# Talk:Just intonation point

## Explanation

Would anyone who understands the first part of this page be able to revise it a bit for clarity and/or extend it until it actually explains what JIP is? I'm completely lost. Here's my experience reading this text. It tells me that J is a point in a space. I am now in eager suspense about which point that is. Instead of answering that, a new object M is introduced. Whatever it is, it might be a monzo, it might not. This begs the question: what else could it be? And if it's not a monzo, it's not evaluated in octaves? Who cares if it is or isn't -- what does that have to do with JIP? We then do a "shift" which is weird because we weren't in any acknowledged state or action to shift away from yet, and we take my favorite arbitrary monzo I was implicitly asked to imagine as M (maybe!), which we haven't even used yet, and throw it away, now "representing" it as something using a variable "e" which is certainly not Euler's constant but isn't explained at all, and the grand conclusion is that J "becomes" something. But I don't want to know what it becomes; I want to know what it is in the first place. And the thing that it is shown to become doesn't make any sense from the typical interpretation of val: what kind of val could map all the primes to a single step? If you're going to use a bizarre val like that, certainly it has to be explained. --Cmloegcmluin (talk) 15:58, 6 May 2021 (UTC)

The original text dates back to Gene Ward Smith, who was a mathematician, and - as far as I know - rarely in the mood to make his ideas understandable to non-mathematicians, unfortunately! --Xenwolf (talk) 16:17, 6 May 2021 (UTC)
I also didn't understand much of the article, but let's see if someone is willing to make it even more accessible for non-mathematicians. So I wouldn't suggest to remove anything by now. Thanks so far for Flora, Inthar and you. --Xenwolf (talk) 11:41, 8 May 2021 (UTC)
It's just the tuning map which maps monzos to cent values; I added a high-level blurb. Mike Battaglia (talk) 23:12, 9 May 2021 (UTC)

## The logarithm and generators

Math rant: The p-limit is a submodule of Q (the rational numbers) under multiplication. The only reason to take a logarithm is because addition is easier for us (and allows us to use the tools developed in linear algebra). So really, the logarithm is an isomorphism between p-limit JI and the free Z-modules under addition we use in RTT. The generators of JI are just the primes, so the JIP is nothing more than the generators under this isomorphism. I know this sounds pretty abstract but maybe this helps: you can think of the p-limit JI as a temperament with the identity matrix as its map, and the JIP is its generator (list). As such there should probably be a mention of generators, and I propose renaming JIP to something like "just generators".

EDIT: I have written up an explanation here.

- Sintel (talk) 22:20, 18 December 2021 (UTC)

The JIP isn't just a list of generators; it's a function that maps from monzos to their size in cents (or whatever unit you want). In non-weighted coordinates, the coefficients are the sizes of the basis monzos in your subgroup, in cents; in weighted coordinates it'll typically be <1 1 1 1 1 ...| if you're in some subgroup generated by primes. Mike Battaglia (talk) 10:58, 19 December 2021 (UTC)
Yes, this fact follows directly from the definition. Sintel (talk) 14:35, 19 December 2021 (UTC)
It doesn't if we go with saying the JIP is just a list of generators. Mike Battaglia (talk) 17:00, 19 December 2021 (UTC)