"Maximum Clarity" and Other Writings on Music

Scalar Order as a Compositional Resource

scalar order as a compositional resource 1962–63 When listening to music we hear changing sound qualities in rhythmic patterns which create an illusion of growth.Most people hear music most readily as rhythmic gesture. Their musical present moment is the beat, the bar, the phrase (or the equivalents of these in less traditional music). Tone qualities,noise textures,and pitch combinations make up the musical “objects” which are composed into rhythmic gestures. These different kinds of phenomenal gestalts are, physically speaking, different modes of vibration. Qualities and relationships of sounds are our way of perceiving great numbers of tiny events (vibrations) on a molecular scale. We cannot hear these individual events, but we can easily detect order in the patterns they make.1 The rhythmic gestures composed of these qualities and relationships are in turn composed into larger patterns. These larger contexts are not directly perceptible. Memory reconstructs images of them once we have heard them. Even as we listen to a musical composition for the first time,expectations can grow in us which result from an intuitive grasp of the larger design patterns of the music. The act of musical composition relates the order and pattern of sound vibrations to the order and pattern of musical shapes of larger duration. A composer makes the two interdependent by means of his construction and deployment of musical order on the scale of ordinary rhythmic perception.2 When we listen for practical purposes, we identify objects and actions by their sounds. This recognition depends upon a recognition of similar patterns of sound vibration. To listen musically is to turn one’s attention to details of the sound patterns and to interrelations of these patterns on different time scales. For everyday needs we usually need only to compare the similarity or difference of sounds or at most to classify them loosely in terms of their qualities; for aesthetic purposes we need to understand relationships more precisely. We need as a basis an intuitive grasp of more sophisticated systems of relationship. The depth of musical understanding depends upon the ability to hear orderly relationships and upon the precision of interrelationships implicit in the various kinds of scalar order used to organize the sounds. S. S. Stevens presents four kinds of scales of measurement: nominal, ordinal , interval, and ratio.3 A nominal scale is a collection of equivalent and interchangeable items.An ordinal scale is a collection which is rank-ordered in terms of some attribute.An interval scale is a rank-ordered collection in which the intervals of difference between items are equal. A ratio scale is a rank-ordered collection in which the items are related by exact ratios. A meaningful conception of zero value of the attribute in question is necessary before such a scale can be formed. Each of these scales includes all of the measurement possibilities of its predecessors, plus one more. “Thus an interval scale can be erected only provided we have an operation for determining equality of intervals, for determining greater or less, and for determining equality (not greater and not less). To these operations must be added a method for ascertaining equality of ratios if a ratio scale is to be achieved” (Stevens, Handbook of Experimental Psychology). The assignment of letters to thematic sections in traditional musical analysis (e.g., ABA, ABACABA, etc.) is an example of analysis by nominal scale. We are here concerned with the determination of same and different. The conventional use of dynamic markings in music (pp, p, mp, mf, f, ff) is an example of ordering by ordinal scale, since it is in practice very difficult to decide what an “equal increment” of loudness is, and in musical scores all that is usually implied by mf is that it is louder than mp and not so loud as f. The melodic use of pitch (rather precisely stepped contours of pitch variation ) is an example of ordering by interval scale. So also is the establishment of a regular metrical beat (recurring equal durations). The harmonic use of pitch (carefully tuned simultaneous pitch combinations) is an example of ratio scale ordering, as is, in general, the practice of tuning by ear. The application made in this paper of Stevens’s scale types is based upon musical usage rather than upon controlled psychophysical experiments. The assumption has been that much is to be gained by exploring the nature of the audible order employed in musical composition, from the dual viewpoint of traditional conceptions of...