…triple units almost always come under the tyranny of our biological duple compulsion…a waltz is     performed on two legs: left-2-3, right-2-3, left-2-3, right-2-3…in the larger rhythmic sense a waltz is     every bit as duple as a march.     ---Leonard Bernstein

If all adjacent pulse streams in duple metric structures are in 2:1 relationships, we might assume that all pulse streams in triple metric structures will be related by 3:1 proportions. This, however, is not so.  In the overwhelming number of cases, there is only one pulse stream heard that communicates the strong-weak-weak triple accent pattern. The remaining streams are most often in 2:1 relationships. [The more infrequent instances of a metric structure with two pulse streams exhibiting triple groupings will be taken up later.] What we will call the “triple metric structure,” then, is so named because it contains a single pulse stream heard in a strong-weak-weak pattern defined by the slower level above it. The name is justified by the fact that this triple pulse stream usually stands out clearly, permeating the entire metric structure with its unique triple feel. The triple stream, however, will not always be chosen as the beat. In Example 32, the arrow indicates the level of the beat. In a) the triple pulse is the beat, and the music would be conducted in three. In b) the triple pulse is faster than the beat; the music would be conducted in 2 or 4. In c) the triple pulse is heard as slower than the beat; the music again, would be conducted in 2 or 4. Notice in c) that a fourth level is added to the metric structure to define the slow triple pulse (see section XII B. for more on pulse definition).

Ex. 32 a)

Ex. 32a triple stream as beat.png

           b)

ex.32b-triple-stream-faster-than-beat.png

           c)

ex.32c-triple-stream-slower-than-beat.png

Conducting Triple Metric Structures

Earlier, in Example 13, the conventional pattern for conducting triple metric structure was shown; by now it is surely familiar to you. Other options exist; for instance, if the triple stream is extremely fast, the meter may be conducted “in 1,” that is, by providing a (usually spirited) single ictus. When the triple stream is slower than the beat, the 3 pattern may be used with a subdivision of 2 (see Ex. 17).

Choosing a Beat and its Note Value 

Now listen to the third movement of Haydn’s Symphony #101. The triple metric structure is shown in Example 33, with the single triple stream at level C:

Ex. 33 

ex.33-triple struc lettered levels.png

Choosing a quarter note for level C, the notation will appear as follows:

Ex. 34
                                

ex.34-triple-metric-levels-lettered.png

The above notation is very frequently encountered in symphonic Minuet movements. Depending on the performance you are hearing, either level B or level C may be perceived as the beat. Keep in mind, however, that any note value can be chosen for level C. Alternatives are shown in Ex. 35, still with level C as the beat.  

Ex. 35  
 

Ex. 35 Haydn iii notation options.png

How would the notation change if the triplet (slur with the number 3) were used in Examples 34 and 35?

Choosing a time signature for triple metric structure

Triple metric structure may be represented in several ways. Like duple structure, time signatures will give the same information about the score notation: a note value will appear as the bottom number in the signature, while an upper number will show how many of those notes are to appear in a measure. For triple metric structure the top numbers will be 3, 6, or 12 (9 as a top number will be taken up later). Remember that there is no conventional way to indicate a dotted note value or triplet as the bottom number in a time signature—the bottom numbers will still be 2, 4, or 8, (less often, 16). This results in time signatures like those shown in Example 36, 3/4 and 6/8 being the most common:

Ex. 36
                       

ex.39-triple-time-signatures.png

 [6/2 and 12/2 are unlikely to appear]

Should we be able to decide whether the music is “in 3,”  “in 6,” or “in 12” through listening? The answer is “yes and no.” If we recognize the style and know something of the historical context of the music we’re hearing, we can in most cases assign a time signature. For example, minuets in the 18th century were most often notated in 3/4, the signature Haydn chose for the third movement of Symphony #101. Yet if the style of the music does not suggest a conventional time signature, i.e., if we are aware only of the number of pulse streams and the fact that one of them is triple, it is likely that one time signature will not emerge as the best. Like the relationship of duple and quadruple groupings (two duple groups = one quadruple group), two triple groups combine to form a sextuple group, and two groupings of six combine to form one grouping of twelve (a duodecuplet?). Ex. 37 shows how the “compounding” of these groups arises.

Ex. 37         

Ex. 40 version 2.png

Translating this structure into notation with time signatures shows this process clearly (See Example 38).

Ex. 38

ex.41-triple-compounding-in-notes.png


Again, style and historical period may dictate the signature. Motive length, points of harmonic change, and textural factors may favor one time signature over another. However, there are many pieces written in 3/4 in which two measures are clearly linked, suggesting a grouping of 6. If you have ever danced a waltz, which is thought of as being “in 3,” you know that it takes two groups of three—six steps—before the dancers begin to repeat the pattern (see Leonard Bernstein’s comment, above). Listen to the Haydn Minuet again; there is clear evidence of 6-beat (2 measure) grouping.   Can you hear 12-beat (4-measure) groupings as well?  

Look back at Ex. 9. It demonstrated how melodic contour can contribute to metric structure. What are possible time signatures for each example?

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