The tools are very simple, or can be very simple. What is needed is a way to accurately measure and graph a curve that begins from a flat surface. The flat surface is the "table" of the mouthpiece and the curve is the "lay" of the mouthpiece. To this end, a feeler gauge is used to measure the height the curve rises above the table and a ruler is used to measure the distance from the tip of the mouthpiece where that height occurs. Sounds a little complex, but actually all you are doing is getting X and Y coordinates for purposes of plotting a simple graph. I use Microsoft Excel as a spreadsheet program that has an automatic graph or "chart" function.
One of the traditional methods for measuring was developed by Erick Brand, hence the term "Brand numbers" used in comparing mouthpiece facings. Mr. Brand used a glass ruler etched in millimeters. The original Brand ruler markings started at the end of the ruler, so if the tip of the mouthpiece was even with the end of the ruler, you could begin measuring by using the feeler gauges. http://www.musictrader.com/clarinetmouthpiecerefacing.pdf (Shown in Fig. 95). Those types of rulers are difficult to find. Other rulers, which are not "end indexed," are available, sometimes as part of a kit.
When the ruler doesn't start at the edge, you have to relocate the tip over the zero line several times, and there will be some error (more on that later). And although the Brand ruler is etched in millimeters, the Brand "numbers" are really half millimeters, meaning that if the distance measured is 4.7 millimeters, the Brand number for that distance would be 9.4. Confused yet?
What is being done is that, for graphing purposes, the measurement is being made in .5 mm increments. That adds another element of error because almost every measurement is going to require interpolation between the lines on the ruler. Add to that the fact that the ruled lines themselves can be 3/10ths of a millimeter thick and it gets kind of silly to think that you can measure 20ths of a millimeter using a ruler with 1mm markings and no way to ensure that the mouthpiece is always positioned the same for each subsequent measurement.
One thing that might help is a glass ruler that is in .5mm increments. Here's one. It's from Germany, probably close to 100 years old, and harder to find than an original Brand ruler. It isn't indexed to zero on the end, so if the mouthpiece is moved during measuring (and it will be), it has to be re-indexed to zero for each measurement and some additional error is possible. You can see the zero line and the next line of the same length is the 1 cm line, with 20 lines in between, thus the very thinly etched lines are .5mm. You can click on the picture to enlarge.
If you click on the above picture, you may be able to read this ruler in .5mm increments or actual "Brand numbers." To help you, the long ruled line just left of middle on the feeler gauge is the 10mm mark (meaning a Brand number of 20). So the Brand measurement shown here is approximately 39. When I measure, I use a high-powered lighted desk magnifier. Sometimes, I even use a jeweler's loupe with the desk magnifying glass. I record Brand numbers to the 10ths (i.e., increments of 1/20th of a millimeter), which, as I noted at the beginning of the blog, is probably a little optimistic as to accuracy. The reading above might be plotted on the graph as 39.2 for the .010" feeler.
A word about feeler gauges. Like most measuring devices, the largest and most common source of error is going to be operator error. Inexpensive gauges can be as accurate as expensive gauges, although they may have to be used with more care. They can also be modified to increase accuracy. Here's an example of an inexpensive set ($5 including shipping). There are sets with longer blades and you can purchase individual blades in various thicknesses for about $4 to $5 each. I prefer the set, for reasons I'll get to.
If you click on this feeler gauge set, you'll see that it has some thickness that aren't used in the Brand system, which will only use feelers of .0015, .005, 010, .016, and .024 of an inch for graphing points. This set is also "missing" some required thicknesses, i.e., .035, .050, .063, .078, .093, and .0109. The "missing" thicknesses are measured by stacking proximate blades. Stacking .017 and .018 equals .035. Add the .015 and you have .050. Stack .020, .021, and .022 and you have .063. 18, 19, 20, and 21 is .078, etc. I think that the original "Brand feeler gauge increments" are what they are because they were easy to get from stacking a commonly available mechanic's feeler gauge set. If you buy individual feelers, you're looking at 11 or more feelers to get the Brand numbers and spending between $50 - $200.
There can be a problem with accuracy when using a set and stacking the blades. The first problem is cleanliness, which is a problem with all feeler gauges. You have to make sure that nothing gets on the blades and between the blades if you are stacking. Second, if you simply slide two or more blades between the ruler and the mouthpiece, a blade may be cantilevered out, or a top or bottom blade may be back a little from the leading edge, which can affect the measurement. It's easy to prevent this and should become routine for every multi-blade measurement. If you have the set that has a tightening screw (as shown below), tighten it down good before evening the blades. If you have a set without a thumb screw (like the one above), you simply pinch on the outer case to hold the blades tightly together (which also works for the thumbscrew types).
Here are the aligned blades. Click on the picture and you can see that the ends of the feeler blades don't align perfectly. The other side blade edges are probably also out of whack, but we don't care. The edge that we are going to use for measuring thickness has the blades all perfectly aligned and held in position.
