The Geats wrote like the Danes – at the border the stones fell silent

Hrefningr and Gjalli and Brynjulfr and Gjafulfr placed this stone in memory of Fótr, their father, a very good thegn. … Hjalmr and Hjalli cut the runes.

So reads a runestone at Norra Härene church in Västergötland, Vg 59. Nearly everything in it is Danish: the stone was placed, as in Denmark, rather than raised or had raised, as in the Mälaren valley, and the dead man was a thegn, a title at home in the Danish realm. By then the runic script was already eight hundred years old in the North. But the custom of raising memorial stones with runes in great numbers was new, and it came from Denmark. How did it reach Sweden? And how sharp was the border between the realms – does it show in the runestones? We measured how Danish every runestone in Denmark and Sweden is in its wording and spelling, and we counted the stones and the grave fields on both sides of the border.

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The runes were older than the custom

The runic script is much older than the runestones. The oldest certain runic inscriptions, on a comb from the Vimose bog on Funen and on a spearhead from Øvre Stabu in Norway, date from about the year 160. Where the script came from is debated; most think it was created on the model of the alphabets of the Roman Empire. No carver of that time can be traced, and no one can say who brought the script to Sweden.

But the oldest runestones with the younger rune row already show that Denmark and Götaland belonged together. Around 800 the carver of the Rök stone in Östergötland wrote that Varinn fáði, Varinn coloured the runes, and on Funen a carver at about the same time wrote that Ávarr fáði (DR 190 Helnæs and DR 192 Flemløse). The same word for writing runes is found at Oklunda in Östergötland and at Gursten in Småland. According to Lisbeth Imer, the Danish runestones of the eighth and ninth centuries stood mainly on Funen and Zealand and in Scania.

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The great wave came in Denmark after the conversion. Harald Bluetooth raised the Jelling stone, by the usual dating around 965, and most Danish runestones were raised within two generations, around 970–1025. That is the wave that reaches Sweden.

Measuring a Danish stone

To follow the wave we needed a measure of how Danish a stone is. We let a statistical model learn to tell Danish from Swedish runestones by thirteen features of the wording of the memorial formula and of the spelling: whether the stone was placed, raised or had raised, whether the monument is called kumbl, whether the dead has the title thegn or drengr, whether the word stone is spelled stin or stain, whether "after" is spelled æft or æftiR, whether the carver wrote his name and whether he used dotted runes. Faith and journeys were left out, so that the measure does not merely tell Christian from pagan stones. The model learnt only from stones of the same time, 147 Danish and 576 Swedish from about 970–1050, so that it learns the difference between Danish and Swedish practice and not the difference between early and late stones. It tells a Danish from a Swedish stone correctly in 82 of 100 pairs.

Each stone then gets a Danish likeness between 0 and 1. Above 0.5 it is worded and spelled more like a Danish than a Swedish stone. That does not mean that the carver was Danish – only that he wrote the Danish way.

The measure passes a test it has never seen. Rundata's notes call 8 Danish stones Swedish-made or Swedish-influenced, for example the Simris stone in Scania, which according to Rundata was "made by a Swedish rune carver". The model has not seen the notes, but it gives just those stones a low Danish likeness, on average 0.37 against 0.61 for the other Danish stones. A difference this clear would arise by chance in about 1 cases in 100. Eight stones are few, so the test shows that the measure works, no more.

The charts show two of the features that differ. To place the stone is Danish and is found on the early stones of Götaland, but then disappears. To have it raised is the Swedish contribution: rare in Denmark, but on more than half of the late stones in the Mälaren valley.

The custom took root in Götaland

The earliest Swedish stones of the new kind belong to the style group RAK, with a plain rune band without an animal head, about 980–1015 in Anne-Sofie Gräslund's dating. They stand above all in Götaland. In Småland 87 % of the dated stones belong to RAK, in Västergötland 73 % and in Östergötland 66 %, but in Södermanland only 14 % and in Uppland 7 %. Gräslund has shown that the custom flourished in Västergötland from the end of the tenth century to the middle of the eleventh. In Uppland the great mass of stones came later.

The Danish imprint is strongest on the earliest stones and then fades, style group by style group.

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With the province held constant, the odds of a Danish wording roughly halve every half century. An association this clear would arise by chance in fewer than one case in a million, and it holds in both halves of the material.

But time does not explain everything. Västergötland is the most Danish province on Swedish soil: 50 % of the stones there are worded the Danish way, against 24 % in Östergötland, 29 % in Småland and 8 % in Uppland. Even among stones of the same style group the odds are 2.5 times as high in Västergötland as in the other provinces, and that holds in both halves. Scholars have long debated whether the difference between the runestones of Götaland and of the Mälaren valley is a matter of time or of region. Hans Christiansson held in 1959 that the South Scandinavian ornament, in Jutland, Scania and Västergötland, was a regional style; Gräslund has read it as an earlier stage. Measured by wording and spelling, both are partly right: the Danish imprint belongs both to the early time and to Västergötland.

