an open source architectural beadwork project from Kate McKinnon and a worldwide team of innovators

*Hello all! We are just finishing the HyperLoops and HyperLines chapter here at CGB Central, and should have news on the books soon- stay tuned. HyperThings are the last to be integrated into the concepts and patterns. Thanks to our pre-order folks for their support of this beautiful project. ❤*

We’ve been talking on team and on social media about our increases and decreases, and how we notate them, how we think about them, and whether or not the original names for corner increases apply to those placed in curves, lines, or asymmetrically. Is *Triangle Increase* the best term to describe a herringbone stack?

Maybe not, but quite a few people know the name, and I can certainly see many places in pieces like this where the geometry of the peyote triangle is expressing.

Above, you can see the soaring increase lines of the classical *Triangle Increase* building an 8-Point *PodCast Bead (multicoloured and black)* and an asymmetric *Rick-Rack Bangle* (the red and white section, soon to be removed). Podcast bead by Ingrid Wangsvik, Rick-Rack by Kate. Below are a few more pieces using this same technique.

*two-bead Herringbone or Triangle Increases placed into MRAW Bands
Left, beadwork by Kate McKinnon, right by Sarah Loudon*

In the upcoming new CGB books, we use two main increase progression patterns to build our peyote-stitched pieces. The *Triangle Increase,* shown above,is a herringbone stack, with two beads added at a time in each round. The second pattern we use a lot is a three-round progression, a 2/1 stepped increase often called the *Hexagon Increase*.

You can in fact see the soul of the flat hexagon in this gorgeous spiral built using the Hexagon Increase. So I think the names are just fine.

*Design and beadwork Claudia Furthner, Austria*

Below is a little sample of my own that shows how the 2/1 *Hexagon Increase* progressions look over the first five rounds. The tail is just a *Casting Spine*, and the blue and gold beads are the result of the increase progression. You can see the spiral building and the clean geometry taking over the line.

*Casting Spines* are really neat, and they are one of the recent finds we had during team review sessions, and all of us said “we must add this to the book”.

Joy Davison (Jay Dee on social media) created our first one when decided to add a *Stitch-In-The-Ditch* round to three rounds of flat peyote stitch. It formed a remarkable rope, with a central core and three spiny lines of beads around it. We will have a few pretty patterns for them in the book.

Here is one made by Nico Williams, using black beads for the core (the middle of the three flat rows) and Picasso Delica beads for the other two flat rounds and also the *Stitch-In-The-Ditch* round. It looks like a real spine.

If we aren’t starting off of Casting Spines, we like to do a PodCast build or a peyote start. Each gives a different feel of HyperLine or HyperLoop.

*above: two Hyperloops beaded by Kate McKinnon – at left, growing on a tiny PodCast, at right, from a peyote start. Both have their advantages.*

*HyperLoop design Joy Davison & Claudia Furthner*

You can see the 2/1 pattern of the *Hexagon Increase* clearly in these two *HyperLoops*; the one at left growing on a *PodCast Bead*, and the one at right grown from a peyote start.

We make things like this fabulous, entirely wearable bangle out of *HyperLoops, *and as you can see any notion of hexagons in this piece has given way to the *Geometric Capture* of pentagons instead. The 2/1 increase easily accommodates many shapes.

*Anemone Bangle by Karen Beningfield.
You can choose to Capture ellipses, triangles, squares, pentagons, hexagons, or any other shape that you have room for in your HyperLoops.*

Increases can be alternated, spiralled, switched, and placed off-center. Below is an asymmetric *Rick-Rack Bangle* from Ingrid Wangsvik, Norway, with herringbone increases going three different ways in three different layers. They stack like ocean waves.

*Above, Ingrid Wangsvik, Asymmetrical Rick-Rack Bangle*

We can now show you how to do this off of a line of triangles, or loops thrown off of the tips of a *PodCast Bead, *much like Christina Vandervlist did to make the* Helix Bangle *from *CGB Volume I. *

Here are two such Helix-Loop starts in progress.

