developing an idea

 I haven't posted in an age, but I felt like doing a post that shows how my ideas sometimes grow and develop.  A while ago, I decided to step back from making a new piece, and just focus on finding 2 types of workable units for my work.  What I wanted to find was octahedrons that would have adjacent faces at right angles to one another, i.e.where the overall shape of the oct would be a rectangle.  That way I could have a chain of octs that would be a straight line.  The 2nd shape I wanted was octs that would make symmetrical

trapezoids.  That way you could make an oval shaped necklace by using the rectangular octs for the long straight sides and trapezoidal ones for the curves at front and back.  I came up with several of each that I could make with the lengths of tubes that I cut, and I am amazed at how many times I've gone back and used the units I came up with.  But also in the course of doing this, I happened on an oct I could make where 3 of the sides  formed the angles I've pictured--a right angle with an adjacent 45 degree angle.  This meant that eight of them joined at the 45 degree angle would make a square, one with a sort of star shaped center.  You can see it at the center of the 1st necklace shown.  Also one of my symmetrical trapezoids had an angle of (roughly) 60 degrees between the 2

angled sides, so 6 of them made a circle (actually more of a torus, as the center is open).  I really liked having these 2 regular shapes.  But I thought I could accent the geometry by using some gold tubes in the middle layer of each shape.   That way there's a silver square and circle (hexagon actually, but it reads as a circle) and a gold triangle and diamond.That's necklace 2 and I thought it was an improvement. 
  I wanted to make a pendant of the square shape, but I wanted it to be bigger than what I had.  The square I had so far was a bit over 2" on a side.  But I found that if I turned it 45 degrees so it was a diamond and then added 2 right angle tetrahedrons on each edge I'd get a square that was almost 3" on a side, which was more like what I wanted. I also changed the arrangement of gold tubes, putting them on the inside star shape and on what used to be the outside edge, but was now an intermediate diamond. 
  Finally, I wanted to make a whole necklace using the square as the focal point, but I wanted to go still bigger.  As I've worked out the tube lengths that I want as stock units, I've

found that lengths that approximate multiples of the square root of 2 are useful.  So since my smallest length is 10mm, I'd ideally want one of 14.15xxx...mm, then 20mm then 28.3xxx...mm then 40 mm.

Obviously my tube cutting jig and ruler will only approximate that so I use 10, 14, 20, 28 and 40mm.  In between those I have another series that's 12, 17, 24 and 34mm. Again in an ideal world the 2 series would fit together so that the relationship between each length and its neighbor would be the same, i.e. 12/10 would be the same as 14/12, 17/14 etc.  If that were the case you could come up with a shape, and then you could scale it up or down and it would work at any place on the series, just the way that in music a melody stays the same as you move it up or down an octave ( or a fifth or whatever). 

As I've said, my ratios are close, but not exact, particularly between the 2 series.  So it took a fair amount of trial and error, but I finally found that if I scaled everything up 1size on my tubes except for one on the outside that I left the same, I could make a square that was the size I wanted, almost 3.5" across. Then there was a fair amount of trial and error to get a good curve that got gradually smaller so as to not be too bulky in the back, but I'm really happy with the result, and with all the steps along the way as well.

