2004 Student Research Conference:
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


Presentation Type: Oral Paper

Session: 21-5
Location: VH 1232
Time: 11:00

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