Quire formulas

An important part of any manuscript description concerns the question how many quires of what kind the respective codex is composed of, and whether there are any leaves lost or added later. Two systems are used internationally to summarise this information by so-called collation forulas, and both are used on this Wiki.

English system

Under work

The codification below is based on that offered by N.R. Ker in his Catalogue, p. xxii. Anders Winroth has adapted it to reflect his practice, which is based on the descriptions found in Barbara Shailor, Catalogue; this is the standard commonly used in the U.S.A.

Collation. The formulas used to show the construction of a quire are these:

1. 1⁸. The eight leaves forming the quire are four conjugate pairs (i.e. four sheets or bifolia), 1 and 8, 2 and 7, 3 and 6, and 4 and 5. In some cases it is not possible to absolutely positively determine that all four are complete bifolia (because the binding is too tight or for other reasons), but careful examination respecting the integrity of the material manuscript has revealed no reason (e.g., stubs) to suspect otherwise.
2. 1⁸ (3 and 6 are singletons). Six of the leaves are conjugate pairs, 1 and 8, 2 and 7, and 4 and 5. Two of them, 3 and 6, are not conjugate.
3. 1⁸ (+1, after 5). Six of the leaves are conjugate pairs, 1 and 6, 2 and 5, and 3 and 4. A seventh leaf lies between 15 and 1° and is an original part of the quire. ??
4. 1⁸ (+1, after 5). This differs from (c) in that the odd leaf is not an original part of the quire, but has been inserted at a later date.
5. 1⁸ (-1, 2nd leaf). Formally this quire is identical with (c), but a gap in the text or some other evidence shows that the odd leaf, 17, was once paired with—but may not have been actually conjugate with—a leaf now missing after 1¹.
6. 1⁸ (-1, 8th leaf, probably blank). The scribe finished writing his text on or before the seventh leaf. The eighth leaf of the quire, now missing, was presumably blank. Formally the collation 1+-1 before 1 is equally possible, but it seems unlikely that a scribe would deliberately begin his quire with a half-sheet. More probably he, or another scribe, or a binder, or a later owner or librarian in need of parchment removed the blank leaf at the end. -- This example illustrates the flexibility of the English system, which allows any explicatory brief not to be added in parenthesis.
7. 1⁵ (singletons). The quire consists of five leaves, which appear to be singletons (half-sheets). The same circumstances may also be indicated with "1 five".

Example

We describe the quire structure in Firenze, Biblioteca Nazionale Centrale, Conv. soppr. A I 402 (a copy of Gratian, siglum Fd) thus:

Fascicoli: 1⁸ 2⁸(-1, 7th leaf) 3-5⁸ 6⁴ 7-21⁸ 22⁴ 23⁸ 24¹ 25² 26³(singletons).

In cleartext this means:

The first quire (or fascicolo, plural fascicoli in Italian in this multi-language description) in the book (as preserved) is a regular quire of eight leaves, presumed (or known) to be made up of 4 bifolia, a quaternion. The first quire, at least, of the book was in fact lost, but quires that are entirely lost are not accounted for in the collation formula.

The second quire had the same structure when the book was first made, but the seventh leaf has been cut out. The second quire contains, thus, now only 7 leaves. Since no peculiarities in the pagination has been pointed out, we can calculate that the missing leaf once was between f.14 and f. 15, and that f.10 is a singleton (half-sheet). As it happens, no text is missing here, so the leaf must have been cut out while the manuscript was being written. This is not indicated in the collation, but the formula does in fact allow such information to be added, e.g., thus: "2⁸ (-1, 7th leaf, without missing text)".

The third through fifth quires each are regular eights (quaternia).

The sixth quire consists of 4 leaves = 2 bifolia.

The seventh through twenty-first quires each are regular eights (quaternia).

The twenty-second quire consists of four leaves (two bifolia).

The twenty-third quire is a regular eight (quaternion).

The twenty-fourth quire is a single leaf (singleton). Technically, this could have been considered a part of quire 23, in which case the notation would be "23¹⁰ (-1, the 1st leaf)". It could also have been considered a quire together with what now is quire 25, in which case the notation would be "24⁴ (-1, the 4th leaf)". The author of the collation opted not to follow either of these two alternatives, since this leaf (f.176) in his judgment is an inserted leaf with no connection to either quire 23 or 25. It is a single leaf from the Compilatio quinta. The describer thus considered that this leaf comes from a complete (or at least fuller) copy of that collection and for some reason has been inserted into this volume.

