Often the question arises whether mouthpieces are meant for classical or for jazz music. A certain view on the matter goes along with that. Jazz mouthpieces come from America and bear names like Brilhart and Otto Link. Mouthpieces for classical music come from Europe and from Selmer in particular, to name only one such a view.
It is a fact that the Selmer company over the years served a number of classical musicians of fine reputation. Yet, it is not a fact that the products of this company also show a unity of design. Marcel Mule (* 1901) has set a standard for a classical saxophone tone in France before and after the Second World War with a Selmer metal mouthpiece with a round interior. (Incidentally, John Coltrane used a similar mouthpiece on soprano.) More than thirty years later Londeix did the same with an ebonite mouthpiece with a square interior. How did the concept of classical material change in such a short time in France? How does that compare with those 'staying behind'? A classical musician will find himself in circumstances in which he should be able to act purely on his own as a soloist before a symphony orchestra: he has a great interest in his sound being large and penetrant. The more he plays in large concert halls instead of playing chamber music, the heavier these demands weigh. This has certainly played a role in the changes french mouthpiece construction went through and in the concepts of the sound to be obtained.
I own a couple of Rascher mouthpieces. Interesting pieces in the debate about what is actually classic (material). Rascher certainly was a classical musician, no doubt about it. But his material is not directly what you call mainstream even among contemporary classical saxophonists. Even that niche apparently is at least divided into two streams.
Sigurd Rascher (* 1907) grew up in prewar Germany and learned to play with the then current material. His mouthpieces were still relatively close to Sax's original design. In the wastebaskets with 'disposable mouthpieces' you can still sometimes find them: the nameless mouthpieces from that period. Wide and round in chamber form, of stocky build and with a fairly narrow tip opening. At that time similar models were made in America by Buescher and Brilhart, among others. Rascher left his country in 1939 (because the Nazis considered the saxophone to be a non-German and objectionable instrument) and, through various teaching assignments and an impressive musical career, he for decades executed great influence on the formation of classical musicians. They took along with them his articulate belief on mouthpieces, which had to stand close to Sax's original design. They took his beliefs back again to Germany for example, the current home of the Rascher saxophone quartet. This famous quartet there exerts an influence on other musicians, such as for example the Tetraphonics saxophone quartet, which plays with similar material.
If you consider this story in a bird's-eye view, you get the clear impression that the answer to the question "What is classic?" depends on musical geography: those who are under contemporary French influence (such as the Belgian school) will, mainly following Londeix, consider a narrow mouthpiece (Selmer S80 and S90, Yamaha and Vandoren) with a clear tone classic. In contrast, Rascher set up a different school. This school actually continues an older tradition and considers a much wider and round mouthpiece to be classic. It bases itself on what it considers to be the original concept of Sax. The tone is darker and sweeter.
The question remains whether that in itself makes any sense, to rely on what is supposed to be the original concept of Sax. Sax himself redesigned his saxophones around 1866 and thereby unknowingly paved the way for a narrower mouthpiece as well. Besides, an invention goes its own way, the child grows away from its parent and such a development is probably irreversible. As far as the saxophone is concerned, it's in part the followers who have further developed the instrument (Feuillet, Buffet-Crampon / Evette-Schaeffer, Adolphe Edouard Sax, later Buescher and Selmer) and, admittedly, have changed its shape in more than one aspect compared to the the original. All through the 19th century mouthpiece design has been fairly stable and when mouthpiece design began to shift, the instrument was to a large extend already in its modern shape. Both classical and jazz music is being played with the wider and the narrower types of mouthpiece. Therefore you cannot really answer the question whether a mouthpiece is designed for jazz or for classical music. Only in facings classical and jazz musicians make different choices. Just the extreme designs which are meant for funk and pop music really stand apart.
In the MEASUREments–section in this website you will find dimensioned sketches and facings of the Rasher mouthpieces. The comparison between these mouthpieces and a few of those old nameless ones on the one hand with modern French mouthpieces on the other speaks volumes. Most American mouthpieces are somewhere in-between, but in general concept they are more akin to Sax and Rascher than to the modern French mouthpieces.