Does the realm border show in the runestones?

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The realm border between the Danes and the Geats ran roughly where the medieval provincial borders between Scania, Halland and Blekinge on the one side and Småland and Västergötland on the other ran. We counted the runestones on both sides in bands by the distance from that border, and compared them with the grave fields in the Swedish National Heritage Board's register. The grave fields show where people lived and were buried; Scania, Halland and Blekinge belong to Sweden today, so the same register covers both sides of the old border.

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The border shows. On the Danish side, within 50 kilometres of the border, there are 446 grave fields but only 3 runestones – 0.7 per 100 grave fields. Further into Scania, 50–100 kilometres from the border, there are 31.1 per 100. A difference this large would arise by chance in fewer than one case in a million, and it holds in both halves. Two of the three stones in the belt, at Sölvesborg and Färlöv, belong to the earliest time, about 800; the third, at Lösen in Blekinge, is from after 1050 and according to Rundata made by a Swedish carver. During the great wave, about 970–1025, not a single runestone was raised there. The people of the belt buried their dead, but they raised no runestones.

On the Swedish side it is different. There the runestones stand right up to the border: 10.7 per 100 grave fields within 50 kilometres, in southern Småland and Västergötland. And at the border between the Geats and the Svear, through the forests of Kolmården and Tiveden, there is no silent belt at all: 13.1 and 9.1 runestones per 100 grave fields within 50 kilometres on either side.

So the realm border was not a line in the landscape, but a broad belt where the Danish custom never took root.

Does the border show in the language too? We looked for a place where the spelling changes: how "stone" and "after" are spelled, and whether the stone was placed, raised or had raised. At the realm border none of them changes with certainty. The spelling of "stone" changed mostly with time – the early stones write stin in Götaland and in Uppland alike – and so cannot show a dialect border. The largest difference in how "after" is spelled does not lie at the realm border, but within Denmark; we return to it among the hypotheses.

Scania

Scania belonged to the Danish realm, and its runestones are part of the Danish corpus. At the same time the Scanian stones are Danish in their wording: of the stones from the post-Jelling period, 67 % are worded the Danish way in Scania and 74 % in Jutland and on the islands, a difference that may easily be chance. They stand in southern and central Scania, far from the border.

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Scania was nonetheless bound to the Svear. The Hällestad stone and the Sjörup stone say of the dead that they "did not flee at Uppsala", and the Högby stone in Östergötland, carved by Þorkell, says that "the brave valiant man Ásmundr fell at Fœri". Since the nineteenth century the stones have been connected with the battle of Fýrisvellir near Uppsala, by tradition around 985. Men from both sides fought in the same battle just when the custom came.

The Swedish influence shows later. The stones in the east of the realm that Rundata calls Swedish-made stand at Simris in eastern Scania and at Lösen in Blekinge, and they date from after 1050. The Simris stone (DR 344) says that the dead was Gunnulfr's lad in Sweden. And on Bornholm the late stones write like the Swedish ones: none of the 27 Bornholm stones is worded the Danish way, and so it is in both halves. Laila Kitzler Åhfeldt has used 3D scanning to compare the carving technique of the Bornholm stones with Swedish stones, to test the question of carvers from elsewhere.

Who carried the custom across?

No single person can be pointed out. Danish carvers seldom signed their stones – only 13 of 239 Danish runestones name the carver – and no carver's name can be followed between the countries. But some stones show in which circles the custom moved.

• Fótr, a very good thegn. The titles thegn and drengr are found on 19 % of the Danish stones and on 14 % of the early stones in Götaland, but on only 2 % of the late ones in the Mälaren valley. The most common reading is that they denoted men in the circle around the Danish kings, but this is debated.
• Þorkell in Östergötland, whose Högby stone remembers a man who fell at Fýris and one who was killed at "Holmr", perhaps Bornholm.
• Júti on Björkö. A stone from the tenth century on Björkö, where the trading town of Birka lay, says that Dóttir ordered this monument to be made in memory of Júti (U 4). The monument is called kumbl, as in Denmark, and the dead man's name means "the Jute".

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Three bold hypotheses

What holds points to three hypotheses. They are bolder than the findings, but each has a basis that can be set out – and each can be tested.

