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Understanding the Persian Family
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Understanding the Persian Family
Article © MAIL User: Tesserex
The M.A.I.L. weaves page defines Persian weaves as those characterized by a "stacked" ring orientation. However, I highly disagree. It is so far my most educated opinion that Persian weaves can be defined as employing both "through the eye" and "around the eye" connections with each and every ring in the weave. A "Persian stitch" is one that involves a ring using both of these connections.
I am going to take a look at some of the primary Persian weaves, both chain and sheet, to see how this definition applies, and then explore some interesting characteristics that make these weaves similar and some that make them different. First I will look at the patterns of connections, and then I will go through handedness and symmetry / asymmetry. I refer to symmetry as that with respect to the plane in which the weave lies (It is symmetric if you can flip it upside down and have the same layout, like with HP 4-1 (Half Persian 4 in 1). Handedness reverses but that is not a concern.)
Let's begin by taking a look at the simplest piece that defines a weave as Persian. I call it a figure 8, I don't really care what you call it, just know it's basically four rings as two cells of HP 3-1 (Half Persian 3 in 1).
Notice the colors I used. They will follow through the rest of this article. Red coloring is used to highlight the "eyes" that define the connection. Green segments are "through the eye" connections, and blue are "around the eye", which I will call TE and AE. It is important to note that you will find both blue and green on the same ring, as that is part of the definition of Persian. The only place this does not hold true is at the ends of a chain where the eye itself is not completed. In this piece, every ring is at the end of the chain, so only one color shows on each ring. Also note that the blue and green segments define another eye and the right ring makes an AE connection, and the left makes a TE.
Now let's look at FP (Full Persian 6 in 1) to see where these connections can be found.
Now we can easily see the definition of Persian played out. Each ring that has not been defined as an eye has both green and blue on it. The green, on the inside, passes through the eye, and then the blue, on the outside, passes around it. Obviously, you could not have one ring do the same connection on both sides because that would require fitting completely over another ring in the perpendicular plane, or squishing inside it, and that requires different sized rings. Basically, that would make it orbital family instead. Also, there are variations of this weave that move the connections around. Since the eye is narrower at the edges, putting the TE on the outside, split by the AE, makes the weave tighter. This weave was named "Full Persian - Dense". The official Full Persian 6 in 1 Grizzly applies this method to one side, so the grain is reversed on one side. If you're thinking "what about making a grizzly where both sides put the TEs in the middle?" just like I did for a while. The thing is, when you flip TEs and AEs in one side, you do the same in the other, so when you take one side and reverse the grain, and then try to pull the rings back by one to put the TEs back in the middle, you're just putting the rings on top that were once AEs inside them, making them split TEs. Sorry.
Now we cut this in half and look at a chain of HP 3-1. Remember that FP is just two chains of HP 3-1 combined with matching eye connections.
Now we can see the separation of blue and green more clearly. I noticed while coloring the picture that the TE connection requires far less of the ring than the AE. Logically this is because TE goes in a near straight line, while AE has to circle around.
It is my estimate that such rings are 2/3 AE and 1/3 TE. As to what this conclusion could lead to, I have no idea.
Next, HP 4-1...
What we have here is something slightly more interesting, but alas more complicated. The first thing you probably notice is that there is a blue segment of the rings, and green on BOTH sides of the blue! I would have colored in the opposite side of the ring blue as well but you can't really see it in the picture anyway. Do take note that the rings in this weave are split into four sections. There is TE on two sides opposite each other, and AE on the other, what we could say is the "middle" of the ring.
We can deduce from this information that as you increase x in a weave "HP x-1", the rings will go "through the eye, around that eye, through the next, around that one", etc, while one side is always a TE. If x is odd, one extreme is a TE and the rest of the ring goes around (x-1)/2 eyes. But now you're thinking, "where did that formula come from?" Well, each eye is two rings. A TE connection means one of those two goes through the ring in question. For the AE connections, both of the eye rings pass through. So, that -1 in the formula is the "through the eye" ring. Divide the rest by two rings per eye to get the number of eyes. Now, if x is even, it goes through an eye on each side and goes around (x-2)/2 eyes.
