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TRIPLE METRIC STRUCTURE
"...triple units almost always come under the tyranny of our biological duple compulsion. ...a waltz is perfomred 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 communicating the strong-weak-weak accent pattern; the remaining two, three, or four streams are most often in duple groupings. [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. The name is justified by the fact that this triple pulse stream usually stands out clearly, permeating the entire metric structure with its distinctive triple feel. Frequently encountered triple metric structures may be represented in dot notation as follows:
Ex. 35
a) the triple stream is heard as the beat:
b) the triple stream is heard as faster than the beat:
c) the triple stream is heard as slower than the beat:
Triple metric structure can exist with only two pulse streams, the triple stream and one other level, necessarily a (higher) slower one. Three levels are shown above in Ex. 35 a) and b); the fourth level in Ex. 35 c) is necessary to show a triple pulse stream slower than the beat.
CONDUCTING TRIPLE METRIC STRUCTURES
When the triple stream is heard as the beat, the conventional 3-pattern may be used. When the triple stream is not heard as the beat, as in Ex.35b) and c) above, the beat streams chosen will necessarily be duple. For triple streams faster than the beat (Ex.35b), the 2- and 4-patterns may be used. If the triple stream is extremely fast, the meter may be conducted "in 1," that is, by providing a (usually spirited) single ictus. 6/8 is very often conducted in 2; the triple quality, however, is still quite evident. When the triple stream is slower than the beat, the 3-pattern may be used with a subdivision of 2 (see Ex. 11).
NOTATING TRIPLE METRIC STRUCTURE
Listen to the third movement of Haydn's Symphony #101. The triple metric structure is shown below, with the single triple stream at level 3:
Ex. 36
Choosing the quarter note for level 3, the notation will appear as follows:
Ex. 37
The above notation is very frequently encountered in symphonic Minuet movements. Depending on the performance you are hearing, either level 2 or level 3 may be perceived as the beat. Keep in mind, however, that any note value can be chosen for level three. Alternatives are shown in Ex. 38, with level 3 as the beat.
Ex. 38
a)
b)
TUPLET NOTATION TRIPLE METRIC STRUCTURE
Triple metric structures can be notated using tuplets. Although seen less frequently--you are more likely to encounter this notation in nineteenth-century music--it is worth looking at. Here are the three versions of triple metric structure shown earlier, with their triplet representations:
Ex. 39
a)
becomes:
b)
Ex. 40
a)
becomes:
b)
Ex. 41
a)
becomes:
b)
Notice how using tuplet notation at some level eliminates dots from the slower streams, but requires using tuplet notation for faster streams. Although the pulses notated in triplets may be heard as primary beats because of tempo, we must remember that the bottom number in a time signature represents a note value not contained in a tuplet and without a dot, typically an eighth, quarter, or half note. So the time signatures chosen when the beat is notated in triplets might be: Ex. 39b), 2/2; Ex. 40b), 2/4;Ex. 41b), 2/1 (rare).
*In Ex. 41 b), level 4, the quarter note grouping is shown with the number 6, while the eighth-note and sixteenth-note tuplet groups in all other examples are shown with the number 3. The beaming allows for either a 3 or 6 to be used for eighths and sixteenths:
but it is confusing to see a 3 below a series of six quarter notes:
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 established 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 the following, 3/4 and 6/8 being the most common:
Ex. 42
[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 may be 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 link to form a sextuple group, and two groupings of six link to form one grouping of twelve (a duodecuplet?). Ex. 43 shows a dot structure with the triple pulse as the beat. The "compounding" of these groups may be thought of in two ways: beginning with the short groupings of three linking to form the larger six and twelve groupings, or beginning with the long twelve grouping and dividing into the six and three groupings.
Ex. 43
Translating this structure into notation with time signatures shows this process clearly.
Ex. 44
a) using the eighth note as the beat (`x' in the above):
b) using the quarter note note as the beat (`x' in the above):
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 left foot of the leader begins to repeat the pattern. Listen to the Haydn Minuet again; there is clear evidence of 6-beat (2 measure) grouping. Can you hear 12-beat or 4-measure groupings as well?
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