Humming through a folded handkerchief is an excellent method of teaching the correct way to balance vocal tone with breath pressure and it is simple to do.
Place a folded handkerchief, folded four times, over your forefinger. Place the forefinger parallel with your mouth, gently close your lips over the finger so that they seal against the handkerchief and will not allow breath to pass by them. Breath into the cloth of the handkerchief. The warm breath passes through easily but it meets some resistance from the cloth.
Now do the same breath but phonate (sustain a tone) as you do so. You will feel not only the breath through the cloth but also some resonance of the phonated tone, that is, a buzz.
As you sustain this tone take away the finger and handkerchief. You will be surprised at how loud you are actually singing.
Now do it again but make sirens up and down. You will pass through your passaggio with little notice of its existence. This is because the resistance of breath through the cloth creates a back pressure in the vocal tract and this assists in balancing the pressure beneath the vocal folds (sub-glottal) with the pressure above the vocal folds (supra-glottal) and in doing so regulates the breath pressure at the folds (the glottal area) such that they operate more efficiently.
If you remove the forefinger and cloth quickly the breath pressure will be, at that instant, quite excessive and you will have to reduce it by adjusting the management of the breath.
But if you remove the forefinger and cloth gradually the body will automatically adjust the breath flow so you can maintain the quality of tone achieved with the cloth at the mouth.
Another variation on this is to place the back of your hand, that is, the space between your thumb and your forefinger, against the mouth and seal it with your lips. Then hum into this part of the back of your hand and do sirens up and down. Then slowly remove the hand from the mouth but keep it close to the lips as if you might want to put it back once more to the lip seal. This encourages the voice to maintain a proper breath pressure to sustain tone. You will notice that you feel only a gentle warm breath on the back of your hand.
Finally, breath as if you were “steaming” your glasses to clean them. The breath is gentle and moist. You are achieving this because you are automatically controlling your breath through a balance of the action of the exhaling muscles and the inhaling muscle. Now start a tone (onset of tone) using only this gentle, warm, moist breath. This is the core breath for singing. If you place your fingers almost touching your lips you will feel only a gentle, warm, moist breath and this is as it should be.
Now sing that tone louder and louder keeping its quality of tone consistent. You will notice there is a slight increase in breath but it is still warm and moist and still surprisingly gentle. This all the breath that is needed to sing well.
This breath exercise allows the vocal folds to oscillate using only enough breath for this sole purpose. Any time more breath pressure than is needed is applied to the vocal folds they must close more and more tightly to resist this extra breath pressure and their ability of oscillate easily and freely is compromised. A common example of this kind of singing is the young singer trying to sound like an opera singer by squeezing or pressing on the voice. It is not good singing, no one wants to hear it, and if continued over time, will damage the voice.