These weaves have so far all followed the "stacked ring orientation" rule, but now we are going to break it.
This is a weave I developed, and then made into a sheet, only to find that Lorenzo had made the sheet first. He had not, however, made the chain. You will notice that this weave follows the same connection pattern as regular HP 3-1. For right now, there is not much more to see here, so lets move on.
This is X-weave (X-weave / Spring Chain / Forars Kaede). It is the 4-1 version of the previous example. Once again, see that the rings are divided into four sections, two green and two blue. The angling of the rings is only because they couldn't quite fit side by side in the eyes the way they should. Try to ignore it.
Ahh, the sheet weaves.
Just like 4-1, the rings in the Half Persian 3 Sheet 6 in 1 are divided into four sections. In the front row, there is a green section on the left and then a blue. After passing around the eye in front, it turns green and goes through the eye behind it, and then around the eye in the back. Basically, the back row is an mirror image of the front row. If you flip the sheet upside down, that's exactly what you see. The handedness is reversed because the through the eye connection is on the opposite side. Notice that this is because you can't have "green, blue, blue, green". They have to alternate. What would happen if this sheet tried to do "green, blue, blue, green", you ask? I will explain soon enough...
Wow. Now this sheet has more red eyes in it than the entire Lord of the Rings series. Ignore the gold ring, it's flipped the wrong way. You're probably a bit confused, since what we have here is a 4-1 sheet weave... but it's Persian... but even though it's even numbered, it's asymmetric... how did that happen? Well the trick is that each "unit" can be pictured as a + of four rings in the same plane - the ones facing you, making the X of eyes. A single ring interacts with those eyes. It passes through two in a row on one side, and then goes around both on the other side. With the TE connections, the ring that the eyes have in common is the only one passing through the main ring. On the other side, it goes around two eyes with one ring in common - the other three. That adds up to 4-1. The asymmetry happens because the main ring is only split into blue and green sides, which are not symmetric. A ring split into four sections is symmetric. Another cool thing to see about this weave is that if you look at it horizontally or vertically, you see the usual alternating of green and blue, and with it the usual flipping of two ring units. However, when you look at it down an angle, you see that it is a row of all blue, then a row of all green, and so on. You could construct this weave by starting with a 1-1 chain (2 in 1 Chain), laying it out so it appears to be all of one kind of connection, then joining a new row with the other kind, then do the first kind again, and repeat.
It may be difficult to see this one, since the rings facing us are almost entirely red, but I know you're smart enough to follow. Like X-weave, a lot of the rings in this picture should be side by side but didn't quite fit. Now, where 4-1 sheet had a "unit" of 4 coplanar rings and a fifth intersecting ring, mystic maille has 6 coplanars intersecting a seventh ring. The unit is kind of like a sideways A, or o8o8, if you imagine that squished together horizontally. The main ring passes through two eyes on one side with a common ring in the center (the 'o'), and then goes around two eyes with the next middle ring in common (the "8o"). It then goes through the last two eyes on the other side. My writing alone is probably very confusing, so just look at the picture and try to pick out one of these units.
A Look at Handedness and Symmetry
We've all done it. We try to make a chain one way, and it comes out the other. Two chains don't line up. Your sheet changes direction suddenly. Why? Your handedness flipped. Here I will show what causes specific handedness and how you can control it. I will also show that symmetry and handedness are actually closely related.
Handedness only affects odd numbered chains. It is present in evens, but if you flip the chain the handedness is the other way, because it is symmetrical. There is no "top" side. However, with odd, like 3-1, you refer to a "top" and "bottom". Handedness is in relation to the "top" side.
Look at the "top" here. The reason it forms is because the TEs like to form in the center of the eyes because it is the most easily fitting location. When this happens, the AEs move to one side, based on the their stacking. The "top", therefore, is the meeting of the AE connections. These two rings that are both AEs at that point make the narrow almost vertical eye in the chain (the gold areas in the picture).
