Rotola: Setup, Outcomes, and the Future

In early November of this year, over a month ago now, I finished the final assembly on the rotola, completing a design and fabrication project of more than three years.  Whoot!  

After making the bow and fitting the crank, there were some small details to add, the most involved of which was getting the instrument to rotate freely but not sloppily in its cradle by placing felt in the yokes supporting the axle and adjusting the play between the ends.  I also cut a small walnut spacer, like a thick washer, to fit between the nut and the left yoke so as to keep the strings' anchor pins from scraping against the inside of the yoke.  I then added thin felt to the outside of the nut spacer and to the surfaces on the inside of the right yoke, which would contact the face of the cap on the pinblock.  Altogether, these cushions let the instrument rotate very comfortably and silently.  

Next step was to string the instrument.  Following protocol for stringing a gayageum, the Korean zither-like instrument (and its Japanese and Chinese cousins) which was one of the main inspirations for the rotola, I initially attached and roughly tuned the strings without the bridges.  The idea here was to keep the tension across the instrument as even as possible, which is especially important in a cylindrical instrument like the rotola.  Imagine a radio tower, which is essentially a rigid frame held in place by wires pulling radially around it:  if the wires are not pulling equally, the tower could lean, bend, or even break.  Similarly, the longitudinal tension of the rotola's strings should be at least roughly even so as to reduce the risk of warping or, less likely but more problematically, cracking or breaking the instrument.  

With the strings on, I had to find what tension would be ideal.  This was tricky -- and I'm still unsure of the optimum -- as it is determined by trade-offs between desired pitch, length of the string, gage (diameter) of the string, and stiffness of the string.  My initial aurelization for this instrument was as a deep drone, but this prototype is relatively small and therefore necessarily will have a higher base pitch.  Since I had determined the material and gage of my strings based on the length and pitch of the strings on the bowed psaltery, an acoustically similar instrument, its pitch could not be lower than middle C.  Material (steel) and gage (.012") were thus determined.  Length of the string was constrained, of course, by the length of the instrument, but also by another factor which I had not considered previously:  in order for the bridges to transfer their energy most effectively to the body of the rotola, they had to be tall enough for the tensioned string to exert a sufficient down-force.  This, in turn adds tension to the string and, as the bridge is moved toward the one end (in order to maximize the length of the resonating section of string and to find its lowest pitch), this tension increases, such that within a certain proximity to the end, continuing to move the bridge begins counterintuitively to raise the pitch.  Thus, there is a range, surprisingly wide (couple of inches on the rotola) within which the pitch of the string remains roughly stable, despite moving the bridge one way or the other.  This range takes up length of string and so the maximum resonating length of the string ends up being much shorter -- and thus the minimum pitch higher -- than I had expected.  

To illustrate, here is a schematic of the setup (not to scale).  The string runs between the nut and the tuning pin, across the bridge.  The bend in the string created by the bridge presses the bridge down against the soundboard, which allows it to transfer the vibrations of the resonating section of the string into the soundboard.  

If we move the bridge such that the resonating section of the string is shorter, the pitch goes up:  shorter string, same tension, higher frequency.

If we move the bridge in the other direction, the pitch goes down...

... until the angle between the string and the bridge on the non-resonating section gets steep enough to begin to increase the tension in the string significantly, ultimately faster than the lengthening of the resonating section of the string lowers the pitch, and so raises the pitch.  

The end result of this was, as concluded above, that the lowest playable pitch of the instrument was much higher than I had intended because the length of the resonating section turned out to be much shorter than I had counted on.  After much experimentation, I finally settled at F above middle C (F3 or F4, depending on the system you're using).  

The images below show the final assembled instrument and how it is bowed:

All that is well and good, you might say, but how does it sound?  That, of course, is the critical question. Pleased as I am with how it looks (as Bob Emser says, "If you're going. to make it, make it beautiful!"), ultimately, it is a musical instrument and its music-making capabilities are its raison d'etre.   The short version is that it sounds better than I had hoped.  The steel strings, both massive and high-tension, mean it is very resonant, which was a primary desideratum.  The rotola was intended to be a multi-string monochord and tuning it thusly means that its tone is rich and filled with overtones.  It is also louder than I had expected; indeed it has more of a dynamic range than I had hoped.  Overall, its sound exceeded expectations and I plan to have some recordings of it up on my Bandcamp site in the coming months.  

That said, as I spent more time with the instrument, I began to discover some problems, some of which seemed embarrassingly simple, some of which were really interesting.  One issue was that the non-resonating section of the string -- between the bridge and the tuning pin -- was, in fact, resonating and doing so inharmonically.  This was addressed easily enough by weaving a strip of terrycloth among the strings next to the tuning pins; I have some better quality piano dampening felt on order to replace this.  

