In A Practical Guide to French Horn Playing Milan Yancich notes with regard to mouthpieces that
Special care should be taken in the selection of the correct mouthpiece for the student.….
In my opinion the student should start with a large-bore mouthpiece. This will automatically force the learner to take bigger breaths and use the necessary muscles for the development of his entire breathing apparatus.
Start large? Or start small?
While I generally like the Yancich book, I disagree with this point. One goal with younger students is that they not quit horn, and really a smaller bore mouthpiece is easier to play, some early success will help them stick with the instrument. You can work on breathing better later — if they don’t quit the horn!
And an interesting note from Carl Geyer
Yancich also references Carl Geyer in relation to the secret of a successful mouthpiece — but pretty generally, this quote is one you can’t easily apply directly to your teaching or playing. More recent mouthpiece designs have largely solved the problems he describes.
According to the great horn maker, Carl Geyer, two-thirds of the horn players today use the straight cup mouthpiece, but in fifty years of observing hornists who have played for him, he states that there is no one mouthpiece. With the straight cup mouthpiece the problem of intonation is more easily handled than with the other two types of mouthpiece. If the cup of the mouthpiece is too short, the low notes of the horn register are difficult to play. If the cup is too long then the high notes suffer. The throat of the mouthpiece is of great importance to tonal production. The greater the development of the breathing apparatus in playing the horn the larger the opening required in the mouthpiece. The throat opening is, in essence, the secret of the successful mouthpiece.
Milan Yancich had his own series of mouthpieces produced, the MY models made by Alexander. They are classics and were innovative products, as they were produced with a larger inner diameter than commonly seen at the time.