another mathematical rabbit hole

     I've been having fun playing with a new area of mathematics.  Up to now my explorations have had to do with building polyhedra.  But I do look occasionally at Kate McKinnon's peyote stitch based work done in seed beads. Under the heading Contemporary Geometric Beadwork, she's produced several books, as well as lectures and lots of other stuff.  I admit I don't have the books.  Since I don't do peyote stitch and I no longer do seed bead based work, I thought lots of it wouldn't apply to my work.  But I do look at the pictures of what she and her group do, and find it quite interesting (as an aside--since the people who read this blog are mostly beaders with a mathematical bent, if anyone knows which of the books in the Contemporary Geometric Beadwork series would have a good coverage of the theories for someone who doesn't actually do peyote stitch with seed beads, I'd love a recommendation). I've often thought I should play around with the hyperbolic plane that she uses. She calls it a warped square, and it's made of 4 triangles.  If they were right triangles it would be a flat square but since the "hypotenuse" is longer than it would be in a right triangle there's more perimeter and the structure isn't flat.  It has always seemed to me that my way of making triangles has much more flexibility than the peyote stitch way.  It seems to me the shape of her triangles is determined by the shape of the seed beads--the relationship between the height and the diameter of the bead used sets the shape of the triangle.  In that way I have much more flexibility. I can  cut any length tubes and get whatever triangle I want.  Of course it's also much faster, but on the other hand I can't do the great stuff with colors and patterns that she can.
   Above is a single warped square made into an earring, and another earring with 2 of them.  I said my way of working  gives me more flexibility, but on the other hand my "stock" lengths are sort of set to be able to build right triangles. For example, I cut lengths of 10, 14, 20, 28 and 40 mm. Each one is more or less the one before it times the sq root of 2. So 10/10/14 makes a  right triangle ( or would except that the sq root of 2 isn't 1.4 but 1.4xxxx to infinity), as does 14/14/20 or 20/20/28 etc.  I also do 17, 24 and 34mm lengths, which fill in the gap and work the same way.  But to jump to 14/14/24 makes a very warped square,
(similar to what's in the earrings, which use triangles of 10/10/17) and more than I wanted.  So I decided to try making squares where just one of the outer edges was 24 and the rest were 20s.Here's a double row of these squares.

I liked it, and thought it could make a good bracelet ( you can see on the left end an additional structure I added where I could put a clasp). But there was 1 problem.  There are 2 versions of the square.  If you arrange the "plane" so that the tube on the bottom is horizontal, the tube on top can either go from high on the left and low on the right or vice versa.  Since the triangles are theoretically rigid you can't change it once it's made. In this way it's different from the peyote triangles which are inherently flexible. In the top pic I arranged the squares so that each is the mirror image of the ones beside it, which is the way it would have to be for a bracelet.  But since the hyperbolic-ness ( hyperbolicity? no idea what the proper word is) is fairly minimal, if you push on one of the high points in the center of the structure you can flip it, and then it turns into pic 2.  You can just as easily flip it back, but a potential customer wouldn't know that and I didn't want to get bogged down in long explanations. So I changed it, making essentially warped rectangles, where the outside edges were 2 20s and 2 24s.  That made the bumpiness more extreme and hence more stable. 
   I also tried a structure where the warped squares didn't go back and forth between the 2 versions, but were all the same version.  That made the warping spiral.  That's the last picture, but you can't see what's happening very well. In order to make it work, I'd need to replace 1 tube in each square with a gold or colored one so that you could see it spiral around.
  There's another way to make a hyperbolic plane. Instead of adding length to the tubes that make the perimeter of the structure you can add an extra triangle, i.e, where 4 right triangles would make a flat square, 5 of them would make a hyperbolic pentagon.  That's the sort of structure that will get progressively more wavy in the way of a lettuce leaf.  But doing it with 5 right triangles was too extreme.  Each pentagon was very non-flat. And if the first row had n structures the next would have 2n, and then 4n etc.  Again too  extreme and fast a progression.  I did it several years ago (you can see it in a post on hyperbolic planes from that time) using equilateral triangles, and where 6 would make a flat hexagon, 7 makes a hyperbolic heptagon. And each row will have 4 units for every 3 units in the one before, so the progression is still fast, but not so very fast. I really liked the one I did in colored glass beads back then, but had some trouble with the glass cutting the thread. I'd like to try one in silver tubes, possibly bright silver, but haven't gotten it done yet. 
  