Another issue was that, as can be seen in the above pix, the placement of the bridges was not as consistent from string to string as I expected; they looked like a set of bad teeth.  I had anticipated that the bridges would alternate closer to and further from the nut in parallel with the tuning pins, as these are staggered for efficiency of space.  However, try as I might to tune the strings without the bridges, once I put the bridges in place to produce an F, their location varied greatly; I still don't know why.  This was not a great problem initially, but as the next -- and most serious -- issue developed, it became at least potentially more relevant.  

The most significant and, indeed, design-changing issue was wolfing.  Bowed-string instrument players are probably most familiar with this phenomenon, although I believe all musical instruments are subject to it:  a string, or more commonly a specific note, refuses to sound or sounds very poorly, instead making a kind of choking sound.  After much experimentation, I discovered that every string attached to a left tuning pin -- those closer to the nut -- wolfed at least a bit.  In the end, six of them were so bad I had to remove them, leaving the rotola now with ten strings in a pattern of two groups of three strings with two sets of single strings in between each (3-1-1-3-1-1).  The two groups of three each have a string with a left tuning pin in the middle, but, for whatever reason, their wolf is very mild and not problematic; it may be noteworthy that these two are on opposite sides of the instrument.  

My working hypothesis for what is causing the wolfing is based on what I know causes wolfing in violin-family instruments:  due to the unique properties of the wood from which an instrument is constructed and the minute imperfections of its construction, any given instrument has frequencies at which it will resonate more readily than others.  (This is not desirable; keeping the frequency response of an instrument as even as possible across the audio spectrum is the goal of any instrument maker.)  These same imperfections will also necessarily make an instrument idiosyncratically unresponsive at other frequencies; this is the wolf.  

I believe that, in the case of the rotola, this effect is exacerbated by its cylindrical construction.  In a violin, guitar, or banjo, the interface between the bridge and the soundboard is concentrated in one place; all soundwaves travel through that spot and propagate freely out across the soundbox from there.  The rotola's bridges, in contrast, are concentrated in a ring around the waist of the cylinder and at least half of the instrument's strings are being played at once; it is plausible that these factors combine to significantly increase the likelihood that a given bridge's vibrations will be interfered with by waves from another.  

Another hypothesis is that the shallow break angle of each string over the bridge (i.e., the relatively low height of the bridges relative to the pins and nut) along with a relatively low string tension means that the downward pressure of the bridges onto the soundboards is weak, making it easier for the two to lose contact as they vibrate together, in turn increasing the chance that they could vibrate at different frequencies and interfere with each other.  

As to why it is just the left-side pinned strings that do this, it could be that the wolf has nothing to do with the placement of the bridges per se, but rather an inharmonicity between the length of the shorter strings and the resonating body.  Whatever the case, removing most of the offending strings seems to have addressed the issue; it may be that a given bridge needs a certain minimum available space on the sounding body in order to resonate.  

That is it for this project and related posts.  I do have ideas about the next iteration of rotola:  I want it to be longer, such that the resonating length of the string can produce at least a C two octaves below middle C (C1 or C2).  As I said, a deep drone was what I originally had in mind.  With the working hypothesis that each bridge needs a certain minimum amount of real estate, a larger diameter seems useful (indeed, I recently discovered a similar instrument which is much larger and grants each string much more room between itself and the next), a greater circumference seems useful, too.  Also, I plan to increase the break angle at the bridge, increasing the contact pressure there.  Additionally, since I had so much trouble steam bending the curve of the cylinder into the sections of soundboard, I am also thinking about carving the sections instead.  Only the future will reveal... 

Thanks for coming along on this journey with me!

Rotola: The Crank and the Bow

When I originally started this project, I had some fantasies about creating my own YouTube channel to document my musical inventions and their progress; it didn't take much experience, though, to conclude that videography entailed much more work than I wanted to do.  Still, I wanted to share my ideas and efforts with whomever might be interested (there are a surprising number of makers of unconventional instruments out there, if widely scattered), thus my decision to include the rotola on my blog.  

However, even doing this has been more of a challenge than I expected, largely because I find it very difficult to manage the split-focus required to maintain a record of my process while I am in that process.  (I increasingly admire the folks who can maintain a video log of their work as they go; indeed, those that share about it say they actually have to focus on making a video first, then on its content.)  So, you may notice that, as my posts have progressed, they have become not only more patchy in their content, but also more retrospective.  I will complete my sharing of the balance of this instrument making project, but in the future, it might make more sense for me simply to post when I have completed a thing; I just can't keep proper track of all of it.  

