Abstract Nonsense Appreciation

Since the start of 2021, I've massively turned down the composing and transcribing to focus on maths. I'm up to my MSc now, and hopefully, by the time I don't have to grind coursework any more, MuseScore 4/MuseSounds, or FL Studio, will be able to do xenharmonic/microtonal stuff, so that I can start diving into that kind of theory, and making that kind of music in earnest!

Then again, maybe maths was supposed to be my music all along - I would focus so much on coming up with "interesting" chord changes that everything else in my music would suffer. Conversely, if I had to make music that didn't have "interesting"-enough chord changes (whether due to a music assignment deadline or whatever), it would sound even worse because I'd stop working on it ASAP from how much my inner-critic would beat me up! They will never get the message that the point of music is not chord changes that span an interesting mathematical structure, so I've trapped them where they belong - polishing my maths with rigour after all the big ideas are down.

I found this album for the first time while surfing the hooktheory's theorytab database (I wish they let you filter music by the complexity/novelty metrics they already have in place!)

I wonder what it was like to make vgm in that era. Too bad intricate chord progressions/melodies/etc. (I guess I'll call it pitchsmithing) just don't have that kind of influence anymore. Now that computers are powerful enough to do all these automation curves and samples to make the timbre interesting, it's clear that most people only turned that much attention to those metrics as a last resort.

Take a completed sudoku, and append an identity row to the top, and identity column to the left.

You now have the Cayley table of a magma with identity. Is the magma also monoid? a group?

What if you relax the subgrid condition? (idk if there's an official name for it, but you know...)

Is that true for \(n\times n\) grids for all \(n\in\mathbb{N}\)?