If a mouthpiece with inner diameter of the cup of 13,5mm-14mm is attached to an oboe, it will give a modern type of cornetto (diatonic trumpet) with keys and more or less the fingering ofthe oboe. The sound compared to the trumpet is less loud because of the smaller bell and more sweet because the oboe is not made from brass metal.
The same applies if instead of an oboe we utlize a soprano saxophone with a cornetti mouthpiece with 14,5mm-15mm inner diameter of the cup. Even a french horn mouthpiece would fit and would give a very good 1st octave! It will become a DIATONIC FLUGELHORN OR CORNETTO with fingering chart more or less that of the soprano saxophone. The sound is very close tthe flugelhorn sound , and compared to it is slightly more instrospective and less loud because of the smaller bell compared to a flugelhorn. The pitch is a bit more volatile with the soprano sax body, when the same french horn mouthpiece is utilized both in the flugelhorn and the soprano sax, and easy changing in the embouchure compared to a flugelhorn, because of the smaller length tube of the soprano saxophone. But with a smaller mouthpiece of 14,5mm-15mm of inner diameter of the cup,as in wooden cornetto this pitch variability is improved. The fingering system of the saxophone played in such a way as a flugelhorn with a cornetto or french horn mouthpiece is by far more intuitive and straight forward as a diatonic instrument compared to the valves system of the flugelhorn which is better for the chromatic 12-notes scale rather than 7-notes diatonic scale.