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ISSN : 1226-0401(Print)
ISSN : 2383-6334(Online)
The Research Journal of the Costume Culture Vol.24 No.6 pp.873-885

Symmetry, ratio and proportion in Scottish clan tartans
- Templates for modern designers -

Michael Hann†, Chaoran Wang
School of Design, University of Leeds, UK
Corresponding author: (
November 28, 2016 December 22, 2016 December 28, 2016


It is common knowledge that a conventionally woven textile consists of two assemblies of parallel threads (warp and weft), one interlaced with the other at ninety degrees. Where each of the two assemblies is arranged in a particular colour sequence, a check design, known as a ‘tartan’, may be created. Although similar check-type cloths have been produced worldwide, it is the tartans of Scotland which have received most attention and it is here that a complex set of rules evolved and tartans of different types became associated traditionally with different regions, family groups or 'clans'. There is an impressive array of publications focused on the identification of tartans and their clan associations. This paper explains the nature of tartans, analyses typical surface structures, ratios and proportions, and suggests possible avenues of use for modern designers. The principal sources of data were a collection of tartans held at ULITA - An Archive of International Textiles (University of Leeds, UK) and Stewart's 1974 publication The Setts of Scottish Tartans. Based on the observation that divisions into halfs and thirds were dominant, a series of templates is presented with the intention of developing an awareness among designers that ratios and proportions used in familiar or traditional frameworks can be employed in a modern context.



    Although tartan-type textiles have attained popularity the world over, it is in Scotland where this category of woven textiles underwent an evolution in design up to modern times and various design types (or setts) became associated with particular families, clans or geographical regions. There is an impressive array of publications focused on the identification of tartans and their clan associations. Probably the best known early works are those by Logan (1831), Stuart and Stuart (1842, 1845), Smith and Smith (1850), Simbert (1850), Grant (1886), Whyte (1891), Stewart (1893), Whyte (1906), Adam (1908), MacKay (1924) and Innes (1945); most of these are available for reference only at relevant specialist libraries. An interesting series of monographs, each focused on a particular clan, its tartan, armorial crest and related matters, was published in the 1950s and early 1960s, under the general title of Johnston's Clan Histories; examples included Grant (1952), Moncreiffe (1954), Stewart (1954), Dunlop (1957), Fraser (1954) and Dunlop (1960). Readily available publications, focused specifically on tartans, include: Bain (1938), McClintock (1943), Innes (1945), Hesketh (1961), Dunbar (1962) and Scarlett (1972, 1973). Stewart (1974) provided a useful explanatory bibliography of these and other important publications. Subsequently, notable treatese were produced by Dunbar (1984), Teall and Smith (1992), Way and Squire (2000), Urquhart (2000, 2005), Martine (2008), and Zaczek and Phillips (2009). More recently, Hann (2015) provided an explanatory section on tartans, including thirty-two colour plates of rarer tartan types, in the publication Stripes, Grids and Checks.

    Tartan cloth famously displays a checked feature, comprised of squares and other rectangles created by interlacing two series of threads (warp and weft), with each series arranged in a particular colour sequence and to a particular thread count and density (e.g. threads per centimetre or per inch); this sequence or order of different coloured threads is known as the ‘cloth sett’ or simply ‘sett’.

    It is the contention here that the modern designer has much to learn from considering the design of textiles such as these and, with this in mind, consideration is given below to aspects of space division associated with a selection of tartans as well as common geometric ratios and proportions associated with the finished textile.


