Never underestimate the power of humming to warm up/cool down/relax/revitalize the singing voice. And it’s not just any every-day hum, but a specific kind that I’ve grown to call “hummy-yummy.”
Try it: take a low, slow, easy breath and hum as if you were smelling or tasting something delicious, like you just put a spoonful of decadent dessert in your mouth and the flavor hits your tongue like a bomb. It’s that kind of hum. The vibration should be felt in the roof of the mouth, just around and behind the nose. The jaw is relaxed, not clenched, and the teeth are separated.
James C. McKinney has a more clinical-sounding procedure for this in his book, The Diagnosis and Correction of Vocal Faults:
Take a comfortably deep breath and think of starting to hum. You will find your mouth and your vocal cords closing in preparation for the hum….As you begin the hum, bring your teeth together firmly and try to feel a lot of “buzzy” vibration in the roof of your mouth. This type of hum is somewhat penetrating in quality but seldom breathy.
Now, with your mouth still closed, continue humming while separating your teeth by dropping the lower jaw down freely. Try to maintain as much vibration in the roof of the mouth as possible. This type of hum is more relaxed and has a better quality than the first one; it will not be breathy if it is properly produced.
And when you go further and open your mouth to sing a vowel, you want to maintain that “hummy-yummy” sensation in the mouth. It’s like riding the wave into the vowel, as a surfer would transition from lying down to standing up on a surfboard when the support of the wave is felt. A good vocal exercise to try this would be “Sol-Fa-Mi-Re-Do” on a hum, but when you reach “Do,” open to the vowel of your choice. And you just separate the lips; don’t let the jaw drop down suddenly, because the vowel will drop too and make the sound go “ka-chunk.” Make it one smooth gesture; the hum vibration should glide easily and seamlessly into the vowel.