Rhythmicity

Obviously, you can start the first note on the start of the beat. This produces rhythm. (Actually, the story is more complicated than this, but we will ignore the complexities and note that at least to your ear, you can start the note on the start of the beat and it will sound rhythmic.)

First of all, singers sometimes do not do this. Instead, they let the background musicians carry the beat, and they sing off beat. Or, more usually, some notes are on the beat and some are off the beat.

But suppose the singer puts the start of the note on the start of the beat. When does the singer stop the note? A musician will give the note the normal length (whatever that is), or the music might mark the length as shorter (stacatto) or longer (legato). Add interpretion and it's the end of the story.

If the note ends in a vowel, the singer is in the same position. But if the note ends in a constant, then the singer has to decide when to end the note. This ending note can add (or subtract) rhythm from the song.

There is one clear-cut example of an ending sound adding rhythmicity. In one of her songs, Karen Carpenter clearly and distinctly pronounces the t at the end of a syllable, she puts it right on the beat, and everything else is on the beat too. This is discussed here.

More commonly, the rhythmic effect is to put the sound in the second half of the beat (or even the second third of the beat). These are, at least to my ear, never clear cut, but I am pretty sure they exist. Presley's use of ending consonants to produce rhythmicity is discussed here.

Given the difficulty detecting these, it is difficult for me to say how often they occur. My guess is that they are not common, because singers do not know about them and because they are difficult to produce.

I think that some singers deempasize the ending sound, because they do not want to produce stray rhythmic markings that actually do not fit the music. The charitable interpretation would be that they do not want any rhythmic markers; it is also possible that they do not know how to make the ending sounds rhythmic.

Producing this Effects

There is probably a trick to producing these effects. First, putting an ending consonant on the beat presumably is not a problem; the problem is putting them on the inside of beats, say where the second or third note of a triplet would occur.

Basically, your body just has one rhythm. That is why beating your foot to the beat helps you keep the beat -- your foot establishes the beat, then the rest of your body follows along. So, if you move something at, say, three to the beat, your actions will tend to occur then. That means you will tend to sing the consonant on those thirds of the beat.