Bird's‐Eye Views of the Musical Surface: Methods for Systematic Pitch‐Class Set Analysis

Abstract

Articles systematic pitch-class set analysis huovinen and tenkanen erkki huovinen and atte tenkanen of the appropriate set classes. We can therefore reformulate Lester's assertion by concluding that a surprisingly small number of these simple detectors are required to cover the surface of Mozart's well-known theme. More complex detectors will be similarly sensitive to more complex properties of the musical surface.The other, and equally important, aspect of systematicity pertains to the way in which the detector is deployed throughout the relevant field of objects. Just as a minesweeper has to move systematically across an entire minefield in order to ensure that every explosive device has been found, so the musical surface has to be scanned in a similarly exhaustive fashion if the quantitative results are to be of any value. In the Mozart example, such systematic scanning requires only that the successive simultaneities be checked for features of interest; however, larger compositions and less transparent musical textures tend to render the issue much more involved. Now, it is well known that the systematic core of pitch-class set theory has often been supplemented by less than systematic analytical procedures, especially when it comes to the question of segmentation and the further identification of key structural features (Apajalahti 1994; Pople 2004b). Merely pointing the detector towards some intuitively salient aspect may perhaps engender pertinent results, yet may just as easily lead to more sweeping implications that are insupportable.The second section of this study will concentrate on this latter aspect of systematicity, namely the means by which the detector is applied. This is a task which entails the use of computer algorithms. 2 At the same time, we will attempt to establish a framework for developing various kinds of detectors, each sensitive to the differing properties of pitch-class sets. Although our contribution can be seen as a continuation of the tradition of statistical music analysis, the pitch-class set-theoretical approach widens the perspective from the primitive characteristics of individual notes (pitch, duration and so on) to more complex relational features. This change in scope carries a clear advantage: put simply, its findings are more open to qualitative interpretation. For example, whereas early informationtheoretic approaches to the analysis of music were concerned, in the main, with the amount of musical information generated (for instance, Winckel 1964;Fucks and Lauter 1965), it now seems that greater attention should be paid to the musical character of the pitch materials being analysed. Even if the differences between musical styles may only be approached fruitfully using information regarding the frequency distributions of various musical elements (Beran 2004; Manaris et al 2005), we prefer a form of statistical style analysis that attaches some musical meaning to these elements from the outset.For example, the third section of this survey will seek to explore the use of ...

Hierarchical multi-scale set-class analysis

“…Since no average is performed by computational means, it is up to the analyst's criteria to focus on different salient features, facilitating the interaction with the data. Unlike the approach in Huovinen and Tenkanen (2007), our temporal indexing method makes possible the precise inspection of each individual class.…”

“…Among the most systematic approaches to set-class surface analysis, Huovinen and Tenkanen propose a segmentation algorithm under the concept of "tail-segment array", whereby every note in a composition is associated with all the possible segments of a given cardinality that contains it (Huovinen and Tenkanen 2007). This segmentation is combined with certain "detector functions" to obtain summarized information from music pieces and collections.…”

“…In this study we address the four descriptive issues in Huovinen and Tenkanen (2007), mentioned in Section 2.2, by conceiving systematization from a more holistic perspective. Our method extends the systematization of the multi-scale segmentation and representation methods in Sapp (2005) It is important to clarify that our technique is intended to provide assistance to human analytical decisions.…”

“…The class-matrix, thus, summarizes information from all the time-scales simultaneously. Unlike the approach in Huovinen and Tenkanen (2007), which also accounts for several time-scales in a single tail-segment array, the class-matrix preserves a strict separation of classes. This feature can be exploited in more subtle descriptive tasks, as discussed next.…”

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“…25 25 For a different, but in some ways more thoroughgoing, approach to mapping the global distribution of set classes across a whole musical work, see Huovinen and Tenkanen (2007). …”