What I Learned Writing an Album in Just Intonation

Thanks for posting this. The approach of keeping the traditional 12 notes while changing the tuning on-the-fly is really interesting and maybe the right tradeoff. This is so spot-on because adaptive JI is mentioned as a possible solution at the end of the article. It's the classic HN move where a weird topic is being discussed and someone says "why yes, I've made tools that happen to exactly match the niche topic being discussed!"

In fact, it's probably not my business, but this topic is so profoundly niche (and likely to remain so for a while) that I personally wouldn't make this commercial. My reasoning (and the reason I open-sourced some projects) is that it will limit adoption while changing almost nothing about my income. Obviously I hope I'm wrong, maybe these techniques will pick up in popularity. It's also possible that I think this way simply because I'm bad at marketing.

If the author is here, the audio clips don't play for me. Firefox console has: Uncaught (in promise) TypeError: document.querySelector(...).contentDocument is null

yeah, in general I do want to open source it, but for the time being I’m a student and every little bit counts

Speaking of Jacob Collier, this is a good time to mention the song where he “hacks” equal temperament to modulate to G-half-sharp without anyone noticing.

https://www.youtube.com/watch?v=Xd54l8gfi7M&t=3m17s

If I may provide some constructive criticism as someone who also has a background in tuning and tuning theory: I believe the article is pretty cool and you clearly have a good background on modern microtonal music. However, it is also clear that you do not have a good background on historical tunings (there are some factual errors in this regard).

Modern sources often implicitly assume that you understand tuning theory before teaching it, I agree. The understanding they often expect is this historical theory, though. I find that understanding historical tuning based on the idea of scales to be sort of tough to understand, while the circle of fifths is a lot more useful, and before 1900, pretty much nobody wrote about tuning in terms of scales since for all practical purposes it is very easy to hear frequency relationships in fifths and fourths rather than hearing them from steps.

Just Intonation is built on top of the harmonic series (not the circle of fifths), and I would suggest that you introduce the concept of the harmonic series before thinking about scales and fixed temperaments (your "boring" solution). As someone who does understand Just Intonation pretty well, I found the idea of going straight to a concept of scales very confusing, personally. The scale for true just intoned tunings is built on top of the harmonic series relationships you showed later, and those don't all have nice intervalic ratios.

Factually, the intervals were wrong for a typical Pythagorean scale: your fifth is 2^18/3^11 when the correct relationship for the typical notion of Pythagorean tuning is 3/2. Your scale stacks fourths based on 4/3 relationships, leaving the most important interval in the scale as the so-called "wolf" fifth. Most practical notions of Pythagorean tunings used fourths going one way and fifths going the other from the tonic, leaving the F#-C# relationship as the "wolf" (if the tonic is C), while all other fifths are pure. If you illustrate this with a circle of fifths rather than a graph showing scale degrees, it's a lot easier to understand. Pythagorean tuning also isn't really a type of just intonation since it doesn't use a harmonic series on a single note, but the exact definition of "just intonation" varies by source (some would say that even a temperament like Werckmeister is "just intonation").

All that said:

I would suggest you start with some ideas about tuning, introduce the harmonic series, introduce that "just intonation" is about preserving harmonic series relationships, and then go straight to your "freestyle" section. Eschew the notion that you need to understand the history of unequal temperaments to understand the present concept of the tension between the equal-tempered compromise scale and the just-intoned harmonic series.

Since you're more interested in modern theory, and your innovation and interests are there, I think you can skip the history and just get straight to the math and the lattices. Whether you use circles of fifths if you do this is up to you (I'm guessing you shouldn't - they are not so useful for modern tuning ideas).