I'm studying lullabies right now, and am just left wondering about a few things. Why is a common element of a lullaby that it has a slow tempo? Also, why is having a high tessitura so important?
Studying lullabies? That sounds kind of interesting, actually!
The lullaby is typically a soothing song, and it's typically used to help someone fall asleep. Indeed, the German word (Schlaflied) is literally "sleep-song." As such, I think it only makes sense that it would be a slow tempo instead of a fast one, don't you?
As for the high tessitura, I can't say definitely, I can only guess: perhaps historically speaking it was the mother (or a mother figure) singing the lullaby, and thus culturally we've come to associate it with a high tessitura on account of the (typically) higher vocal range of the female gender.
I'll just present to you my observations with this kind of music without any findings from a formal study. I just want to throw out some ideas to help lead your research.
We're supposed to be in a peaceful state when we're about to fall asleep. Music too fast may be too stimulating, which will more likely wake us up. It only makes sense for lullabies to be in a slower tempo.
Dynamically, lullabies are supposed to be relatively quiet, with the loudest at f, and used sparingly. Also, the 8th note triplet should be the fastest rhythm in the piece (assuming quarter note gets one beat), and used sparingly. 16th notes would be too stimulating, especially if there are enough of them in a row. You can use faster rhythm, but use sparingly.
Chords should last at least an entire measure as much as possible. Chords may last 1 beat, but avoid two or more consecutive 1-beat chords. Some use exotic chords like IIb, IIIb, VIb, and VIIb, which seem to induce state of dreaminess. Again, no study.
Instrumentation may vary, but flute, oboe, and french horn are great for counter-melody. The singing is mostly soft.
The following example below oddly places the child falling asleep as the singer. There is mention of sleep, bed or cradle, quietness (hush), the mother, the child, mother-child relationship, moon and stars, night scene, reminiscing the good past.
Listen to this lullaby medley. It's not in English, but it does a very good job in exemplifying a lullaby.
Very small babies are more sensitive to higher pitched sounds; this is related to how people tend to use high pitched voices/sounds when talkint to them. This is probably related to the tessitura of the lullabies.
We tend to relate to tempi through an association with comparable paces (generally, not as a hard-and-fast rule). Play at a brisk walking pace and you'll normally feel a bit of push to movement, and faster than that communicates more energy. Slower music correspondingly tends to evoke associations of slower phenomena.
So, in short, tempo evokes periodic motion, and certain periodic motion is rousing.
A lullaby ideally corresponds to a gentle rock. Rocking infants is a widespread practice which serves to stimulate in a lulling manner, and autistic individuals, epileptics after a seizure, and individuals under stress may instinctively resort to rocking. The repetition provides familiarity and predictability, yet isn't slow enough to remind of walking tempo.
Also characteristically prerequisite for your typical lullaby is a major key, emphasis on proximity and/or consonance between consecutive notes, and predictability. By the latter, I mean repetitive phrases and common progressions such as emphasis of the tonic, optionally moving to the subdominant, and fairly direct resolution through the dominant back to the tonic. It's pretty common to head straight for the dominant then return, for a sense of a simple cycle lacking complexity as it repeats.
As for high tessitura, I'll again answer from conjecture: Firstly, it's been established that infants and several young animals react instinctively to low voices and sounds. Also, babies respond more to high sounds, but I suspect that the real reason for the high tessitura is that we associate lullabies with a mother's soft voice, music boxes, and smallness, so that many arrangements of lullabies strive to conjure these associations with similarly high sounds.