by any other name, for example, “major-seconds” or “minor–seconds.” Proper
interval identification for whole steps and half steps shall be addressed in
.
Throughout the history of music, various systems of referential tuning have
evolved, been adopted, been modified, and been discarded in favor of other
systems. It is not within the purview of this discussion to examine these various and
sundry systems of tuning.An exceptionally clear and concise discussion of the
history and theory of tuning systems may be found in Chapters 1 and 2 of
Chromaticism: Theory and Practice
, Howard Boatwright, Walnut Grove Press, 1994.
For our purposes, we shall limit the discussion to the standardized tuning system
known as
equal temperament
4
. Music in the transitional period between the
Renaissance and Baroque employed different tuning systems that limited
compositional resources. A “compromise” tuning system was proposed and
gradually adopted, whereby pitches were slightly altered enabling the division of
the octave into twelve equal portions or
semi-tones
(half steps). This “evenly-tuned,”
or “equal-tempered” system allowed composers to employ the full resources of the
chromatic collection.This will come into focus in
Signatures, and The Cycle of Fifths"
and
Therefore, the source collection for Western music is the
Chromatic Scale
5
.The
Chromatic Scale, so called because it contains all the pitch “colors,” is also known as
the
Duodecuple scale
(Latin:
duo-deca
, “two and ten”). It is also labeled the
Non-
Selective Scale
, so-called because, all pitches being of equal quality, no one pitch
asserts itself over the others.
The Chromatic Scale
Figure 3.1
The Chromatic Scale
Audio 1
The Chromatic Scale
4. The current system of tuning
whereby pitches have been
adjusted to allow division of
the octave into twelve equal
portions.
5. The source set or collection for
pitch materials as defined
within equal temperament.
Chapter 3 The Foundations Scale-Steps and Scales
3.1 Scales and Scale-Steps
89
