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Half Persian Weaves: Balanced; Unbalanced; and Sheet Progressions
Article © MAIL User: Chainmailbasket_com

Intro

The Persian weave family, like the European one, has many basic types that are scaleable in terms of how many rings pass though how many others. While the Japanese family offers the same 'x in y' paradigm, it doesn't have as many options since it has a limited number of tessellation types without losing purity. The Persian family utilizes "around the eye" and "through the eye" connection types which open up many options and allow for quite a few potential variants. This article covers the possibilities presented with the Half Persian (HP) weave types, and their (unbalanced) sheet weave progressions.

Half Persian weaves are either unbalanced or balanced (symmetrical). Unbalanced HPs have a chevron (^)-shaped cross section and have different appearances on the top and bottom. The most basic and common of these is Half Persian 3 in 1. These weaves offer the potential to be easily expanded into one of two different styles of sheet weave: Half Persian Sheets, and Three Quarters Persian Sheets.

Balanced HPs appear the same on the top and bottom and thus have a rectangular (or possibly square in extreme cases) cross section. The most common of these is Half Persian 4 in 1. These weaves offer less options in terms of lateral expansion for sheeting purposes.


Half Persian Chains:

Half Persian chains are named thusly because they are Half of a Full Persian. Half Persian 3 in 1 is contained within a Full Persian 6 in 1 (FP) chain. If you were to remove all of the rings off one face of FP, you'd end up with a Three Quarters Persian (TQP) chain. If you were to remove all the rings from one of the two outside faces of TQP, you'd end up with HP3-1. It becomes a 3 in 1 weave at this point. The same concept applies to Persian chains with a larger number (x) in 1.

When you build a HP weave from scratch, it's done by passing a ring up through, and then down through a certain number of rings on the opposing face. This ratio is very important as it defines what type of HP chain is being made. The following is a chart showing the possibilities:


HP3-12:11:2
HP4-13:12:21:3
HP5-14:13:22:31:4
HP6-15:14:23:32:41:5
HP7-16:15:24:33:42:51:6
HP8-17:16:25:34:43:52:61:7
HP9-18:17:26:35:44:53:62:71:8

...and so on. Unbalanced HP chains contain a ratio with two different numbers. Reversing the numbers (e.g. 1:2 vs. 2:1) doesn't create an independent weave. It simply yields the same weave with a different handedness. (Naturally) balanced HP chains are those with the same number on each side of the ratio.

Unbalanced:

Most unbalanced HP chains are an odd number in 1 (e.g. Half Persian 3 in 1, Half Persian 5 in 1, etc. However, it is possible to unbalance an HP(even)-1 by changing the offset. Half Persian 4 in 1 Unbalanced, for example, is the result of using the 3:1 or 1:3 ratio of up vs. down rings instead of 2:2, which constitutes the balanced Half Persian 4 in 1.


HP3-1Half Persian 3 in 1 (2:1/1:2)
Image: 0hp3-1.jpg
HP4-1Half Persian 4 in 1 Unbalanced (3:1/1:3)
Image: 0hp4-1u.jpg
HP5-1Half Persian 5 in 1 (3:2/2:3)
Image: 0hp5-1.jpg
Half Persian 5 in 1 Unbalanced 4:1 (4:1/1:4)
Image: 0hp5-1u.jpg
HP6-1Half Persian 6 in 1 Unbalanced (4:2) (4:2/2:4)
Image: 0hp6-1u.jpg
HP7-1Half Persian 7 in 1 (4:3/3:4)
Image: 0hp7-1.jpg

In the table above, you'll notice there are two HP5-1's. Even though both are unbalanced, the second one is referred to as such in its name because of its extreme offsetting. It needs a very large AR and isn't completely stable. Regular HP5-1 is made at its most easy and forgiving 3:2 or 2:3 ratio. HP4-1U is unbalanced by using the 1:3 or 3:1 ratio, and HP6-1U is made unbalanced by using the 4:2 or 2:4 ratio. A 5:1 or 1:5 is logically possible, but would require an excessively high AR. The HP7-1 utilizes 4:3 or 3:4, and while a 5:2 version is possible (or 6:1, for that matter), it is excessive and would require a very high AR.

Naturally Balanced:

Half Persians with an even number in 1 are naturally balanced, but only if the ratio they use has the same number on each side, which in every case, is the easiest version to construct.


Half Persian 4 in 1 (2:2)
Image: 0hp4-1.jpg
Half Persian 6 in 1 (3:3)
Image: 0hp6-1.jpg
Half Persian 8 in 1 (4:4)
Image: 0hp8-1.jpg

Note: Half Persian 10 in 1 is also in the weave library, but I've never personally made it.