    In the popular imagination, tartans are believed to be of very ancient lineage. This may well be the case with checked wool textiles in general, and it may be the case also that thread colours used in a particular region, in ancient times, were derived from dyestuffs available locally; so there may have been a tendency for certain colour palettes to dominate in different regions, depending on local dye-stuff availability. Detailed classification of Scottish clan tartans, and the specific use of a particular tartan design and colour palette by a particular family group, however, is of relatively recent origin (within the past two-hundred years). Often commentary on tartan origins will make reference to various historical documents, paintings or illustrations. Famously, a woodcut image, dated to 1631, showing checked textiles being worn by figures reputed to be Scottish highland soldiers (and volunteers to the army of Gustav Adolphus of Sweden), is cited as early evidence for tartan use (Hampshire and Stephenson, 2007; Moxon, 2016). Meanwhile it is pointed out often that Bonnie Prince Charlie’s armies were organized into tartan-clad regiments (Hann, 2015) and, after the defeat of the Jacobites at the Battle of Culloden, in 1746, a range of repressive legislation was enacted by the English authorities banning the wearing of highland dress (Hampshire and Stephenson, 2007; MacInnes, 2000). This was under the Act of Proscriptions which came into force on 1st August 1746 and made the wearing of ‘highland dress’, including tartan or a kilt, illegal in Scotland (Moxon, 2016). The law was repealed in July 1782, presumably because the Jacobites were no longer regarded as a threat (Moxon, 2016). During the nineteenth century the use of tartans gained in popularity in the wake of various visits to Scotland by English royalty, initially George IV in 1822 and Queen Victoria with her husband Prince Albert in the 1840s (Moxon 2016). In the twentieth century, tartans were famed worldwide, new designs were commissioned by major multi-national companies and eminent fashion designers launched tartan collections at key international fashion shows (Hann, 2015). By the early-twenty-first century tartans had retained their popularity and were a well recognised textile category worldwide.

    III.Tartan Setts

    There are many publications (some listed in the introduction to this paper) which identify different tartan types and provide interesting historical backgrounds to Scottish regional clans. By comparison, only a few publications have focused on actual production issues, including the identification and enumeration of setts and the precise orders of differently coloured yarns in given tartans. Stewart’s (1974) publication is one of these few and gave sett details for over twohundred- and-fifty designs, though it was remarked that this list was not exhaustive and by no means accounted for all tartans produced (Stewart, 1974). Issues such as weaving tension, yarn crimp and postweaving relaxation shrinkage in warp and weft directions, as well as orders of shrinkage which may occur during finishing, are of great importance in manufacture, but seem to have been ignored largely in published work.

