Just intonation doesn't have to have 12 notes, does it? I've never heard that before, and I play lots of just scales that have 7 notes.

@ScottWallace yes you are correct. When you start building off of the different intervals inside just intonation, things compound and get out of hand fast which is why ET is very prevalent today. I'd rather not make this more complex than it needs to be.

@Dom- yes, but it's misleading to imply that there's only one just scale, and that it has 12 notes.

@ScottWallace I never imply either thing. I only say what the system defines. ET defines 12 tones that are always uniform so they're always the same. JI can theoretically have infinite tones if you keep using the system on each create interval since the system is non uniform. The only thing I state is the initial building of the 12 intervals in cents in JI.

You say, and I quote, "So for example both Equal Temperament and Just Intonation (which is a tuning) have 12 notes".

@ScottWallace I'll change it to say 12 defined intervals if that makes more sense, but again as long as you're not modulating and reusing the formula it's accurate.

Thanks. Another problem (sorry!) is that you say "So in the other question, the OP defines a set of notes by ratios which neither come up in Just Intonation nor Equal Temperament. " But the ratios given are all small integer ratios, so that qualifies as a just scale by any definition I know, even if it's an unfamiliar one. It's important to note that there is not only one "true" just scale, and that the number of notes can vary.

Or you can have a just scale of fewer tones.

Yes, there's a lot to play with.

But your answer implies that there is one just scale with twelve tones, which is of course not true.

The distinction I'm trying to get across is the communication aspect of this question. Which was lacking in the original question.

I don't understand your distinction.

Just intonation does not have a fixed set of notes due to the nature of it, but when comparing and trying to get the name of a scale we have to have a way to talk about them.

Yes, and there's nothing wrong with your example of the 12-tone just scale. But I think you should have made it clear that that's only one possibility.

The other question just asked what scale which the answer based on the information given lies in the temperament/tuning of the set of notes whether it be a subset of a just scale or something different.

Do you mean the list of ratios at the beginning of the OP's question?

I don't see how that is not a just scale.

It's really not

Why not?

If it is it's not complete.

Why not?

Because the ratios have to come from somewhere.

Typically determined by the limit.

Where do the ratios have to come from? As far as I understand it, a just scale simply means a scale of integral (typically small integer) ratios.

That scale was a 13-limit just scale.

1, 15/14, 15/13, 5/4, 15/11, 3/2, 5/3, 15/8

A rather peculiar just scale, but a just scale nonetheless.

I think we're just going to go down a rabbit hole if we keep going. If you can find a reference for his scale being a defined 13-limit just scale I can reopen the original question and you can add this as an answer.

I don't see how that rules out this scale as being one of many possible 13-limit just scales.

There's a lot behind Just Intonation and the possibilities are next to infinite.

Why do I need a reference? This scale has ratios, the largest prime denominator is 13.

I know about the possibilities. I do a lot of just tunings myself.

The possibilities are endless, but the definition is simple.

So let's think of this from a communication standpoint: how would you define the OP's 13 limit scale versus a defined version in the question above?

What do you mean, "a defined version"?

I would simply call it "a 13 limit just scale".

But how do you differentiate?

By listing the ratios.

I mean between different 13 limit scales.

That's the only way, with so many possibilities.

Listing the ratios is the only way.

I do it all the time.

Again, we're going down the rabbit hole that the other question set up.

I don't see a rabbit hole. The definition of a just scale is pretty simple, even if we can't name them all except by listing the ratios.

I will fix the wording on the question a little later and ping you to see if it's any better, but the point I'd like to get across it to be able to talk about a scale you need to understand the tuning or intonation.

So the OP of the first question wanted a name for his ratios.

Even if we're saying it's a 13 limit just scale that's not really specific enough to uniquely identify it.

The ratios are the only thing that will identify it uniquely.

We can't have a name for every scale.

Okay, I'm off to bed. Thanks for the chat and your consideration. Happy musicking!

If you're interested, here's an example of my stuff, this one in an 11-limit scale:

soundcloud.com/scott-wallace-189088488/cauliflower

@ScottWallace loving the cauliflower!

we really need to get more of people's music posted around the place...