new piece after a hiatus

   It's been quite a while since I've posted anything here. First there were 2 months on a canal boat in England. Then I came home at the end of October to the aftermath of hurricane Michael.  By the time I got back to Panama City the roads were mostly clear, and we had power and water.  But our house, though liveable, has holes in 1 wall which are only covered with plastic.  Also until a week or so ago we didn't have internet, except for slow data on our phones.  Finally, my computer crashed, taking with it all my jewelry pics as well as the copy of Photoshop that I had used to edit them.  So I've had to learn to use Gimp, which is open-source.  I'm pretty sketchy at it, but I finally got a picture of a piece I like.
   I decided to think back over the last 4 or 5 months, pick my favorite piece from that period, and post a picture of it.This is it.  It's done mostly in RAW ( I guess it's technically CRAW, but since that's the only kind of RAW I ever do I don't usually specify it).  But I wanted to break it up, make it less regular than I usually do in my RAW pieces, and I was quite pleased with the way it came out.  I hope you like it. As I get more pictures "gimped" I'll try to post some.  It feels good to get back to normal in one more way.
 

some new bracelets, and a technical advance

Just finished some new bracelets, and I like them a lot.  It also provided a start of a solution to a technical problem I've had with bracelets. 
  Up until recently, I have sort of avoided bracelets for several reasons.  One is that I don't wear them myself.  Like most everyone else, I start out by making something for myself, and I've just never been a bracelet wearer.  The second was the lack of a good clasp.I've written about this before, but I've finally found 2 clasps that work for me and don't use up too much of the bracelet length.
    It still left the major problem with bracelets--they have a very narrow range of usable lengths.  The difference between a 7" bracelet and an 8" one is pretty big.  When you are making modular structures, as I usually am, if you come out too short, you can't just add another module, or you'll be much too big.  Over time I've found out that 10 modules using 20mm lengths or 6 modules using 28mm lengths make a workable length when a short clasp is added.
    Now about the bracelets shown here--it started with the idea of a common Brancusi structure which is column with a square cross section that alternates small and bigger waists.  He did that a often and I wanted to reproduce in in a RAW structure.  My first attempt failed, because since my structures aren't rigid the way a wooden column is, they tend to straighten out on one side or another unless you exaggerate the in-and-out-ness quite a bit.  As you can see, the top bracelet is more exaggerated than the bottom one, but both of them work pretty well.  What I discovered, though, and thought was pretty cool, was that because of the zigzaging in and out on the inside of the bracelet, which is there when not stressed, but can go away if you push on it, the bracelet fits comfortably on a small wrist, but will also accommodate a larger wrist by straightening out the zigzag.  The outside distorts to allow that, but it looks fine either way.  Pretty cool. 

new work and galleries

I thought I'd do a post of what I've been up to lately.  Another piece where individual structures are interlinked to form a chain. For each link, I made an octahedron out of gold filled tubes, then added 8 long oxidized silver tubes to form another octahedron on the outside of it.  It took a while to get it right because so many tubes were ending at the same place.  Eventually I added a small round silver bead to separate the outer oct from the inner one, and that seemed to make it work.
The other thing I've been working on this summer is getting my work into galleries.  I traveled around and talked to places, and I've gotten a few new ones, so if you're in any of these areas, I hope you'll stop by and take a look:
Albuquerque--Mariposa Gallery, 3500 Central Ave, mariposa-gallery.com
New Orleans--Ariodante Gallery, 535 Julia St, ariodantegallery.com
Chicago--Pistachios, 55 E Grand Ave, pistachiosonline.com

new collar with gold

I love this piece!  A few posts ago I talked about using some long beads on the outside of one of these collars and how it made the outside edge scallop. I had done it with stone and marble beads and didn't like the mix, but mentioned I might do it with gold tubes. Just finished this one and I really like it. I'm doing more these days with the gold (actually gold-filled) tubes as accents. and I think the contrast with the dark silver really works. For my own use, I mostly stick to the plain oxidized silver pieces, as they're less dressy, as is my lifestyle. But I do like making these silver and gold pieces. They tend to be simpler, and less funky, because when I piece has lots of different shapes and structures, then I think the contrasting color is  distraction.  But it makes a more classic piece pop.
By the way, after writing the earlier blog post about this structure, I forgot to read it before making this piece, and so had to redo it  after getting around 1/3 of the way around.  In the post the dark tubes were 28mm and the stone tubes on the outside edges were 20-35-20.  In this one I started out using all 28s except for the long 35mm ones on the outside, so no 20s on the outside.  That made the outside too long relative to the inside, so it curved was too tightly to fit your neck into it. So I changed the inside tubes to 31mm.  It's still a pretty tight circle.  If I wanted it a bit longer, instead of round, I'd make2 of the inside tubes in each side 35s instead of 31s.  That would add a bit more length, but mostly it would make the curve shallower at that point. There are 12 inside tubes, so I'd change 3,4, 9 and 10. Actually I might just change 3 and 10 (talking to myself here) because you really want to do it when the line of the necklace is 90 degrees from the center point, so you're making it just longer, not wider.

