JOHN GRESCHAK
PLATONIC DICE: HEXAHEDRON
for 2 violins, 2 violas and 2 cellos
(1999)
11:48
Program Notes
The musical material for this piece was derived from the
mathematical properties of a
hexahedral die.
Melodic Phrases
Counterpoint
Instrumentation
Textures
Musical Characteristics
Melodic Phrases
In this piece,
streams
are used to generate melodic phrases. Each edge
of a stream generates one or two notes of a phrase.
Counterpoint
At each point at which a given (parent)
stream
turns, it is possible to begin
another (child) stream that follows the edge that was avoided by the parent.
For example, if a parent stream makes a right turn, a child stream may begin
along the left turn that was not taken by the parent. Each stream generates
a melodic phrase. In this way, contrapuntal textures are formed.
Instrumentation
Instruments are assigned to the 6 faces of the die in the following way:
|
Face
|
Instrument
|
|
1
|
1st cello
|
|
2
|
1st violin
|
|
3
|
1st viola
|
|
4
|
2nd viola
|
|
5
|
2nd violin
|
|
6
|
2nd cello
|
Textures
A given melodic phrase may be
presented homophonically or melodically. Homophonic textures are used
primarily at the beginning and end of the piece and also serve
structurally as punctuation. Melodic textures are used extensively
throughout the piece. Some melodic phrases appear in a single instrument
while others are divided across several instruments (klangfarbenmelodie).
The instruments upon which a given phrase is played is determined by
the faces that are touched by the
stream
from which the phrase has been derived.
Musical Characteristics
There are 62 different
types of streams
on a cube. In this piece a primary and secondary musical characteristic is
associated with each type of stream. Loud and soft are used as primary
characteristics while con sordino and senza vibrato are secondary
characteristics. In addition to these, many other primary and secondary
characteristics are used.