The twenty-fifth quire is a single bifolium.

The twenty-sixth quire is not really a quire, simply three single leaves (singletons, half-sheets).

Folio numbers

In the English system, folio numbers are not directly indicated in the formula but may be derived with a simple algebraic formula. To calculate the folio number of the last folio of a set of quires, perform the following operations: For each component in the formula multiply the number of quires with the number of leaves in each quire. Then subtract or add the numbers within parenthesis. For example, to calculate the folio number of the single leaf making up quire 24 in the example collation above, perform the following operation:

(1*8)+(1*8)-1+(3*8)+(1*4)+(15*8)+(1*4)+(1*8)+(1*1)=176

When formulating the formula, it is more convenient to count all quires of the same size together:

(21*8)-1+(2*4)+(1*1)=176

(There are 21 quires which contains or once contained 8 leaves each, namely quires nos. 1-5, 7-21 and 23, plus 2 quires that contain 4 leaves, namely quires 6 and 22, minus 1 leaf that has been removed, in quire 2. The last parenthesis is the leaf for which we are looking for the folio number.)

If the manuscript is paginated rather than foliated, one multiplies the result by 2., which gives the page number of the last page.

German system (Chroust)

In German-speaking scholarship, the most common form to describe the quire structure of a codex is that developed by Anton Chroust around 1900 (known as Chroust'sche Lagenformel). In this system, the focus is on the type of quires a codex is composed of. If a codex (as it is very commonly the case) consists of medieval parchment quires with modern paper fly leaves, only the parchment folios are taken into account. Roman numbers are used to indicate the different quire types (I for a bifolium, II for a binio, III for a ternio, IV for a quaternio, and so on). If there is a series of quires of the same type, preceding Arab numbers indicate how many. A plus sign is used between the individual series of quires. A codex composed of one ternio followed by three quaterniones is thus described as follows:

III + 3.IV

Leaves that were cut out or inserted later are notated with a plus or minus sign after the quire type which is placed in brackets in such cases. To retain the same example, if the ternio lost a leave but the last quaternio was later supplemented with two more single leaves, the formula would be:

(III-1) + 2.IV + (IV+2)

Finally, to make it easier to check the quire structure, the folio number of the last folio in a series of quires of the same type is indicated by superscript Arab numbers.

(III-1)⁵ + 2.IV²¹ + (IV+2)³¹

The Chroust formula for Firenze, BNC, Conv. soppr. A I 402 (the Gratian copy mentioned above) would be:

IV⁸ + (IV-1)¹⁵ + 3.IV³⁹ + II⁴³ + 15.IV¹⁶³ + II¹⁶⁷ + IV¹⁷⁵ + (I-1)¹⁷⁶

and translates as follows:

The first quire is a quaternio and ends fol. 8, the next already at fol. 15 because of the one leave being lost; after three more quaterniones we are at 15+(3*8) = fol. 39, the binio ends after four folios at fol. 43, the series of fifteen quateriones (15*8 = 120 folios) ends at fol. 163, the binio at fol. 167, the quaternio at fol. 175, the leave we treat as a separate quire is fol. 176.

The remaining folios (a binio and three singletons, see above) are not foliated, and thus conventionally are not counted for the Lagenformel.

From this formula, it is easy to see that the quires together contain 176 folios, and that Fd mainly consists of quaterniones; also, it is relatively easy to see that there are only two biniones (the two "II" stand out) and where to find them (fol. 40-43 and 164-167, respectively), but it is less straightforward to say how many quires there are in total (1+1+3+1+15+1+1+1 = 24), and one simply cannot tell where between fol. 9 and fol. 15 the lost leave originally was.

Literature

N.R. Ker, Catalogue of Manuscripts containing Anglo-Saxon (Oxford 1957) esp. p. xx. - J.-P. Gumbert, L'unité codicologique, ou : à quoi bon les cahiers ?, Gazette du livre médiéval 14 (1989) pp. 4-8. - Franz M. Bischoff, Methoden der Lagenbeschreibung, Scriptorium 46 (1992), pp. 3-27. - Barbara Shailor, Catalogue of medieval and Renaissance manuscripts in the Beinecke Rare Book and Manuscript Library, Yale University (Binghamton, N.Y., 1984-2004) (the first three volumes are online: vol. 1, vol. 2, vol. 3).