Johann Sebastian: A Tercentenary Celebration

By Seymour L. Benstock | Go to book overview

4
Hemiola in the Eighteenth Century

Vincent Corrigan

Hemiola is a general term used to indicate the ratio three=to=two, and its musical applications are varied. It may refer to the interval of the fifth, whose frequencies and string lengths show the 3:2 relationship. It is also used to describe triplets. ( 1) As a notational term, it indicates coloration, particularly the use of blackened notes in tempus perfectum. ( 2) During the late eighteenth and early nineteenth centuries, it even indicated the time signatures 5/4 and 5/8. ( 3) However, it is now used most often to describe metric shifts that occur when, for instance, two dotted half notes are replaced by three half notes: d.d. = d d d.

The result, in this case, is a shift in meter from 6/4 to 3/2, characteristic of the French courante. This is only the simplest example, however; in eighteenth century musical sources, hemiola is widely used and appears in much more complicated ways. Studies dealing with hemiola in the works of individual composers have pointed the way to a more comprehensive view of the subject, but questions still remain about how eighteenth century musicians thought of hemiola and how they used the technique in their compositions. ( 4)

The definitions in dictionaries of the period are curiously antiquated. ( 5) They describe hemiola in terms of coloration, and use breves and semibreves to illustrate the patterns. Two types of hemiola are recognized. In the major hemiola, three blackened, imperfect breves replace two normal perfect breves; in the minor hemiola, the altered note value is the semibreve. Analogues to these two types occur in the musical sources. In some cases, two measures of simple triple meter, for instance 3/4, are combined to form one measure twice as long, in this case 3/2. In others, the accentual pattern within a measure of compound duple meter (e.g. 6/8) is altered to produce a measure of simple triple meter (3/4). In this discussion I will use the term major hemiola to describe situations in which two measures are combined into one. The term minor hemiola will refer to hemiola that operates within a measure. Table 4.1 lists the most frequently encountered metric shifts, and Example 4.1 provides some characteristic passages. ( 6)


T 4.1
Major hemiola Minor hemiola
2 × 3/4 -- 3/2 6/4 -- 3/2
2 × 3/8 -- 3/4 6/8 -- 3/4

-23-

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Johann Sebastian: A Tercentenary Celebration
Table of contents

Table of contents

  • Recent Titles in Contributions to the Study of Music and Dance ii
  • Title Page iii
  • Contents vii
  • Preface ix
  • 1: The Contemporizing of Scripture in the Cantatas of Johann Sebastian Bach 5
  • 2: J. S. Bach: The Flauto and the Traverso 11
  • 3: An Odd Couple: J. S. Bach and A. S. Huxley 19
  • 4: Hemiola in the Eighteenth Century 23
  • Notes 32
  • Notes 122
  • Index 157
  • About the Editor and Contributors 161
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