playing with tube lengths

This is a post that, more than most, is just me talking to myself to remember something, because it's about a piece I started to make, but don't like too much and plan to take apart.  I've always liked the piece pictured first.  It was made with 25mm tubes and quartz beads of around 20mm.  I recently bought some malachite beads that are a sort of pinkish tan, and wanted to use them on the outside edges, but I wanted to use 28 mm silver tubes everywhere else. This was partly to make the piece a bit bigger, and partly because I 'm low on 25mm tubes just now. But I found that that combination of lengths made a curve that was way too shallow (obviously, the tightness of the curve is just a matter of how much longer the outside edge is than the inside edge).  The outside edges consist of 3 beads in a sort of a straight line and then and then a shift to a new angle. So I went back and put a long(35mm) marble bead in the middle of each set of 3, in place of one of the pink ones.  I liked the way it made the set of 3 curve, so you get an interesting outline, as you can see in the bottom picture.  But I didn't like the 2 colors.  Too jumpy.  If I'd used all 28s on the inside I was headed toward a piece that was about 21" on the inside and 26" on the outside.  No Pythagorus here, I just laid it on top of a salad plate and the outside curve was pretty close to the outside curve of the plate.  A saucer (21") fit the inside. That seems pretty big, so I needed to shorten the inside edge some more.  I tried substituting a 20mm on the inside, but you have to do it in pairs, and 2 20mm tubes would have made the curve too tight (there's one 20 in the sample).  It looked like the curve with all 28s would have led to a piece with 9 units (maybe 8 and a clasp).  If I'd used all 25s on the inside that might have worked.  Or, to get a more oval, less round shape, 28s with 4 25s, to sort of make 4 "corners".  You could do it with gold tubes on those outside edges, and it would be pretty interesting too.

Another neckwire piece

I liked playing around with shapes on a neckwire a few weeks ago, so I thought I'd try another.  I think the rectangles with gold zigzagging down them worked well.  makes for a pretty wearable piece, as well as an attractive one.

Developing an idea

 I've been making lots of pieces like the first one here: repeats of a structure like an oct, separated by biggish stone beads.  And I've varied it by using different structures, but always a repeat of the same one.  I've wanted to do 2 things--eliminate the beads and vary the structures.  Leaving out the beads means you don't have the color limitation, i. e. you're not limited to wearing it with an outfit that goes with red. There are 2 ways to do this.  One would be to put a closed ring between the octs (or whatever structures) Or they could interlink directly with one another.  Here I interlinked them. It means that you need to build more structures, as they overlap, but it makes the design tighter. I like this one, and I think pretty soon I'll make another one with the pentagonal shapes done in gold filled beads.
   As with most of my ideas, I start out being rigidly symmetrical, and then later I play with the idea in a freer, asymmetrical way.  Picture 3 shows me doing this design in that way.  I think its my best one so far.  I also think adding the gold makes the piece more interesting, without limiting the colors you can wear it with.  Now I'd like to extend that more asymmetrical, more random approach to some of my very structural pieces.

