17th Annual Student Research Conference
Mathematics and Computer Science
The Mathematics of Musical Tuning Systems
Erin M. Gibeson
Dr. Scott Alberts, Faculty Mentor
Musical pitches sound different because they all have different frequencies, and scales are constructed by comparing the frequencies between pitches. In modern music, we think of scales being cyclic (returning to their starting point), but a scale constructed solely of frequency ratios will never return to it starting point. Thus, musicians and sometimes mathematicians temper intervals to keep the scale more in tune. This dilemma has led to the development of many different tuning systems. I will discuss several of these systems and the drawbacks of each. I will also explain with continued fractions how we can best approximate several tuning systems that not only sound pleasant but are accurate.
Keywords: music, tuning, temperament, mathematics, frequency ratios
Topic(s):Statistics
Presentation Type: Oral Paper
Session: 21-5
Location: VH 1232
Time: 11:00