We use the mathematical 12 tone chromatic scale as a framework for an expanded view of modes in music, focusing first on minor scales, and then branching out to other scales. This frees us from the somewhat limiting pre-occupation with the usual Dorian, Lydian, Mixolydian etc modes for the major scale.

We use the notation introduced in the last videos for describing general scales and the associated interval sequences. Some basic mathematical concepts relating to transformations, typically rotations and powers are found to be useful here in this purely musical context.

And we start to see some non-trivial mathematics emerging from this purely musical set up also. Some interesting classification questions are just around the corner from this thinking. So Maths and Music do really interact with each other!

This is indeed part of the Maths and Music Playlist: please check out the other videos in the series at    • Maths and Music  

Artwork created with the help of Midjourney, an amazing Bot that stands ready to put half of the planet's graphic designers out of business in the next few years. It's a new world coming, and us pure mathematicians are not immune, as we shall discuss in our Sociology and Pure Maths series!

You can check out my TikTok (music) channel: www.tiktok.com/@njwildberger

Video Contents:
00:00 The importance of scales
00:50 The 12 tone clock - Major scale
02:14 Rotating an interval sequence (rho)
04:09 Quick review of modes of a major scale
06:40 Modes of a minor (harmonic) scale
10:15 Names of modes of a scale type
13:50 Examples of obtaining modes of a scale

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Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.

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 will be 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! :)

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Here are all the Insights into Mathematics Playlists:

Elementary Mathematics (K-6) Explained:    / playlist  
list=PL8403C2F0C89B1333
Year 9 Maths:    • Year9Maths  
Ancient Mathematics:    • Ancient Mathematics  
Wild West Banking:    • Wild West Banking  
Sociology and Pure Mathematics:    • Sociology and Pure Mathematics  
Old Babylonian Mathematics (with Daniel Mansfield):    / playlist  
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History:    • MathHistory: A course in the History ...  
Wild Trig: Intro to Rational Trigonometry:    • WildTrig: Intro to Rational Trigonometry  
MathFoundations:    • Math Foundations  
Wild Linear Algebra:    • Wild Linear Algebra  
Famous Math Problems:    • Famous Math Problems  
Probability and Statistics: An Introduction:    • Probability and Statistics: an introd...  
Boole's Logic and Circuit Analysis:    • Boole's Logic and Circuit Analysis  
Universal Hyperbolic Geometry:    • Universal Hyperbolic Geometry  
Differential Geometry:    • Differential Geometry  
Algebraic Topology:    • Algebraic Topology  
Math Seminars:    • MathSeminars  
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And here are the Wild Egg Maths Playlists:

Triangle Centres:    • ENCYCLOPEDIA OF TRIANGLE CENTERS  
Six: An elementary course in pure mathematics:    • Six: An elementary course in Pure Mat...  
Algebraic Calculus One:    • Algebraic Calculus One  
Algebraic Calculus Two:    • Algebraic Calculus Two  
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