Table of Septuplet Partitions

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(a) 7
(b) 6+1
(c) 5+2
(d) 5+1+1
(e) 4+3
(f) 4+2+1
(g) 4+1+1+1
(h) 3+3+1
(i) 3+2+2
(j) 3+2+1+1
(k) 3+1+1+1+1
(l) 2+2+2+1
(m) 2+2+1+1+1
(n) 2+1+1+1+1+1
(o) 1+1+1+1+1+1+1

= 64 possibilities

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Partitions of 7

The table above displays all possible "unique patterns" derivable within 1 = using only the , or whole multiples thereof, as the building block.

As with the Quintuplet partitions (the explanation for which should be read first), patterns are classified vertically according to their component durations, or partitions.

In the particular case of (n = 7) there are 15 partitions, but 64 "unique patterns".

The table can be used for note values other than the by doubling or halving the internal values. By removing the septuplet superscripts and brackets, the table can also be used as the basis for studying , , .

For study purposes one MUST begin with the bottom classification, becoming comfortable saying, thinking, or tapping 1,2,3,4,5,6,7, many many times, at various speeds. We are not accustomed to thinking in 7, and it is imperative that we become. In principle one should try to think of the 7 as a whole, and not break it up into smaller units for counting purposes (although counting/saying 1,2,1,2,1,2,3, or 1,2,3,4,5,1,2, when learning patterns such as and , and generalizing this idea for all the patterns, may prove helpful to the learning process). Ultimately, however, one should escape from this stricture, and be able to think 7, although that is easier said than done.

As with the quintuplets, once comfortable with the patterns individually it will prove of use to create random chains of patterns, using a methodology similar to that suggested for the quintuplets. It will also prove of use to "hocket" the patterns within a group of students, as that is one of the tasks they may expect to encounter in the so-called "real world".

Paul Zukofsky

March, 2004