Скачать с ютуб Pythagorean intervals in music and the magic of numbers | Maths and Music | N J Wildberger в хорошем качестве

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 *********************** My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses are being developed at openlearning.com. The first one, already underway, is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated. Here are the Insights into Mathematics Playlists:    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист   Here are the Wild Egg Maths Playlists (some available only to Members!)    • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист      • Плейлист   ************************