The top and bottom appear to have one set of rings leaning left and the other leaning right. The sides have both sets appearing to lean the same direction, making "arrows". Viewing from the side with the top facing up, both sides run the same way, that is in the direction of the row closest to you. As you look from the side, the opposite row's lean is changed in view. If this sounds confusing, pick up an HP 3-1 strand. Look down onto the top of it, then turn it until you are looking at the side. You will see what I mean.
Now, since there is no definition of what "left handed" and "right handed" actually mean, I won't use them specifically. However, it depends on which set of rings leans which way when viewing the top of the chain. To reverse the handedness, reverse the stacking of one set of rings. It will turn what was once the top into a side (because now all the rings lean the same way) and the new top will be in the direction you just pointed the rings you moved. What was once the lower row is now the upper, and the handedness is reversed. When you restacked the rings, you think you're changing the lean, but once again, because the top is moved, when you turn it to face up again, the row you moved will now appear to lean the other way again. Yes, it sounds confusing. Try it. Still confusing? Try figuring this out by staring at the chain for three hours! Just teasing.
Remember when I asked what would happen to sheet 6 if the rings went "TE, AE, AE, TE"? Well, the last TE would place itself in the middle of the eye, as is the natural tendency. Because of the lean towards the top of the sheet, the back row with which it intersects would be forced downward. Take a look.
With the blue/green rings, AE on the right is above the next TE, pushing the ring upward and towards the back of the sheet. In the next row, they make and TE and then AE. The AE there is below the next TE, pushing them to the bottom of that red set of rings, and conversely, pushes the red set of rings upward. The sheet continues in a zig-zag pattern.
If we turned the back AE into a TE and the TE into an AE, for example by sliding the back red row to the left by one ring, the TEs would locate themselves in the middle. The AEs would be pushed to the top of the red set, and, conversely, the red set would be pushed downward, toward the front of the sheet. Instead of zig-zaging, the sets would circle around. I'm sure you already figured it out by now. You would have FP.
Well I hope I have been informative and enlightening. The Persian family, in all its simplistic beauty, is just that - simple yet beautiful. It takes some work to understand how it behaves, but the interactions, at their heart, are just a matter of two terms - TE and AE. Learn to use them to push the rings however you want, you can probably come up with dozens of arrangements that no one has tried before. Good luck.
-Tesserex
I am going to take a look at some of the primary Persian weaves, both chain and sheet, to see how this definition applies, and then explore some interesting characteristics that make these weaves similar and some that make them different. First I will look at the patterns of connections, and then I will go through handedness and symmetry / asymmetry. I refer to symmetry as that with respect to the plane in which the weave lies (It is symmetric if you can flip it upside down and have the same layout, like with HP 4-1 (Half Persian 4 in 1). Handedness reverses but that is not a concern.)
Let's begin by taking a look at the simplest piece that defines a weave as Persian. I call it a figure 8, I don't really care what you call it, just know it's basically four rings as two cells of HP 3-1 (Half Persian 3 in 1).
Notice the colors I used. They will follow through the rest of this article. Red coloring is used to highlight the "eyes" that define the connection. Green segments are "through the eye" connections, and blue are "around the eye", which I will call TE and AE. It is important to note that you will find both blue and green on the same ring, as that is part of the definition of Persian. The only place this does not hold true is at the ends of a chain where the eye itself is not completed. In this piece, every ring is at the end of the chain, so only one color shows on each ring. Also note that the blue and green segments define another eye and the right ring makes an AE connection, and the left makes a TE.
Now let's look at FP (Full Persian 6 in 1) to see where these connections can be found.
Now we can easily see the definition of Persian played out. Each ring that has not been defined as an eye has both green and blue on it. The green, on the inside, passes through the eye, and then the blue, on the outside, passes around it. Obviously, you could not have one ring do the same connection on both sides because that would require fitting completely over another ring in the perpendicular plane, or squishing inside it, and that requires different sized rings. Basically, that would make it orbital family instead. Also, there are variations of this weave that move the connections around. Since the eye is narrower at the edges, putting the TE on the outside, split by the AE, makes the weave tighter. This weave was named "Full Persian - Dense". The official Full Persian 6 in 1 Grizzly applies this method to one side, so the grain is reversed on one side. If you're thinking "what about making a grizzly where both sides put the TEs in the middle?" just like I did for a while. The thing is, when you flip TEs and AEs in one side, you do the same in the other, so when you take one side and reverse the grain, and then try to pull the rings back by one to put the TEs back in the middle, you're just putting the rings on top that were once AEs inside them, making them split TEs. Sorry.
