Course  Introduction to Pitch Systems in Tonal Music
This series is one part of UC Irvine's Musicianship 15 ABC sequence for music majors. An understanding of music notation and basic musical terms is helpful but not required for these presentations. The math involved is basic.
Pitch systems use mathematics to organize audible phenomenon for creative expression. The cognitive processes we develop through exposure to music comprise a kind of applied mathematics; our emotional responses to musical nuance grow out of a largely unconscious mastery of the patterns and structures in music. This series of presentations covers the basic mathematics and cognitive phenomenon found in the tonal system used in Western music and much of the music of the world. Over the course of several presentations we will explore basic concepts of pitch and frequency, the organizing rules of tonal systems, and the mathematical construction of basic scales and chords. The reasoning and purpose of equal temperament, the standard tuning system for tonal music, will be explored in this context. Presentations will include graphics and computer applications designed specifically to illustrate these concepts.
  Music notation

Lecture 1  Introduction to the Course

Lecture 2  Basic Concepts

Lecture 3  The Octave and Just Intervals

Lecture 4  Octave Equivalence and More

Lecture 5  Circular Pitch Systems and the Triad

Lecture 6  Building a Diatonic Set with 3 2 Ratios

Lecture 7  Pythagorean Tuning and the Pure Triad

Lecture 8  The Minor Triad and a Circular System of Thirds

Lecture 9  Tuning with Pure Major and Minor Triads

Lecture 10  A 12Tone Pythagorean Set