There is one final thing that should be done to improve accuracy. The individual blades are stamped out, causing the edges of the gauge to not be at a perfect 90 degree angle to the width of the blade. The generally have one edge slightly "rolled over" as a result of the stamping. The general "thickness" of the gauge is accurate for its intended use, but we are using it in a little different manner. We need the very edge of the blade to be accurate. To ensure that, look at the picture above where the blade is on the granite slab. I usually remove the blade from the set and, holding it perpendicular to the granite slab, draw it over emory paper. I can examine the edge with my jeweler's loupe and make sure that I have put a 90 degree edge on the blade. Then I wipe the edge with steel wool to remove any burrs. Be careful not to erase the chemically etched numbers that show the blade's thickness! When you are done, the edge of the blade will feel kind of sharp compared to the original undressed stamped edge.
Now we are going to insert the blades between the ruler and the mouthpiece. A little wiggle and you'll get the hang of it. You want the blade(s) flat against the ruler and the same force each time so that you are measuring "apples to apples."
Hey, wait a minute! That's not an expensive, rare, scratched glass ruler. Right, this is an inexpensive, easy to find and replace, accurate ruler. It's a rigid "mechanic's ruler" that is end indexed, just like an original Brand ruler, and ruled in .5mm increments (or Brand increments), just like the Brand ruler didn't have. These are also made in a flexible version and that isn't what you want, as that type will flex away from the feeler gauge and screw up the measurements. These are about $10 off of the web, including shipping.
Hey, wait another minute! I can't see through it! Well, you can't see through the feeler gauge or the mouthpiece either, so what's your point?
Here, we zero it out using a flat surface to accurately get the same starting point every time. That's one of the nice things about a mechanic's ruler, it's edge indexed.
I've offset the mouthpiece so that you can see what's going on. The ruler would normally be lined up down the center, or it can be lined up running closer to the rail as long as the piece is perpendicular to the ruler. If you are off by three or four degrees, it can make a measurable difference (which is another source of error that negates any supposed accuracy in reading to 20ths of a millimeter).
The Brand article above at Fig. 95 shows the author using a finger to align the mouthpiece tip with the end of the ruler. That would basically be using the inaccurate eye-ball method that will change a little each time the piece is re-positioned. What good is a super accurate .5mm ruler with ruled lines exactly .2mm thick help you measure in .05mm increments if you start each measurement by saying to yourself "Does that look like it's lined up at the zero line?" Or, "Does the tip appear even with the end of the ruler this time?"
Three additional notes on accuracy. First, if you are trying to eyeball up to a zero line, you need to decide which side of that line is zero. The thicker the line, the more important that is. It isn't just the area in between the lines that is .5 mm (or whatever the particular metric of your ruler), it's the space and the thickness of one of the adjacent lines. On the ruler shown above, it is the leading edge of the ruled lines (the lower edge in the picture) that is exactly 1mm from the edge. Then there is a line that is .2mm thick, then an open space that is .8mm, and you are back to the next full millimeter beginning on the leading edge of the next line. Likewise on the .5mm scale. The line is .2, the open space is .3, and you are back to the face of the next line. Your ruler type may vary, but use it properly to maximize its accuracy.
Second, I don't think that an exact zero starting point is as important as a uniform zero starting point. By that I mean that the importance of whether a facing curve is 22.5 mm long (45 in Brand numbers) or 22.75 (45.5 in Brand numbers) pales in comparison to whether the curve is accurately measured over its length so that the fairness of the curve can be analyzed. If you index to zero "inaccurately," but uniformly inaccurately for every measurement, meaning, for example, that every single Brand reading you recorded is uniformly high by exactly .2 mm because of your inaccurate zero point, you will still have an accurate map of the curvature. If you eyeball your zero for each measurement, and your Brand numbers look perfect, but your eyeballed zero point varied by plus or minus .2 mm for each reading, you've got an accuracy problem. For purposes of refacing a mouthpiece, I'm concerned about attaining a smooth curvature and not necessarily attaining some magic numbers. An accurate curve requires a uniform zero, which doesn't have to be an exact zero, and won't be easy to achieve using a repeatedly eyeballed zero reference.
The same is true for just mapping the piece for analysis. Think of mapping a mouthpiece as making a geological topographic map. You start out by marking sea level as your zero point and start mapping your contours at 20 foot height increments. Every contour is indexed to the same sea level marker. 20, 40, 60, 80, 100, 1,000 feet, etc. Now let's create a map a different way. To establish the 20 foot contour, we put a marker at sea level. For 40 foot, we put in another marker to establish sea level and measure from that marker. Each time we measure, we put in a different marker for sea level using our best technology. Let's say that our best GPS technology is accuracy within 6 inches. Given that the purpose of the map is to show contour in relationship to one point (sea level), it doesn't make sense to re-establish sea level for every measurement. And given the fact that we are interested in the overall topographic detail, whether our single sea level marker was off by 6 inches is not as important from a mapping point of view as the accuracy provided by using a single point starting point for every measurement. That's my theory.