So, with all that said, here are bits of what I did to make the crank and the bow.  

My initial visualization for the crank was for a relatively straightforward handle attached to a ring that clamped to the axle with a knob at the other end to hold while turning.  I played with several designs for this and all of them either didn't look very good (one of which was vaguely obscene) or weren't sufficiently robust.  After some time, I was struck with the idea that the crank didn't have to be a handle, but could be wheel-like, which solved the problem of robustness and opened new approaches for design.  I came up with several designs I liked, but they were either too difficult to fabricate or did not match the overall look of the instrument.  I finally settled on one that echoed design aspects of the stand:  

The handle would be located near the rim between the cutouts (darkened areas).  I liked this one a lot -- until it struck me that the cutouts looked a little too much like a certain famous cartoon mouse.  I solved that problem by addressing another one:  I hoped to make the cutouts exclusively with drill bits (as opposed to having to hand-draw individual curves)?  You can see the solution in the next pic below.  

To create the crank, I first built a jig that kept the disc blank centered so that, after roughly cutting it out on the bandsaw, I could use the the oscillating belt sander to get the outside edge concentric with the axle hole.  I then mounted the jig and disc on the drill press, where, guided by a printout spray-glued to the disc, I used two different sized Forstner bits to make the cutouts.  

I wanted a chamfer on the inside edges to add interest and make the wheel look thinner.  Here is a shot of that work in progress.  

Workholding took some time to figure out, but, more importantly, I had never done that kind of free-hand, curved chamfering, so I picked which side would be the (less visible) inside and did that one first.  The piece of walnut I was using was pretty brittle and splintery, making it especially challenging for a beginner.  I'm very glad I started with the mostly hidden face, as there was not only workholding and carving techniques to sort out, but also learning which tool to use, how to hold it, and keeping it sharp.  (I ended up mostly using a sloyd knife.)  While the outside came out better, it's still best not to look to closely at it.  

The end result.  The two small dots next to the axle are bamboo pins; I wanted to keep the crank removable, but my local big box store did not have small enough brass screws, so I used some shish-kabob skewers to make a friction fit.  It has worked fairly well so far.  

The bow presented some unique problems.  First, because I wanted it to wrap around the instrument and contact as many strings as possible, it necessarily would not be structured as bows typically are, placing tension on the horsehair to keep it taught.  Instead, it needed to act more as a frame, anchoring the ends of the horsehair strands such that they could stretch around the instrument and press against the strings as they rotated through their arc of travel.  This meant that the horsehair could not be attached to the bow (frame) as it might normally be, using the tension of the hair against the bow to keep it in place.  I would have to come up with some system that both held the hair securely while allowing it to be removed and changed when it wore out, yet do so independently of the degree of tension on the hair at any given time (which would hang loose when not being used).  I had some ideas for how to do this, but testing them would not be possible until after the second problem was solved.  

That second problem was that, in order for the bow maximally to wrap the horsehair around the instrument, it would have to be semicircular.  This presented strength issues, as there is no single cut possible from straight-grained wood in which the grain would follow the shape of the bow closely enough to prevent weak sections across the grain (this problem is called grain runout).  My first solution to this was to glue together three pieces of wood, in this case walnut, to make an arc blank such that the grain more or less followed the curve of the bow; thus no part of the bow would have significant grain runout.  I managed to get two pix of this attempt:

Here you can see the three pieces being butt-jointed together (just glued with no special joinery) to create the blank from which the bow will be cut; the cardboard template is in the foreground.  

This rather blurry shot is the best image I have of the almost-finished bow (it's from the background of another pic).  It has yet to have the attachment points for the horsehair cut into it, but it is otherwise complete.  If you look closely, you can see the joints where the grain direction changes between sections.  

The problem with this design is that, although it is unlikely to break due to grain runout, it actually did break several times -- under embarrassingly little stress -- at the joints, because butt-joints, especially with such thin wood, tend to be fairly weak.  Additionally, I had trouble clamping them properly, which undermined the strength of the glue.  A better solution would have been to have some sort of floating tenon connecting the sections, like splines or small dowels; these could even have been decorative, using a contrasting light-colored wood.  However, for whatever reason (I think I was just impatient and in denial), I did not take the time to do that.  After the sickening sound of the last snapped joint, I threw my hands up and started over with a different approach:  steam bending.  

I liked the walnut from the first iteration, as it would contrast nicely against the spruce of the soundboard, but none of the walnut I had was sufficiently straight-grained for steam bending and I was getting impatient:  by the time I had reached this stage, the rest of the instrument was completed and I wanted to get this project, beloved and exciting as it was, off my bench.  So I let go of my dreams of color contrasts and grabbed a chunk of ash from which I had cut the axle and drew a new design for the bow.  

