Mouthpiece Measurements and Terminology

Below we show a trumpet mouthpiece in cross-section:

We have immediately introduced several terms and measurements that begin to characterize the geometry of the mouthpiece.

The cup and backbore, as shown, are terms widely used to describe the parts of the mouthpiece shown.

The overall length is fairly sef-explanatory.

Tangent point is terminology that is, we believe, unique to VennCAD.

The tangent point is the point that was measured to be the left-most extent of the mouthpiece in the orientation shown above. We call it the tangent point because if the mouthpiece were placed cup-down on a table, that point would be where the mouthpiece was tangent to the table surface. Of course, in practice, for a mouthpiece with a flat rim, the mouthpiece remains quite flat near the tangent point, and it’s more of a tangent line in cross-section. But for a mouthpiece with more curvature or sharpness in the rim, it really is a pretty tiny point. Consider the following comparison:

In the Schilke 13A4A shown on the left, picking the exact location of the tangent point is rather imprecise, since the mouthpiece would follow our theoretical table closely along the extent indicated by the white line before peeling away. In the Bach 7C, the curvature of the rim allows us to indicate with much more confidence an exact tangent point. So how do we determine the exact location of the tangent point for a flatter rim like the one on the left? Well, it’s all down to our mouthpiece profiling machine and our proprietary software that zooms in and applies our mouthpiece parsing algorithms to what the profiling machine has measured. We look for the absolute minimum point. The machine can resolve down to 0.00002” (about 1/20 the width of a human hair), but zooming in to that level reveals a pretty bumpy surface due to surface imperfections. We obtain multiple (usually 8) traces, average them, mathematically account for any angular bias (as due to a tiny bend in the mouthpiece somewhere along its length), and, voila! There is your tangent point.

The throat point is how we refer to the narrowest point of the mouthpiece. Traditionally, the mouthpiece throat is thought of as a cylindrical region with some finite length. In our experience analyzing existing models, we have found that in some cases (as shown above), there’s not much of a cylindrical region at all. In others, it is extensive. Consider this comparison:

In the top example, the throat point’s location is harder to determine. After all, the mouthpiece remains at a fairly constant diameter for quite a while. As before, the profiling machine plus our algorithm chew up the geometry and assign a throat point. In the bottom example, the throat point is quite singular: the diameter tapers down from the cup, briefly “kisses” its minimum at the throat point, and immediately begins flaring back out again in the backbore.

Before we move on, can we just pause and reflect for a minute on how cool mouthpieces are?! Can we just ponder the amazing variety and unique shapes and limitless room for experimentation? The mouthpiece safari can be a lifetime journey. We at Vennture hope that you will read VennCAD as a love letter to you, our fellow gear-obsessed, fiddling, tinkering, nerdy, brass-playing brethren and sistren (is that a word?). Whether you become our best customer or never order a thing, we will be very gratified if you derive joy and insight from looking at mouthpieces, measuring them, comparing them, and tweaking them in the software. Whether you customize something and buy from us or simply use VennCAD as a way of comparing things you know to things you’re thinking of buying and then buy from another manufacturer, we hope to help you find what you need to help you use your embouchure and technique to perform the music you want to play. Everyone will experience both the cup and backbore of the top mouthpiece as “tighter” than the bottom or, put another way, will experience the bottom example as more “open” or “free-blowing”. But is this good or bad? Too constricting to one player may be experienced as efficient by another. Or, to quote the inimitable Macklemore in his seminal 2012 opus “Thrift Shop,”

“One man’s trash, that’s another man’s come up.”

OK, misty-eyed nerd moment over. Let’s move on.

We have had to make some executive decisions to chop up geometries into sections and then provide tools for investigating, tweaking, and designing your own geometries. We have decided that once we assign a singular throat point (again, that point in the horizontal axis is a bit more arbitrary in something like the Marcinkiewicz above that has a long cylindrical region), everything to the left of it is “cup” and everything to the right is “backbore.” In general, in instances where the throat is “cylindrical” for a while, we assign the throat point as far to the left as we can, so most/all of the cylindrical part is considered part of the backbore when it comes to calculating the length of the backbore versus depth of cup, or the volume of backbore versus volume of cup. This is indicated in the following diagram:

This drawing also introduces another important executive decision we made, and another piece of terminology we use: inner rim height.