1. The custom followed the king's men. The runestone custom did not spread as a fashion from one neighbouring district to the next, but with a network of men in the circle of the Danish kings, those called thegns and drengs.
The basis: Västergötland writes the most Danish way, also at the same time. The titles thegn and drengr are found on 19 % of the Danish stones and 14 % of the early ones in Götaland, but hardly ever in the Mälaren valley. Men from both Scania and Götaland fought at Fýris. And on the Danish side the runestones stand in the inner districts of the realm, not in the belt nearest the border.
The test: If the hypothesis holds, the early stones of Västergötland should stand by magnate farms and royal estates, and the carving technique on them should resemble that on Danish stones more than that of their neighbours. Both can be tested.

2. The border was a border of custom, not of language. The Danes nearest the border spoke and wrote like their neighbours, but the Danish runestone custom never reached them.
The basis: The silent belt on the Danish side holds in both halves, and people were buried there. At the border none of the spellings we could measure changes with certainty.
The test: More linguistic features, from the Danish database Danske Runeindskrifter and from the medieval inscriptions and place names on both sides, can show whether the language really ran across the border.

3. Scania wrote like the Swedes. The language border that shows in the runestones did not lie at the realm border, but ran through Denmark, between Jutland and Scania.
The basis: The word "after" is spelled short, æft, on 62 % of the stones in Jutland but only 13 % in Scania, with time held constant. Scania writes æftiR instead, as the Swedish stones do. A difference this large would arise by chance in about 1 cases in 100. The difference goes the same way in both halves, but is certain in only one, since the stones are few.
The test: With the Danish and Scanian inscriptions in Danske Runeindskrifter, including those not on runestones, it can be tested on more stones.

Caveats

• The datings rest on different systems: the Swedish stones on Gräslund's style groups, the Danish on Rundata's periods after Jacobsen and Moltke. The years are approximate, and the dating of the Jelling stone has recently been questioned.
• The border is drawn after the medieval provincial borders. The border about 1025 was probably a zone, and its exact course is unknown.
• Most grave fields are dated no more closely than to the Iron Age. In the plains of Scania many grave fields have been ploughed away, so the ratio of runestones to grave fields further into Scania is higher than it would have been. That does not change that the belt has many grave fields and almost no runestones.
• The patterns read Rundata's English translation and the transliteration, which are made the same way for all the countries. Crosses cannot be compared, as Rundata describes the crosses almost only on Swedish stones.
• Danish likeness is a measure of wording and spelling, not of the carver's origin.
• The Norwegian stones are too few to place Norway. They lack both the Danish features and the Swedish ones, which may suggest a Norwegian tradition of its own.
• An association is not a cause. The hypotheses explain the patterns, but other explanations are possible.

See for yourself

The comparison is in Vitki under the map, in the tab Compare countries, with the borders of the realms around 890, 1025 and 1200. On how the prayer came to the runestones and left them: The prayer fell silent – but the cross remained.

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The maps, curves and models come from Vitki, an open tool for runestone research that you can download and run on your own computer from GitHub. The method is described in METHODS.md.

Sources and data

• Scandinavian Runic-text Data Base (Rundata), Department of Scandinavian Languages, Uppsala University. Open Database License.
• The Swedish National Heritage Board's register of ancient monuments (Kulturmiljöregistret, via K-samsök): the grave fields. Open data.
• Fund og Fortidsminder, the Danish Agency for Culture and Palaces (find places for Danish stones without coordinates in Rundata). OpenStreetMap contributors (ODbL) and Natural Earth (borders and coast).
• Christiansson, H. 1959. Sydskandinavisk stil. Studier i ornamentiken på de senvikingatida runstenarna. Uppsala.
• Gräslund, A.-S. 2006. Dating the Swedish Viking-Age rune stones on stylistic grounds. In: M. Stoklund et al. (eds), Runes and their Secrets: Studies in Runology. Copenhagen: Museum Tusculanum Press, pp. 117–139.
• Gräslund, A.-S. 2015. The Late Viking Age Runestones of Västergötland: On Ornamentation and Chronology. Lund Archaeological Review 20 (2014), pp. 39–53.
• Imer, L. M. 2014. The Danish runestones – when and where? Danish Journal of Archaeology 3, pp. 164–174.
• Jacobsen, L. & Moltke, E. 1941–42. Danmarks runeindskrifter. Copenhagen.
• Kitzler Åhfeldt, L. 2019. Provenancing rune carvers on Bornholm through 3D-scanning and multivariate statistics of the carving technique. European Journal of Archaeology.
• Sawyer, B. 2000. The Viking-Age Rune-Stones: Custom and Commemoration in Early Medieval Scandinavia. Oxford: Oxford University Press.
• Wideen, H. 1955. Västsvenska vikingatidsstudier. Arkeologiska källor till Vänerområdets kulturhistoria under yngre järnålder och äldsta medeltid. Gothenburg.
• Photos: Wikimedia Commons, with photographer and licence in the captions. Figures: Vitki's analysis in R.