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xenharmonic-devs / scale-workshop

Design and visualize microtonal scales and play them in your web browser. Export your scales for use with VST instruments. Convert Scala files to various tuning formats.
MIT License
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Better support for LCJI and MCJI approximation #770

Open frostburn opened 1 month ago

frostburn commented 1 month ago

All of the approximate by ratios options produce too many complex ratios and miss plausible low-complexity interpretations.

arseniiv commented 1 month ago

Ooh I’m curious what ideas do you have about this. How to even search this enormous space? Trying out simple lattice skeletons and growing on that if one of them fits especially nice?

frostburn commented 1 month ago

You can count LCJI with fingers and toes if you bring a friend. MCJI should be entirely enumerable by machines too. Then it's just a matter of arranging the results in an efficient search tree for cents ranges.

arseniiv commented 1 month ago

I mean even for intervals in all non-default modes of the scale? It’s typical that if we simplify the written mode then other ones can become unnecessarily complicated. And being bad at JI I can’t fathom how to work with that (well except using frameworks for creating already good scales, like MOS, GS, nice small lattices and all that). But when we’re JI-ifying a scale, how to make the entirety of expressible intervals not unnecessarily disbalanced?

Though I feel that I can’t state the measure of balancedness right now. It’s a bit a design choice and an art, though there should be some sensible default.

frostburn commented 1 month ago

That's an entirely different problem. SW3 can create topology and maintain topology, but it cannot as of yet strategically break topology while maintaiing cohesion. That's a global problem.