The Spiral of Fifths (or - pythagorean drift study)

Maybe not so practical, but fun anyway! Maybe you've already heard about how our "Perfect 5ths" aren't so perfect - they're flattened or "tempered" down two cents in order to fit them within an octave and avoid the kind of endlessly repeating chaos you see here. This video poses the question - what if they weren't? Microtonal chaos ensues, not to mention the notation, my goodness! just look at all those double sharps and double flats and.. what else?

Well, we can derive a ton of stuff from the perfect fifth - the inversion is the perfect fourth, the harmonic mean is the 5-limit minor third, the arithmetic mean and first sum tone is the 5-limit major third, and by taking the mean of the perfect fourth we get a 7-limit minor 3rd.

Confused? Check out this cool pic here: https://imgur.com/DO9sZyE

About the software: If you're interested in software, I would say it's much better to use something you're already familiar with that might already have microtonal support - seriously check your vsts against this list, you might be surprised, a lot of stuff has it these days:
https://en.xen.wiki/w/Software
This is a better approach than like, doing what I do because what I do is convoluted and I can't really recommend it as a process or set of tools for anyone else in good conscience, seriously my workflow is terrible.


Still confused? Follow this channel for more videos, in the mean time why not check out some of these resources:
  / discord  
https://en.wikipedia.org/wiki/Just_in...
https://www.kylegann.com/tuning.html
https://marsbat.space/pdfs/JI.pdf
https://www.plainsound.org/pdfs/HCD.pdf
https://www.amazon.com/Harmonic-Exper...
https://www.amazon.com/Arithmetic-Lis...
https://www.press.uillinois.edu/books...