musical development.  Some examples:

Setting (of a statement) versus Passing (“Satz versus Gang”) e.g. passing through to reach a goal)

Suspension versus Release; corresponding to Friction versus Flow

Metric Conflict versus metric Affirmation

Disappearance of H-beats versus Re-emergence, Effacing versus Filling

Collapse/Destruction of metre versus Restoration


Notating oblique metres: a composer’s postscript

Most music theoreticians deal with metre on the basis of musica recta: the regular time of notated music. This paper, however, has presented a number of observations pertaining to the musica ficta of actual performance.

In the interpretation of contemporary music, the exact reading of the score is indeed regarded as basic, since no general performance praxis of rhythmic modification exists. During the second half of the twentieth century musical notation has been developed both in the direction of increased specificity and complexity (e.g. Messiaen, and Boulez), and in the direction of non-specificity and simplicity (e.g. spatial notation, and the ‘aleatoric’ notation such as used in Lutoslawskij’s music). Both strategies have served the purpose of making possible the rendition of oblique and irregular rhythms. If an aesthetical objective were to render oblique values in musical notation without a fine, explicit mensural unit, the challenge would be to find good compromises between the notational necessity of a regular counting unit and the aurally perceived duration of oblique beats. This is what I have been attempting to achieve in my own compositions. [11] If I would like a rhythmic character of the kind that Rachmaninoff produces in the discussed interpretation, I would have to notate my rhythmic intentions much more precisely than Chopin has done, since most modern pianists would never dare to approach a modern score with the requisite degree of rhythmic freedom, or might end up making arbitrary or irrelevant modifications.


Below (ex. 2) is a rather exact transcription of Rachmaninoff’s interpretation of the theme phrase. The ‘resolution’ is a pulse MM 480, the thirty-second notes. The vertical lines show the H-metre (compare example 1 and 2 above):

I find such a transcription useless for performance purposes. It is technically exact, but it invites a mechanical attitude to the performance. The silent counting of an implicit mensural unit in the tempo of M.M. 480 would be a disturbing occupation that would the draw the performer’s attention and energy away from listening to the music and from a more intuitive and expressive form of timing.

A transcription such as the following one (Example 3) might work considerably better:

This type of notation indicates first of all the number of beats in a bar, then their individual durations by means of an implicit, regular mensural unit (one which is never played and never heard as such). The small x occurring after the notes in the time signature of the second bar add a fourth to the preceding value, so that the duration of a fourth note with an x equals five sixteenth notes. Beams are turned so as to show to which beat they belong. A performer rehearsing such a rhythm would have to learn the beats as a spontaneously mastered rhythm, and then approximate their subdivision when in actual performance, with a certain leeway for expressive deviations. Importantly, the notation maintains focus on the four beats of the metre. Possibly, it could be simplified even more in order to give the performer enough of a leeway for interpretation, while giving sufficient suggestions to avoid arbitrary choices. Such a simplification should never the less take into account that the bars need to have the same duration.

[1] The present text is based on my presentations at the Orpheus Institute 30 and 31 April 2015.

The methods have been published in L. Thoresen ‘Emergent Musical Forms.  Aural Explorations. Studies in Music from the University of Western Ontario. Volume 24., London CA. See also www.auralosonology.com.   Previous publications: L. Thoresen, ‘An Auditive Analysis of Schubert’s Piano Sonata Op. 42’, in: Semiotica, 66(1–3) (1987), pp. 211–37. L. Thoresen, ‘Form-building Transformations: An Approach to the Aural Analysis of Emergent Musikal Forms’ in: Journal of Music and Meaning 4; section 3 2007, http://www.musicandmeaning.net. L. Thoresen (with the assistance of Andreas Hedman), ‘Form-Building Gestalts and Metaphorical Meaning’ in: Organised Sound, 15(2) 2010, pp. 82–95. [back]

[2] The basic velocities in most music occupy a certain range of velocities that we have dubbed gesture-time. Gesture-time velocities are the one that musicians prefer to use as a basis for musical time coordination, – thus the range of tempi from the slowest to the fastest that a conductor would choose to mark with his beats. Gesture time is usually found in the range from appr. 25 to 200 bpm.

The quickest pulse-speed we have called flutter-time. Sound-events moving in this speed approach a continuum: a stepwise passage will be perceived as an iterated glissando; a chord arpeggiated in flutter-time suggests the simultaneous presence of all the tones or sound-events involved. Flutter time is usually found in the range above 500 bpm. [back]

[3] Ripple-time is the name we have given to velocities between gesture-time, where sound-events are clearly individualized, and flutter-time, where they tend to merge. These are velocities that often serve as subdivisions of the main musical pulse that normally is in gesture-time. Ripple-time may take the role of a quick clock-pulse: orchestral musicians often subdivide units mentally using a pulse in ripple-time as their mensural unit. Ripple time is usually found in the range from appr. 200 to 500 bpm.

Ambient-time is the slowest of the velocities; it is called ambient, since sound-events in this time are often shoved into the background by sound-events in gesture-time.  Ambient time is usually found in the range below appr. 25 bpm.

Pulses in gesture-time and ripple time can be categorized as being regular  (thus even), irregular (unpredictable) or something in between (oblique; e.g. pulses in time proportions of 3:5). [back]

[4] These observations seem generally to be confirmed by empirical research, see e.g. J. London, 2012, pp. 28-47. [back]

[5] Flux is an endosemantic isotopy that can be defined as the impression of musical flow versus friction, which in the extreme means arrest of movement.  Arrows pointing to the right mean flow, arrows to the left friction; the more arrows, the stronger the tendency. [back]

[6] The Acousmograph and the Aural Sonology plug-in can be freely downloaded from INA/GRM’s website. This and the following examples are displayed as tiny html movies at www.auralsonology.com [back]

[7] The dynamic form is analysed by identifying form-building functions: presence-oriented of stable (notated by a square square ), forward-oriented or increasing (crescendo-shaped triangles), and backward-leaning or decreasing (diminuendo-shaped triangles). Vaguer or secondary tendencies are notated with perforated lines. [back]

[8] For further definitions see www.auralsonology.com/the-signs/chapter-8-dynamic-forms/ [back]

[9] A. Schoenberg, Fundamentals of Musical Composition, Faber & Faber, London 1967, pp. 20–28. [back]

[10] Note that the dynamic form analysis synthesizes event-tempo, dynamics and accentuation, harmonic functions and linear directionality, but includes also to a limited degree the inherent energy shape of the constituent sounds. A piano sound is by itself a diminuendo, so a long, exposed piano note can potentially influence the overall impression, resulting in a receding time-direction. [back]

[11] Examples are found in a number of my compositions such as YR (solo violin), AbUno (chamber ensemble), The Descent of Luminous Water (Piano Trio), all published by Pizzicato Verlag Helvetia. [back]