Béla Bartók’s Music for Strings, Percussion, and Celeste highlights Bartók's mastery of orchestration, and innovation with rhythm. However, the opening movement perhaps least exemplifies these features (relative to the other movements). The first movement of the work instead showcases his mastery of counterpoint with a particularly praiseworthy example.

While Lendvai’s position may leave room for scholars to debate, this fugue is doubtless a demonstrably taut, elegant and balanced work of art. It is a piece of music that forms a cohesive and coherent whole without aid of conventional tonality or metric regularity. Bartók instead uses techniques and tools creates unity and direction through constructing a subject that is internally self-referential in contour, and form, and by achieving formal balance at the micro and macro level through careful structure of subject entrances as well as placement and pacing of dynamics and contrapuntal variation techniques to create a coherent arch form.

Subject: Segmentation and Affinity. Self-reference.

As Smith notes, “The most distinguishable part of any fugue has to be its first subject entrance.” The structure of the fugue subject alone deserves considerable attention and comment.

Figure 1. Fugue subject: mm. 1-4

Figure 1. Fugue subject: mm. 1-4

First and perhaps most immediately noticeable is the ambiguity created through shifting meter: each measure is constructed using a different time signature than the bar preceding or following it. The first and third measures both make use of 8/8, but this does not violate that principal. Each musical segment consists of one measure initiated by its anacrusis; the first two segments use one eighth note anacrusis (both of which are performed by the violas at A3, hereafter referred to as 9 using pitch class notation) and the latter two use two eight notes. Each of the four segments is separated by an eighth rest. 

Figure 2. Fugue subject segment and pitch class annotation.

Figure 2. Fugue subject segment and pitch class annotation.

Second, and with closer attention to pitch organization (see fig. 2), it becomes clear that the first two segments begin identically with ordered pitch-class set (9T1); this could ordinarily be called a motive. The latter two segments vary both with regard to rhythmic and pitch-class content, yet show significant affinity. Indeed the fourth segment perfectly transposes the third segment down a half-step and then modifies the rhythmic frame. In this way, the segments are hereafter called a1, a2, b1 and b2 respectively.

While beginning with identically, segments a1 and a2 have many other layers of symmetry. First, a2 can be interpreted as merely an interpolated version of a1. This is best visualized when comparing the measures vertically (see fig. 3)

Figure 3. Vertical analysis: segments a1 and a2.

Figure 3. Vertical analysis: segments a1 and a2.


Alternatively, these segments can be viewed from the perspective of ordered pitch-class intervals. This approach reveals additional layers of quasi-motivic unity and affinity between each segment. 

Figure 4. Ordered pitch-class interval analysis (with direction)

Figure 4. Ordered pitch-class interval analysis (with direction)

Looking at only measures 1 and 2 in tabular form, further conclusions may be drawn. As previously noted, a1 and a2 begin with (9T1), ergo they begin with identical intervals. They also conclude with two identical downward half steps (labeled D1). However the remaining interior intervallic content of the longer segment a2 can also be analyzed against that of a1. 

a1 U1 U3 D1 D1
a2 U1 U3 U1 U1 D3 D1 D1

Figure 5. Interior interval class comparison. U=up, D=down, 1=one half-step, 3=three half-steps.

As shown in fig. 5, the interior of a2 is itself a transposed retrograde of a1. Therefore, every interval of a1 can be said to have an intelligible form of affinity with the slightly lengthier a2. This type of work can be repeated in detail across the following two segments. Of b1 and b2 (whose interval contours are identical), the most noticeable affinity can be found by comparing a1 with its anacruses omitted. With that omission it is easy to see that all three segments relate very cleanly to the head. Segments b1 and b2 thereby represent a form of musical pig-latin. These overlaps and affinities can also thought of as self-referential.

Subject: Pitch Content

Upon still closer analysis, the subject yields a clear sense of the harmonic structure to come. Interestingly, the subject does make use of eight pitches, just as would any diatonic major or minor scale (including the necessary resolving octave). However, the eight pitches used are eight consecutive chromatic neighbors, those being A3 through E4.  As traditional tonality has, therefore, given way to what many post-tonal analysts refer to as centricity, one may need to explore “the entire spectrum of centric effects”.  Indeed, alternative analyses are required here. 

Pitch Class Frequency only Duration included
9 2 2
T 4 5
E 4 5
0 5 7
1 5 6
2 3 4
3 2 2
4 1 1
rest (3) 3
Total 27 35

Figure 6. Pitch Salience: with and without considering duration

Under the lens of pitch class salience, the fugue subject yields additional data. Taking the eight pitch classes in a tabular form (see fig. 6), one may observe its content in a statistical sense. The “frequency only” column lists the number of occurrences of each pitch class while the “duration included column awards “additional points” for quarter notes (double the duration=double the points). In the chart in fig. 7, these relationships help clarify the prevalent pitch classes.

In this light, PC0 is clearly the dominant class, and also happens to be roughly in the center between PC9 and PC4.  This is puzzling, at least in part, because the subject entrance (both for segment a1 and a2) is PC9, yet these are the only two occurrences of that PC. Historically, entrances of fugue subjects are tracked using the first pitch of each entrance, even in myriad cases where the first pitch is not the same as the tonic. This ambiguity may lead one to ask whether PC9 is meant to be heard as central. This question will resurface at the end, both of the movement, and of this document.

Figure 7. Subject Pitch Class Content

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This has been an online sample. Read the complete paper below:


Bartok Key Plan. Recreated from Source: Lendvai, Ernő. Bartók's Style. Edited by Katalin Fittler. Translated by Judit Pokoly. Budapest: Akkord Music Publishers, 1999. Download as PDF.


View the accompanying presentation.

Jordan Randall Smith is the Music Director of Symphony Number One.