Measure up

In the wind...

July 2011

Measure up.

When I was an apprentice working in Oberlin, Ohio, we had a particularly bad winter with several heavy storms and countless days of difficult driving conditions.  As part of our regular work, my mentor Jan Leek and I did a great deal of driving as we serviced organs throughout northeastern Ohio and western Pennsylvania.  Jan owned a full-size Dodge van – perfect for our work as it was big enough to carry windchests, big crates of organ pipes, and long enough inside to carry a twelve-foot stepladder with the doors closed if the top step was rested on the dashboard near the windshield.  All those merits aside, it was relatively light for its size and the length of its wheelbase, and it was a simple terror to drive in the snow.  There can’t have been another car so anxious to spin around.

Jan started talking about buying a four-wheel-drive vehicle and one afternoon as we returned from a tuning he turned into a car dealership and ordered a new Jeep Wagoneer – a large station-wagon shaped model.  He wanted it to have a sunroof but since Jeep didn’t offer one he took the car to a body shop that would install one as an aftermarket option.  As we left the shop, Jan said to the guy, “I work with measurements all day – be sure it’s installed square.”  It was.

Funny that an exchange like that would stick with me for more than thirty years, but it’s true – organbuilders work and live with measurements all day, every day they’re at work.  A lifetime of counting millimeters or sixty-fourths-of-an-inch helps one develop an eye for measurements.  You can tell the difference between nineteen and twenty millimeters at a glance.  A quick look at the head of a bolt tells you that it’s seven-sixteenths and not a half-inch and you grab the correct wrench without thinking about it.  Your fingers tell you that the thickness of a board is three-quarters and not thirteen-sixteenths before your eyes do.  And if the sunroof is a quarter-inch out of square it’ll bug you every time you get in the car.

And with the eye for measuring comes the need for accuracy as you measure.  Say you’re making a panel for an organ case.  It will have four frame members – top, bottom, and two sides – and a hardwood panel set into dados (grooves) cut into the inside edges.  The drawing says that the outside dimensions are 1000mm (one meter) by 500mm (nice even numbers that never happen in real life!).  The width of the frame members is 75mm.  You need to cut the sides to 1000mm as that’s the overall length of panel.  But the top and bottom pieces will fit between the two sides, so you subtract the combined width of the two sides from the length of the top and bottom and cut them accordingly: 500mm minus 75mm minus 75 mm equals 350mm. 

You make a mark on the board at 350mm – but your pencil is dull and your mark is 2mm wide.  Not paying attention to the condition of the pencil or the actual placement of the mark, you cut the board on the “near” side of the mark and your piece winds up 4mm too short.  The finished panel will be 496mm wide.  Oh well, the gap will allow for expansion of the wood in the humid summer.  But wait!  It’s summer now.  In the winter your panel will shrink to 492mm and the organist will have to stuff a folded bulletin into the gap to keep the panel from rattling each time he plays low AAA# of the Pedal Bourdon (unless it’s raining). 

You can see than when you mark a measurement on a piece of wood you have to make a neat clean mark, put it just at the right point according to your ruler, and remember throughout the process on which side of the mark you want to make your cut.  If you know your mark is true and the length will be accurate if the saw splits your pencil mark, then split the pencil mark when you cut!

I’ve had the privilege of restoring several organs built by E. & G.G. Hook and never stop delighting at the precision of the hundred-fifty year old pencil marks on the wood.  The boys in that shop on Tremont Street in Boston knew how to sharpen pencils.

Another little tip – use the same ruler throughout the project.  As I write, there’s a clean steel ruler on my desk that shows inches with fractions on one edge and millimeters grouped by tens (centimeters) on the other.  It’s an English ruler exactly eighteen inches long, and the millimeter side is fudged to make them fit.  The last millimeter is 457, and the first millimeter is obviously too big.  If I was working in millimeters and alternating between this ruler and another I’d be getting two versions of my measurements.  While the quarter-millimeter might not matter a lot of the time, it will matter a lot sometimes.  I have several favorite rulers at my workbench.  One is 150mm long (it’s usually in my shirt pocket next to the sharp pencil), another is 500, another is 1000.  I use them for everything and interchange them with impunity because I know I can trust them.  With all the advances in the technology of tools I’ve witnessed and enjoyed during my career I’ve never seen a saw that will cut a piece of wood a little longer.  The guy who comes up with that will quickly be wealthy (along with the guy who invents a magnet that will pick up a brass screw!). 

My wife Wendy is a literary agent with a long list of clients who have fascinating specialties.  In dinner-table conversations we’ve gone through prize-winning poets, crime on Mt. Everest, multiple personalities, the migration of puffins, flea markets, and teen-agers’ brains(!).  Her client Walter Lewin is a retired professor from the Massachusetts Institute of Technology who is famous for his rollicking lectures in the course Physics 8.01, the most famous introductory physics course in the world.  On the first page of the introduction to his newly published book, For the Love of Physics; from the end of the Rainbow to the Edge of Time – A Journey Through the Wonders of Physics, Lewin addresses his class:

“Now, all important in making measurements, which is always ignored in every college physics book” – he throws his arms wide, fingers spread – “is the uncertainty of measurements… Any measurement that you make without knowledge of the uncertainty is meaningless.” 