*above, PodCast- based Helix-Loop starts to asymmetrical Rick Rack
Joy Davison and Franklin Martin, Jr.*

*Below, a Warped Hexagon made using a Triangle Increase, Nico Williams, Quebec*

We’ve had a huge amount of innovation in the past year, and that’s a fact. Every time we sit down to review our conclusions, we have new earthshaking discoveries. The only solution for me to finish these books was to declare victory, go into hiding, and try to bang this all out before one of us has another golden idea that cannot be ignored. See you soon!

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We are close to singing in concert…when I looked up the definition of “null” it said it means zero. Also, I believe the hyperbolic strips are made of a flat shapes… sort of reminds me of doing differential equations. Does this mean the flat-landers can come to the party? 😉

Decreases could simply be noted as -1.

Hi! The hyperbolic things like Claudia’s gorgeous spiral and Karen’s beautiful bangles start out as lines, and then take on a very definite 3D curve. After the first increase round, they are really never flat again, but instead make a curved spiral like a seashell. Sometimes, though, if the tension is soft enough to defeat the curve, they can be *folded* flat along the increase lines, and they make a little tube-like stack of pentagons or hexagons, mostly depending on the tension of the beader.

Our only difference in my mind is that you and yours are notating only the increase round, and we are notating each entire line. When you do the whole line, there are no spaces that get 0 beads. But I don’t think this matters too much, it’s just a difference in what part of the work is described. I should be able to tie them together in a natural way. I’ll be sure to loop you into the edits.

You know what occurred to me this morning – our Pierced Arrow is a second flat shape made from the herringbone/Triangle increase. It is just a single increase line, and it makes an arrow shape.

It’s been fun thinking about this for sure.

With all due respect…may I suggest that nearly everything I’ve seen so far produced by the CGB followers is composed of flat shapes…wouldn’t you agree?

and perhaps we are on the same song sheet…the definition of null is zero according to a couple online dictionaries. All the best…

Flat shapes? Sometimes we make flat peyote triangles and put them together, but usually we are placing increases in straight lines, or making spiky or winged things. We should talk more about this!

It might not be obvious from viewing the finished work that most of our pieces are grown organically in one piece, not assembled from flat pieces. I think the Cycles are the only things that we use flat forms in an assembly method. Most things spring up from a flat line, and the increases we place in the flat line create our entire architecture.

So the *concept* of 0 in an increase pattern in a straight line, such as MRAW is null, but the count is not.

; )

I understand that your 0 means “no beads at the corner” or “no beads in the increase stack” but to us, that third round, which we call a Fill Round, is a part of the progression. So we describe the Hexagon Increase as 2/1/Fill, not 2/1/0, because there is no space that we place 0 beads in.

The only real difference we have in this (I think) is that you prefer to notate only the beads in the increase line, and I prefer to notate all three rounds in the progression. If the third round in the progression has a bead in every slot (and it does) then we would never use a 0. My solution is to use your and Julia’s name for the increase, but describe the third round as what it is, a plain peyote fill round. That way we have overlap, which is the truly important thing I think.

I’m just not free to describe the third step as “add 0 beads”, because that doesn’t describe the progression, which is three steps, each of which place beads. Hoping that makes it more clear?

Also may I add that I am *so grateful* for all of the conversations with you and others on this, because they bring clarity to my writing for the new book. I want to be able to refer to the solid knowledge you and others have built, but do our notation in a way that makes sense to other fields – I have to do that, because we are working cross-field.

Using the original names for the increases won’t make sense to our people immediately, because what we make from the “Hexagon Increase”, for example, is nothing like a flat hexagon. But as I studied this issue over the past week, as I said, I saw the *soul* of the flat geometry in every curve and every line of the work. So I can call that out, and make a true connection, I think.

It goes back what you said about the angles – if we only looked at the resulting ANGLES in the fabric from each increase pattern, we could name them that way. But the old names are good. It was nice to go on the journey with that, and see how pure the information that Julia hunted down was, how the geometry sang out.

