Scale Adjacency, Sharps and Flats | Maths and Music | N J Wildberger

[@kendebusk2540]

Absolutely wonderful, Norman! I started on piano over 60 years ago, know all the sharps and flats, but never once did I realize the clock face with the evens being "right" and the odds being "anti-right" so to speak. Please keep up this series, I continue to learn and be amazed at how complicated it is in relation to mathematics!

[@FergalByrne]

Hugely enjoying this, as you also seem to be!

[@mrborisak]

love your work, thank you

[@Drbob369]

Very unique stuff you mske

[@mattbennett277]

Another thing that seems arbitrary from a mathematical perspective is the preference for the Ionian mode. Dorian mode is symmetric and perhaps highlights certain relationships better. For example, the first adjacent scale either raises to a major third (#3) or lowers to a minor sixth (b9 = b(-3)); so there is an inverse relationship with respect to 0 mod 12. Also, it can highlight the relationship between the modes better - Dorian moves to Mixolydian by raising the third (#3) or lowers to Aeolian by lowering the sixth (9b). Slide 3 shows the relationship between the raising note and the starting note of the scale - the Dorian version demonstrates a relationship where the notes leading into an augmented triad {x, x + 4, x - 4} are a raising or lowering of the same note. For Ionian, if the starting note is x then the raising/lowering note is x + 2. For Dorian, the raising/lowering note is x. For example, if the starting note of the scale is 2 then the notes leading into 6 & 10 are 4# & b4, respectively. But for Dorian, with starting note 2, the notes leading into 6 & 10 are 2# & b2, respectively.

[@WhoIsThisIDontKnow-b5n]

I'm still confuzzled, I'm not sure if this has to do with this video, but how do I do 4#8? It was in a mathcounts competition. I don't know how to do sharps, flats, and naturals in math...