How to Add More Repeating Segments to a Folded Paper Scale Strip

Before opening your folds, choose what you want to preserve: the size of each segment or the overall paper length. That choice determines the method.

Your goal	Best approach	What changes
Add segments of the existing size	Attach matching paper and continue the pattern	The strip uses more paper
Add segments without a join	Start again with a longer strip	The original strip becomes a reference
Fit more segments into the same paper length	Divide the paper into smaller sections	Each segment becomes smaller
Keep the same size and use only the existing paper	Check for an unused tail	The number of additions depends on the remaining paper

A joined strip is a practical construction method. The Clyfford Still Museum’s accordion instructions begin by joining paper strips at their short ends and applying tape to both sides. That provides a useful foundation for extending a simple folded strip. The placement and alignment checks below adapt that method to an existing repeating pattern. Create an Accordion Book — Clyfford Still Museum

Partially unfold two or three segments near the end. Keep the rest folded so you retain a clear reference. Place the strip with its intended display side facing up and keep that orientation throughout the extension process.

Find two equivalent points in neighboring repeats: for example, the first mountain crease of one scale and the first mountain crease of the next. Measure the distance between them on the flattened paper. This is the repeat length: the amount of flat paper consumed by one complete repeat.

Do not assume that the visible width of a folded scale equals its repeat length. A tucked or overlapping section includes paper hidden underneath. Copying only the exposed face would omit that allowance.

For a plain concertina, distinguish a panel from a full directional repeat. A panel is the paper between neighboring creases. The sequence of fold directions repeats after a mountain fold and a valley fold. Chandra’s folding instructions explicitly describe fan folding as alternating mountain and valley creases, with folds reversed where necessary. Science + Origami — Chandra X-ray Observatory

Record the strip width, the flattened repeat length, the crease positions within that repeat and the direction of each crease. A pencil sketch on scrap paper is enough. If you cannot identify where the sequence starts again, unfold one more segment before cutting an extension.

Use this planning rule: extension length = number of additional repeats × flattened repeat length + joining allowance. The joining allowance is the paper hidden in an overlap; it does not count as an additional segment.

For an illustrative example, suppose your decorative strip has a complete repeat every 20 mm when flattened. You want six additional repeats and plan a 10 mm overlap. Prepare an extension 130 mm long: six times 20 mm gives 120 mm of usable pattern, plus 10 mm for the join. These dimensions illustrate the calculation; measure your own strip before using them.

A join made by bringing the ends together without overlapping them needs no overlap allowance. In that case, the example would require 120 mm of additional paper. Tape would bridge the meeting edges.

Check whether the existing end is a complete repeat. If it stops halfway through a unit, first determine how much paper is needed to finish that unit. Keep that amount separate from the allowance for six entirely new repeats. This avoids counting a partial end as a finished segment.

Gather matching paper, a ruler, pencil, scissors and either tape or a glue stick. Use the same paper as the original where possible. As a practical check, fold a short scrap into two or three segments and compare how it sits beside the existing strip before preparing a long extension.

Cut the new strip to the same width. Place the two strips beside each other on a flat surface and align their long edges. Correct a taper now; otherwise, the extension will introduce an obvious step along the finished edge.

Mark the crease positions on both long edges of the extension. Connect corresponding marks lightly across the width. Measure from one fixed starting point rather than repeatedly measuring from the previous mark: this makes it easier to spot a misplaced line before folding.

For equal divisions, a separate paper template is another option. Origami Resource Center demonstrates transferring divisions from an evenly spaced template and notes that preprinted lined paper can serve the same purpose. Use a template that matches your measured spacing when preserving existing segment sizes. Dividing Paper: Easy Method — Origami Resource Center

First arrange the extension without adhesive. Open enough of the existing end to lay the connection flat, then position the new strip so its crease sequence continues the original. Fold the first two new segments provisionally and compare them with the last two old ones.

Choose one of these two joining arrangements:

• Edges meeting: Bring the short ends together without overlap. Apply tape across the meeting edges, then turn the strip over and tape the reverse. This follows the museum’s basic joining method and preserves the calculated paper length.
• Overlapping ends: Mark the joining allowance and place that portion beneath the existing end. Keep the overlap within a flat panel where the design permits, leaving neighboring crease lines free. Apply a thin, even layer of adhesive and maintain the alignment while it sets.

For either arrangement, align both long edges and check that the join does not create an extra-wide panel. An overlap must occupy paper reserved for joining; laying one complete patterned segment over another changes the segment count.

Close the nearby folds gently before committing to the whole extension. If the join catches, creates an unintended crease or makes the first new segment a different size, reposition it. Once the adhesive has set according to its instructions, continue folding. For a strip with tightly tucked scales, consider placing the join before the tucked area or making a new, longer strip if the added layer prevents the unit from closing.

Work outward from the existing strip. Fold along each marked line, matching the direction required by the established sequence. For a simple concertina, a mountain crease rises toward you and a valley crease recedes from you when viewed from the same face.

Make only two or three new segments at first. Bring them together loosely and compare their edges with the original folded stack. This short check reveals spacing and alignment errors before they affect the entire extension.

Inspect three things: whether the upper and lower edges remain aligned, whether equivalent segments have equal widths, and whether the fold sequence passes smoothly through the join. For a scale pattern with extra shaping, complete each unit’s diagonal folds or tucks before assessing its appearance.

If the segments begin drifting sideways, reopen the affected portion and compare the crease endpoints with your pencil marks. Correct the first misplaced fold rather than adding a compensating slant farther along. If two neighboring folds face the same way in a plain concertina, reverse the incorrect crease and resume the alternating sequence.

If you want more divisions without attaching paper, the repeat size must decrease. Repeated halving produces equal divisions such as quarters, eighths and sixteenths; Origami Resource Center describes this approach for dividing paper. Dividing Paper: Easy Method — Origami Resource Center

For example, a 240 mm usable length divided into eight equal panels gives 30 mm panels. Dividing that same length into sixteen gives 15 mm panels. This calculation concerns flat paper; it does not specify the displayed length of the folded strip.

To change an existing eight-panel concertina into sixteen panels, open it and mark the midpoint of every panel. Fold at the new divisions, then reassign all crease directions into an alternating sequence. Some original folds will need reversing. Simply adding midpoint folds while preserving every original direction will not produce a regular concertina.

If each scale has additional shaping, test one complete smaller repeat on scrap paper first. Its internal fold positions must shrink proportionally as well. Halving only the main panel width leaves the rest of the design mismatched.

Open the finished strip gradually, then bring it back together. Inspect the join in both positions. Look for a stepped edge, an unusually wide segment, adhesive extending into a working fold or an incomplete final unit.

Finish at a complete repeat whenever the design allows. Leave any required end flap intact, and trim only surplus paper beyond it. If the extension matches in width, crease spacing and fold direction, the new segments should read as a continuation of the original pattern.

For the most straightforward extension, preserve one measured repeat, calculate the added paper from that repeat and test the join before folding the full length. Those three checks give you a clear way to add segments without gradually changing their size.

• Create an Accordion Book — Clyfford Still Museum
• Science + Origami — Chandra X-ray Observatory
• Dividing Paper: Easy Method — Origami Resource Center