Insights into Mathematics | Tones, notes, duodecimals: and a Eureka moment for arithmetic | Maths and Music | N J Wildberger @njwildberger | Uploaded 1 year ago | Updated 23 hours ago
Can music teach us something about basic arithmetic? In this video we will begin to appreciate that the answer might be: YES! We start by making the distinction between tones (of which there are twelve possibilities in our Western system) and notes, which are associated rather to frequencies and are in principle unbounded as we go up and down the keyboard (or fretboard etc).
We've seen that tones are best named in a duodecimal fashion, and then the question arises: how do we best name notes? This is an important issue that has not been given enough thorough attention in musical circles. However by clarifying it, we are let to a "eureka" moment where we suddenly realize that our own familiar arithmetic has a crucial bias in it towards negative numbers, and that there is actually an interesting "musical" alternative for negative numbers that ought to be given careful consideration. There are bound to be lots of potential repercussions from this simple insight!
To check out my TikTok (music) channel: www.tiktok.com/@njwildberger
A big shout-out to my Patreon supporters and Members of the Wild Egg mathematics courses channel! Thanks so much.
***********************
My research papers can be found at my Research Gate page, at 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 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 patreon.com/njwildberger Your support would be much appreciated.
Here are the Insights into Mathematics Playlists:
youtube.com/playlist?list=PL55C7C83781CF4316
youtube.com/playlist?list=PL3C58498718451C47
youtube.com/playlist?list=PL5A714C94D40392AB
youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
youtube.com/playlist?list=PLIljB45xT85D94vHAB8joyFTH4dmVJ_Fw
youtube.com/playlist?list=PL8403C2F0C89B1333
youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
youtube.com/playlist?list=PLIljB45xT85DH__ZzGQWQrVRxlbKh-Nsa
youtube.com/playlist?list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
youtube.com/playlist?list=PL6763F57A61FE6FE8
youtube.com/playlist?list=PLBF39AFBBC3FB30AF
youtube.com/playlist?list=PLIljB45xT85DSrlV6NX8RMBksZhdTHtwW
youtube.com/playlist?list=PLIljB45xT85Bmcc9ksBOAKgIZAl0BwPg7
Here are the Wild Egg Maths Playlists (some available only to Members!)
youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
youtube.com/playlist?list=PLzdiPTrEWyz4VlOppC5CN0D0GjrjvBGKy
youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-
youtube.com/playlist?list=PLzdiPTrEWyz6zpIZ4Y_RK9zyJ9OufqNJv
youtube.com/playlist?list=PLzdiPTrEWyz7hk_Kzj4zDF_kUXBCtiGn6
youtube.com/playlist?list=PLzdiPTrEWyz5j1BJdXBw1MFst_nQAqzZ_
youtube.com/playlist?list=PLzdiPTrEWyz5HWgaVkhIwpGVKi6fciRxW
youtube.com/playlist?list=PLzdiPTrEWyz5HBT_Yo1G4DfeqUfI9zkKM
youtube.com/playlist?list=PLzdiPTrEWyz7LKbuJAHaXAhRj2ylD0OoX
youtube.com/playlist?list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
youtube.com/playlist?list=PLzdiPTrEWyz6MwUTOHRgC0oIxVtaHGQBd
youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
youtube.com/playlist?list=PLzdiPTrEWyz4IknbwXMEVwxOWS3z1Ch3C
************************
Can music teach us something about basic arithmetic? In this video we will begin to appreciate that the answer might be: YES! We start by making the distinction between tones (of which there are twelve possibilities in our Western system) and notes, which are associated rather to frequencies and are in principle unbounded as we go up and down the keyboard (or fretboard etc).
We've seen that tones are best named in a duodecimal fashion, and then the question arises: how do we best name notes? This is an important issue that has not been given enough thorough attention in musical circles. However by clarifying it, we are let to a "eureka" moment where we suddenly realize that our own familiar arithmetic has a crucial bias in it towards negative numbers, and that there is actually an interesting "musical" alternative for negative numbers that ought to be given careful consideration. There are bound to be lots of potential repercussions from this simple insight!
To check out my TikTok (music) channel: www.tiktok.com/@njwildberger
A big shout-out to my Patreon supporters and Members of the Wild Egg mathematics courses channel! Thanks so much.
***********************
My research papers can be found at my Research Gate page, at 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 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 patreon.com/njwildberger Your support would be much appreciated.
Here are the Insights into Mathematics Playlists:
youtube.com/playlist?list=PL55C7C83781CF4316
youtube.com/playlist?list=PL3C58498718451C47
youtube.com/playlist?list=PL5A714C94D40392AB
youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
youtube.com/playlist?list=PLIljB45xT85D94vHAB8joyFTH4dmVJ_Fw
youtube.com/playlist?list=PL8403C2F0C89B1333
youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
youtube.com/playlist?list=PLIljB45xT85DH__ZzGQWQrVRxlbKh-Nsa
youtube.com/playlist?list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
youtube.com/playlist?list=PL6763F57A61FE6FE8
youtube.com/playlist?list=PLBF39AFBBC3FB30AF
youtube.com/playlist?list=PLIljB45xT85DSrlV6NX8RMBksZhdTHtwW
youtube.com/playlist?list=PLIljB45xT85Bmcc9ksBOAKgIZAl0BwPg7
Here are the Wild Egg Maths Playlists (some available only to Members!)
youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
youtube.com/playlist?list=PLzdiPTrEWyz4VlOppC5CN0D0GjrjvBGKy
youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-
youtube.com/playlist?list=PLzdiPTrEWyz6zpIZ4Y_RK9zyJ9OufqNJv
youtube.com/playlist?list=PLzdiPTrEWyz7hk_Kzj4zDF_kUXBCtiGn6
youtube.com/playlist?list=PLzdiPTrEWyz5j1BJdXBw1MFst_nQAqzZ_
youtube.com/playlist?list=PLzdiPTrEWyz5HWgaVkhIwpGVKi6fciRxW
youtube.com/playlist?list=PLzdiPTrEWyz5HBT_Yo1G4DfeqUfI9zkKM
youtube.com/playlist?list=PLzdiPTrEWyz7LKbuJAHaXAhRj2ylD0OoX
youtube.com/playlist?list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
youtube.com/playlist?list=PLzdiPTrEWyz6MwUTOHRgC0oIxVtaHGQBd
youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
youtube.com/playlist?list=PLzdiPTrEWyz4IknbwXMEVwxOWS3z1Ch3C
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