Pythagorean intervals in music and the magic of numbers | Maths and Music | N J Wildberger

Let's introduce the remarkable connection that the ancient Greeks, in the school of Pythagoras, discovered between ratios or proportions between small natural numbers and pleasant sounding harmonic intervals.

The relation is perhaps best introduced by discussing notes on a guitar string, and applying some affine geometry (not metrical, or Euclidean!)

However we need to realize that all is not quite so pleasant mathematically as the Pythagoreans would have liked, as such a tuning system ends up having some inconsistencies when we try to translate from one key to another. This is an obstacle that generated a huge amount of analysis in the history of Western music -- and we will be discussing this in our next video.

This video is one in a series where we look at the foundations of music from a mathematical point of view, and is complemented by my Tik Tok channel www.tiktok.com/@njwildberger .

Video Contents:
00:00 Foundations of music from a mathematical point of view
00:52 Context to the guitar
00:59 Mass and tension of the strings
04:13 Relationship between the extents of strings and intervals
08:22 Perfect fourths and perfect fifths
13:24 Transposing keys

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Видео Pythagorean intervals in music and the magic of numbers | Maths and Music | N J Wildberger канала Insights into Mathematics