Sadly, this is yet another bit of the build from which I have only sporadic images, so description will have to do for much of its explication.  Given that eliminating grain runout was now the goal (the bent wood approach would allow it, where butt-jointing only minimized it), I selected the most straight-grained section of ash I could identify and drew a pattern that allowed for continuous grain along the entire length of the bow, all the way through the handle.  After a few iterations, I had one that succeeded at this, looked good, and also took advantage of the curve of the handle to minimize the stress of the bend, which was tight (less than a 4" radius, as you'll see labeled in the next pic).  I milled a blank 10mm thick and then cut the pattern such that the "stick" of the bow would be 10mm square in cross-section.  I then chamfered all four edges of this to make an octagonal cross-section; I wanted to leave the final rounding until after the steaming so that I might have a little extra wood to work with if there were any splits from the bending (this turned out to be a good idea).  

Here is a shot of the bow in the bending frame ("r=95mm" refers to the radius of the form around which it is clamped).  

Here, I've begun to round off the handle-end of the bow, but you can still see the octagonal cross-section of the stick.  

This shows the slot cut into the end of the stick that is intended to keep the horsehair from spreading out too much.  You can also see that the stick is rounded now and the end has been cut in a curved slant.  Eventually, I drilled a small hole roughly perpendicular to this curve and drove a short brass rod through it such that the rod extended a few mm out the other side (opposite the camera view); to this the horsehair was anchored and tied off after a few wraps around the stick.  

Here is the slot at the end of the handle into which the other end of the horsehair would be set.  Once the hair was pulled into it, a shim of walnut was forced in behind, keeping the hair in place; the shim, being a press-fit, can be removed when it is time to change the hair.  

Here is a shot of the shim blank, prior to being inserted and flush sanded to the ash handle.  

Finally, here is the completed bow, finished with shellac, hair installed, and in position against the instrument's strings.  The design ultimately was very satisfactory, allowing good sensitivity in pressure and movement along the strings, important factors affecting the instrument's timbre, while being firm, robust, and fairly easy to hold.  Although small changes might be appropriate for different sized instruments, I expect future iterations of the rotola bow will closely resemble this.  

That concludes my posts about the fabrication of the rotola!  It was a long project and the most complex and challenging I've done so far, but very educational and rewarding.  My final post on the rotola will cover setting the instrument up, small tweaks, and end results.  

The Numinous Atheist

"I took the lamp and, leaving the zone of everyday occupations and relationships where everything seems clear, I went down into my inmost self, to the deep abyss whence I feel dimly that my power of action emanates. But as I moved further and further away from the conventional certainties by which social life is superficially illuminated, I became aware that I was losing contact with myself. At each step of the descent a new person was disclosed within me of whose name I was no longer sure, and who no longer obeyed me. And when I had to stop my exploration because the path faded from beneath my steps, I found a bottomless abyss at my feet, and out of it came — arising I know not from where — the current which I dare to call my life."

-- Pierre Tielhard de Ghardin, The Divine Milieu, Part Two, 2. The Passivities of Growth and the Two Hands of God, pg. 77

I recently reread Bless Me, Ultima by Rudolfo Anaya.  It's even more wondrous and amazing than I remember from when it was a middle-school reading assignment.  The main character, Antonio, a seven-year-old boy growing up in southeast New Mexico during World War II, struggles to reconcile the divergent ways of understanding the world that are pressed on him by his elders with those he discovers on his own.  Mystical, magical, horrifying, and inspiring, his experiences are grist for the mill of his young mind sorting the paradoxes of being human.  The story resonates with me because Antonio's confusion and drive to understand his world describe my own lifelong experience of wonder, fear, and hunger for certainty.  

Some of my earliest memories of my childhood are of moments of what I now call the numinous:  standing on the brick porch entry of my family's Upper Michigan Air Force Base quadruplex apartment -- as mundane a place as any -- and having an intense experience of being ready to die, expecting to be "taken up," even spreading my arms and looking skyward toward ascension.  I was probably four.  At age 10, playing in a stream in the North Carolina backyard of my best friend Beth, I remember a certainty that there was something magical about the place, that we were part of and witness to something bigger than us, something immense and incomprehensible.  As a young man watching the sunrise and writing in my journal as I dangled my legs off the edge of a lava flow atop Albuquerque's West Mesa, I surprised a wandering coyote who didn't see me sitting there until he was just a few dozen yards away; the moments we gazed at each other before he trotted off felt both matter-of-fact and transcendent, a magical space that would endure in my mind for the rest of my life, yet passed as quickly as a sandgrain meteor.  These, for me, are incontrovertible experiences of the numinous.  