Now we cut this in half and look at a chain of HP 3-1. Remember that FP is just two chains of HP 3-1 combined with matching eye connections.
Now we can see the separation of blue and green more clearly. I noticed while coloring the picture that the TE connection requires far less of the ring than the AE. Logically this is because TE goes in a near straight line, while AE has to circle around.
It is my estimate that such rings are 2/3 AE and 1/3 TE. As to what this conclusion could lead to, I have no idea.
Next, HP 4-1...
What we have here is something slightly more interesting, but alas more complicated. The first thing you probably notice is that there is a blue segment of the rings, and green on BOTH sides of the blue! I would have colored in the opposite side of the ring blue as well but you can't really see it in the picture anyway. Do take note that the rings in this weave are split into four sections. There is TE on two sides opposite each other, and AE on the other, what we could say is the "middle" of the ring.
We can deduce from this information that as you increase x in a weave "HP x-1", the rings will go "through the eye, around that eye, through the next, around that one", etc, while one side is always a TE. If x is odd, one extreme is a TE and the rest of the ring goes around (x-1)/2 eyes. But now you're thinking, "where did that formula come from?" Well, each eye is two rings. A TE connection means one of those two goes through the ring in question. For the AE connections, both of the eye rings pass through. So, that -1 in the formula is the "through the eye" ring. Divide the rest by two rings per eye to get the number of eyes. Now, if x is even, it goes through an eye on each side and goes around (x-2)/2 eyes.
These weaves have so far all followed the "stacked ring orientation" rule, but now we are going to break it.
This is a weave I developed, and then made into a sheet, only to find that Lorenzo had made the sheet first. He had not, however, made the chain. You will notice that this weave follows the same connection pattern as regular HP 3-1. For right now, there is not much more to see here, so lets move on.
This is X-weave (X-weave / Spring Chain / Forars Kaede). It is the 4-1 version of the previous example. Once again, see that the rings are divided into four sections, two green and two blue. The angling of the rings is only because they couldn't quite fit side by side in the eyes the way they should. Try to ignore it.
Ahh, the sheet weaves.
Just like 4-1, the rings in the Half Persian 3 Sheet 6 in 1 are divided into four sections. In the front row, there is a green section on the left and then a blue. After passing around the eye in front, it turns green and goes through the eye behind it, and then around the eye in the back. Basically, the back row is an mirror image of the front row. If you flip the sheet upside down, that's exactly what you see. The handedness is reversed because the through the eye connection is on the opposite side. Notice that this is because you can't have "green, blue, blue, green". They have to alternate. What would happen if this sheet tried to do "green, blue, blue, green", you ask? I will explain soon enough...
Wow. Now this sheet has more red eyes in it than the entire Lord of the Rings series. Ignore the gold ring, it's flipped the wrong way. You're probably a bit confused, since what we have here is a 4-1 sheet weave... but it's Persian... but even though it's even numbered, it's asymmetric... how did that happen? Well the trick is that each "unit" can be pictured as a + of four rings in the same plane - the ones facing you, making the X of eyes. A single ring interacts with those eyes. It passes through two in a row on one side, and then goes around both on the other side. With the TE connections, the ring that the eyes have in common is the only one passing through the main ring. On the other side, it goes around two eyes with one ring in common - the other three. That adds up to 4-1. The asymmetry happens because the main ring is only split into blue and green sides, which are not symmetric. A ring split into four sections is symmetric. Another cool thing to see about this weave is that if you look at it horizontally or vertically, you see the usual alternating of green and blue, and with it the usual flipping of two ring units. However, when you look at it down an angle, you see that it is a row of all blue, then a row of all green, and so on. You could construct this weave by starting with a 1-1 chain (2 in 1 Chain), laying it out so it appears to be all of one kind of connection, then joining a new row with the other kind, then do the first kind again, and repeat.