    As indicated above, the ‘cloth sett’ (or simply ‘sett’) of a tartan gives the planned colour order and numbers of warp threads and weft threads. Full production details would include also a precise statement of yarn (or thread) count and the number of threads per unit length (inch or centimetre) in both warp and weft directions. It seems that all traditional tartan fabrics are of square (or balanced) sett, when in the finished state, which means that they have identical numbers and orders of yarn types, counts and colours (per unit of measurement) in both warp and weft directions. Further to this, setts may be classed as either ‘symmetrical’ or ‘asymmetrical’. The importance of symmetry in crafted and industrially manufactured objects has been recognized by numerous observers. A detailed explanation with relevant illustrations was, for example, provided relatively recently by Hann (2015). The concept may be used in the description of various figures, objects and images, all of which are either symmetrical or asymmetrical. Where symmetry does exist, two or more identically sized and shaped versions of each identical component of the figure, object or image, can be identified within the whole, and the placing of each identical component can be visualized most easily in terms of ‘symmetry operations’ of which reflection is probably the most common. Symmetrical setts have a series of pivots (in both warp and weft directions), with each pivot (denoted in notation form as an oblique stroke) acting like a two-sided mirror (or reflection axis) reflecting the order of threads in a warp or weft direction. So a pivot is where the colour and number of threads is reversed or reflected. With different pivots operating at similiar points in warp and weft directions, an identical order of colours and yarn counts will occur in both directions; reflection symmetry is thus a dominant characteristic of the majority of traditional tartans. For example, a MacKeane tartan has warp threads ordered as follows: 4/yellow, 2 black, 24 red, 16 black, 8 red, 16 black and 8/red (considered at the ‘sett’ or, occasionally, with symmetrical tartans, as the ‘half sett’) which is reversed or reflected to continue in reverse order as 16 black, 8 red, 16 black, 24 red and 2 black; reflection occurs therefore at each of the two pivots (4/yellow and 8/red), and the yarns at each pivot are not themselves reflected (Stewart, 1974). In shortened form this order of threads (in both warp and weft directions) can be represented as 4/Y, 2 Bk, 24 R, 16 Bk, 8R, 16Bk, 8/R which is reversed at either of the two pivots (each shown as an oblique stroke) to produce a ‘symmetrical’ arrangement of twelve bundles of yarn which repeat in the same colour sequence in both warp and weft directions. Meanwhile an ‘asymmetrical’ arrangement has no pivots, and the sett or order of threads will simply repeat across and down the cloth; so although the colour, order and types of threads in warp and weft directions are identical, groups of threads are not reversed through the use of pivots. Examples of asymmetrical arrangements include the Buchanan and MacAlpine tartans (Stewart, 1974), though it appears that the vast majority of tartans are organised on a symmetrical basis. Thus symmetrical tartans appear largely identical when viewed along the cloth (from top to bottom or bottom to top) or across the cloth (from right to left or left to right). It is worth noting that traditionally tartans were woven using a 2/2 twill (in a ‘Z’, or ‘right-hand’, direction); a minor consideration is the direction of the twill lines, which will differ when viewed in either a warp or a weft direction, though in the vast majority of cases this is only detectable at a close range of less than twenty centimetres (Hann, 2015). As a general rule, when in use, the ‘Z’ twill orientates vertically (with the upper and lower bars of the ‘Z’ oriented horizontally). Weaving is perceived often as a restrictive means of production, with patterning in the conventional process dependent on the manipulation of setts of threads interlaced at ninety degrees. Despite this, tartan checks (which are, after all, only a sub-category of woven textiles) show immense variation, through the numbering and ordering of yarn colours in warp and weft directions. Importantly, the repeating unit for all symmetrical tartans is in a square format, with equal numbers of warp and weft threads, to the same count and woven to equal density (threads per centimetre or inch). Within this square, further squares and other types of rectangles are created, as threads of the same or differing colours interlace.

    IV.Sources of Data and Sample Size

    All data were collected from the analysis of samples of finished tartans, selected from a collection held at ULITA - An Archive of International Textiles (University of Leeds) and cross referenced with the various publications listed in the introduction to this paper. Numerical details of setts were taken from Stewart (1974). Further comparisons were made with web-site based material (provided, for example, by the Scottish Tartans Authortity at Occasionally, where contradictions were apparent, samples were not included for analysis. Twenty-five symmetrical tartan designs (in their finished cloth state) were selected, with this sample size determined by the number of examples for which dependable cross referencing was available; the selected tartan types are listed with their half setts (not allowing for reversing of numbers at pivots) and colours in <Table 1>. It is readily apparent that all except one of the sett numbers in the sample are even numbers; this is apparently because working practice among traditional hand weavers was to work from left to right and the insertion of an even number of weft threads in each given colour allowed the shuttle to return to its original box at the left-hand side of the loom, in readiness for further use. The one exception is the Robertson tartan sett which contains three red threads within its half sett (Stewart, 1974); the authors have been unable to find a reason for this apparent annomoly.

    It should be noted that warp- and weft-ways measurements were carried out on finished historical textiles and that it was not possible to assess the degree of post-weaving shrinkage, though it should be noted that where the known setts suggested square ratios (as with all symmetrical tartans in the sample) this indeed was always evident. It may be the case that warp- and weft-ways shrinkage were largely similiar and, as a result, did not affect ratios and proportions to any visually detectable degree. It should however be stated further that the assessment of warp and weft-ways shrinkage, in the absence of knowledge of production conditions, is not readily attainable, and this is an obvious weakness of examining historical collections.