Today, I hunger for that numinosity as much as I did as a child and youth, but an entire other self has developed, too.  My father had no room for mysticism, disdaining anything that smacked of magic or even the impractical, so I was taught early on that such ideas were for fools and, thus, if I wished to be anything other than a fool, I needed to eject these notions at their first showing.  Was it provable?  Demonstrable?  Repeatable?  If so, it might have merit; beyond that, it belonged in the trash bin of the gullible.  My father was not harsh, but he had a way of conveying disappointment that made clear my childhood fascination with ESP and spells and hexes was worthy of shame.  The most devastating blow to my obsession came in sixth grade, when a group of classmates conspired to convince me that one of them was brilliantly clairvoyant and the teacher, rather than interrupt their cruel joke and admonish the conspirators, simply rolled her eyes at me and let them play it out until I was utterly humiliated.  After that, I basically exiled my numinous and mystical self.  

Instead, I came to worship the empirical.  Without knowing it for what it was at the time, I took up the skeptics' great question:  how can we know what we know?  What can we learn with our imperfect and incomplete senses?  How can we augment our senses or account for their imperfections?  Given that, even with such augmentations or accounting, we nonetheless process all information with limited minds, how can we know if there is even anything "out there?"  Am I the only being in the world, the rest an illusion (the solipsist's conclusion)?  This makes no intuitive sense, but then can I trust my intuition?  

After years of such wandering, rejecting the numinous yet being unsatisfied with the empirical alone, my undergraduate studies in epistemology and skepticism helped me find a happy, workable (while still imperfect) solution:  there is a world "out there" and, although we cannot know it perfectly, we can know enough about it to operate effectively in it.  Indeed, there are ways that we can work to make our knowledge ever less imperfect and these ways are called science.  

Today, I am a trained scientist, an empiricist, materialist, and practical skeptic.  I do not believe in the existence of god(s), the spirit or soul, nor, by extension, ghosts (spirits with no body) or zombies (bodies with no spirits) and their ilk.  At the same time, it feels wrong to invalidate and shame others who do believe.  Moreover, how do I reconcile my own experiences of the numinous?  Again, my father, unwittingly perhaps, pointed me in a useful direction:  wonder.  As an engineer and a true geek's geek, my father had that childlike, "gee-whiz" excitement when it came to the sciences he studied and the gadgets he built.  His commitment to the empirical was not absent of wonder and, indeed, wonder drove all of his passions, whether flying airplanes, studying advanced mathematics, building race cars or personal computers (before they were a thing), or touring the Great Parks of North America in a 1961 Greyhound bus he converted himself.  Perhaps wonder is sibling to the numinous.  

Even after being shamed and argued into rejecting the mystical, I never stopped having mystical experiences.  In my late 20s, after I broke up with a woman I thought was my One Great Chance at True Love, I spent a (completely sober) day and night filled with music and visions, following a call that ultimately led me crashing nude into midnight ocean waves on an empty city beach, feeling that an old skin was being beaten off of me.  In my late 30s, following the birth of my daughter, I went through a period of introspection and transformation that changed the course of my life, a deep dive into religion and art that ultimately led me to becoming a psychologist.  Change and clarity arising from I know not where have punctuated my life, leaving me convinced in the moment that I am a mere vessel or conduit for some greater power.  

In studying the human brain, I've come to understand that such incongruous experiences have their origins in the fact that the conscious mind is but the thinnest of veneers over the vastness of the psyche:  the consciousness that the brain produces is but a fraction of its output and its greatest products appear to be outside conscious reach -- perception, identity, meaning, even decision-making.  Thus, what some people call God or spirit -- the experiences I call numinous -- likely, in my empirical cosmology, arise from these deep workings of the mind and brain.  Yet, that explanation of their origin does not make them less wondrous -- or numinous.  

Now as ever, I strive to stay in touch with the numinous in my life.  The breathtaking spectacle of the sugar maple in my autumnal backyard, the shivering insight that melts from a patient's face down through their body, the bottomless space beyond the planets on a moonless night, the derealized moment when a tarot card reveals its meaning, the joy and wonder in the eyes of loved ones, the sudden Knowing of a personal Truth, all these are part of it.  The numinous is a human birthright, from wherever it springs.  Christianity, Judaism, Islam, Buddhism, Taoism, Paganism, Wicca, spirituality, science, all of these are ways of explaining the how of our experience, but the what cannot be denied.  