Consider this: if we put our mouthpiece on our theoretical table and that tangent point made a perfect seal against the table, we could consider everything “inside” the seal to be part of the cup. And the diameter of that cup would then be the same as the diameter of the circle made by that tangent point as our cross-sectional view is rotated into three-dimensional reality. But nobody quotes cup diameters like that. In the mouthpiece industry, cup diameters are measured at some distance into the cup for a very sensible reason: our faces are not flat, rigid objects like our theoretical tabletop. To form a seal with the mouthpiece, we have lip engagement with the inner rim, reducing the cup diameter that we experience from the theoretical tangent diameter to something smaller. Our lips protrude somewhat into the cup, filling up some of the theoretical cup volume.

How much do our lips engage the inner rim or protrude into the cup’s volume? Well, you will surely recognize that this varies greatly from player to player. It surely even varies for a given player depending on the volume they’re playing with, or what register they’re playing in, or their level of fatigue, or even the alignment of the planets. It’s variable. We are not machines.

It is entirely possible that you may experience a mouthpiece with a larger tangent diameter to be smaller than one with a smaller tangent diameter, depending on the curvature of the inner rim and your level of lip engagement. Consider the following example:

The Schilke shown has a flatter rim, so while it has a somewhat larger tangent diameter than the Bach 5C (examine where the small dots indicating the tangent points lie; the Schilke measures 0.814” at the tangent point, whereas the Bach measures 0.791”), many (if not all) players will experience the Bach as having a wider cup diameter because it has a narrower rim and “peels off” into the cup faster.

So where do we measure the cup diameter? In some ways, picking a point at which to measure the diameter is arbitrary, and not the best way to compare different geometries. That is why VennCAD allows you to open up and overlay geometries, and then use a measurement cursor to measure the diameter at any level of protrusion into the cup you want.

But, forced to plant a flag somewhere, we decided to adopt a standard apparently originally devised by Marcinkiewicz. In the anatomy of a mouthpiece section of their website, they state that they measure mouthpiece diameter at 0.032” protrusion into the cup for trumpet/cornet/flugelhorn/French horn, 0.047” for trombone, and 0.064” for tuba. We haven’t been able to determine where these numbers came from or whether they are used by other manufacturers, but we have found them to be useful parameters that jibe with our measurements and play testing of other mouthpieces. By the way, in our considered opinion, Marcinkiewicz makes some of the most hella comfortable rims out there. Not too flat, not too sharp. Super nice. Everyone should have some Marcinkiewicz in their collection.

Anyway, when measured 0.032” into the cup at the “Marcinkiewicz point,” the Schilke 13A4A above measures 0.652” and the Bach 5C measures 0.678”, squaring with what most people would perceive: the Bach has a wider cup diameter as we experience it when playing, even though it has a narrower tangent diameter.

So when we measure cup diameters, we measure them (for trumpets) at .032” into the cup (i.e. 0.032” to the “right” of the tangent point when viewed in the orientation of all of our diagrams). When we measure cup depths, we measure from that .032” point to the throat point (as defined above). We measure the volume starting at 0.032” up to the throat point. All of this is easier seen and understood by a diagram, so here you go:

We have added a few new terms as well, but hopefully they are fairly intuitive.

The inner rim height is that Marcinkiewicz distance of 0.032” (for trumpet/cornet/flugelhorn/French horn) that we’ve been discussing.

The rim-cup point is located at exactly that depth, and represents the semantic division between “rim” and “cup.” Of course, this is rather arbitrary, and your experience of the cup may vary depending on your lip engagement/protrusion. But it helps to at least have some terminology. And as always, you can fire up VennCAD and measure stuff at shallower or deeper points.

The rim-cup angle is the angle of the mouthpiece at that rim-cup point, as shown above. This measurement is also referred to by Gary Radtke of GR Mouthpieces as alpha angle.

