This is a quick and dirty introduction to the logic that produced the tie-ups used to create the drawdowns in the tie-up comparison gallery and the galleries for the individual threadings.

Star fashion vs. Rose fashion

This determines the location of pattern blocks in the resulting drawdowns, and is the standard definition of star and rose fashion from traditional overshot.

Star fashion tie-ups have the pattern blocks on the bottom-left-to-top-right diagonal. Rose fashion tie-ups have the pattern blocks on the top-left-to-bottom-right diagonal.

This is only one way of creating a rose fashion design, but since my focus is not on treadling fashions but halftone placement, this is the only one I’ve used.

Due to limitations on the number of images I can include in each gallery, only some threadings have rose fashion designs in their galleries. Galleries that include drawdowns from multiple threadings only include star fashion tie-ups.

Tie-up profiles

Each of the structural tie-ups in the drafts are specific examples of a tie-up profile. A tie-up profile indicates where pattern, background, and halftone are located in the tie-up, but does not specify which halftone is to be used. Therefore, a tie-up profile represents a collection of specific structural tie-ups.

For example, these some tie-up profiles:

Each square of the profile represents a 2 shafts x 2 treadles section of a structural tie-up.

The shading of the profile squares indicate what kind of block that section of the tie-up produces: black squares indicate pattern blocks, white squares indicate background blocks, and grey squares indicate halftone blocks.

Pattern and background blocks can only be tied up one way. I have named them P for pattern and K for background.

Halftones

The grey squares can be any one of these four possible halftones, which I have named S, R, E, and O:

The S and R halftones create checkerboards in the drawdowns that look like plain weave. The R halftone connects pattern blocks together, whereas the S halftone does not. Each one has a different effect on the dimensionality of the design.

Where S and R halftones meet, the checkerboard is interrupted along edges and/or at corners, which can add interesting texture to the design

The E and O halftones create vertical pinstripes, as in traditional overshot. The POKE tie-up is the closest analog to that of traditional overshot woven with four blocks on four shafts:

When two blocks of E or two blocks of O are adjacent, the pinstripes connect across blocks.

When a block of E is adjacent to block of O, the pinstripes are offset.

Halftone shading

Even though all four halftones have the same 1:1 proportion of pattern to background, the smaller “dots” of the S and R halftones blend the two together more evenly, whereas the stripes in the E and O halftones concentrate the two colors. This creates interesting differences in values and shading when the two are combined:

Halftones in regular and irregular tie-ups

Regular tie-ups use all four halftones. Irregular tie-ups use only the S and R halftones, in every possible combination given the number of places halftone can appear in each given tie-up.

Regular vs. Irregular tie-ups

All the tie-ups can be classified as either regular or irregular.

Regular tie-ups

Regular tie-ups have the same sequence of pattern, background, and specific halftone on all treadles. These are the five regular tie-up profiles:

The drawdowns produced with regular tie-ups are also fairly regular, with the halftone and background “echoing” the pattern on expected diagonals. Here are two examples:

There are 116 regular star fashion tie-ups for each threading. Some threading galleries also include the 116 rose fashion counterparts.

With and without background

The first of the regular tie-ups above has no white background blocks, and therefore the 64 structural tie-ups based on this profile also have no background. Their drawdowns have only pattern and halftone visible on the front. Here’s an example:

These drawdowns are darker than the others. Note that the reverse side of these drawdowns have only background and halftone and are therefore much lighter than the front, and also lighter than other drawdowns that have both pattern and background on both sides. There are no drawdowns for the reverse side of the drafts in the galleries.

The 52 structural tie-ups based on the other regular tie-up profiles do have background blocks.

Even vs. uneven

The 64 regular tie-ups based on the first regular tie-up profile (those without any background) are also uneven: more shafts are left down for each pattern pick than are raised.

The last regular tie-up profile is also uneven: it has two background squares vs. only one pattern square. That makes the four regular tie-ups based on that profile uneven as well. Here’s an example:

Naming convention

Images of drawdowns with regular, star fashion tie-ups include _reg_ in their names, followed by the sequence of background (K) and specific halftones used to create them.

For example, tieup ‘PEKR’ means that the first profile treadle is tied up with [P]attern, followed by the [E]ven halftone, followed by bac[K]ground, followed by the [R]ose halftone. Treadles to the right are rotations of this first one, in which the pattern block moves up one position with each step to the right.

Regular rose fashion

Regular rose fashion tie-ups were created by flipping the corresponding star fashion tie-up horizontally. Therefore, the tie-up ID refers to the sequence of pattern, background, and specific halftones on the fourth profile treadle (in the fourth column), and the remaining treadles are rotations up and to the left.

Irregular tie-ups

Irregular tie-ups have a different pattern of background and specific halftone from one treadle to the next. There are nine different irregular tie-up profiles:

You may notice that Tieups 0, 312, and 624 are also in the list of the regular profiles. The difference is in the way that the halftones are applied. In regular profiles, the halftones are applied the same way in each column; in irregular profiles, the halftones are applied differently in each column.

To create the irregular structural tie-ups, the S and R halftones were applied in each permutation that produced a diagonally symmetrical tie-up. The first of each set has the S halftone applied in each location. The last of each set has the R halftone applied in each location. When only one halftone (S or R) is used in all locations, the halftones in the drawdown come together in a uniform checkerboard, like so:

Notice that in the first of the above drawdowns, the blue pattern blocks are not connected to one another at their corners, instead appearing as little “island archipelagos,” whereas in the second drawdown the pattern blocks are connected. This is always true: the pattern blocks in all “first” tieups – that is, anything numbered tieup.X.1 – are disconnected, and pattern blocks in all “last” tieups – that is, the final structural tie-up from each profile – are connected.

The other structural tie-ups for each irregular profile – the ones between the first and last – combine the S and R halftones in various ways. When that happens, the checkerboard halftone is not ones in between have a combination of S and R, which creates “blips” where the two checkerboards meet and do not align.

Bagatelle, Tieup.0.8, with white “blips”. Some blocks are connected, some are not.

Naming convention

Each irregular tie-up profile has a profile ID which comes from the process used to enumerate all possible tie-up profiles. These IDs refer only to the profile’s position in the full list of 624 profiles so enumerated; the numbers, digits, and order are not meaningful otherwise.

Each irregular tie-up profile has been expanded into a set of 2 to 16 structural tie-ups. These are numbered in order from 1 to 2, 4, 8, or 16 depending on how many structural tie-ups each profile represents.

Since the structural ID number of the final tie-up in each set is not consistent from one set to the next, it is always given the tag ‘last’ for ease of filtering. Even though the structural ID number of the initial tie-up in each set is consistent (it’s always 1), it likewise has the tag ‘first’.

Similarity and dissimilarity of irregular tie-ups

The 2-16 structural tie-ups that come from the same irregular profile are all very closely related; all that changes from one drawdown to the next is the presence and position of interruptions in the halftone checkerboard.

Structural tie-ups from different irregular tie-up profiles are unrelated to one another and their drawdowns look quite distinct.