And so I could continue to indefinitely citing voice authorities and fail to find complete agreement. Some say there are no registers. Others say there are two; and still others say that there are three. Some declare falsetto cannot be used in the development of the voice, but that the head voice can, yet they give us no clue as to what they mean by their use of the term “head voice.” There are those who would convince us that the soft, high tones of the tenor can only be sung in chest voice, and that after a long period of study one will be able to do all that is necessary in singing high pitches in that voice. Now, in the face of all this confusion and disagreement among those who should know, is it any wonder that the pupil, eager and ambitious, wanders about as in a fog, going from one teacher to another in the hope of finding a solution to his problems? You have young tenors who need help in producing high tones. They try to get them, but cannot because the chest register will not go beyond the limit of its particular range or series of tones. You have heard that the head voice is legitimate, but you are not certain just how to get the pupil to sing it. My experience convinces me that the head voice is attained through falsetto. If head voice is legitimate, then falsetto is legitimate, for they are one and the same thing. The only difference is in the degree of development. 

[…]

When it is in the beginning stage, the breathy soft high tone is called falsetto. When the breathiness is eliminated and the tone develops some character and power, we call it head tone. When the tone is resonated and resisted so that the registers blend one into the other at will, and can be employed interchangeably in pianissimo, it becomes known as mezza voce or half voice. Mezza voce is rather difficult to explain in so many words, but it is an Italian term and is taken by most singers to mean “soft” singing. However, this is only partly correct. Rather does it mean a half power of voice, not chest and not falsetto, but midway between the two, produced through a balanced breath resistance or with restrained force. Do not confuse mezza voce with messa di voce. 

Mezza voce has a different feeling than chest or falsetto, though it is the result of expert tone production in both registers. It has the feeling of being resisted at the larynx with no breath escaping. It feels sharp and pointed in placement. I cite as my authority for this, my teacher, Jean de Reszke, though the choice of words is mine. I think Mr. de Reszke had the most beautiful mezza voce I ever heard, with the possible exception of Lucien Muratore.

[…]

I know the practice of falsetto is helpful in laying the foundation for the young tenor’s high tones, whether he ever continues to sing falsetto or not. Falsetto in, and of itself, is of no value to the singer. It must be developed and resonated out of the falsetto state and blended into the chest register. To be convinced that this is the proper way to begin the treatment of the young tenor voice, one must lay aside his prejudice long enough to learn something about how it works and what it will accomplish. One may not be able to prove its value in one semester or one year, but if you stick to it you will get results if the voice is a tenor.

Carpenter, Allen Ray. “Developing the High School Tenor.” Music Educators Journal 27.6 (1941): 34-39.