The outer rim height is the farthest point (measured horizontally and starting at the tangent point) of the outer rim that VennCAD considers. We set this by royal decree at 0.20” for trumpet/cornet/flugelhorn. Now some makers (e.g. Marcinkiwiecz) start tapering their pieces down before this point (i.e. following the curvature of their outer blank, eventually ending in the shank). Others (e.g. Bach and Schilke) carry their max outer diameter past this point, or maybe don’t even reach max OD until after this point. In VennCAD, we extend those truncated outer rims or trim “longer” outer rims to this standard dimension. We figure, your chops don’t interact with this outer rim anywhere past 0.20”. Unless you have a really weird embouchure. Like, weird enough to creep us out.

The reason for this 0.20” is that it’s plenty of space to finish the geometry far from the reach of your chops, but not so much that they blank gets unnecessarily heavy/chunky. 0.20” is where our blank starts its relentless taper down to the shank. More on that later. So it follows directly that the outer rim width is the vertical distance from the tangent point to the “end of the line,” where the OD is measured. And the inner rim width is the vertical distance from the tangent point to the rim-cup point, which we discussed earlier. Do you see how it all fits together?

The upshot of this is that the outer diameter (O.D.) that we quote may be smaller than if you measured the max OD of the physical piece, since we are not measuring anywhere past that 0.20” cutoff. But we should agree with what you’d measure if you took the diameter 0.20” in from the tangent point.

When we say throat, we mean “diameter at the throat point,” which we discussed at some length above. It is, as we said, the very narrowest diameter of the whole geometry.

In VennCAD™, for reference models from the library we only show what we consider the “wetted” surfaces of the mouthpiece: the entire backbore, the cup, the inner rim (up to the tangent point) and the outer rim (which ends at the point where we quote mouthpiece OD). This is the active geometry of the mouthpiece.

However, for mouthpieces designed in VennCAD™ to be manufactured, we must also design the shank geometry (for where the mouthpiece seats in the receiver) and the blank geometry (i.e. the method of tapering from the outer rim point down to the taper).

In the diagram below, we show the throat point, inner rim point, tangent point, and outer rim point for reference.

Our convention at Vennture is to consider the blank to begin right at the end of the outer rim and blend seamlessly into the shank:

The shank is a perfectly conical taper. A conically tapered section (geometrically speaking, a frustum) has four important dimensions:

• A starting diameter
• An end diameter
• A taper rate (expressed in degrees or slope)
• A taper length

Note that if you know any three of the dimensions above, you can figure out the fourth.

For nearly every modern brass instrument (note the straight Flugelhorn “taper,” used on older Couesnon instruments, as the sole exception below), the taper rate is the same: 5%, meaning that the diameter expands at 5% of the change in length. Thus, for every inch of shank length, the diameter expands by 0.05″. (Or, for every cm of shank length, the diameter expands by 0.05cm.)

Bach has helpfully published on a page of its mouthpiece manual the starting diameter dimension for all the mouthpieces it makes. This information has been entered in the table below along with the industry-standard taper rate’s and Vennture’s choices for taper length and the resultant end diameter. Vennture bases its manufacturing on these numbers.

Note that for all lines of the table above, we have listed all four taper elements (starting diameter, taper rate, taper length, and end diameter). For any line, note that if you multiply the taper rate by the taper length, you get the amount of change in diameter, and if you add that to the starting diameter, you get the ending diameter. For example, consider the trumpet line. It tapers for a length of 1″ at a rate of 0.05 inches (of expansion) per inch (of length). Thus, the diameter expands from 0.382″ at the start to 0.382″+0.05″=0.432″ at the end of the taper.

Below, we introduce several new terms relating to the shank of the mouthpiece:

Shank Starting Diameter and Taper Length are as defined in the table above.

Starting Inner Diameter is the widest part of the backbore.

