The sax was invented in 1846. Withing jazz, one of the first famous saxophonist was Frank Trumbauer and he became popular around the 1920s. So to answer your question it took about 70 years after the sax's invention before it became mainstream. There were other sax players before then, but most switched over from clarinet around this time. It wasn't uncommon though for musicians to play clarinet at sax within the same song. This multi-instrumentalism can be see during musicals where sax players will also be asked to play clarinet. I've been playing upright and electric bass myself for about 9 and a half years now.
Trumpet, cornet, and fluglehorn all have the same fingerings (if I'm not mistaken). The main difference between them is that they all have different tones. I'm not sure why the cornet was more popular back then, but I have to guess that it was because the cornet was more accessible in that it was probably a cheaper option. From what I understand most who chose one of these three typically stuck with it.
This is awesome, thanks for sharing it! I play more upright than electric and I'm always so fascinated by the technique and precision of tone required to make tapping sound this good.
Haha oh yes. Here's a link to my quartet's site.
Haha well thank you. We've improved individually as a whole since that, but it's still nice to listen to.