I honor your numinosity as I honor my own and I wish for all humans to be in touch with theirs, however that may occur.  

Rotola: The Bridges and the Stand

 In my last post about the rotola focusing on the construction of the nut, I included an overview of basic string instrument construction; for review:  

In this post, I'll focus first on the other end of the resonating part of the string, the bridge, and then on something unique to the rotola, the stand on which the instrument rotates.  

The rotola has 16 strings and each string has its own bridge.  Here's a drawing of the bridges' front and side views:

They are not big, about 18mm high and maybe 6mm thick at the base and ~1.5mm at the top.  I decided to make them out of purpleheart, of which I have a large chunk.  I like the wood a lot, although I don't often use it, as it's really difficult to work with due to its extreme hardness and density; however, those same properties make it good for this application.  Additionally, while I have some hard maple, which is a more typical wood for string instrument bridges (particularly the violin and viol families), I wanted something that would contrast visually with the spruce of the soundboards.  

Fabricating these would be a challenge:  I needed to make at least 16 of them (spares would be nice, too) and they needed to be uniform and precise (note the curved base that fits exactly on the soundboard), plus, being small, they are hard to hang onto while working.  After much thought, I figured a way to make them from a long strip as a starting blank.  I could plane the strip at an angle along one face, then, supporting the planed side to keep the centerline correct, plane the same angle along the other face.  Next, I would mark out the width of the bases using a pair of dividers and then sand the correct radius between those marks.  Finally, I could saw out the rough triangles and clean up the sides using sandpaper on glass and file the notches for each bridge's string.  This more or less went to plan, although I mades some mistakes while working it out and had to start over.  

Here are some views of the process:

The purpleheart blank after it was cut, milled, and planed to size as precisely as I could make it.  

Two views of the jig I built to run the blank through the surface planer:  

For the second run (which I neglected to photograph), I had a shim with same angle as the cut, so the second side would be held at the same angle as the first going through the planer.  (For my first attempt at this, I used a hand plane and struggled to get the angles correct and consistent; the above success was due to having purchased a surface planer.) 

This is the setup I used to cut the radii into what would become the bases of the bridges.  The wheel is cut from 1 1/2" MDF (actually two 3/4" pieces glued together, leftovers from another project); I cut it initially on the bandsaw and then rounded it against the oscillating belt sander by rotating it on a fixed dowel inserted into the center hole.  I then stuck 120 grit sandpaper to the edge using spray adhesive.  I was able to raise the work surface by cutting some 1/8" plywood to fit around the disk and clamping it to the drill press table; this prevented leaving a ledge of unsanded wood where the bridge blank might slip under the spinning disk.  The setup worked fairly well, being only a bit off of parallel to the table.  

Here you can see the scallops made with the sanding disk.  

Next step was to cut the bridges out, which I did using this jig (left) and a pull saw.  The vertical piece of the jig had a magnet embedded in it to keep the saw at the correct angles (defining the side of the trapezoid and keeping the edge square to the centerline).  This also worked fairly well and you can see some of the cut bridges in the cup at center, but, unfortunately, I seem to have neglected to get any close-up pix of the finished bridges; you'll see later how they fit onto the instrument.  

Next, I went to work on the stand for the instrument.  As it is intended to be played by a single person, cranking with one hand and bowing with the other, it needs to be supported at the axle ends so that the pins and bridges have clearance from the stand, but not so high as to raise the business side -- the strings rotating across the top -- inconveniently high.  The simplest design would be some basic yokes at the ends and a plain platform spanning between them; however, I wanted the stand to be a part of the presentation and be attractive enough to compliment the instrument.  

I started out by hand milling down a large piece of fairly warped but beautifully figured walnut given to me by a friend.  This was before getting either a jointer or a surface planer and became an exercise in confronting my amateurism, ending with turning most of a 6/4 piece of wood into sawdust or shavings; you can see the resulting piece in the middle of the bench, below -- it's less than 5/8" thick.  

The two square pieces with holes drilled in the center will be the end supports.  These were resawn from 3/4" pre-milled stock and so was much less disastrous.  

I spent quite a bit of time experimenting with different designs before settling on these profiles.  

After routing roundovers on the stand's components, I rabbet-jointed them together with glue; I did not want any hardware or dowels showing.  Next, I cut two knees for each end to add strength to the joints.  

Here you can see the knees being glued in place.  

In the end, the joints were plenty strong enough and I am very pleased with the overall appearance of the stand.  

