A friend had a dog (a Pomeranian) that would howl when she played the flute. I just watched a video of a dog howling at piano notes (that it itself was accidentally playing with its paws).
I feel a little guilty being amused by these things because I don’t know really why they are howling. It’s not because their ears are hurting, is it? Or is it just them misinterpreting the musical notes as another dog howling and they are trying to howl back?
I’m fairly sure some of it is conditioning. They realize people laugh and love them when they do it, so they do it.
Our dog has learned that when he makes a Chewbacca noise he becomes the center of attention.
Our dog howled when the fire sirens went off, or when I practiced my trumpet. I’m fairly sure that it’s a built-in response – he’s joining in the howling. Nothing he did is consistent withn it being pain.
My sister, of course, always said it was pain, an editorial commentr on my trumpet-playing.
Our newest dog howls when my son plays his clarinet (we say she is singing along), but only when he plays certain songs or notes. Low notes, to be specific. Once he hits those, she’ll hop up all excited and run in and sing along. She in no way seems to be in pain; in fact, she seems to really enjoy it. We can also get her going by singing certain songs. I’m pretty sure she likes it, since she runs towards the sound rather than away from it (which would make a lot more sense if it was hurting her ears).
Our dog howls at any sirens, including ones that are so faint we can barely hear them. She doesn’t appear to be in any pain, and looks embarrassed if we catch her howling (I know, I’m anthropomorphising). She definitely isn’t conditioned to do it based on positive feedback. It might have been cute the first couple times, but 10 years later at 3:00 AM we aren’t impressed.
I’m going with the idea she’s instinctually responding to calls from other “dogs”.
My dog howls at two main sources - fire/ambulance/police sirens (all three of which have depots right near our house, so we get a lot of them) and the ice cream van’s badly-recorded, high-pictchy music warble.
The former, he just howls to. A very melodic, wolf-like howl (Malamute). The latter, he howls to with a very sharp, whiny pitch. It’s hard to elucidate, but it sounds more like he’s in pain than his “Fire Siren” howl. I don’t know that he’s in pain, but the pitch and tone of his howl seems to give that impression, and he genuinely seems to find the ice cream van distressing when it comes around.
So the answer is - yes and no. Sometimes it does seem to hurt them, sometimes it’s just them joining in with the noise.
Well yeah…you aren’t buying him any ice cream. 
Grandma was always singing - church hymns, bawdy (for her generation) saloon ditties, etc. - and Candy (her dog) wouldn’t give her a second thought. But sometimes Grandma would sing “Where’s [Aunt who moved away]?” over and over again, and Candy would howl and howl.
Amused us grandkids to no end. 
Dogs don’t howl when they’re in pain. A dog in pain whimpers, has very altered body language, quits eating, goes quiet, does all sorts of things but howling because they hurt isn’t one of those things. So the notion that certain noises “hurts” dogs’ ears and makes them howl is way off-base, a classic old wives’ tale.
Dogs howl because they feel bereft or lonely, or because they want something (usually company), because they hear someone else howling or making a noise in their pitch, because they’re distressed, or want to say “hi”…but howling is always a cooperative thing, or an effort to communicate something. NOT because “it hurts.”
dogs howl as part of being in a pack. they hear howls (or something close) and they respond.
Ha, chiroptera, that’s true about pain response, unless it’s a Malamute or Husky recovering from anesthesia. OMG they will not shut up. I know it’s partially altered mental state, but part of it is - they’re amazing wimps about surgery!
As to the OP, yeah, they’re just joining in.
OK, I’ll amend my response to “this applies to any dog except Malamutes and huskies.” I know they are really, really talky woo-woo dogs and normal rules don’t apply to them! I know people with both breeds and the woo woo is so endearing. 
I’ve had a lot of dogs over the years, and admit to being spoiled by “Spoiled Rott’n weilers” - Rottweilers as a general rule are very quiet and absolutely refuse to exhibit pain response to anything, they are extremely stoic dogs typically, and don’t vocalise much at all.
I think they are emotional and feeling something of bond/kinship when they howl when you sing, ie, unless you are a terrible tone-deft: howl of pain for sure then.
In other words: They’re singing along.
I wonder if you could train a dog to carry a tune?
My mother’s dog howled at the opening theme song of M.A.S.H. Not immediately, but starting at a spot partway thru the music. She did this every time, even if nobody was in the room with her. We always assumed there was some part of that music that she was responding to.
My next-door neighbor thinks it is pain, but I think it is solidarity. (This is when our two dogs are howling together. It’s usually a siren that starts them, but they go on from there and I swear they are trying to out-sing each other.)
Also, when in pain, at least when I know about it, my dog yips. And then after that he’s pretty stoic.
ETA: But, the flute? I don’t know. I had to quit playing the flute when my firstborn was an infant, because he screamed. I think in that case, it was pain.
My friends’ dog would scream at the sound of a fire or police siren. He didn’t bark, and didn’t howl, exactly: it was a more desperate, frantic, frenzied reaction. He also showed lots of other behavior evidence of distress… Anyway, the dog emitted unending sharp, short, howl-like screams, and shook and shuddered, and his eyes rolled, and he absolutely could not be comforted. Weird, and very disturbing. If it wasn’t pain, it sure looked like it.
Obviously, I might well be anthropomorphizing… But dogs’ moods seem so very easy to interpret in most other ways. Or not?
Perhaps they are trying to train us to carry a tune, their tune? “Look ya big tailless dog that doesn’t know how to walk on all fours, ya may be the pack leader and have opposable thumbs but this is how you sing!”
I’m sure some sounds make dogs distressed or frustrated, but that’s not the same as physical pain. My Lab gets inordinately distressed, agitated and woo woos pathetically and loudly if he’s in the vehicle and I leave to go into a store or something; but that’s a manifestation of his mild separation anxiety, not physical pain.
BTW, “comforting” a dog who’s distressed because of something like a siren, or being left alone in a vehicle momentarily, reinforces the behaviour. Actually the worst thing you can do, besides getting angry and punishing the dog for being distressed. By comforting a distressed dog, you’re telling him it’s OK to be distressed. Better: divert attention with food or play, or ignore it and make a happy show of telling him he’s silly.
I’ve brought more than one dog into the house (I foster) that didn’t react to sirens or certain pitches of music, but if a resident dog is a howler, the new one usually picks up the habit.
It awakes in them the call of the wild.