A new inspiration

 I was looking at the current issue of Metalsmith magazine the other day.  They had an article about Betty Cooke, who's been a well known jewelry designer for decades now.  Besides loving her work, I'm interested because my niece Kate has worked for her off and on for several years at her shop, The Store, Ltd., in Baltimore.  Anyway the piece shown here is one of her better known pieces, and I've seen pictures of it before.  But the magazine picture was bigger, and I noticed that there are silver tubes over the neckwire at the bottom to control the spacing of the oval elements.  That got me thinking, and luckily I have some tubing large enough to go over 16 ga. wire.  Of course for me the tubes would be part of structures of some sort.  After playing for a while, I came up with the piece below.  I'm pretty pleased with it, although it's not quite as clean and minimalist as the other one.Actually, thinking about a more minimalist look, I experimented with what it would look like if I had left out the 2 small diamond shaped pieces that ard between the 3 larger pieces.  What I did was to take my photo of the necklace and photoshop them out to see what It would look like.  The photoshopping was really crude, but it did give me an idea of what it would be.  I decided I liked it better the way it is, but it was an interesting experiment.  I'll be doing more with this idea.

changing necklaces

This post is essentially an addendum to my last post.  I've done a couple of art festivals in recent weeks, and I'm reacting to some problems that showed up.  Basically, I tend to size things to myself.  I have a pretty small neck, so that means that what I think of as a short necklace is actually too short for lots of people.  For starters, the necklace I just wrote about, the one with octahedra and floating pearls--as I said, it was based on a necklace of 22 octahedra, but, because I was running out of 25mm tubes, I made this one out of 20 octs. Then I made up some of the lost length by making the tets at either end longer.  Mistake.  I've now redone it with an extra oct at each end that ends with a 14mm equilateral triangle to get some taper.  That gets us back to 22 octs, and I put a 20mm tet at each end.  Even for a small neck, it's a better size.  Then, to accommodate larger people, I added a 2" extender chain.  I'm going back and adding extender chains to lots of my necklaces.

I've also had a tendency to continue a structure or pattern right up to the hook and eye at the back, without any taper or change of structure.  This one is a good example. I look at it now and say "What was I thinking?"  It makes a good picture, but when you put it on there are these big elephant ears poking out  in back.  They don't want to lie flat the way the ones in front do, and they're just awkward.  More redoing.

octahedra and pearls

  Recently I bought some pearls with holes big enough to slide them over my tubes.  I decided I wanted to make a neckpiece that was a simple series of octs, ornamented by the pearls.  I had made a similar structure using bright silver and colored aluminum tubes a few years ago, and wanted to repeat that structure.  So I went to my handy blog, where I keep track of my structures.  Here's what I found, from August, 2014:  "It's a simple chain of octahedrons.  But a chain of octahedrons would normally form a straight line.  In order to get the curve you need for a necklace I had to make the triangle on the outside edge longer than the triangle on the inside edge.
Here's where some trig would have come in handy in figuring out just how much longer, but I managed to figure it out with "lesser" math, and it came out right."
  It would have been really handy if I had written down just what the lesser math had given me so that I could have reproduced the shape.  That, after all, is one of the main reasons I write this blog.  Since I didn't do that I started and ripped apart the new piece over and over trying to get the curve I wanted.  As you can see I didn't get the same curve as last time; it's a little pointier at the bottom and straighter across at the back but I like it OK.  It's also just a bit shorter.  That's only because I was running out of 25 mm tubes, so I did just 20 octs instead of 22.  Then I made the 2 tets at the back by the clasp longer.  Also I now make my own hooks and they're longer than the one I used in the earlier piece.  So the overall piece probably isn't that much shorter, but I do think it's a bit shorter.
  So as not to make the same mistake twice I'll put down the plan for the curve.  The outside triangles are mostly equilateral 25mm triangles.  To get more curve I used 28/28/25 mm isosceles triangles at position 1 (at the center), 3, 9 and 10.  On the inside the triangles are either 20mm equilateral or, at inits 1, 2, 3 and 6, to tighten the curve, 20/20/25 isosceles.  It actually doesn't change things all that much.  If I didn't want it to be so pointy at the bottom I could have spread them out more.  Also triangle 6 is an equilateral 25mm oct.  I CHANGED SOME OF THIS AND WROTE ABOUT IT IN THE NEXT POST.