I’m impressed that Professor Lewin thinks that inaccuracy is such an important part of the study of Physics that it’s just about the first thing mentioned in his book.

The thickness of my pencil lines, my choice of the ruler, and the knowledge about where in the line the saw blade should go are uncertainties of my measuring.  If I know the uncertainties I can limit my margin of error.  I do this every time I make a mark on a piece of wood.  And by the way, if you’re interested at all in questions like “why is the sky blue,” you’ll love Lewin’s book.  And for an added bonus you can find these lectures on YouTube – type his name into the search box and you’ll find a whole library.  Lewin is a real showman – part scientist, part eccentric, all great communicator – and his lectures at once brilliantly informative and riotously humorous.

Now about that panel that will fit into the dados cut in the frame members.  Given the outside dimensions and the width of the four frame pieces, the size of the panel will be 850mm x 350mm (if your cutting has been accurate).  But don’t forget that you have to make it oversize so it fits into the dado.  7.5mm on each side will do it – that allows for seasonal shrinkage without having the panel fall out of the frame.  So to be safe, cut the dados 10mm deep allowing a little space for expansion, and cut the panel to 865mm x 365mm – that’s the space defined by the four-sided frame plus 7.5mm on each side which is 15mm on each axis.  Nothing to it.

Now that you’ve all had this little organbuilding lesson, look at the case of a good-sized organ.  There might be forty or fifty panels.  That’s a lot of opportunity for error and enough room for buzzing panels to cover every note of the scale.

§

For the last several days I’ve been measuring and recording the scales and dimensions of the pipes of a very large Aeolian-Skinner organ that the Organ Clearing House is preparing to renovate for installation in a new home.  I’m standing at a workbench with my most accurate measuring tools while my colleague Joshua Wood roots through the pipe trays to give me C’s and G’s.  Josh lays the pipes out for me, I measure the inside and outside diameters, thickness of the metal (which is a derivative of the inside and outside diameters – if outside diameter is 40mm and the metal is 1mm thick, the inside diameter is 38mm.  I take both measurements to account for uncertainties.), mouth width, mouth height, toehole diameter, etc.  As I finish each pipe Josh packs them back into the trays.  With a rank done, we move the tray and find another one.  Now you know why I’m thinking about measurements so much today.

When studying, designing, or making organ pipes we refer to the mouth-width as a ratio to the circumference, the cut-up as a ratio of the mouth’s height to width, and the scale as a ratio of the pipe’s diameter to its length.  If I supply diameter and actual width of the mouth, the voicer can use the Archimedian Constant (commonly know as π - Pi) to determine the mouth-width ratio, and so on, and so on.

Here’s where I have to admit that my knowledge of organ voicing is limited to whatever comes from working generally as an organbuilder without having any training or experience with voicing.  My colleagues who know this art intimately will run circles around my theories and I welcome their comments.  From my inexpert position I’ll try to give you some insight into why these dimensions are important.

The width of the mouth of an organ pipe means little or nothing if it’s not related to another dimension.  Using the width as a ratio to the circumference of a pipe gives us a point of a reference.  For example, a mouth that’s 40mm wide might be a wide mouth for a two-foot pipe, but it’s a narrow mouth for a four-foot pipe.  A two-foot Principal pipe with diameter of 45mm might have a mouth that’s 40mm wide – that’s a mouth-width roughly 2/7 of the diameter, on the wide side for Principal tone.  The formula is: diameter (45) times π (3.1416) divided by mouth-width (40).  In this case, we get the circumference of 141.372mm.  Round it off to 141, divide by 40 (mouth-width) and you get 3.525 which is about 2/7 of 141.  Each time I adapt the number to keep things simple I’m accepting the inaccuracy of my measurements.

The mouths of Flute pipes are usually narrower (in ratio) than those of Principals.  Yesterday I measured the pipes of a four-foot Flute which had a pipe with the same 40mm mouth-width, but the diameter of that pipe was about 55mm. That’s a ratio of a little less than 1/4.  The difference between a 2/7 mouth and a 1/4 (2/8) mouth tells the voicer a lot about how the pipe will sound.

And remember, those diameters are a function of the scale, the ratio of the diameter to the length.  My two example pipes with the same mouth width are very different in pitch.  The Principal pipe (45mm in diameter) speaks middle C of an eight-foot stop while the Flute with the 40mm mouth speaks A# above middle C of an eight-foot.  Now you’re a voicer.