Notice that the left-hand end of the stand, for the nut-end of the rotola and over which the bow will rest, has a longer squared end than the right (below).  This is because, at the time, I was still considering anchoring the bow at the left end and making a hinge so that the bow -- and presumably some weight -- could rest on the string and not require a player to manipulate it; the hinge would connect to the stand somewhere along that straight edge.  I have since changed my mind on that bow design, but I still like the asymmetry.  

The right-hand end of the stand.  

Again, I neglected to photograph the finishing process, but the results will be seen in later posts when the instrument is fully assembled; it looks pretty good.  

Next post I will cover the fabrication of the crank and the bow -- and then it will be done!

Rotola: The Nut

So far, I've talked about the rotola's construction fairly idiosyncratically, discussing what I'm doing as I'm doing it, but, apart from sharing pix of the original design, I haven't contextualized what I've done within the instrument overall or within the principles of chordophones generally.  We're coming to a point where a little of that background might be useful.  

On most stringed instruments, the string runs between two anchor points that keep the string in tension and across two contact points that define the length of the resonating section of string.  Thus:

Note that the  contact points are by definition between the anchor points.  This is true of all stringed instruments in one way or another, with variations in how their different jobs get done.  

There can be some further specialization, however, within these jobs.  One of the anchor points will usually have a mechanism for adjusting the string tension and one of the contact points usually has the additional purpose of transferring the vibrations of the string to a resonating body.  We name these different points according to their roles:  

The anchor point responsible for adjusting the string tension may be called a tuner, tuning pin, tuning peg, etc.  The anchor point that holds down the other end of the string, usually immobile, is sometimes called an end pin (in some instruments, instead of a pin, there is a hole into which a thickened part of the string catches).  The contact point that transfers string vibrations to the resonating body is usually called the bridge and the contact point that holds the other end steady is the nut.  Most string instruments have some version of all of these, although sometimes a piece might do more than one job, as in the bowed psaltery, in which the end pin also serves as a nut.  The most important job of the nut is to provide a solid point against which the string can vibrate, i.e., by being a rigid surface, it inhibits the string's movement as minimally as possible.  (This property is necessary for the bridge, too, but I would say it's first job is to transfer sound to the body.)

Whether the bridge and the end pin are located at the same end of the instrument or not is usually dictated by the structure of the instrument and how it gets played.  In violin, viol, and guitar family instruments, for example, the tuners and the nut are usually near each other and the bridge and end pins/holes are together at the other end.  But it can be the other way around, which is the case for the rotola:

More precisely, per my initial design:

So, as you can tell from both the end of the previous post as well as the title of this one, I'll be talking here about the design and fabrication of the nut.  

Despite the octagonal cross-section seen in the above initial design, as discussed elsewhere, I decided as I began to build the instrument to aim for a cylindrical shape instead; thus, the nut will need to be circular as well.  However, the grain of the wood comprising the nut, in this case walnut, will need to run perpendicular to the strings it supports.  As no trees grow with the grain in a circle (growth rings don't count, as the fibers are still longitudinal), the nut will have to be assembled similarly to the pinblock -- what I came affectionately to call pizza slices, as I struggled to get yet again perfect 22.5° cuts.  Using a bandsaw, this is tricky:

The one on the left, you see the cuts are too shallow and on the right, too steep.  These are just two of my many attempts to get the jig set right using scrap wood.  In the end, I finally got one close enough:

You can still see some small gaps, artifacts of having to use the oscillating belt sander to get the angles just right, but I had wasted a good deal of wood already, and my tools and my skill with them were not going to let me get more precise than this anyway, so I glued it up:

Next step was to round it off, which entailed first circularizing the center hole and then using that as a pivot to do the same with the circumference.  

I spent quite a bit of time laying out and fashioning a jig that would allow me to center and hold the nut on the drill press; unfortunately, I neglected to capture that work, but here is a shot of the completed center hole with the nut correctly placed on the jig:

The slots in the frame allow the jig to be bolted to the drill press table; the alignment marks have complements on the table and those on the nut then line up with the jig.  Using this system, I was able to place the 3/4" blade bit precisely in the center of the inner octagon and make a perfect pivot hole.  It's amazing what good marking up can yield.  

Next was to make a jig for circularizing the outside of the octagon.  Using a scrap bit from a practice axle, I set up a way to hold the nut firmly in place on the table of the oscillating belt sander sufficiently precisely at the radius I wanted:

The long edge allowed me to keep the whole thing square, which was the key to controlling the radius (from the center pin to the sander face).  Thus:

I was very pleased with the end result:

In working with the walnut thus far (this was the first part of the rotola that used walnut), I began to realize that, while it is a relatively hard wood, it's not as dense as a nut really needs to be.  My original plan was that the strings would be supported directly by the nut, draping across its edge (as you can see in the third figure, the one labeling the various string supports), but I began to think that the walnut was just soft enough that it could have a dampening effect.  Given that the rotola's strings should be highly resonant in order to create the sound I aurelize, this was a risk I was unwilling to take.  

