It's an Old Italian School of Singing term, one that was used by Anna E. Schoen-René, for which she was derided by none other than Corneilus L. Reid on pages 164-166 of his book Bel Canto: Principles and Practices (1950), only a few years after her death in 1942.
For those who are new to this blog, Anna E. Schoen-René was a student of Pauline Viardot-García and Manuel García, with whom Schoen-René studied for a special course in training the male voice. No small potatoes that. In fact, Schoen-René was very successful in teaching men, the famous tenor Florencio Constantino being one of them.
Reid's book delineates the way in which he believes the training of the voice should proceed, one of his ideas being that the registers should be separated before being joined back together. Never mind that Schoen-René went on record as saying that this was not what García taught: Reid had his own ideas about the matter, which I saw up close at a vocal pedagogy event for the New York Singing Teachers Association some years ago. Very curious indeed, the esteemed gentleman had invented his own terminology, which is what all pioneers endeavor to do when they chart new territory. However, it occurred to me then, as it does now, that his eschewing of traditional terminology didn't exactly clarify matters. Rather, it only seemed—to these ears anyway—to obfuscate things further. Did Reid think that Schoen-René and other students of great teachers were just making things up as they went along? I mean, it's certainly possible, but it strikes me that Reid's broad swipes against his vocal elders did not educate the ear as much as give us his own theory, which was something else entirely.
Let me put it another way: there's a reason why there is a picture of an ear on this post. Open throat? To be simple about the matter, the ear can hear whether the throat is open or not. Nasal singing? Not open. Guttural singing? Not open. You get the picture.
You see, the term has empirical origins. It's meant to signify an aural impression, one where the voice sounds "open throated." Making an open throat? That's a whole other matter, one which is often doomed from the start. Why? Because creating "space" in the throat is better felt as a result, rather than a cause. The Old School teachers were a great deal more simple about such things, whereas we apply our science and tie ourselves in knots of knowing.
How did those Old School teachers get their students to "open" their throats? By calling on vowels with Italian tonal values, /a/ being considered the preeminent vowel. Nothing more complicated than that. Of course, this has be heard to be understood. And by "heard," I mean given to the student in the voice studio via the voice of the teacher. You don't open your throat mechanically to sing, but rather, call with Italian tonal values and hear and feel the result, which is an open throat—a very different thing. Then there is the Old School saying which places the whole matter in context: The Italian singer has no throat. Isn't that a kicker? All this talk about opening the throat, and tradition maintains that when you are singing really well you should not even feel that you have a throat!
To be clear in terms of Mr. Reid: he's hardly alone in the pet theory department, seeing that I yammer on and on about the ear, while he makes much of registers. Be that as it may, my take is this: You can work on separating the registers all you want, knock yourself out, singing in chest and then in falsetto. However, will this procedure open your ear, and lead you to vocal nirvana? That's an interesting question. My perspective and experience is that when the ear is fully open, distinctions between registers are secondary in importance. Getting the ear open? That's a whole other matter. Did Reid's procedure do this? Of that I have no knowledge. However, Reid asserts on page 166 of his book that García and Lamperti "were obliged to accept as pupils only those who were exceedingly gifted and whose advanced technical status made the problem of registration and register development a matter of secondary importance." There's a fascinating clue in his assertion, one which Reid didn't intend, but which stood out to me. It's this: Schoen-René tells the story of being with García when he heard two would-be students from America. She relates the story in her book, America's Musical Inheritance: Memories and Reminiscences (1941), on page 109.
Once in García's studio, I was given a most instructive lesson in the diagnosing of voices. He asked me to listen with him to two singers who had come from America. They were under the impression that they had studied with a teacher who was a representative of the García technique, but in the singing that followed there was no trace of it. Manuel García then asked them to sing some exercises and vocalizations, which seemed to them a strange request. It was a most amateurish exemplification of tone production. When asked to project the pure Italian vowels, they could not do so (my emphasis). One—a baritone—had a very throaty voice, and the other—a tenor—sang with a nasal quality. The climax came when the poor fellows asked whether they might take lessons from him, during the few weeks of their stay in London. "No, no," he exclaimed emphatically, "I do not want to commit a sin!"
Pure Italian vowels? Now how do you suppose one acquires them? By manipulating your throat? By separating the registers? Pushing your larynx down? Raising your soft palate? Grimacing for all you are worth? I rather doubt it. Rather, one has to have an ear for them, which is as obvious as the nose on one's face, but is missed because you can't see it unless you look in a mirror. This is why García did not accept these two men as students. They couldn't sing pure vowels, vowels which, I dare say, sound "open throated."
There is more to address with Reid I suppose, especially his quoting García's statement in the Musical Herald in 1894 on page 167, which Frederic W. Root also referenced in an interview in American newspapers, but to be succinct: I addressed this matter in the introduction to my book: Hidden in Plain Sight: The Hermann Klein Phono-Vocal Method Based Upon The Famous School Of Manuel Garcia (2013). Interested readers can find my thoughts on the matter there.