Tones, notes, duodecimals: and a Eureka moment for arithmetic | Maths and Music | N J Wildberger скачать в хорошем качестве

Tones, notes, duodecimals: and a Eureka moment for arithmetic | Maths and Music | N J Wildberger

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. Video Contents: 0:00 - Introduction: Mathematics and Music 2:45 - Understanding Tones Through Frequency 7:19 - Combining Octave and Tone for Unique Note Labels 10:38 - Connecting Note Naming to Base-12 System 13:23 - Applying the Dozenal System to Piano Notes 14:00 - Comparing Number Lines in Different Systems *********************** 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.