Unnaturally Balanced:

It is possible to take an otherwise naturally unbalanced HP and force it to be balanced by alternating the ratio with each set of two rings added. This doesn't seem to work with HP3-1, but works with all subsequent HP(odd)-1's. As far as naming conventions go, these variations have the word 'Symmetrical' appended to them.


Half Persian 5 in 1 Symmetrical (3:2/2:3, alternating)
Image: 0hp5-1s.jpg
Half Persian 7 in 1 Symmetrical (4:3/3:4, alternating)
Image: 0hp7-1s.jpg


Half/Three Quarters Persian Sheets

By continuing HP3-1 laterally and adding rows, with each row using the same connection method as the previous, Half Persian 3 Sheet 6 in 1 is made. Other types of HP sheets exist too, them being Half Persian 3 Sheet 5 in 1, and Half Persian 3 Sheet 4 in 1, but they are less pure and use European-style connections between rows. They are not covered in this article.

Using any of the unbalanced Half Persian chains, it is possible to expand these into their logical Three Quarter Persian sheet progressions. TQP Sheets are more dense than their HP Sheet counterparts.


Half Persian 3 in 1
Image: 0hp3-1.jpg
becomesHalf Persian 3 Sheet 6 in 1
Image: 0hp3s6-1.jpg
orThree Quarters Persian Sheet 6 in 1
Image: 0tqps6-1.jpg
Half Persian 4 in 1 Unbalanced
Image: 0hp4-1u.jpg
becomesHalf Persian 4 Unbalanced Sheet 8 in 1
Image: 0hp4us8-1.jpg
orThree Quarters Persian Sheet 8 in 1 Unbalanced
Image: 0tqps8-1u.jpg
Half Persian 5 in 1
Image: 0hp5-1.jpg
becomesHalf Persian 5 Sheet 10 in 1
Image: 0hp5s10-1.jpg
orThree Quarters Persian Sheet 10 in 1
Image: 0tqps10-1.jpg
Half Persian 5 in 1 Unbalanced 4:1
Image: 0hp5-1u.jpg
becomesHalf Persian 5 Unbalanced 4:1 Sheet 10 in 1
Image: 0hp5us10-1.jpg
orThree Quarters Persian Sheet 10 in 1 Unbalanced
Image: 0tqps10-1u.jpg
Half Persian 6 in 1 Unbalanced (4:2)
Image: 0hp6-1u.jpg
becomesHalf Persian 6 Unbalanced 4:2 Sheet 12 in 1
Image: 0hp6us12-1.jpg
orThree Quarters Persian Sheet 12 in 1 Unbalanced
Image: 0tqps12-1u.jpg


Half Persian - Full Persian

Any of the Half Persian weaves, balanced, or unbalanced can be made into a Full Persian weave by adding two more faces, and having the fourth face attach back onto the first. It is generally easier though, especially with progressions beyond standard FP6-1, to assemble these weaves segment by segment.


Half Persian 3 in 1
Image: 0hp3-1.jpg
becomesFull Persian 6 in 1
Image: 0fp6-1.jpg
Half Persian 4 in 1
Image: 0hp4-1.jpg
becomesFull Persian 8 in 1
Image: 0fp8-1.jpg
Half Persian 4 in 1 Unbalanced
Image: 0hp4-1u.jpg
becomesFull Persian 8 in 1 Unbalanced
(Full Persian Gobi Chain)
Image: 0fp8-1u.jpg
Half Persian 5 in 1
Image: 0hp5-1.jpg
becomesFull Persian 10 in 1
Image: 0fp10-1.jpg
Half Persian 5 in 1 Unbalanced 4:1
Image: 0hp5-1u.jpg
becomesFull Persian 10 in 1 Unbalanced
Image: 0fp10-1u.jpg
Half Persian 6 in 1
Image: 0hp6-1.jpg
would becomeFull Persian 12 in 1
(didn't bother attempting)
Half Persian 6 in 1 Unbalanced (4:2)
Image: 0hp6-1u.jpg
becomesFull Persian 12 in 1 Unbalanced
Image: 0fp12-1u.jpg
Half Persian 7 in 1
Image: 0hp7-1.jpg
becomesFull Persian 14 in 1
(not in weave library)
Image: 0fp14-1.jpg


With Full Persian chains, versions based on unbalanced HPs are more stable, as those based on balanced HPs start to develop strange flexibility properties as the AR increases.


Special thanks to Daemon_Lotos for explaining the offsetting concept to me.
Original URL: http://www.mailleartisans.org/articles/articledisplay.php?key=755