MAPPING MUSIC

Author: thomasclarkumich

  • CONSTELLATIONS: Pitch Space, Arrays, Tonality

    Introduction

    Galileo revolutionized astronomy, in part by using a new tool: the telescope. Schoenberg revolutionized harmony by evolving an existing concept, the chromatic scale, into a new tool: the 12-tone scale. (He also devised the compositional tool of the 12-tone row — but that’s another story.) Allen Forte took Schoenberg’s ideas to another level of abstraction: defining Pitch Class and applying basic math to the 12-tone universe. Christman focused on intervallic essence of pitch patterns: defining the “successive interval array.” I am merely another explorer using their maps but choosing my own creative path. In doing so, I will define some of my own terms, while adapting and clarifying some established terms that fit what I’m thinking and expressing.

    Topics

    • Tuning
    • Constellations
    • Interval Arrays
    • Scales
    • Scale prototypes
    • Scale patterns and set classes
    • Harmonic complexity
    • Constellation streams
    • Constreams and 12-tone sets
    • Progressive alterations of arrays
    • Clusters
    • Cells – melodic molecules
    • Cell class

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    Mapping the Music Universe by Thomas S. Clark . . . CONTENTS

  • STARS: Time points, periodicity, perception

    We start with time. Everything in music involves time, is of time, sound events occurring in our perceived flow of time. Sound itself is periodic, a repetition of compression waves in air (or water).

    Repetition of an event or series of events, establishing a frequency of repetition and the period or cycle length of the elapsed time duration from each event’s starting time point (moment) to the starting point (moment) of its repetition.

    We perceive the frequency of the waves as pitch if they are faster than 20 per second and slower than about 4,000. Frequency is typically measured in cycles per second, called Hertz.

    Non-periodic waves faster than about 20 Hz are perceived as noise. Events or time cycles slower than 20 Hz are perceived as pulses, tempo, rhythm, phrase structure, etc. At these slower sub-sonic event speeds, it is more convenient to identify the duration of the cycle, its period, than the frequency.

    Periodicity, this repetitive aspect of sound events in time, gives us a dimension to map all the possibilities, from extremely fast to almost frozen slowness, and from simple, highly regular repetitions to a very complex succession of variants.

    Topics

    • Defining time
    • Time perception
    • Periodicity
    • Meter
    • Definitions
    • Stress and accent
    • Rhythmic molecules
    • Harmonic rhythm
    • Beyond meter
    • Prime numbers

    To read more, request a password from tc24@txstate.edu

    Mapping the Music Universe by Thomas S. Clark . . . CONTENTS