Somewhere between Binary Form and Ternary Form lies the often mentioned, but also misunderstood Rounded Binary Form.

Rounded Binary is a stupid name. It's not really Binary - it's Ternary. But it's not "truly" Ternary. Some theorists call Rounded Binary "Incipient Binary" - incipient means "almost" - the problem is, if anything, it's actually Incipient Ternary. Or is it already Ternary, and beginning to devolve into Binary?

Oh who cares. The important thing is that's it's a very common Form and as composers, we should be able to recognize it and use it.

If you haven't already read my articles on Binary and Ternary Form, you should (for background). That said...

Binary Form is:
A B
and Ternary is:
A B A

Rounded Binary is also:
A B A
BUT with one important distinction:

In Rounded Binary, only approximately HALF of the A material returns after the B section. Now this is important: HALF of A returns - not A half as many times! It is literally, HALF of the original A section's material (usually the latter half). So Rounded Binary is usually written:
A B 1/2A

And like Binary and Ternary, a Two Reprise repeat pattern is common:

||: A :||: B 1/2A :||

Now again, be careful here:
A B A - Ternary.
||: A :||: B :||: A :|| - also Ternary.

Repeats don't affect form, so:

||: A :||: B :|| A || is written out:

A A B B A

This is STILL a Ternary Form (a side note here, there are many "in-between" forms such as "asymmetrical binary" or "simple ternary" into which many of these "non-standard" versions fit). It may LOOK like 1/2 of A is here after the B sections, but that's not the case - it's just one less repeat of the FULL A section! If the A sections where 16 bars (without the repeat) above, then the last A (which is not repeated above) is ALSO 16 Bars. It would only be Rounded Binary if the final A section was approximately 8 bars!

Back to the name game - why "binary"? Well, it is closer to Binary for a couple of reasons:

1. It is not repeated like ||: A :||: B :||: 1/2A :|| - that makes the last A "double", and therefore the length of the original, and thus basically a Ternary form (A A B B A) again.

2. It is an "quasi-open" form, which is closer to Binary than Ternary. Ternary Forms tend to have a complete A section and B section - that is, they cadence in their own key and could stand alone as complete little pieces. Rounded Binary Forms usually have an A section that is sectional - ends on the Tonic of the home key - so that when the latter half of A returns later, the final cadence will be on I (so this is an idea from Ternary). The B section commonly is not "complete" as in Ternary (so an idea from plain Binary).

So really, it's basically a Binary Form that's been "rounded off" by having some of the A material come back to "close off" the piece.

Rounded Binary might be seen (and has been seen by many) as taking the best attributes from Binary Form (open structure) and Ternary Form (idea of Home-Away-Home with a Return) and combining them.

It is also seen as the precursor to Sonata Form, which if you've heard anything about form, you've probably encountered.

Modulation Schemes for Rounded Binary are as easy as Binary and Ternary:
A: Home key - usually closes on I in Home key (so when material reappears later, the final cadence will be correct).

B: If Home key is Major, usually key of Dominant (relative minor common as well), if minor, usually key of Relative Major (minor dominant common also). Typically, the B section will feature a modulatory build-up to take us back to the Tonic of the Home key when the A section returns - thus the B sections are typically "less final" at their final cadence, modulate back to the original key, provide a half cadence in the original key, and so on. This "setup" for the return of the original material in the original key is an important aspect of larger forms like Sonata Form. Rounded Binary pieces don't necessarily play this up to the same degree, but one can usually find inklings of the idea.

1/2A: Usually the latter half of the A section so the final cadence is correct. In many cases, it is LITERALLY the second half of the A section, though sometimes it's the first phrase of A coupled to the last phrase of A (i.e. if the original A section began it's second half in a modulated-to key etc.).

Rounded Binary, like Ternary, seems to be the more favored form than Binary from the Classical Period onward. In fact, true Rounded Binary is rare before the Classical Period. In fact, Rounded Binary (or forms derived/evolved from it) is even more common than Ternary (or its related forms) in the Classical era.

And again, this doesn't mean a composer should automatically default to using X form because it was common in X period. What it means is, if you have some material, you should be able to make an informed decision about which form it's going to be cast in (assuming you'd only be using Binary, Rounded Binary, or Ternary). An interesting experiement is to take a piece you've written in one of these simple forms, and see if it can be cast successfully in the other two types as well - or if one is more successful than another for a particular type of material.

fine.