The Connection Between Pythagorean Intervals and Music | 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/Norman_Wildberger 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/algebraic-calculus-one/ 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 https://www.patreon.com/njwildberger Your support would be much appreciated. Here are the Insights into Mathematics Playlists: https://www.youtube.com/playlist?list=PL55C7C83781CF4316 https://www.youtube.com/playlist?list=PL3C58498718451C47 https://www.youtube.com/playlist?list=PL5A714C94D40392AB https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp https://www.youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf https://www.youtube.com/playlist?list=PLIljB45xT85D94vHAB8joyFTH4dmVJ_Fw https://www.youtube.com/playlist?list=PL8403C2F0C89B1333 https://www.youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK https://www.youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e https://www.youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH https://www.youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua https://www.youtube.com/playlist?list=PLIljB45xT85DH__ZzGQWQrVRxlbKh-Nsa https://www.youtube.com/playlist?list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov https://www.youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse https://www.youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb https://www.youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP https://www.youtube.com/playlist?list=PL6763F57A61FE6FE8 https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF https://www.youtube.com/playlist?list=PLIljB45xT85DSrlV6NX8RMBksZhdTHtwW https://www.youtube.com/playlist?list=PLIljB45xT85Bmcc9ksBOAKgIZAl0BwPg7 Here are the Wild Egg Maths Playlists (some available only to Members!) https://www.youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB https://www.youtube.com/playlist?list=PLzdiPTrEWyz4VlOppC5CN0D0GjrjvBGKy https://www.youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG- https://www.youtube.com/playlist?list=PLzdiPTrEWyz6zpIZ4Y_RK9zyJ9OufqNJv https://www.youtube.com/playlist?list=PLzdiPTrEWyz7hk_Kzj4zDF_kUXBCtiGn6 https://www.youtube.com/playlist?list=PLzdiPTrEWyz5j1BJdXBw1MFst_nQAqzZ_ https://www.youtube.com/playlist?list=PLzdiPTrEWyz5HWgaVkhIwpGVKi6fciRxW https://www.youtube.com/playlist?list=PLzdiPTrEWyz5HBT_Yo1G4DfeqUfI9zkKM https://www.youtube.com/playlist?list=PLzdiPTrEWyz7LKbuJAHaXAhRj2ylD0OoX https://www.youtube.com/playlist?list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM https://www.youtube.com/playlist?list=PLzdiPTrEWyz6MwUTOHRgC0oIxVtaHGQBd https://www.youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS https://www.youtube.com/playlist?list=PLzdiPTrEWyz4IknbwXMEVwxOWS3z1Ch3C ************************