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SECTION I: THE FOLDED SHEET

Let us start with the single idea that defines what a book is.

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A book was never printed as pages. It was printed on large sheets, and each sheet was folded. The number of folds is what we call the format. Folio, quarto, octavo, these are not sizes. They are fold-counts dressed with Latin names, and almost everything about antique books falls out of this one act of folding. 
 

Let us now shift our focus to vocabulary. We only require six words. A sheet is the whole piece of paper as it left the mould. Once it is folded, it becomes leaves. A leaf is one folded page-unit with two sides. A page is one side of a leaf. Therefore, a leaf always equals two pages, unless it is particularly a thick leaf, a three dimensional rectangular cuboid, giving us six pages. For our purposes, since we are not a Mesopotamian scribe that fills all six sides of a clay tablet, we ought not entertain this idea further. The front side is the recto, and the back is the verso. A single sheet folded once gives a bifolium, two leaves that are still physically one piece of paper, and those two leaves are said to be conjugate. Conjugacy is a crucial concept: it is the thread that will let us catch a made-up copy because a leaf that should have a conjugate twin and does not is a leaf that has been operated on.

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The folding law

Each fold doubles the leaves and that is all there is to it in terms of arithmetic. If n is the number of folds, then leaves = two to the power of n, and pages = two to the power of n+1. One fold gives two leaves, and four pages, and that is a folio. Two folds give four leaves and eight pages, a quarto. Three folds give eight leaves and sixteen pages, octavo. The names are simply the leaf-count per sheet. Octavo takes its name from octo, eight, because the sheet yields eight leaves. The physical process is the following: fold the sheet, watch the counts, and watch two other things: the chain lines and the watermark.

Above is a full sheet. It has no folds, is a single sheet, has two pages, and the chain lines are vertical. Chain lines are the widely-spaced lines, roughly an inch apart, visible in the paper's texture; wire lines are the finer, closely-spaced lines running perpendicular to them. To truly understand what these lines are, one can observe them by placing a light source behind a piece of 'antique laid' paper that dates from the twelfth to the nineteenth century. Prior to the introduction of mechanised paper-making, paper was manufactured manually, with each sheet formed individually using a rectangular mould fitted with a wire mesh, the fine laid wires bound at intervals by thicker chain wires that held the mesh taut against the mould's frame. The papermaker submerged the mould into a vat containing a diluted mixture of hemp or linen fibres suspended in water. Once removed, the mould was tilted to ensure the fibres were spread evenly across the mesh while excess water drained away. The mould was then gently shaken to bind the fibres together, transferring both the dense wire pattern and the wider chain pattern onto the surface of the finished paper. Every sheet of hand-press paper carries this double grid as an involuntary signature of its own making. When we fold, the paper does not mind which way is up, but we read the finished leaf in one orientation, and relative to that reading orientation the chain lines turn ninety degrees with every fold after the first. The first fold runs with the chain lines, so a folio keeps the vertical lines of the unfolded sheet; the second fold crosses them, so a quarto reads horizontal; the third turns them back, so an octavo reads vertical again. Chain lines running up the page therefore point us to a folio or an octavo, and chain lines running across point us to a quarto. The watermark, visible in the graphic above, sat in the middle of the half-sheet, and the folding carries it toward the spine and then into the corner. We can see this from the interactive widget above. In order these are the folio, quarto, and octavo. A tiny worked case would be the following: imagine we are handed a leaf. Chain lines run horizontally, and a fragment of watermark peeks out of the gutter at the top. That is a quarto, and we have not touched a ruler. Now consider a tall book and a short book that both do this. They are both quartos. Their difference in height is a difference in the sheet they were folded from, not in the format.

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Size is a liar

This is the counterintuitive crux of the matter, so let us be blunt. A common phrase one might say is 'a big book, so it must be a folio,' and this is usually right, and never to be relied on. Format is fold-count. Size is the sheet-size reduced by that folding. A folio printed on a small sheet (a pot-paper folio) can stand shorter than an octavo printed on a large one (a royal or imperial octavo). The names Chancery, Pot, Foolscap, Crown, Royal describe sheet dimensions. Folio, quarto, octavo describe foldings. We need both words to describe a book, and confusing them is the beginner's tell.​

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A table summarising folds, leaves, pages, chain lines and watermark of a folio, quarto, octavo and sextodecimo.

Three complications

First, the format is not always the gathering. A gathering (the unit that gets sewn, which later will be called a signature) is often more than one sheet nested inside another. An octavo is usually gathered in eights, one sheet per gathering, so format and gathering coincide. But a quarto can be gathered 'in eights,' meaning two quarto sheets tucked one inside the other, giving eight-leaf gatherings from a four-leaf format. So when we eventually read a formula like 4°: A–K⁸, that superscript 8 is the gathering size, and the little degree sign is the format. They are answering two different questions. We ought not let the eights fool us into calling it an octavo. This is precisely the confusion Section III will tackle.

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Second, half-sheet imposition. Sometimes a printer laid out a whole gathering's worth of pages on one side of the sheet, printed it, then printed the same forme on the other side and cut the sheet in two, getting two identical gatherings from one sheet. It saves paper on short sections. The tell is a gathering whose two halves are conjugate to nothing, and it matters enormously later, because half-sheet imposition creates leaves that look like cancels but are not.

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Third, duodecimo, the format that breaks the tidy powers of two. A 12° does not come from clean halving. The sheet is cut and folded in a more involved pattern (commonly a strip of one-third folded off and tucked in), yielding twelve leaves and twenty-four pages, with signature and watermark evidence that is genuinely messy. When we meet a book whose arithmetic will not resolve into 2ⁿ, we should suspect a twelves, and know in advance that the chain lines and watermark fragments will argue with each other. That mess is normal. Most cheap Elzevir-style pocket editions are twelves, since the whole commercial point of the Leiden and Amsterdam trade was cramming a lot of readable text into a small, cheap, well-imposed format.

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Notice that the arithmetic is also an economic argument. A single sheet costs the same to buy whether we print four pages on it (folio) or sixteen (octavo). So format is a lever on cost per page, and the drift of the whole European trade from grand folios toward octavos and twelves across the sixteenth and seventeenth centuries is, underneath the bibliography, a story about paper being the expensive input and printers learning to fold it harder. When Aldus standardised the octavo for portable classics, he was not making an aesthetic choice so much as a manufacturing one that happened to also make books we could put in a pocket. The Estienne folios and the Elzevir twelves sit at the two ends of that same lever.​​​​​​​​​​​​​​​​​​​

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