§

You can imagine that the accuracy of all these measurements is very important to the tone of an organ.  The tonal director creates a chart of dimensions for the pipes of an organ including all these various dimensions for every pipe, plus the theoretical length of each pipe, the desired height of the pipe’s foot, etc., etc.  The pipe maker receives the chart and starts cutting metal.  Let’s go back to our two-foot Principal pipe.  Diameter is 45mm.  Speaking length is 2-feet which is about 610mm.  Let’s say the height of the foot is 200mm.  The pipemaker needs three pieces of metal – a rectangle that rolls up to become the resonator, a pie-shaped piece that rolls up into a cone to make the foot, and a circle for the languid.

For the resonator, multiply the diameter by π: 45 x 3.1416 = 141.37mm (this time I’m rounding it to the hundredth) – that’s the circumference of the pipe so it’s the width of the pipemaker’s rectangle.  Cut the rectangle circumference-wide by speaking-length-long: 141.37 x 610.

For the foot, use the same circumference and the height of the foot for the dimensions of the piece of pie: 141.37mm x 200. 

Roll up the rectangle to make a tube that’s 45mm in diameter by 610 long and solder the seam.

Roll up the piece of pie to make a cone that’s 45mm in diameter at the top and 200mm long and solder the seam.

Cut a circle that’s 45mm in diameter and solder it to the top of the cone, then solder the tube to the whole thing.  Now you’re a pipe maker – except I didn’t tell you how to cut the mouth or form the toehole.

But Professor Lewin’s adage reminds us that no pipemaker is ever going to be able to cut those pieces of metal exactly 141.37mm wide.  That’s the number I got from my calculator after rounding tens-of-thousands of a millimeter down to hundredths.  You have to understand the uncertainty of your measurements to get any work done.

§

As I take the measurements of these thousands of organ pipes, I record them on charts we call scale sheets – one sheet for each rank.  I reflect on how important it is to the success of the organ to get this information accurately.  I’m using a digital caliper – a neat tool with a sliding scale that measures either inside or outside dimensions.  The LED readout gives me the dimensions in whatever form I want – I can choose scales that give inches-to-the-thousandth, inches-to-the-sixty-fourth, or millimeters-to-the-hundredth.  I’m using the millimeter scale, rounding hundredths of a millimeter up to the nearest tenth.  As good as my colleagues are and as accurately as they might work, they’re not going to discern the difference between a mouth that’s 45.63mm wide from one that’s 45.6mm. 

And as accurately as I try to take and record these measurements, what I’m measuring is hand made.  I might notice that the mouth of a Principal pipe is 16.6mm high on one end and 16.8mm high on the other.  A difference of .2mm can’t change the sound of the pipe that much – so I’ll record it as 16.7.  I know the uncertainties of my measurements.  I adapt each measurement at least twice (rounding to the nearest tenth and adapting for uneven mouth-height) in order to ensure its accuracy.  Yikes!

§

Earlier I mentioned how people who work with measurements all the time develop a knack for judging them.  I’ve been tuning organs for more than thirty-five years, counting my way up tens of thousands ranks of pipes, listening to and correcting the pitches, all the time registering the length of the pipes subconsciously.  With all that history recorded, if I’m in an organ and my co-worker plays a note, I can reach for the correct pipe by associating the pitch with the length of the pipe.

Π (pi) is a magical number – that Archimedes ever stumbled on that number as the key to calculating the dimensions of a circle is one of the great achievements of the human race.  How can it be possibly be true that πd is the circumference of a circle while πr² is the area?  Here’s another neat equation.  A perfect cone is one whose diameter is equal to its height.  The volume of a perfect cone is exactly half that of a sphere with the same diameter.  How did we ever figure that one?

There are no craftsmen in any trade who understand π better than the organ-pipemaker.  When you visit a pipe shop you might see a stack of graduated metal rectangles destined to be the resonators of a rank of pipes.  The pipemaker knows π as instinctively as I can tell that the first millimeter on my ruler is too big.  Imagine looking at a tennis ball and guessing its circumference!

§

When you’re buying measuring tools you have to pay attention to accuracy.  Choose an accurate ruler by comparing three or four of them against each other and deciding which one is most accurate.  Choose an accurate level by comparing three or four of them.  You’ll be surprised how often two levels disagree.  Just as mathematics give us the surety of π, so physics gives us the surety of level.  There is only one true level!

I’ve been showing off all morning about how great I am with measurements in theory and practice, so I’ll bust it all up with another story about van windshields.  I left the shop to drive to the lumberyard to pick up a few long boards of clear yellow pine.  They had beautiful rough-cut boards around thirteen-feet long, eight and ten inches wide, and two inches thick.  Each board was pretty heavy and as they were only roughly planed it was easy to get splinters from them.  I put the first one in the car, resting the front end on the dashboard right against the windshield.  Perfect – the door closed fine, let’s get another.  I slid the second one up on the first, right through the windshield.  Good eye!