(musTh 212) Lecture Notes: Basic Concepts for Atonal Theory

These concepts are taken from Introduction to Post-Tonal Theory by Joseph Straus.

Basic Concepts

Octave Equivalence. Pitches separated by one or more octaves are regarded as equivalent.

Pitch Class. Distinguishes between a specific pitch (a single note on a staff) and a pitch class (all the notes with the same letter name, in any octave).

Enharmonic Equivalence. Without tonal context, there is no difference between C# and Db, etc.

Integer Notation. Using integer notation simplifies enharmonic and octave equivalence.

Pitch Intervals, Ordered and Unordered. Pitch intervals specify a distance between two specific pitches (not pitch classes). An ordered pitch interval also tells you the direction of the interval (+ = up; – = down).

Pitch-Class Intervals, Ordered and Unordered. The interval between two pitch classes. Ordered pitch-class intervals move to the right around the clock face. Unordered pitch-class intervals move whichever way is shortest.

Interval Class. Intervals larger than an octave are considered equivalent to their intervals within the octave (i.e., a pitch interval of a 15 //minor 10th// is the same as a pitch interval of a 3 //minor third//). Intervals larger than a 6 (a tritone) are the same as their inversion within the octave. Subtract the interval from 12 to get the inversion. In this manner, an interval of 9 is larger than 6. Subtract, 12 – 9 and the result is 3, the interval class for nine.


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