Pythagorean Tuning

A musical tuning system that based on using simple integer ratios to define the intervals between notes

"Pythagorean Tuning" is a musical tuning method based on using whole number ratios to define the relationships between musical intervals. In this system, intervals are adjusted using simple integer ratios, but switching between different keys may result in dissonance.

Pythagorean Tuning originates from the viewpoints of the ancient Greek philosopher Pythagoras (570-490 BC), who believed that musical intervals should be defined based on whole number ratios to achieve the purest harmonies. In this tuning method, intervals are adjusted based on simple integer ratios such as 1:1, 2:1, and 3:2. For example, the perfect fifth interval has a ratio of 3:2, meaning the higher note's frequency is 1.5 times that of the lower note.

However, Pythagorean Tuning presents challenges, especially when modulating between different keys. Since different keys have distinct interval ratios, modulation may result in intervals no longer being pure, leading to dissonance. This restricts the practical use of Pythagorean Tuning in performance and playing.

Although Pythagorean Tuning is less common in modern music, it still finds applications in certain specialized music genres and experimental music. It emphasizes the purity and harmony of intervals but is limited by its inability to accommodate flexible modulation.

Example of Pythagorean Tuning

How Pythagoras Broke Music (and how we kind of fixed it) [see comments for corrections]