JOHN GRESCHAK
THE TOWER OF HANOI
for string orchestra
(UNFINISHED)
(1997)
4:03
Program Notes
To some extent, the structure of the piece is based upon the
legend
that is associated with the
Tower of Hanoi.
Section 1
Section 2
Section 3
Section 1
The first section (bars 1 through 3) is a musical representation of God
hammering 3 pegs into the ground. Pitches were chosen to create a
metallic sound.
Section 2
The second section (bars 4 through 15) is composed of 2 subsections.
The first is a musical
representation of God placing 5 disks on the 3 pegs that were installed in
Section 1. The second is a
musical representation of God moving disks in order to perform
a quality assurance test on the puzzle.
Each move of a disk generates one note. Notes for larger disks are lower
in pitch and longer in duration.
A pitch class is assigned to each of the 3 pegs in the following way:
|
Peg
|
Pitch Class
|
|
p0
|
C
|
|
p1
|
E
|
|
p2
|
G#
|
The pitch class of a note is given by the
pitch class of the peg to which a disk is moved.
Section 3
The third section (bars 16 through the end) is a musical representation of
priests attempting to solve
The Tower of Hanoi
puzzle.
A note is generated each time a disk is moved. Except for the largest disk,
the pitch of the note is a function of both the disk size and the peg to
which the disk is moved (the target peg). The following table gives
the pitches for each combination of disk size and target peg
(d0 is the smallest disk):
Pitch Classes for Moving Small Disks
|
|
Target Peg
|
|
Disk
|
p0
|
p1
|
p2
|
|
d0
|
C
|
E
|
G#
|
|
d1
|
C#
|
F
|
A
|
|
d2
|
D
|
F#
|
A#
|
|
d3
|
D#
|
G
|
B
|
The pitch of a note that is generated by moving the largest disk is
dictated by the peg from which the disk is moved (the source peg).
Pitch Classes for Moving the Largest Disk
|
Source Peg
|
Pitch Class
|
|
p0
|
D#
|
|
p1
|
G
|
|
p2
|
B
|
The cellos open section 3 with the following 6 bars which are generated
by moving all 5 disks from p0 to
p1:
Had the piece been completed, this section would end with a musical
representation of a thunderclap in accordance with the
legend.