Scott Wallace

@Tim - iirc, I have said when I've disagreed with you. But I've agreed far more often.

@Tim - I often disagree with you, but I agree with you here: people who downvote should explain why. After all, the point of this forum is education, isn't it? And although as a traditionalist, I would say the "primary" meaning of M.M. is "Mälzels Metronom", I don't see any reason not to replace that with "Metronome Marking". So what? The important thing is that it just means the tempo according to a metronome.

@leftaroundabout- what do you mean by a "high-intonated" third? I find the resolution of a just dominant chord to its tonic- say 12/15/18 to 8/16/20, to be just as convincing, and with less cringeworthy dissonance. But maybe that's just me....

I'll just second all the opinions here about A=432. I've been following the movement (yes, I'm weird) for some time now, and it's revealing. There are even conspiracy elements to it: the Nazis (or the Rockefellers) supposedly introduced 440 as a means of mind control. The 432ers even have a rival sect in the C=256ers, which puts an equal tempered A even higher, at around 444Hz. Amusing but also disturbing.

@phoog - what is "optimal" tuning for a keyboard (or any other fixed pitch instrument)? You are obviously of the opinion that the sour D-A fifth disqualifies the JI scale under discussion from being "optimal". As I've pointed out, with all due respect, that's simply your opinion.

@phoog - well, it's obvious that you're no fan of JI. That's fine. But that doesn't render JI useless for others who don't share your preference, does it? I could say that the sour JI fifth of D-A is more than countered by the sour thirds (all of them) of 12TET. In the JI discussed here, we have three perfectly in tune major triads 4/5/6, and two perfectly in tune minor triads, 10/12/15. Can't do that in any equal temperament. But as I said, there's a place for all these temperaments.

@phoog - I agree with goblin, it depends entirely on what you deem necessary for a key (or mode) to sound good. For some music, I can either do without the D-A fifth altogether, or use it as a dissonance. I recognize that JI with a fixed scale is never going to be the best choice for, say, Chopin, but as I said, it has its place. And a 4/5/6 triad is simply heavenly, imho. Suum cuique.

@phoog - Yes, I know exactly what just intonation entails. Among other things, it means not expecting to be able to have a perfect fifth above every scale step. So what? It's a trade off, just as I said.

@ToddWilcox Well, cellists can march with their instruments, albeit awkwardly. I played in a group at the Dickens' Fair with a cellist who not only walked but danced with her instrument, supported by a band around her neck. But yeah, awkward at best.

@Tim - at least the way I'm used to using the terms, "accidental" means "a tone within a piece that's been altered away from the key (or mode) of the piece, by means of a sharp (or flat, etc) sign". I wouldn't call the F# and C# signs in a key (or mode) signature "accidentals". And while I find the distinction between "keys" and "modes" to be an historical artificiality, I usually go along with convention and say "the key of C major" and "the mode of D dorian". I don't know what's considered "correct", but as far as I know, there's no "correct" usage that doesn't fall apart somewhere.

Isn't it normal and clear to say "D major has the key signature of two sharps, G Dorian has the key signature of one flat", and so forth? That's what I do.

@topomorto - nope, not yet. I'm hoping to get my daughter to film me. I'll let you know. Thanks for the interest- what I do is definitely on the fringe.

And look at typical jazz instruments: saxes, horns, are almost all in relatively flat keys. It's just history.

Also a factor here: look at the tuning of the guitar. Doesn't even have a C string- everything's sharper (in the circle of fifths).

Actually, for me, the problem doesn't arise much any more: since I nowadays play almost exclusively heptatonic music, either tuned justly (usual scale: 8 9 10 11 12 14 15) or in some sort of meantone (C D E F G A B, the tuning being either more thirdy or more fifthy depending), then I'm never faced with the problem of denoting tones in a value (key) free way.

@Tim - depends on the flat. Bb is okay, but Fb is definitely depressing.

@supercat - sounds plausible to me. In any case, I don't see why there's anything to worry about here.

@Stinkfoot - I don't know. Aren't flats a bit depressing?

@supercat - I haven't checked out the German electronic tuner conventions. But I'm willing to bet that it would be A, A#, H, C, with no B.

I'm never jocular. Jovial perhaps.

Sounds guitarish to me too, but I've seen it in other contexts as well. Flats just don't have the uplifting feeling of sharps....

I agree- I'd like to see more examples of what people are doing posted somewhere.

@topomorto - thanks. I have fun doing this weird stuff.

soundcloud.com/scott-wallace-189088488/cauliflower

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

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

We can't have a name for every scale.

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

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 do it all the time.

Listing the ratios is the only way.

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

By listing the ratios.

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

What do you mean, "a defined version"?

The possibilities are endless, but the definition is simple.

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

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

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

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

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

That scale was a 13-limit just scale.

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.

Why not?

Why not?

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

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

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.

I don't understand your distinction.

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