I played with several ideas for solutions, including remaking the nut with ebony or maple on its edges or even fashioning a new one out of those materials.  However, in the end, I took inspiration from the bowed psaltery, which has a slim bar of brass on its bridge.  Brass is hard enough to support the steel strings rigidly, malleable enough to work with in a woodshop, and looks good, too.  

Having procured some 1/8" brass rod from my local Big Box Home Store, the next step was to mount it onto the nut's edge, most simply by cutting a groove into it.  As with much of this project -- indeed lutherie in general -- this would require making a jig.  Fortunately, I needed only modify the one I'd made to circularize the nut, standing it on its edge and mounting it to the router table.  After some trial-and-error, I came up with this:

A v-bit in the router could be raised (via the black and yellow handled adjustment shaft on the left) into the edge of the nut, then the nut could be rotated on its axle, creating a fairly straight and even groove.  Both the axle and the router bit are seen better from the below angle (seen from the other side of the fence): 

I was pretty happy with the result; it's not perfect, but more than good enough for a proof-of-concept:

Next, I wanted to taper the outside edge, giving a smoother transition for the strings on the end pin side (outside) of the nut.  After more trial-and-error, I came up with a setup that would allow some consistency:  

The rounded nut (here a practice scrap) rests on the bench, with a bench dog through its center hole (serendipitously the same size as the axle), then a guide keeps the plane at the same distance -- and thus the same angle -- relative to the nut; counting strokes and rotating the nut the same number of degrees as I worked my way around helped me rough in a taper:

These large facets (seen below in the nut itself) were smoothed by making smaller facets in between:

These were then blended and rounded over with sandpaper.  

Next step was bending the brass rod.  I expected that, in order to get a good fit, the rod should be wrapped around a cylinder that was somewhat smaller in radius than that nut itself, to account for springback.  I made a form, which turned out to be too large, then a smaller one -- 

-- which was still too large.  Rather than continue to make circles out of wood, I decided to look for ready-made cylinders, like cans of finish:

-- which turned out to be just right.  

I got the brass rod to a rough fit, cut it, and then taped it to the nut to see a) how well it would sit in the groove on the edge of the nut and b) how much pressure from the strings would be required to get it to sit straight and evenly in the groove.  

You can see some of the wobbliness, especially in the lower of these pix.  Masking tape was capable of holding the brass down fairly strongly, but I'm unsure if the strings (even considering that there are 16 of them) will generate enough power to keep it firmly in its slot.  That said, I decided those were problems to resolve another time and I needed to keep going to finish the nut.  

The last fabrication operation with the nut would be drilling the holes for the end pins.  This would require some accurate marking out:

Here, you can see I started by marking out the radii at 1/16th circumference (or 22.5°) arcs.  I'm using the seams between pizza slices as references, which, in turn, I will match up with the seams in the soundboard slats; this will then allow the end pins to line up perfectly with the tuning pins, which were also drilled in with an analogous method at the other end of the instrument.  Then, returning the nut to its jig, I used a compass to draw circles at 15mm and 20mm from center.  These intersections I then marked to indicate alternating drilling points, like so:

The places with the hash marks (or crosses) are to be drilled.  I drilled a few test holes in some scrap to see which of the candidate pins would work best (I had several ideas:  brads, screws, etc.) and settled on brass-plated twist brads (no pix yet; to be revealed later).  To keep the alignment consistent, I returned to the edge circularizing jig (the one I used on the oscillating belt sander and the router table), now mounting it onto the drill press and tipping the drill press bed 5° to give the pins a tilt away from the direction of the pull of the strings.  After drilling the holes, I ended with this: 

And that is as far as I'm taking this blog post.  I have since cleaned up the markup pencil and begun pre-finish sanding on the nut.  Still remaining for the nut is to be glued to the body, which I'm holding off on only because I have this nagging feeling that I'll regret it if I'm too hasty, and for the brass rod to get a final fitting (i.e., hand-bending to get as nearly perfectly circular as possible) and possibly to be glued (epoxy? cyanoacrylate?) in place.  

Next post I plan to be about the bridges, which I have just begun to experiment with.  After that, there will be very little left of the complex, inventive parts of this build:  I'll need to make a support for the instrument (basically a couple of Ys to hold the axle), glue up whatever isn't yet glued and apply a finish (very likely shellac), put the strings on and tune it, and make a bow (the design of which is still unclear).