Clough / Engebretsen / Kochavi -- MTS article

hi Gene,

if you haven't yet read this, i strongly urge you
to do so. i think you'll get a lot out of it

... and then, hopefully, you'll explain it to me! :)

John Clough, Nora Engebretsen, and Jonathan Kochavi
"Scales, Sets, and Interval Cycles: A Taxonomy"
_Music Theory Spectrum_, vol 21 #1, Spring 1999, p 74-104

ABSTRACT

>> Recent studies in the theory of scales by Agmon, Balzano,
>> Carey and Clampitt, Clough and Douthett, Clough and Myerson,
>> and Gamer have in common the central role of the interval
>> cycle. Based on scale features defined in these studies,
>> and an additional feature called *distributional evenness*
>> defined here, a taxonomy is proposed for pitch-class sets
>> (pcsets) the [_sic_: that] that correspond to interval cycles
>> or to certain conjunctions thereof. Pairwise implicative
>> relationships among the features are explored. Of 20 sets
>> of features that are consistent with these relationships,
>> 13 are found to be instantiated by actual pcsets and 7 others
>> are shown to be incapable of instantiation. Most instantiated
>> feature-sets correspond to infinite classes of pcsets which
>> are shown to be enumerable; one such feature-set is found
>> to be uniquely realized (up to transposition) in the usual
>> diatonic pcset.

-monz

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