I think I understand what the previous commenter means by flat – not that the whole piece is flat, but that it could be decomposed into a series of triangles or trapezoids, which are each individually flat. For example, the part of the spiral above excluding the gold beads is made of pink and white trapezoids. This is also related to the conversation we were having on facebook about the definition of hyperbolic…

Sure, but a critical difference in having flat planes and being assembled from flat forms is how the piece grows – and that’s what I’m really talking about. Growing a piece of architecture from a flat line is pretty different from making panels and zipping them together. The process is not the same…

love the posts but am hanging out to get my pre- ordered book… I am 86 so have limited time left to play with beads!!!

Jane! I wish I could hurry faster.

Kate, Thank you for this post and all the information within it. I was a little confused about a few things that I couldn’t figure out from the photos in FB posts in the past few weeks and this post clarified everything! All the best!

I didn’t realize that CGB has excluded flat shapes. To me whether the shape is flat or ruffled, an increase pattern of some kind is used.

Well sure, we use the herringbone or Triangle Increase, and the 2/1 or Hexagon increase all of the time.

But we don’t often have corners (think putting increases in a straight run of MRAW to make a Rick-Rack) and so there is no “0”, in our increase notation it’s just another peyote round, which we call a Fill Round. We only use a 0 in our notation for a decrease stitch – when we have a placement of 0 beads in a live slot.

So what’s a 2/1 increase?

May I expand on your reference to a naming convention for increase patterns?

The increase patterns I refer to were developed by Julia Pretl in her book, “Little Boxes,” published in 2003. In it she refers to “cycles” for each of the four basic flat shapes: triangle, square, pentagon and hexagon.

My suggested abbreviation for each is as follows:

Triangle: to make a flat triangle with three corners or three points of increase, two beads are added at each point of increase (the vertical column of beads at each corner). While some refer to this as a herringbone increase, it is simply a peyote increase of two beads. It could be abbreviated as 222 or simply called the triangle increase.

Square: to make a flat square with four corners or four points of increase, the pattern or cycle would take place over five rows and the number of beads added at the point of increase for each row would be 3, 2, 2, 1, 0. The zero refers to the fact that on the fifth row of the increase pattern, no new beads are added. One simply passes through the single bead added at the corner in the last row. The increase pattern could be referred to as the 32210 increase or simply the square increase.

Pentagon: to make a flat pentagon with five corners or five points of increase, the pattern or cycle would take place over four rows and the number of beads added at the point of increase for each row would be 3, 2, 1, 0. The zero refers to the fact that on the fourth row of the increase pattern, no new beads are added. One simply passes through the single bead added at the corner in the last row. The increase pattern could be referred to as the 3210 increase or simply the pentagon increase.

Hexagon: to make a flat hexagon with six corners or six points of increase, the pattern or cycle would take place over three rows and the number of beads added at the point of increase for each row would be 2, 1, 0. The zero refers to the fact that on the third row of the increase pattern, no new beads are added. One simply passes through the single bead added at the corner in the last row. The increase pattern could be referred to as the 210 increase or simply the hexagon increase.

I have a Quick Reference for Peyote Increases that explains these in more detail row by row and would be happy to send it to anyone who wants it. Please contact me at dmfbeads@bitstream.net.

There are many ways to describe what we do but we are most likely to communicate effectively if we use commonly understood terms. I’d love to hear how others would describe these increase patterns or cycles.

And while we’re at it, if someone could develop comparable increase patterns for an octagon (eight sides) and decagon (ten sides), we sure could use them!

Happy Beading!

Diane Fitzgerald

Hi Diane, and thank you! Honestly we at CGB have little interest in flat shapes, but I do have a deep interest in honoring standing naming conventions. The notation conventions will be harder to mirror, because as we rarely have corners, for example, the “0” of the corner increase notation loses significance.

If we are putting increase rows in a straight line, for example, the idea of 0 is null; there are no corners. So I can go with the names, but I have no way to integrate the concept of 0 in the corner increase notations.

The only time we really encounter true zeroes is when we do a decrease, and skip a live slot by passing through and adding no beads.

Hugs

Kate

Well, as I mentioned, some call it the Hexagon increase. It is a three round progression, and it goes 2/1/Fill. Diane will say 2/1/0, but that is because she is talking about a corner increase in a flat form. We have no corners, so to us, this is a 2/1 FILL progression.