How can I learn to hear counterpoint?

How can I learn to hear counterpoint... without the aid of the piano? Whereas I have no trouble hearing and singing single lines, I'm not quite sure how I should approach hearing counterpoint. When writing counterpoint, it seems to me that it's absolutely essential to be able to hear both voices simultaneously, rather than just choose appropriate notes for the counterpoint part mechanically, following the rules.

Let's say I've got this example:

Is it really possible to hear two voices in your head, rather than hearing them as separate voices? How can I practice this?

Is the underlying harmony as important as the separate voices? By that I mean: what's more important? To hear them as Cantus Firmus: DFE etc and Counterpoint AAG etc or as P5 M3 m3?

Thank you in advance.

Firstly, of course it's possible to hear two voices in your head as being connected rather than just two separate voices. Sing your example, top voice, and then hear it in your head, then do the same for the bottom voice, then (if you really don't want to use the piano, even when practising) try to hear them together in your head, but I would try to play both together on the piano if I could. Even easier and more straightforward than that: listen to

, remember it, hear it in your head, and there you have it. I actually completely understand your confusion, and think, from experience, that it's a result of theoretical study with no practical application; it's in the language that they use when teaching these concepts, and they assume that you'll have no trouble understanding it because most musicians will want to go to the piano and the practical application will sort them out big-time.

If I were to have a go at explaining what I hope I know about what you're asking, I'd say that what you should be trying to do (or, rather, what it is that teachers usually would have you do) is to hear the interval (the harmony) mostly for consonance and dissonance just so you know when you should be resolving and when you should be using some nice V7s &c., and hear where each voice is moving to and from. Listen to a Bach Invention and you'll probably notice that there are two (or three) parts, each of which has its own clear-cut melodic line, but which sounds harmonically with the other voice(s), just like with any other sounds played together. When writing counterpoint, what I think makes it easier, nicer, and more intuitive is to hear the melody of each line on its own - to where it wants to go &c. - whilst still keeping an ear out for no-no's, like parallel and direct perfects, unresolved and harsh dissonances and all that other rulesy stuff.

Briefly, what jumps to my mind in answer to your questions is: listen, play, imagine, and, in answer to your last, both, because, essentially, what you're trying to do is write two melodies that don't sound like scraggy when played at the same time: enter rules.

Well one key to hearing two voices at a time is not to get stuck on hearing each interval as isolated - eg - you don't say at every bar - ok major 3rd, othink hard ok think I got it, then 5th same procedure, etc. What helps is to hear the motion between voioces - is it parallel, contrary, oblique, similar? It makes the process much faster. Of course you gotta know your intervals - especially if it leaps around but again judging whether the top or bottom is moving at a greater distance etc. helps a ton.

Now as you get to more voices, then it is a matter of knowing your theory to lead you eventually to visualizing what you hear, Probably one of the best ways to do it is to solfege chords.