    V.Ratios and Proportions

    In all symmetrical tartans there will always be a strong preponderance of squares in either solid colour or ‘blended’ colour (the latter involving one colour from the sett interlacing with another colour from the sett). Squares will result when equal numbers of warp and weft threads are interlaced. Interlacements involving unequal numbers of warp- and weft-direction threads will produce rectangular forms in differing length and breadth ratios depending on the number of threads used. The most common ratios found in the sample of twenty-five tartans were identified and are listed in <Table 2>. Considering the prepondance of squares of various sizes in all symmetrical tartans, it is not surprising that the most common length to breadth ratio (found in 100 per cent of the tartans examined) was 1:1. The next most common ratio, found in 80 per cent of the sample, was 1:2, followed by 2:3 (48 per cent), 1:3 (36 per cent), 1:4 (28 percent) and 3:4 (24 per cent). Based on these findings a series of six compositional frameworks was created with unit cells in each case conforming to the dominant length to breadth ratios exhibited by the analysed sample of tartans. Further to this, and by way of example, each grid was given a simple checker-board-type design (Fig. 1, to 6) and was subsequently manipulated using commonly available software (Fig. 7b, c and d, 9b, c and d, 11b, c and d, 13b, c and d, 15b, c and d and 17b, c and d). By way of example, a resultant manipulated image was selected and brought into simple repeat (Fig. 8, 10, 12, 14, 16 and 18); the intention is to stimulate further (or alternative) developments among designers.

    VI.Design Layers

    As noted in the introduction and elsewhere in this paper, the dominant aesthetic characteristic of tartans is their checked appearance, based on warp threads in a given order of colours interlacing at right angles with weft threads in the same order. Each colour in a sett can be visualised conveniently as a layer or grid, formed from two series (one warp and the other weft) of parallel threads of the same colour intersecting at ninety degrees. So, in order to understand more fully the dominant aesthetic features of tartans, it was decided to consider each tartan sample in terms of a series of layers or grids, and to ascertain the dominant features of this layering in each case.

    An images of each tartan in the sample was reproduced using commonly available software, making reference to the samples held at ULITA - An Archive of International Textiles and supported by the sett data provided in Stewart (1974). The repeat unit within each tartan was identified. By way of example, black-and-white reproductions for Brodie and MacNeill tartans are presented in <Fig. 19> and <Fig. 20> respectively. The repeat unit of each tartan (comprised of the full sett, which takes into account reflections at pivots) is held within a box labelled ABCD (Fig. 19 and 20). Within this repeat unit, the design in each case can be considered, in three-dimensional space, divided into a series of layers with each layer formed from a grid of warp and weft threads of a given single colour. So the number of layers for each tartan will be equal to the numbers of colours used in the sett (e.g. three for the Brodie tartan and six for the MacNeill tartan). With both the Brodie and MacNeill tartans it was found that warp- and weft-direction stripes (which together give the checked appearance) coincided clearly with vertical and horizontal dividing lines within the square repeat. These dividing lines were positioned at half-way and third way points, and bundles of yarn colours were distributed equally on either side of these dividing lines. Similar results were obtained across the full sample of twenty-five tartans.

    Each repeat unit across the whole sample was considered and it was found in 100 percent of cases that the constituent groups of threads in a given colour were arranged at half way and/or quarter way and/or eighth way line divisions, both vertically and horizontally, within the repeat unit. Half-way division is not surprising as all the tartans in the sample are symmetrical, but further half divisions (or sub-divisions) where bundles of threads are positioned at quarter way or eighth way points within the repeat unit seem worthy of note. Third-way divisions and sub-divisions (at one sixth or one twelfth) of the repeat unit were less common, at 76 per cent of the sample, but still worth noting as this has a great influence on the proportions evident in the relevant check designs.

