Discrete pitch

The orthodoxy of cognitive music theory today, as I pointed out in section 3.1, is that melodies consist of discrete intervallic structures and stable tonal relations. “One of the striking commonalities of musical pitch systems around the world is the organization of

pitch contrasts in terms of a musical scale, in other words, a set of distinct pitches and intervals within the octave that serve as reference points in the creation of musical

patterns.”145 _{This consensus extends to what is proposed as a key difference between}

music and language: that musical melody consists of discrete pitch events whereas

linguistic melody is continuously varying. But this distinction is made on the basis of

instrumental music, not song. I will show that such gradient elements are in fact distinctive of song melody. The problem with discrete categories, as employed by generativists, is that they are rigid and absolute—they are either present or absent and cannot be partial. To base our analysis on these categories would ignore a range of prosodic pitch phenomena and so I introduce several alternative categories instead. In

place of discrete pitch, for instance, I propose the concept of pitch targets. This enables

us to include many features of discrete pitch without reifying discrete tonal identities as absolute.

The idea of discrete pitch emerges from a digital model of cognition in which the mind combines discrete conceptual units into a potentially unlimited number of combinations to produce coherent meanings. In generative theory there are rules and constraints that govern these combinations (see Chapter 2). Discrete pitch categories are assumed to be the fundamental units in these computationist models. Consider Jackendoff’s statement: “Unlike any other cognitive capacities, both language and music involve a sequence of

digitized sounds: speech sounds in language, tones or pitch events in music.”146 But the uses of pitch in music and language differ: “only melodies have discrete pitches, while

prosodic contours usually involve a continuous rise and fall.”147 _{Patel makes a similar}

point: “The lack of a stable interval structure is the single most salient difference between musical and spoken melodies, and is likely why theories of musical melody and theories

of speech melody have had so little conceptual contact.”148Again, these theories of

discreteness are convenient in making a firm distinction between music and language, but they simply ignore features of gradience and variation in pitch organization. After all, the categories of perception need not be discrete. “[N]onmusicians [do] not show strong evidence of categorical perception. This evidence strongly suggests that intervallic

relations and their perception is the product of learning rather than innateness.”149

Diverse pitch categories are possible and indeed probable.

There is cross-cultural evidence of gradience and variation in pitch patterning. J.H. Kwabena Nketia has elaborated this in his studies of African music:

The scales used in vocal music, having from four to seven steps, are not unlike those used in instrumental music. For any given scale step, however, one may not always find absolute correspondence between the vocal pitches and the instrumental tunings. In African musical

146 _{Jackendoff, “Parallels and Non-Parallels Between Language and Music,” 198.} 147 _{Jackendoff, “Parallels and Non-Parallels Between Language and Music,” 199.} 148 _{Patel, Music, Language, and the Brain, 206.}

practice, the areas of tolerance of pitch variation for particular steps of the scale are much larger than those of traditions that base their music on a fixed pitch of 440 vibrations per second for A.150

A cognitive explanation is required for this “tolerance.” If pitch units exhibit a high degree of gradience then there must be a significant degree of perceptual adjustment, a shift in expectations. Were discrete pitch in operation we would expect there to be narrowly defined thresholds beyond which new, distinct categories of pitch units are formed. If we take pitch categories to be more fluid, then this “tolerance” for pitch variation is accounted for by a general cognitive adjustment for a gradual narrowing of tessitura over the course of the utterance. This is a phenomenon phoneticians describe as ‘pitch-span reduction’ and it is common to most speech utterances. There is no reason to believe that it does not operate similarly in song. In other words, the capacity to recognize distorted or reduced pitch contours as possessing the same pitch identity is a crucial feature of music cognition.

Still, the concept of ‘discrete pitch’ has played a vital role in accounting for features of tonality and hierarchical structure for many music cultures, and any new model must account for these functional attributes. Patel reviews the important of intervallic structures to musical melody and makes a comparison with tonal linguistic features as follows:

[A] stable system of intervals allows musical melodies to make use of a tonal center, a focal pitch that serves as a perceptual center of gravity for the melody. An interval system also allows the creation of a hierarchy of pitch stability in melodies. In contrast, the ‘tones’ of intonation have no such organization: Each tone is used where it is linguistically appropriate and there is no sense in which some are more stable or central than others. Another consequence of an interval system is that when combined with a temporal grid provided by beat and meter, a scaffolding is created for an elaborate set of structural relations between tones. This is likely part of what makes musical melodies so aesthetically potent. In contrast, the network of pitch relations in intonation contours is not nearly as rich. As a result, intonation contours are aesthetically inert, as evidenced by the fact that people rarely hum intonation contours or find themselves captivated by the pitch patterns of speech. This is quite sensible, as a musical melody is an aesthetic object, a sound sequence that is an end in itself, whereas a linguistic intonation contour is simply a means to an end, in other words, pitch in the service of quotidian linguistic functions.151

Apart from assumptions about the respective functions of music and language, Patel’s comparison of melody and intonation is problematic in several respects: for one thing, intonation cannot be segregated from other pitch elements in either song or speech. Second, non-instrumental melodies are far more graded than his analysis admits. And even more important is the fact that many linguistic factors impose special constraints on musical melody too. The focus on discrete pitch is problematic in each of these respects and needs to be supplemented. We need to account for the many important elements of melodic structure associated with pitch events but we need to do so while at the same time ensuring that gradient elements are not ignored. This means devising a model of

melodic structure that factors both sorts of categories. To accomplish this task I introduce the notion of pitch targets, thereby retaining the element of combinatorial organization in melody without assuming a rigid structure of discrete elements.