[For a more in-depth writeup and more examples, see Coyote Voicings]
I have made several recordings of coyotes yipping. These recordings are not the classical howls we all know about, rather they are of a very high pitched barking — it has a violin smoothness or purity of sound. The barking has intent, is very intense. Except when howling at sirens, every episode of barking that I have heard was the result of a coyote having been chased or intruded upon on some level by a dog. Howling and yipping which results from having been chased by a dog is easy to recognize because they are much more distressed sounding. A less obvious cause of the barking may be an antagonistic dog which simply came too close to the coyote, say within about 100 feet, without actually chasing it: it turns out that in most cases, the dog chased or intruded on the coyote in the past.
But also, I’m seeing that a coyote will feel intruded upon if specific dogs “eye” the coyote on its perch — possibly in an antagonistic way — something like giving the coyote “the evil eye”. In addition to the vocalized complaining and standing up for itself which I’ve seen when a dog actually chases it, the coyote’s barking at these intrusive dogs appears to be a statement to them of territoriality.
I used to think that the barking might be a warning to other coyotes in the family group, but I have now seen instances where this was definitely not the case. For example, a dominant coyote — the mother — was relaxing on a hilltop when one of her full-grown pups started a barking session not too far off — it had been disturbed by a dog. I immediately started watching for a change in the mother’s behavior, waiting for some type of reaction. There was none. This mother ignored the barking, even though I had previously seen her run to a pup’s defense when she saw a dog — a particular dog which she deemed dangerous — approach too close to one of the pups. In another case, I was on a hillside photographing one of these full-grown pups when I heard the mother barking in distress in the distance — it is a signature bark which I have come to recognize. The young coyote totally ignored the barking and continued its hunt! Now, maybe there are barks and then other barks, but in these cases the barking was not an alarm signal to others.
I have heard that coyotes will howl or bark just for the pleasure of doing so, and I’m sure they do, but I have never heard them under these circumstances. Males have a lower tonal range — barely — but you can tell them apart from the females if you hear them within a short space of time. Coyote “songs” can go on for 20 minutes or longer. I call them “arias”. Here are several videos of them:
Several coyotes barking at the same time can often sound like many more than there really are. They “come in” at slightly different pitches creating dissonances that sound like many.
Coyotes have various other vocalizations. There is the classical howl, there is childlike complaining in high pitched tones, greetings can sound like puppy sounds because they are high pitched, there is grunting which sometimes precedes a barking episode — as if the coyote is trying to decide whether or not to go ahead with it. There are anger grunts and growls.
For a more in-depth writeup and more examples, see Coyote Voicings
Coyote Yipps 
