An Introduction to America’s Music

492 PART 4 | SINCE WORLD WAR II

California assisting Partch as a carpenter and musician. On the faculty of the

University of Illinois from 1951 to 1986, Johnston began to compose microtonal

music only in 1960, beginning with works for specially tuned piano, including

a Sonata for Microtonal Piano (1964) that derives some of its pitch material from

classic popular songs such as “W hat Is This Thing Called Love?” A Suite for Micro-

tonal Piano (1978) includes a movement titled “Blues.” Other works require wind

and string players to play with highly refi ned intonation; to indicate subtleties of

pitch, Johnston expands the traditional sharp and fl at signs (raising and lower-

ing a pitch by a half step respectively) to a total of ten signs, indicating relative

degrees of raising and lowering a written pitch.

Johnston’s String Quartet no. 4 (LG 19.6) is a set of variations on the folk hymn

tune New Britain, better known as “Amazing Grace” (see chapter 3). The four

string players begin with two simple statements of the melody in Pythagorean

tuning, a system favoring perfectly tuned fourths and fi fths (according to the over-

tone series) over thirds and sixths; the sonority, open and rather stark, is distinctly

different from equal temperament, where no intervals are favored, so that all

intervals are slightly out of tune relative to the natural overtones. Attributed to the

ancient Greek mathematician Pythagoras, Pythagorean tuning was widely used

through the Middle Ages in Europe, and is also the basis for classical Chinese scales.

The following variations add more pitches, organized in scales of various tun-

ings. Moreover, the rhythmic relationships mirror the pitch relationships. For

instance, the frequency ratio of the Pythagorean fi fth is 3:2, and in the fi rst vari-

ation the cello, using double and triple stops, plays two simultaneous lines, one

moving at the rate of three notes to every two notes in the other. The score’s highly

precise notation allows Johnston to control minute fl uctuations in tempo and even

construct passages in which the four instrumentalists play in different but coor-

dinated tempos, a technique of metric modulation pioneered by Elliott Carter.

The piece’s melodic ideas also refl ect changes in the tuning system from vari-

ation to variation. The sixth variation uses “undertones,” the reciprocals of the

overtone series; in other words, instead of beginning with a low note and build-

ing pitches above it in the ratios of the overtone series, Johnston begins with a

high note and builds pitches below it in a mirror inversion of the overtone series.

In a melodic analog y, “Amazing Grace” is heard in melodic inversion; that is, the

rise and fall of the tune is inverted, or played “upside down.”

Microtonal music continues to attract musicians eager to look beyond the

twelve pitches of the piano keyboard. Among other benefi ts, it has opened up

Western classical music to the tuning systems of other cultures, ranging from

the blues (since blue notes can be thought of as microtonal adjustments to the

equal-tempered scale) to the traditional musics of Asia and Africa.

QUESTIONS FOR DISCUSSION AND REVIEW

1. How do developments in rock in the early 1970s resemble developments in
   modern jazz in the 1940s and 1950s, and how do they differ?


2. What are the stylistic features of punk rock, and how do they distinguish
   punk from other 1970s trends? W hat makes punk a “reformation” movement
   in rock history?


3. W hat are some similarities and differences between funk and disco?

LG 19.6

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