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Chapter 1 Answer Key

Applications

Exercises

1. Identify the following pitches with letter name and numerical octave designation. Identify the clefs at the beginning of each line.

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2. Notate the pitches. Use ledger lines as necessary.

3. Determine the two enharmonic spellings for each of the five black keys in the C4 octave. Notate the two pitches in the staff, and then write the names of the pitches below each note.

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Brain Teaser

1. Label the pitch notated in bass clef with the correct letter name and oc-tave designation. Then re-notate the exact same pitch in the treble clef to the right.

2. Refer to Example 1-1. How would you label the pitch immediately below C1? Provide its letter name and numerical octave designation.Answer: B0

3. While triple sharps and triple flats do not occur in musical practice, deter-mine an enharmonic note for the following pitches:a. Cbbb = Ab. Abbb = Gbc. G# = A#

Thinking Critically

Why do we experience pitches to be high or low? Pitches are not physical objects in space that we can see or touch, so how is it that we perceive one pitch to be higher or lower than another one?

Discussion

Our brains interpret the frequency (rate of vibration) of a sound as pitch. Although we hear pitches to be high or low, a perceived “high” pitch is not any higher in physical space than a relatively “lower” pitch. Our experience of pitch height is purely metaphorical. How does metaphor structure our experience of pitch?

In the early 1980s, cognitive linguist George Lakoff and philosopher Mark Johnson presented their pioneering work on conceptual metaphor.1 They argue that metaphor is not merely a rhetorical, poetic device but is actually central to human understanding and meaning. Through conceptual metaphor, we structure our understanding of abstract, unfamiliar concepts in terms of more concrete, famil-iar concepts and experiences.

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A conceptual metaphor consists of a source domain and a target domain. The source domain is a form of concrete understanding obtained directly from bodily, environmental, and cultural experience. The source domain is rooted in embodied knowledge, which results from repeated experience with our senses and motor programs. The target domain, on the other hand, is an abstract, intangible, and/or subjective concept—something that we do not learn about directly through sensorimotor activity and environmental interaction. In a process that Lakoff and Johnson call cross-domain mapping, we structure our knowledge of the abstract target domain in terms of an inherently compatible and well-defined source do-main. The result of this mapping from source domain to target domain is con-ceptual metaphor.

Consider the conceptual metaphor “Theories are Buildings.” Here, the abstract notion of a “theory” is structured by the familiar physical aspects of a “build-ing.” Since a theory is not something we can see or touch, we create a mental correlation between a theory and something we can see and touch—in this case, a building. In other words, we map features from the source domain (building) onto the target domain (theory). Numerous linguistic expressions fall out of this conceptual metaphor: “He built his theory on a firm foundation,” “She constructed her theory on a solid framework,” and “His theory did not have enough support and it fell apart.”2 The terms “built,” “foundation,” “construct,” “framework,” and “support” are borrowed from the domain of actual, physical buildings.

Music theorist Lawrence Zbikowski argues that “cross-domain mapping plays [a] very important role in musical understanding…it provides a way to ground our descriptions of elusive musical phenomena in concepts derived from everyday experience.”3 Zbikowski identifies the conceptual metaphor “Pitch Relationships are Object Relationships in Vertical Space,” which structures our conception of pitches as being located somewhere along a continuum from low to high. The source domain of this metaphor, “object relationships in vertical space,” is grounded in our bodily experience of uprightness as well as from activities like climbing a staircase and observing the level of water rise as we fill a drinking glass. But what is the experiential basis for our conceiving of pitch relationships in terms of object relationships in vertical space—why does this particular map-ping work? Consider our embodied experience of producing pitches through singing and speaking: when we make a low sound with our voice, our chest res-onates; when we produce a higher pitch, particularly in falsetto, the sound seems to resonate from the head.4 Our bodily experience of vocal pitch production fur-ther grounds the source domain to help structure our understanding of pitches as having relative height.

This conceptual metaphor is so pervasive that it has become a cultural con-vention reinforced through practice, pedagogy, and everyday conversations about music. (This metaphor, however, is not universal among all musical cultures.5) It

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is from this conceptual metaphor that descriptions of musical events in terms of space and motion derive: “a low B-flat,” “a descending scale,” “the leap of a tritone,” “a closely related key,” and so on. These linguistic metaphors stem from the larger conceptual metaphor and reflect the cognitive mapping of objects and events perceived in actual space (the source domain) onto those in pitch space (the target domain).

Notes

1 George Lakoff and Mark Johnson, Metaphors We Live By (Chicago: The University of Chicago Press, 1980); Mark Johnson, The Body in the Mind: The Bodily Basis of Meaning, Imagination, and Reason (Chicago: The University of Chicago Press, 1987); Lakoff and Johnson, Philosophy in the Flesh: The Embodied Mind and Its Challenge to Western Thought (New York: Basic Books, 1999); Mark Johnson, The Meaning of the Body: Aesthetics of Human Understanding (Chicago: The University of Chicago Press, 2007).

2 Lakoff and Johnson, Metaphors We Live By, 46. 3 Lawrence Zbikowski, Conceptualizing Music: Cognitive Structure, Theory, and Analy-

sis (Oxford: Oxford University Press, 2002), 64. 4 Ibid., 69. 5 Zbikowski points to some non-Western cultures that do not conceive of pitch in

terms of height. In Bali and Java, for instance, pitches are not regarded as “high” or “low” but as “small” and “large,” respectively. The Suyá of the Amazon basin conceive of pitches as “young” and “old” rather than as “high” and “low” (Zbikowski, 67–68). Although these cultures do not structure their understanding of pitch relations with the “Pitch Relationships are Object Relationships in Vertical Space” metaphor, their conceptions of pitch result from other conceptual metaphors grounded in embodied knowledge. The correspondence among these different metaphors is rather obvious: a young child has a smaller resonating cavity and therefore produces a higher pitch (young = small = high).