The Shank Skin Thickness is the minimum amount of material (the “skin”) at the very end on the mouthpiece where the backbore is at its widest and the shank taper is at it narrowest. You may have noticed that this varies somewhat for different mouthpieces. In the trumpet world, “lead” pieces intended for high register work tend to have fairly tight backbores, so this skin is rather thicker. Others with more open backbores feature a thinner skin thickness. For example, the Bach 3E, which features a deep plunge of Bach’s already-roomy #117 backbore reamer (reamers are tapered, and plunging them more deeply into a given mouthpiece creates a larger Starting Inner Diameter and, consequently, a lesser Shank Skin Thickness), has been described by my good friend Kent as “possibly useful for doing lumbar punctures.”

Consider the following diagram:

Note that the vertical axis has been stretched somewhat to make the taper more apparent. This can be done in VennCAD by adjusting X-Magnification – a useful feature for seeing differences in backbores and shanks, where the taper rates are modest.

The mouthpiece gap is defined as the distance between where the mouthpiece shank ends and the Receiver Step in the leadpipe. You can see this step by looking into your leadpipe, possibly with the help of a flashlight.

Note that the seating of the mouthpiece (i.e. where the mouthpiece ends up relative to the Receiver Step) is determined when the taper of the mouthpiece and the taper of the mouthpiece receiver interfere (i.e. when you insert the mouthpiece and bash it with the palm of your hand…just kidding! Please don’t do that; a gentle twist will suffice). The mouthpiece does not butt up against anything.

This gap depends both on the mouthpiece and the mouthpiece receiver. A given mouthpiece seated in different instruments may leave different gaps in those instruments, depending on the geometry of the instruments’ mouthpiece receivers. Likewise, different mouthpieces in one instrument may produce different gaps depending on their starting diameters.

Measuring the gap left by a certain mouthpiece in a particular horn may be accomplished with a gap measurement tool such as the one available here from Warburton.

Vennture allows the user to request a given Gap Adjustment, which is a change in gap from what would be achieved by a mouthpiece that conforms precisely to the table above.

Consider an example of designing a trumpet mouthpiece. A “standard” trumpet mouthpiece shank would start at 0.382″. If we inserted it in the trumpet shown above, it would seat itself leaving the Theoretical Gap shown. This, as discussed earlier, is dependent on the horn’s particular mouthpiece receiver. Let’s suppose for this example that the Theoretical Gap would be 0.06″. Suppose you want your actual Gap (i.e. for the mouthpiece you want to order) to be 0.10″. Your Gap Adjustment would then be 0.04″. (A negative Gap Adjustment would make the actual Gap smaller than the theoretical gap, seating your new mouthpiece closer to the Receiver Step than a standard mouthpiece would seat.)

Of course, it would be nice to be able to simply specify what Gap you want, but it depends on your receiver, so we use Gap Adjustment, since it makes sense as a parameter on its own.

A Gap Adjustment of +0.04″ instructs Vennture to make the mouthpiece’s shank Starting Diameter larger than the standard diameter of 0.382″ by the amount of 0.04″(i.e. the adjustment)×0.05(i.e. the taper rate)=.002″. Thus, we will make the Starting Diameter at 0.384″, thereby pushing the mouthpiece away from the Receiver Step by 0.04″, yielding an actual Gap of 0.10″.

Hopefully you are starting to see how we divide up the parts of the mouthpiece. This may be more detail than you’ve gone into in thinking about mouthpieces before, or it may not be exactly the same as you’ve thought of things before. Perhaps you reckon the cup depth starting at the tangent point and not at the inner rim height. Or you think of the rim as having a single “thickness” rather than an inner and outer width, as we have proposed. But hopefully the measurement cursors in VennCAD and some simple arithmetic will allow your mental models and ours to meet up. Maybe your “rim thickness” is just Inner Rim Width+Outer Rim Width in VennCAD-speak. Or you use the GR term “alpha angle” instead of rim-cup angle.

Here’s your final exam. If you understand these equations/identities and why they’re true (or, at any rate, consistent with the terminology we’ve proposed), then we’re playing in tune!

O.A.L. = inner rim height + cup depth + backbore length

O.D. = cup diameter + 2*inner rim width + 2*outer rim width