It may be difficult to see this one, since the rings facing us are almost entirely red, but I know you're smart enough to follow. Like X-weave, a lot of the rings in this picture should be side by side but didn't quite fit. Now, where 4-1 sheet had a "unit" of 4 coplanar rings and a fifth intersecting ring, mystic maille has 6 coplanars intersecting a seventh ring. The unit is kind of like a sideways A, or o8o8, if you imagine that squished together horizontally. The main ring passes through two eyes on one side with a common ring in the center (the 'o'), and then goes around two eyes with the next middle ring in common (the "8o"). It then goes through the last two eyes on the other side. My writing alone is probably very confusing, so just look at the picture and try to pick out one of these units.
A Look at Handedness and Symmetry
We've all done it. We try to make a chain one way, and it comes out the other. Two chains don't line up. Your sheet changes direction suddenly. Why? Your handedness flipped. Here I will show what causes specific handedness and how you can control it. I will also show that symmetry and handedness are actually closely related.
Handedness only affects odd numbered chains. It is present in evens, but if you flip the chain the handedness is the other way, because it is symmetrical. There is no "top" side. However, with odd, like 3-1, you refer to a "top" and "bottom". Handedness is in relation to the "top" side.
Look at the "top" here. The reason it forms is because the TEs like to form in the center of the eyes because it is the most easily fitting location. When this happens, the AEs move to one side, based on the their stacking. The "top", therefore, is the meeting of the AE connections. These two rings that are both AEs at that point make the narrow almost vertical eye in the chain (the gold areas in the picture).
The top and bottom appear to have one set of rings leaning left and the other leaning right. The sides have both sets appearing to lean the same direction, making "arrows". Viewing from the side with the top facing up, both sides run the same way, that is in the direction of the row closest to you. As you look from the side, the opposite row's lean is changed in view. If this sounds confusing, pick up an HP 3-1 strand. Look down onto the top of it, then turn it until you are looking at the side. You will see what I mean.
Now, since there is no definition of what "left handed" and "right handed" actually mean, I won't use them specifically. However, it depends on which set of rings leans which way when viewing the top of the chain. To reverse the handedness, reverse the stacking of one set of rings. It will turn what was once the top into a side (because now all the rings lean the same way) and the new top will be in the direction you just pointed the rings you moved. What was once the lower row is now the upper, and the handedness is reversed. When you restacked the rings, you think you're changing the lean, but once again, because the top is moved, when you turn it to face up again, the row you moved will now appear to lean the other way again. Yes, it sounds confusing. Try it. Still confusing? Try figuring this out by staring at the chain for three hours! Just teasing.
Remember when I asked what would happen to sheet 6 if the rings went "TE, AE, AE, TE"? Well, the last TE would place itself in the middle of the eye, as is the natural tendency. Because of the lean towards the top of the sheet, the back row with which it intersects would be forced downward. Take a look.
With the blue/green rings, AE on the right is above the next TE, pushing the ring upward and towards the back of the sheet. In the next row, they make and TE and then AE. The AE there is below the next TE, pushing them to the bottom of that red set of rings, and conversely, pushes the red set of rings upward. The sheet continues in a zig-zag pattern.
If we turned the back AE into a TE and the TE into an AE, for example by sliding the back red row to the left by one ring, the TEs would locate themselves in the middle. The AEs would be pushed to the top of the red set, and, conversely, the red set would be pushed downward, toward the front of the sheet. Instead of zig-zaging, the sets would circle around. I'm sure you already figured it out by now. You would have FP.
Well I hope I have been informative and enlightening. The Persian family, in all its simplistic beauty, is just that - simple yet beautiful. It takes some work to understand how it behaves, but the interactions, at their heart, are just a matter of two terms - TE and AE. Learn to use them to push the rings however you want, you can probably come up with dozens of arrangements that no one has tried before. Good luck.
-Tesserex
Original URL: http://www.mailleartisans.org/articles/articledisplay.php?key=328
