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In Chopin's "Heroic" polonaise there is a two-handed ascending scale in the main theme that repeats several times throughout the whole piece (to state the obvious). What kind of scale is this? I never learned it in my theory class.

It's a completely absolutely standard version of one of the very most standard scales.

It's the "ascending melodic minor."
(Not unusual at all.)

I wonder if the fact that you didn't know means that the standard scales aren't as standard as they used to be. Back in the day, we (most of us, I think) used to be routinely drilled on the standard scales from the very beginning:

-- major
-- melodic minor, ascending and descending (the ascending and descending are different)
-- harmonic minor

B flat minor. Pretty common, actually. You were probably thrown off by it starting on the A.

"Melodic minor scale : the melodic minor scale differs when descending from when ascending. When descending, the seventh and sixth degrees are flattened so that the scale is the same as a descending natural minor scale.

The Bb minor melodic ascending is : Bb, C, Db Eb, F, G, A, Bb

Descending is : Bb, Ab, Gb, F, Eb, Db, C, Bb

As Mark_C points out, the scale passage in the Ab Major Polonaise is a textbook example of the melodic minor, ascending.

Regards,

B-flat melodic minor; I didn't enjoy trying to get that up to speed!

BTW, it's the same as the scales at the end of the 1st Ballade, even though it sounds different for various reasons including that it represents a different harmony.

Other examples:

-- end of Mozart Fantasy in C minor, K. 475
-- one of the variations in the middle of Beethoven's 32 Variations in C minor

....and probably 10 billion others that other people could probably mention some of.

It's very common. I think Damon is probably right that a big part of what made it seem unusual was that it starts on the A.

I've given lessons on occasions to students from the local conservatory. I ask them, do you know your scales? They always reply an emphatic ... yes.

OK, play an Ab major scale starting on scale degree three.

There's always a pause while they try and figure out what I meant ... and then they try and figure out what the fingerings are. We then have a discussion on what 'knowing your scales' really means.

My first assignment in the 'keyboard harmony' class back in college was being able to play the following in every key, every major key and all three flavors of minor keys ...

You play the I or i chord in one hand (of the key given) while you play the appropriate scale from scale degree 1 up and down an octave with your other hand. You them move on to the diatonic chord built on scale degree 2 with one hand while you play the scale starting on scale degree 2, up and down an octave, with the other hand .... and so on.

That was the first assignment. It got difficult after that.

Why all the scales? ... (honest question)

There are only 12 major scales at the piano (14 on paper). Each of those major keys only has seven diatonic triads, there's a finite amount of information to digest.

If you just stop at C major, you'll be thrown for a loop when you play in Bb major. Why not simply make yourself comfortable in all keys ... there are only 12, right? (I do admit that the minor scales might seem overwhelming, but then again, there is a finite amount of information.)

When you learned your multiplication tables, did you stop at the 2's? ... the 3's? ... the 4's? ... or did you go all the way to the 12's? ... and why?

This stuff is the basics of music and music theory. Learn it and be well spoken or don't and fumble around in the dark and just see notes on the printed page without any underlying connections ... and you'll keep asking questions like you did in your initial post.

BTW, dunno if this has often been the problem, rather than what they know about scales per se, but....."scale degree" might not be a well-known phrase. In all my 200 years including advanced music theory courses in college, I've never come across it. Sure, I could easily figure what you probably meant, but....I think it's a phrase that many people who really do know scales might trip over.

Mark, you quoted my uncorrected use of the word ... emphatic ...

Well, I guess I have Allen Forte to blame. I thought everyone discussed music, scales, whatever in terms of scale degree.

BTW, I don't get what's the deal about "emphatic"....

(like, what was wrong with how you used it)

I thought emphatic was fine. I just thought "scale degree" introduced a red herring into what you asked them to do.

(OK, now I guess we'll have to get into "red herring"....)

In your quote the spelling is still wrong. I think he'd like you to correct it since he can't in a quote.

Though empathy is a nice thing for a teacher to have, Dave.

Oh!!
Here's the problem: I can't see.

I never saw it as anything but "emphatic"!

Walter Piston uses the term 'scale degrees' in his Harmony book, which I thought was widely read.

I must admit that I never heard the term "scale degree" until I was in college. My teachers before that always taught me to use tonic, supertonic, mediant, etc. Scale degree does seem to be a bit more straightforward, especially if you are just talking about where to start a scale. If you are talking about harmony then the names do help me figure things out a little quicker.

It was.
But we used Siegmeister!

And anyway, the thing is: the term didn't catch on in general, did it? As I said, I had never come across it.

For a question like what Dave asked them, I think all of those sukkk.

Because they introduce an additional variable besides what you're really getting at: you're requiring that the person know some jargon or be able easily to figure it out.

How about just saying something like "the third step" or "the third note"? Anything else, and if the person has trouble, it isn't necessarily about what you're asking.

Dave, I started out knowing only solfege with a vague idea of note names. If you asked me to start on the third degree of Ab major, I would hear Mi, start on C, and want to hear Fa next which would bring me up a semitone to Db. I don't "know" my scales very well and I checked on the piano whether I was right about the Db, or would want to do a quick run-through mentally to make sure. But I think this tool is useful.

Over here rudiments theory for the RCM introduces degrees at the preliminary level on the first page of the chapter on scales. I translated degrees into solfege: La is 6. We memorized which chords are major or minor so if I start with my Mi I also know that the accompanying chord is a minor chord so it should be Cm.

The trouble is that knowing all of this intellectually and working it out is slow and wouldn't make me a pianist. It is likely that Mark would breeze through it as long as he knew what you meant by "degree" while I'm not sure that I can.
Terminology is secondary to ability, and ideally we should have both.

Well of course they do. Every field of study has its own jargon and students are forced to learn that jargon sooner or later, even when that jargon changes over time.