Placement is often taught as a general idea such as put the voice backward or forward. It is also common to name a place such as put the voice into the nose, just behind the forehead, through the tope of the head, on the roof of the mouth etc, etc.
While I was studying with Burton Coffin at the University of Colorado, Boulder, I constructed a vowel mirror similar to the one he used in his studio. His tone came from a small 4 octave electric organ usually using a flute stop. My tone came from an early Korg tuner that produced a square wave. That limited me to just the odd integer harmonics but it still worked adequately. It would have been better if it produced a saw-tooth wave that would contain all harmonics.
I would tune my vocal tract by aiming the small two or three inch speaker into my mouth at a distance of about 2 inches from my lips. I would then take a short breath and close my vocal folds and then, without singing at all I would play the tuner produced pitch into my vocal tract and I would do the gamut of open to closed vowels, /a/ to /i/, gliding smoothly through all the vowels in between. Invariably, the tone being introduced into my mouth would get louder on one or two vowels. I would select one of these louder vowels and see if I could tune more exactly to its center by making adjustments in my vocal tract such as tongue position, lip position, widening the pharynx etc. When the tone became more secure or even louder, I would then stop the tuner sound and sing using the same configuration of the vocal tract that I had just used to ‘find the center’ of the tuner sound.
It took some time to be successful, even with finding a tuner tone-vowel match that worked, as well as being consistent in replicating that vocal tract adjustment when I sang the tone. What really surprised me was how little I was willing to move around parts of the vocal tract. It was as if the tongue, for example, was fixed in its movements and unwilling to do my bidding to move freely. I studied tongue placement from X-ray photos of vowels and later from MRI photos. The early X-ray photos were later proven to often be incorrect (taken from spoken vowels and not from sung vowels) but they still helped me be more flexible in my tongue movements
Later I would do the same exercises going from /a/ to /u/.
Some startling discoveries.
I had to assume an inside smile position of the roof of the mouth. The kind of surprising action one experiences in the mouth when first hearing a juicy bit of gossip or discovering something suddenly pleasant etc. The soft palate raises, the corner of the lips lift slightly but there is little sign of an outward smile, the jaw is open but relaxed Only with this position could I consistently get resonances that were clearly defined.
There was a sense that the tuner sound was bouncing off the back of the roof of the mouth. A definite sense of more pharyngeal space was evident. This was even present on more closed vowels.
In short, the vowel mirror not only made me more aware of what adjustments I could do but it actually, slowly changed the whole sensation I felt during singing.
When I rehearsed a song or aria I would later use the vowel mirror only for troublesome notes. These were usually pitches in my passaggio with vowels that seemed to throttle the voice or require greater breath pressure to produce. I would adjust the vowel mirror tuner to that pitch and try to resonate the tuner sound on that pitch into my vocal tract while silently pronouncing the requested vowel. Almost every time I could get no response. So I would alter the vowel somewhat or try a neighboring vowel until I got a resonance response. I would then use that vowel in the word, even if it was wrong and almost every time I could easily sing that replaced vowel within the phrase. It was “in tune” with that pitch. Then later I would try the required vowel and it was better, not as good in resonance, but better.
I sometimes would record myself doing this vowel replacement exercise. I discovered when I listened to the recording that when I went back to the required vowel I was singing it slightly differently. My pronunciation of it had been influenced by the good feeling I had experienced with the more resonant vowel. I had modified the vowel slightly but I never had any listener tell me such modifications were noticeable.
Consequently, I have little use for the concept of placing the tone. I would rather teach singers how to manipulate their speaking vowel habits into singing vowel habits and how to be more conscious of those slight vowel adjustments that make a difficult note much easier