Drum Composition Example
Multicultural Mathematics
Rachel Hall

time signature = 12 beats per measure
tempo = 370 beats per minute

Rhythm cycle.  This cycle has a length of 12 beats (one measure) and is repeated through most of the piece.
 claves X X X X X X X cowbell X X X X X low bongo X X X low tom X X

Rhythm cycle patterns (for abcdrums)

I:  dzdzddzdzdzd
J:  dzzdzzdzdzdz
K:  dzzzdzzzdzzz
L:  dzzzzzdzzzzz

Polyrhythm.  The rhythm cycle contains the polyrhythm 2 against 3, which is found in the low bongo and low tom parts.

Solo pattern.  The composition is based on this pattern.  It is played by two drums, and has a duration of two measures = 24 beats.
 C: X X X X X X X X X E: X X X X X

Here is the same pattern in abcdrums notation.

C:  dzzzdzzzdzzd zdzddzzzzzdd
E:  zzdzzzzdzzzz dzzzzzdzdzzz

Note:  This pattern is usually played in the form CCEC or EECE.

Intro pattern.  The introduction to the composition is an arithmetic series based on this pattern.

A:  dzzz
B:  zddd

The length of pattern A is 4 and there are 10 A's, for a length of 40.  The pattern would be played

A zg AA zg AAA zg AAAA

where g is the length of the gap between patterns.  To find the length of the gaps, we solve the equation 40 + 3*g = 1 (mod 12).  The smallest value of g that makes this equation true is 3, since 40 + 3*3 = 49 = 1 (mod 12).  Therefore, the duration of the series

A z3 AA z3 AAA z3 AAAA has length = 1 (mod 12)

As required, this pattern starts and ends at the beginning of a measure.

Tihai ending pattern.  The tihai is based on this pattern.

F:  dzdzdzddzdzdd

This pattern has length 13.  To find the gap length g, we solve the equation 3*13 + 2*g = 1 (mod 12).  The smallest value of g that makes this equation true is 5, since 3*13 + 2*5 = 49 = 1 (mod 12).

So F z5 F z5 F has duration = 1 (mod 12).

Melody.  There are two melodic patterns, which can be played together or singly.  Each pattern has length 4 measures or 48 beats.

G:  C3  D3  E6 F2 F2 F2 G6 C3  D3  E6 F2 F2 F2 E6
H:  G,3 A,3 C6 D3  D3   E6 G,3 A,3 C6 D3  D3   C6

The abcdrums entries are preserved below: