"Perceptual
Aspects of Maximally Even and Deviant Maximally Even Sets"
In
this paper, I show how the maximal evenness property can alternately facilitate
or hinder our ability to navigate pitch spaces aurally. Richmond Browne’s
concepts of pattern matching and position finding enable us to evaluate the perceptual
characteristics of these scales. Several common ME sets are modes of limited transposition,
a property that inhibits pattern matching. In many cases, a slight deviation from
ME—a semitonal displacement —results in a set that is much more listener-friendly
by producing a collection with a number of modes equal to its cardinality.
The
second part of the paper applies the notion of ME and deviant-ME to second-order
ME sets. Second-order ME sets are ME subsets of a set that is already ME: the
most common example is the triad with respect to the usual diatonic collection.
Messiaen’s modes and the chords he gives as indigenous to them provide a
point of entry to examine the relationship between ME sets, deviant ME sets, and
second-order ME sets. In cases where the scale is maximally even, a second-order
collection that deviates from ME is desired so as to facilitate pattern matching.
In cases where the scale is not ME, the second-order collection can be ME without
compromising pattern matching. This work serves as a starting point for investigation
into the cognition and perception of neo-tonal music by the likes of Debussy,
Stravinsky, and Messiaen.
“A
Parsimonious Voice-Leading Space for Set Classes”
There has been considerable recent interest in parsimonious voice leading among
pitch-class sets, that is, voice leading in which a single note moves by semitone.
This paper describes an integrated parsimonious voice leading space for all of
the set classes and explores some of its features. The space is multi-dimensional
and thus difficult to grasp in its entirety. This paper offers maps of slices
and chunks of the space in a format that is relatively simple to grasp and thus
to use in analytical descriptions of actual progressions of harmonies. Within
the space described here, the progression between any two harmonies, and harmonic
successions of any length and diversity, can be meaningfully interpreted as easy
or hard, near or far, with particular expressive effects associated with each
possibility.