I've been on a mission to find a more suitable cornet mouthpiece, largely unsuccessfully, but I've learned an awful lot along the way and thought some of it might be useful to others.
Everyone wants a mouthpiece which makes it a breeze to play high notes, is easy to play for long periods and sounds beautiful in the high and low registers. The bad news is that you can't have all of those things at once, and so instead of finding the perfect mouthpiece, you're actually trying to find your own personal compromise between those things.
More bad news is that the different makes use their own numbering and lettering systems which makes it very difficult to compare. If you look at their literature, the manufacturers give some dimensions in mm, which helps. Other factors, such as the cup depth and backbore are either not quoted, or given as 'deep', 'medium-deep', 'medium' etc and I've learned that what one company calls deep is what another calls shallow. Beware of anomolies in these systems, for example the Wick 4 and 4.5 are exactly the same diameter and cup size, it's just the backbore which is different.
The other difficulty with making comparisons is that 2 mouthpieces from different ranges may have the same diameter, but different cup shapes, rim widths, depths, and bores.
The number is the rim diameter, and lower is bigger. '3' is pretty big, '5' is small. No letter means deep - and Wick's deep really does mean very deep compared with other makes. 'B' means medium depth, but this compares well with 'deep' from other makes. 'W' means a wide rim width, and 'S' is their shallow sop mouthpiece.
The number is the rim diameter, starting at '1' (very big) to '20' (very small) The actual diameters vary more widely than Wick, and the numbers don't really correspond. The letter is the depth of the cup, 'A' is deep (although this is not very deep compared to Wick) through to 'F', which is extra shallow. They do a 'V' which is very deep.
Yamaha also use a number to denote the rim diameter, but in their case it works the other way around - ie starting at '16' (very big) through to '7' (small). They use a letter for the cup depth, which again is the reverse of Bach - in Yam's case 'A' is shallow and 'E' is deep. They then add a number for the rim shape, '1' is flat and '5' is round, and then a lower case letter for the backbore - 'a' is narrow and 'e' is broad
Schilke have a remarkably similar numbering system to Yamaha, the diameters varying slightly, but with the rim countour working in reverse - ie '5' is flat and '1' is round.
Alliance cornet mouthpieces have been developed with help from Roger Webster and are supplied with new Besson instruments. Cup diameters range from '1' (large) to '3' (medium) with a letter for cup depth - no letter for deep, 'a' for medium and 'b' for shallow. A couple of sizes are available with a wide rim denoted by a w.
Everything about the mouthpiece design affects the playing and sound. Some of these things have a dramatic effect, others subtle or negligable.
The diameter has a big effect on the sound and how much effort you need to play, especially in the upper register. A smaller diameter means easier playing and a brighter sound in the upper register, but a thin raspy sound down low. A larger diameter makes for a beautiful rich tone but harder work and no brightness up high. A bigger diameter is also said to icrease flexibility (how easily and accurately you can jump from a low note to a high one and vice versa) because your lips have more freedom to move.
It's amazing how much difference a tiny difference in diameter can make . For example, there's 0.25mm difference in cup diameter between a Wick 3 and 4, and 0.5mm difference between the 4 and 5, but they feel and sound very, very different. They do make a number 2, described by them as 'enormous' and suitable for low parts, or possibly for soloists with strong embouchures who want the flexibility and tone and yet it's only 0.5mm bigger in diameter than the 'standard' 4.
This has a similar effect to the diameter, ie a shallow mouthpiece makes a brighter sound and easier to play up high at the expense of tone. For example, there are trumpet mouthpieces called 'screamers' which are so shallow that your lips almost touch the backbore, and allow you to get notes which only dogs can hear. However, the sound in the lower registers is horribly thin and raspy.
This is sometimes called the 'bite' and affects comfort rather than sound. A narrower rim width will obviously bite into your lip if you press too hard or if the instrument is held at the wrong angle, and therefore reduce endurance. It may be round or flat, which makes it feel different and of course a rounder rim will have more bite than a flatter one. A wider or flatter one may be a bit more comfortable but may reduce flexibility (how easily and accurately you can jump from a low note to a high one and vice versa). Wick produce some especially wide rims (marked 'W'). Rim width and shape have a much more subtle or aguable effect than diameter and depth.
This again has an effect on the sound and ease of playing. Trumpet mouthpieces usually have a narrower throat than cornet ones and it's this which is largely responsible for the difference in sound - if you don't believe me, put your cornet mouthpiece in your trumpet (with the adaptor) and hear your trumpet sound much more like your cornet. It's difficult to compare backbores because it's not just the size of the throat which affects things, but the size and shape of the backbore too.
A mouthpiece which is heavier, ie has more metal or is denser, is said to sound darker. Designs such as Bach Megatone or the Wick Heavytops are bigger on the outside. Wick even make an adaptor which slides over their lighter mouthpieces to convert them. Yamaha now do a 'sterling' range which are turned out of solid silver - the material is said to give a darker sound - at a price!
Kanstul Mouthpiece Comparator - a great idea - shows accurate outlines for the insides of lots of mouthpieces and allows you to overlay and compare them
Dimensional Characteristics of Brass Mouthpieces by Renold O. Schilke. A wonderful article, scanned and transcribed for the web.
Brass Horn Mouthpiece Elements and Characteristics ChartWhen You Change A Part of The Mouthpiece What Does It Do To Your Sound? Another great chart.