1. Forte's study of this work was first published in 1983 and subsequently reprinted in 1987. "Motivic Design and Structural Level in the First Movement of Brahms's String Quartet in C Minor," Musical Quarterly, 69 (1983), 471-502. Reprinted in: Michael Musgrave, ed., Brahms 2: Biographical, Documentary and Analytic Studies, pp. 165-196 (Cambridge: Cambridge University Press, 1987).

2. Further discussion regarding this point may be found in Leonard Meyer, Emotion and Meaning in Music (Chicago: University of Chicago Press, 1956).

3. The assumption that lines-of-sound are psychological "real" rather than "reified" is supported by a wealth of perceptual research. As theorists are well aware, not all pitch successions evoke intervals. For an extensive review of the pertinent perceptual evidence see Albert Bregman, Auditory Scene Analysis (Cambridge, Mass.: MIT Press, 1990).

4. This observation is chronicled in detail in David Huron and Jonathon Berec, "A Method for Characterizing Instrumental Idiomaticism: A Case Study of the B-flat Valve Trumpet." MS.

5. See, for example, the discussion of quotation and allusion in Kenneth Hull, "Brahms the Allusive: Extra-compositional Reference in the Instrumental Music of Johannes Brahms," PhD diss., Princeton University, 1989.

6. There are other possible definitions of a good description, although I am not aware of any in the field of music theory. The definition proposed here merely echoes the widespread notion in theory (promoted by Schoenberg) that music and musical descriptions ought to seek an economy of expression. It is noteworthy that this definition of good description is analogous to the concept of efficiency in technical disciplines.

7. An introduction to the historical background of this work may be found in Michael Musgrave and Robert Pascall, "The String Quartets Op. 51 No. 1 in C minor and No. 2 in A minor: A Preface," in Michael Musgrave, Ed., Brahms 2: Biographical, Documentary and Analytic Studies, pp. 137-143 (Cambridge: Cambridge University Press, 1987).

8. Forte's study focuses predominantly on the musical foreground. Similarly, my analytic points will center on foreground features. This focus is merely a matter of convenience and of avoiding undue length. As the reader will readily understand, the inferential analytical approach employed here is as pertinent to the comparative evaluation of proposed background, middleground, and process-related features as it is to foreground motivic features.

9. All of the ensuing measurements were carried out using the Humdrum Toolkit software. All repeats were expanded in the electronic scores prior to processing. See David Huron, Unix Software Tools for Music Research; The Humdrum Toolkit Reference Manual (Menlo Park, CA: Center for Computer Assisted Research in the Humanities, 1995). Extensive online information is available regarding Humdrum, including an online introductory User Guide.

10. A ludicrous comparison to be sure, but one that well illustrates the point.

11. For pertinent experimental evidence see David Huron, "Voice Denumerability in Polyphonic Music of Homogeneous Timbres," Music Perception 6 (1989), 361-382. (An abstract is available online.) For a demonstration of this perceptual phenomenon affecting musical organization see David Huron and Deborah Fantini, "The Avoidance of Inner-voice Entries: Perceptual Evidence and Musical Practice," Music Perception 7 (1989), 43-47. The complete text is available online.

12.  The numbers on this line indicate the total number of unique patterns present in the movement. These numbers are useful for assessing the relatively importance of the rank orderings given for each of the various alpha patterns. For example, the 10th most common pattern might be relatively important in a work that contains 100 different patterns; however, the 10th most common pattern might be deemed relatively unimportant if the work contains just 15 different patterns. (Being the 5th best student in one's class is more significant in a class of 80 students than in a class of 10 students.)

13. The term "significant" is used here in the formal statistical sense of the word. Pooling the data for the two control movements, a chi-square analysis for the ratios of expected to actual instances produces the following results: prime form of alpha (X²=56.47; df=1; p<<0.001 significant); inverted form (X²=1.82; df=1; p=0.18, not significant); retrograde form (X²=53.39; df=1; p<<0.001, significant absence); retrograde inverted form (X²=5.22; p=0.02, significant absence).

14. Forte's motivic description would appear to have only one advantage over the feature developed in this paper and shown in Example 3: namely, the alpha motive is more succinct. However, since the alpha interval-class motive is not distinctive of the work in question, the feature description must be regarded as too brief.

15. Readers familiar with Forte's paper may have noted that our analysis has focused exclusively on Forte's alpha motives without mentioning the innumerable other subsidiary patterns discussed in his analysis. The reason should now be clear. Many of Forte's other motivic sets suffer from the same problems, and other sets appear to be attempts to patch up the shortcomings of the alpha pattern.

16. A number of articles have applied this principle to the study of music, including much of the current author's published research. A useful description of the research approach may be found in the second chapter of Zohar Eitan, Highpoints: A Study of Melodic Peaks (Philadelphia: University of Pennsylvania Press, 1997)--although see comments in the current author's book review (Music Perception, 16 [1999], 257-264).

17. This research was completed in 1994 while the author was a visiting scholar at the Center for Computer Assisted Research in the Humanities, Stanford University. I am grateful to the Center's Director, Dr. Walter Hewlett, for providing helpful feedback and advice.

End of footnotes