    VII.Compositional Templates for Modern Designers

    Based on the observation that divisions into halfs and thirds were dominant, a series of six templates was produced, with the proportions shown in each derived from the most dominant proportions found in the sample (Fig. 21). These proportional templates were subsequently given a checkerboard-type design (Fig. 22), and each of these was manipulated using commonly available computer software (Fig. 23b, c and d, 25b, c and d, 27b, c and d, 29b, c and d, 31b, c and d and, 33b, c and d). A single selection from each was brought into simple (square) repeat (shown as e in Fig. 23, 25, 27, 29, 31 and 33) and each selection is presented in an enlarged format and without the underlying grid-type guideline in <Fig. 24, 26, 28, 30, 32 and 34>. Again the intention is to develop an awareness that ratios and proportions used in familiar or traditional frameworks can be employed in a modern context.

    VIII.In Conclusion

    Often forms from familiar or traditional compositions have an underlying structure which may offer a hidden value to modern visual artists and designers. This brief examination of Scottish clan tartans has highlighted that beneath conventional check designs various ratios and proportions are present. This paper proposes a series of compositional templates based on these observations. Each offers scope for further (or alternative) development or elaboration. The suggestions made here are insufficient to make a dramatic impact on design practices, but the intention is simply to underline the potential value of delving into past compositional decisions, identifying structural principles and utilizing these in a modern design context.



    Checker-board effect on 1:1 grid.


    Checker-board effect on 1:2 grid.


    Checker-board effect on 2:3 grid.


    Checker-board effect on 1:3 grid.


    Checker-board effect on 1:4 grid.


    Checker-board effect on 3:4 grid.


    Checker-board effect on a 1:1 grid (a), manipulations (b, c and d) and tiling (e).


    Tiling design in square repeat derived from manipulations of a 1:1 grid.


    Checker-board effect on a 1:2 grid (a), manipulations (b, c and d) and tiling (e).


    Tiling design in square repeat derived from manipulations of a 1:2 grid.


    Checker-board effect on a 2:3 grid (a), manipulations (b, c and d) and tiling (e).


    Tiling design in square repeat derived from manipulations of a 2:3 grid.


    Checker-board effect on a 1:3 grid (a), manipulations (b, c and d) and tiling (e).


    Tiling design in square repeat derived from manipulations of a 1:3 grid.


    Checker-board effect on a 1:4 grid (a), manipulations (b, c and d) and tiling (e).


    Tiling design in square repeat derived from manipulations of a 1:4 grid.


    Checker-board effect on a 3:4 grid (a), manipulations (b, c and d) and tiling (e).


    Tiling design in square repeat derived from manipulations of a 3:4 grid.


    A reproduction of a Brodie tartan.


    A reproduction of a MacNeill tartan.


    Compositional templates.


    Checkerboard effect on each compositional template.


    Checker-board effect (a), manipulations (b, c and d) and tiling (e) using a compositional template.


    Tiling design in square repeat derived from manipulation of a compositional template.


    Checker-board effect (a), manipulations (b, c and d) and tiling (e) using a compositional template.


    Tiling design in square repeat derived from manipulation of a compositional template.


    Checker-board effect (a), manipulations (b, c and d) and tiling (e) using a compositional template.


    Tiling design in square repeat derived from manipulation of a compositional template.


    Checker-board effect (a), manipulations (b, c and d) and tiling (e) using a compositional template.


    Tiling design in square repeat derived from manipulation of a compositional template.


    Checker-board effect (a), manipulations (b, c and d) and tiling (e) using a compositional template.


    Tiling design in square repeat derived from manipulation of a compositional template.


    Checker-board effect (a), manipulations (b, c and d) and tiling (e) using a compositional template.


    Tiling design in square repeat derived from manipulation of a compositional template.


    The (half) setts and colours of a selection of twenty-five tartans

    Key: Y=yellow; R=red; B=blue; Bk=black; Gy=grey; G=green; W=white; Lv=lavender; Az=azure; Helio=heliotrope (or light purple); Cr=crimson; Res=reseda (or pale green); Dy=dull yellow; P=purple Source: Stewart. (1974).

    Common ratios found in Scottish clan tartan setts

    Sample size: 25 finished tartans
    Source: ULITA - An Archive of International Textiles (University of Leeds, UK)


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