◎ JADH2016

Sep 12-14, 2016 The University of Tokyo

Quantitative Analysis for Division of Viola Parts of Mozart’s symphonies
Michiru Hirano (Tokyo Institute of Technology)

This study focuses on the fact that some of the symphonies by Wolfgang Amadeus Mozart (17561791) include two viola parts. More specifically, the goal of the study is to examine whether separating out viola parts influences the orchestration of violin parts.

Symphony refers to a genre of orchestral composition, that has been actively composed since the eighteenth century [1]. Mozart composed in excess of forty symphonies throughout his life [2]. While symphonies are usually composed for orchestras comprised primarily from four string parts (two violin parts, a viola part and a cello part), some of Mozart’s symphonies require two viola parts. We refer to this phenomenon as a separation of the viola parts within this paper. While acknowledging that the notion of separating the violas within symphonies is not common, still, there has been little discussion of its potential significance and of what Mozart might have been pursuing.

Even for works that contain two viola parts, the parts are frequently played the same and only rarely are the individual notes assigned to the respective viola parts. On the other hand, violins that are basically assumed to be played two distinct parts, are occasionally played together. Separating the violas means that the number of parts increases. For sections where violas are separated, if the ratio for the separation of violins is higher than usual, then separating the violas seem to intentionally increase the number of parts. In contrast, if the ratio is lower, then separating the violas does not imply an intention to increase the number of parts, but rather to give the violas the roles that violins ought to have. If the ratio does not change when violas are separated, then, separating the violas does not influence the orchestration of the violins, which would imply another objective. This study utilizes computational methods to examine whether separating the violas influences the ratio of separation for violins.


There are 17 Mozart symphonies where the initial movement is divided into two viola parts, and this study targets those 17 initial movements.

The following procedure is done for each of the 17 works. First, the scores were obtained from “The New Mozart Edition” by B¨arenreiter Vertrag, which contains the most authoritative scores for all of Mozart’s compositions currently available[*1]. Next, the scores were exported into the MusicXML format, which is a textural representation of the musical notation suitable for digitization. Then, every measure is examined to determine whether or not paired parts (for both violins and violas, respectively) are consistent. Consistency for paired parts means that they are not separated, which inconsistency means that the parts are separated. The durations and pitches of notes are used in determining consistency. If any differences in terms of note durations or pitch are observed within a measure, the parts of the measure would be regarded as being inconsistent. Notes with pitch belonging to the same pitch class, however, are regarded as being consistent, even if there is a gap between octaves. Every measure was examined for the correspondences between consistencies and inconsistencies for the violins and the violas and the frequencies of measures falling under the various conditions are listed in Table 1. Finally, Fisher’s exact tests were conducted to identify whether any significant differences exist between the ratios of A (both violins and violas are separated) to B (violins are not separated but violas are) and between the ratios C (separated violins but violas are not separated) to D (neither violins nor violas are separated) in Table 1.

Table 1: Frequency distribution for the correspondences between the consistencies and inconsistencies for violins and violas: The cells labeled A, B, C and D indicate the numbers of measures conforming to the respective conditions.


Table 2 presents the separation ratios and p-values obtained from the Fisher’s exact tests. There are 11 of the 17 works that have p-values that are lower than the 0.05 significance level (K.43, 112, 114, 132, 173dB, 189k, 385, 425, 543, 550, and 551). Thus, for those works, it is possible to reject that null hypothesis that the separation ratio is not influenced by separating the violas parts.

Table 2: List of materials and their measured values: The number assigned to each work is from the sixth edition of the K¨ochel catalogue, which is a chronological catalogue of Mozart’s compositions. Items labeled A, B, C and D correspond to the conditions presented in Table 1. The rightmost item is the p-value derived from relevant Fisher’s exact test.


The analyses results failed to observe significant relations between the ratios for separating violins and violas for six of the 17 works (K.133, 162, 173dA, 319, 338, 504). Moreover, of the 11 works for which significant differences between the ratio for separating violins when violas are separated, five works (K.43, 173dB, 385, 425, 543) have greater ratios between A and B compared to the ratio between C and D. For those works, separating the violas would seem to intentionally increase the number of parts. For the remaining six works (K.112, 114, 132, 189k, 550, 551), however, there are higher ratios between B and A. In those cases, separating the violas would appear to inhibit any separation for violins. Accordingly, it would seem that Mozart did not have a single reason for separating the viola parts, and the objective varied across different works.


This study conducted a quantitative analysis of Mozart’s symphonies that include two viola parts. Specifically, we examined whether the ratio for separation of the violin parts is influenced when the viola parts are separated. Such influences were found to be significant for 11 of the 17 works. Five works exhibited a tendency for the violins to be separated more frequently when the violas are separated, with the opposite trend observed in the remaining works. Consequently, it would seem that Mozart had different objectives in mind when he separated the viola parts of his symphonies.


[*1] NMA Online Neue Mozart-Ausgabe: Digitized Version, (Retrieved May 5, 2016, http://dme.mozarteum.at/DME/nma/start.php?l=2)


[1] Andr´e Hodeir. Les formes de la musique. Presses Universitaires de France, 1951. ([In Japanese.] Ongaku no keishiki [The forms of the music], Hidekazu Yoshida, trans.,Hakusuisha(1973)).

[2] Neal Zaslaw. Mozart’s symphonies: context, performance practice, reception. Oxford University Press, 1989. ([In Japanese.] Mozart no symphony: context, ensou jissen, juyou, Tadashi Isoyama and Miho Nagata, trans.,Tokyo shoseki(2003)).