BAIN MUSC 525Post-Tonal Music Theory

Straus Ch. 1 OutlineBASIC CONCEPTS AND DEFINITIONS

The page numbers in all outlines refer to Joseph Straus, Introduction to Post-Tonal Theory (Upper SaddleRiver: Prentice Hall, 2000) unless otherwise specified. For other citations, see Course Reader.

In order of appearance…

Termspitch (p. 2)pitch notationstaff notationoctave equivalence (p. 1)equivalence relation (p. 1)equivalence classidentity relation (p. 1)twelve-tone equal temperament

(12TET)enharmonic equivalence (pp. 2-

3)pitch class, abbr. pc (p. 2)pc lettername notationpc integer notation (p. 3)pc staff notationfixed-zero notation, [C=0] (p. 4)movable-zero notation

pc clockface diagram (p.4)mod12 arithmetic (pp. 4-5)modulus (p. 4)arithmetical operations (p. 4)Johann Carl Friedrich Gauss’s

clock calculator (Sautoy2003, pp. 20-21)

pitch spaces (p. 5)pitch-class space (p. 5)

c-space (Morris 1987, pp. 23-26)u-spacep-spacem-spacepc-space

traditional tonal interval names(p. 5)

intervals (p. 6)adjacent intervalsnon-adjacent intervalsdirection and magnitudesigned numberabsolute valuepitch interval, abbr. ip (p. 6)ordered intervals (p. 6)unordered intervals (p. 6)ordered pitch-class interval (p. 7)complement mod12 (p. 7)unordered pitch-class interval

(pp. 7-8)interval class, abbr. ic (p. 9)ic content (p. 10)ic vector (pp. 11-12)unique multiplicity of ic (p. 12)

FOUR BASIC INTERVAL TYPES

In basic atonal theory, 12TET is (usually) assumed so the basic intervallic unit is the semitone = 212 :1.

Interval Type StrausAbbreviation

BainAbbreviation

Description

1. Ordered pitch interval ip opi Distance between two pitches, directionand distance are indicated.

2. Unordered pitch interval ip upi Absolute distance between two pitches,only distance is indicated.

3. Ordered pitch-class interval i opci Distance between two pitch classes,number of units clockwise on the pcclockface diagram is indicated.

4. Interval classAn equivalence class createdby collapsing opci’s underintervallic inversion

ic ic Shortest distance between two pitchclasses, shortest distance (clockwise orcounterclockwise) on the pc clockfacediagram.

“Which one we use will depend on what musical relationship we are trying to describe.”Joseph Straus, Introduction to Post-Tonal Theory

EXAMPLE

Interval opi upi opci icA4 to G#3 -13 13 11 1

QUOTABLE “…pitch is the intersubjective correlate of frequency.”

Robert Morris, Composition with Pitch-Classes