Sackbut mouthpieces
One-piece models
In the last few decades, the standard among serious sackbut players has been to play mouthpieces that are smaller than modern mouthpieces, with an extremely flat rim, a hemispherical cup and sudden, sharp entrance to the throat, and large throat size relative to the cup size. That cup and rim shape is based on surviving 16th and 17th-century examples. The mouthpiece is turned from a single blank, with an expanding backbore within a tapered shank. A select few people had adopted even more historical designs, and some schools of playing use much more modernized designs, but overall this flat-rim, sharp-throat one-piece design has been the broadly-accepted, mainstream sackbut mouthpiece style. Compared to a modern mouthpiece, the sound is much softer, somewhat less focused and with a bit of air, with much less core but much more complex and richer overtones. The colour of the sound can be altered more easily and the mouthpiece is much more sensitive to articulations.
*Makers sometimes introduce a venturi in the backbore (so that the throat is not the narrowest point) to help focus the sound, such as Egger in their "Baroque" line and in the "V" variants (and all bass models) of their "Renaissance" line, or Romera with his Lasalle Tolosa line.
The best and most widely-used of these are built by Van der Heide (formerly) and Egger. They are available in a large variety of sizes and from other makers as well.
Historical models
Now the actual surviving mouthpieces from the 16th until the later-17th century are in fact not made in one piece, but in two or three. You have a turned top that includes the usual flat rim and relatively small hemispherical cup with a sharp throat, but only includes a very short expanding backbore. The shank is built from flat sheet brass rolled into a long, very gently-tapered tube, often reinforced at the large end with a turned sleeve. This means that after the throat, instead of the bore expanding gradually (or tapering to the venturi point and then expanding), the bore first expands much faster, expands again by step where the short backbore ends, and then tapers back down again over the length of the shank. Essentially, behind the throat is a belly, or the opposite of a venturi.
Until recently only few players had adopted that historical design, they tend to take a while to get used to, and can be quite fussy, and it can be harder to match with people who play other equipment. But in the last several years many players, especially in the younger generations, have been experimenting with and ultimately adopting this design, to the point where it is now accepted as a new norm. Compared to modern mouthpieces and one-piece sackbut mouthpieces, this design generally pushes the difference yet further in the same direction (less core but more overtones, less stability but more flexibility, more responsivity to variation of articulations).
I believe part of the problem is that few makers have been making mouthpieces of this type, and usually only as exact replicas of only a couple of originals (one for tenor and one for bass), which is not very practical if those particular sizes don't happen to match your face or the model of instrument you play, or both (despite the fact that size is about the one aspect that varies a lot between different originals). I had made some half-satisfactory experimentations in the last years, but I recently finally worked with Egger to make a solution that works for me (and hopefully will work for others), using the exact rim and cups of the one-piece models that I know work well for me and my horns (RT-6 and RB-4), but making them as just tops, with separate rolled and seamed shanks, and then working out what size and taper the throat/backbore needed to be for them to work.
Here are some pictures of my new tenor mouthpiece to demonstrate what an original would have looked like (the extra sleeve is just an adapter as the receiver on my instrument is not meant for the very small shank size of original mouthpieces):
Now for comparison, left to right: modern 5G size (Ferguson 1), Egger in historical style, Egger RT-6, modern 11G size (Ferguson 11)
Same comparison for bass mouthpieces. Left to right: Modern 1½G size (Ferguson V), Egger in historical style, Egger RB-4. The throat on the multi-part Egger is slightly smaller than the RB-4's, but the RB-4 had a venturi after the throat that is smaller still, so the new one is actually more open. Also the historical style Egger here has a permanent built-in adapter to fit instruments not meant to take original mouthpieces.
Romantic mouthpieces
I don't have any classical mouthpieces to show, but based on printed sources and some surviving trumpet mouthpieces, it appears they still had flat rims and sharp throats, but with cups that were less hemispherical, with more hybrid shapes.
Here are four romantic mouthpieces however, that show that a lot of the early features are still there until quite late.
Far left is the modern 5G size (Ferguson 1) for comparison
2nd left is a ca. 1840 original German tenor mouthpiece. The rim is narrower and its edges are more rounded, but it is still basically flat and the edges well defined. The cup is deeper and more elliptical, like an elongated U with slightly sloped sides. Entrance to the throat is just as sharp as on my sackbut mouthpieces. It has a very subtle venturi a bit after the throat. A colleague owns one almost identical, same size, same cup and throat shapes and sizes, but with a rim that's more rounded and without the venturi in the backbore. These work absolutely fantastic with German romantic trombone, they really bring the horn to life and make it sing. Interestingly, of all my mouthpieces (many of later German make) including modern ones, the best fit for my German bass is actually my one-piece bass sackbut mouthpiece, which essentially has the same overall shape and features as this German tenor mouthpiece (down to the venturi), only bigger.
3rd left is a ca.1890's original French tenor mouthpiece. It is TINY. Again a flat rim, but with a fairly pronounced curve into the cup (no sharp edge). Deep (relative to width) V-shaped cup with a smooth entrance to the throat. With my 1890's Courtois, this makes a gloriously light sound, and Bolero is stupidly effortless. Sadly this size is way too small for me (or anyone I know) so I can't sustainably play this set-up, and I marvel at how different French trombone player's technique must have been to be able to play this.
3rd right is also late 19th century French, but for bass (or possibly saxhorn). More manageable size, actually almost exactly the same rim width, shape and size as my tenor sackbut mouthpieces (which is still smaller than anything most modern trombone players would use), just slightly more rounded on the edges. Hybrid cup shape with smooth entrance to the throat.
2nd right is my ophicleide mouthpiece, based on characteristics of a couple originals, diagrams and printed descriptions. In the size realm of modern bass trombone, but with a narrow and flat rim, a cup that is essentially hemispherical and a fairly sharp throat. Ophicleide mouthpieces tended to be at either extreme, either big and bowl-shaped, or smaller and extremely V-shaped.
1st right is the modern 1½G size (Ferguzon V) for comparison