Third, the accuracy of feeler gauges themselves is often the source of concern, especially when stacking blades. What if by stacking the .017 and the .018 blades to measure the .035" number that results in some inaccuracy? It might really be .0353" thick. Because of that extra thickness, the feelers won't slide in as far, say by .03mm. Or what if the edges of the feeler gauge is not perfectly plumb, but rather, rounded from use? Because it's not properly plumb, it slides in further by .03mm. If you play around with your feeler gauges, say by measuring first with the .024" blade and then .025," you'll see a measurement difference in Brand numbers. That huge difference of going from one blade thickness to the next might make only a .2 difference in the Brand number. Lesser changes, say a .0003 inaccuracy in the blade thickness would be barely visible, barely visible being the key here. An inaccuracy of .0003" in thickness resulting from stacking the blades is easily imaginable, but don't let your imagination run wild. It's going to be your eyeballs and your technique, not your tools, that limit your accuracy.
It is easy to increase the accuracy of indexing to zero by using a flat surface, as shown above. Even better is to zero the piece by holding it horizontal and aligning against a flat surface like the front edge of the countertop (my favorite method). Or, like the picture below, where I am holding the tip upright and coming up under a flat surface, using the smooth overhanging edge of the milled granite countertop.
That way, the mouthpiece and ruler are comfortably oriented in the same way that I will hold them when I take my measurement. Very easy, very fast, very consistent, very accurate.
Here's how I hold the mouthpiece and the ruler. Index finger right up against the beak lip, middle finger over the ligature line, with most pressure between the middle finger and thumb and basically no pressure from the index finger (it's only used to index, yuk, yuk). I've never had a curve start behind the "lip" of the beak, so the thumb is pushing the rigid ruler only on to the flat table (or hopefully flat table, not covered in this blog) right before the lay begins.
This mechanic's ruler is indexed to zero on both ends and ruled on both sides, so if I want to use the .5mm rulings to help in getting direct read Brand numbers for either rail, it's just a matter of flipping the ruler over. Because re-indexing to zero is quick and accurate, it doesn't matter that I've moved the mouthpiece on the ruler or to the other side of the ruler. In fact, this is a good way to double check the accuracy of my readings.
Here, the .5 mm markings (or Brand numbers) are on the left hand rail. The rulings on both edges help in determining whether the rails are even (when the feeler will balance at 90 degrees to the ruler). You've probably noticed that in the above picture the .010 feeler goes in farther on one side than the other. That's because on this tenor mouthpiece the curvature of the rails is uneven. The further the rails are from even, the more difficult it gets to measure them accurately.
That's the basics of measuring the mouthpiece. This is not an exhaustive treatise, therefore, you may have to use common sense to increase the accuracy of your readings.
Finally, we get to the interesting part. Here are numbers from a new "no name" mouthpiece for a BBb contrabass clarinet which, when compared to a baritone saxophone, is physically much larger (its internal chamber is about 1.25" in diameter as compared to a baritone sax at .75"). If you are familiar with lay lengths and tip openings for baritone saxophones, you will notice that this BBb clarinet mouthpiece has a long lay for a relatively small tip opening. And this particular lay is actually very short for a BBb piece. This piece is new old stock (1960's?) and was intended as a student grade mouthpiece. The mouthpiece was about $40 on Ebay. It appears to be plastic rather than the hard rubber used on high-end pieces. I've also written down some other notes to make it easier to compare this piece to other BBb mouthpieces and maybe help in improving this piece if I decide to modify the facing curve.
If you clicked on the picture, you can see that the left and right rail are measured and recorded separately. And on this piece, those measurements are not the same. It is possible for a skilled and experienced craftsman to adjust the rail to differing heights at different locations to improve the piece, but on an inexpensive, mass produced plastic student piece? Nah. This unevenness is just the result of the quality control in the manufacturing.
We then need to graph the numbers to see what's really going on. Excel does this automatically. On this graph, the distance from the tip is on the Y axis and height from the flat table is on the X axis. Remember, the Brand system is 1/1000th of an inch on one axis and interpolated 1/20th of a millimeter on the other, so don't expect the graph to look too much like the curve on an actual mouthpiece. Okay. Ready? Click on it.
This second mouthpiece is a well known, well respected, hand finished piece. It costs in excess of $360 and there is a waiting period if you want one. If you study the graph, you will see that all of the points at which the mouthpiece varies from the computer generated line are "high spots" in the lay, meaning that a careful touch-up on the facing would reduce those spots and make it a perfect match with the curve. In fact, the computer generated line was purposely designed to show the facing curve, given this mouthpiece's measurements, that would require the smallest amount of fairing in order to be "true." Question is, would a perfect curve be better? Again, not covered in this blog.
So there you have it. It is possible to do a self-examination of your mouthpiece. Whether you should then play Doctor is another question. I have talked about how to play Doctor in other blogs, but that isn't for everybody.