Monophthong spellings become rarer on the runestones – from 69 to 22 percent between about 1000 and 1115

There is agreement that the East Norse monophthongisation, in which the diphthongs æi, au and øy became long monophthongs, began in Denmark in the tenth century, and the evidence is the spelling of the runic inscriptions: the digraphs are replaced by a single rune, so that stain becomes stin (Marklund 2018, p. 12, with references). From the spelling of the runestones Elias Wessén assumed that the sound change reached Östergötland and Västergötland around the year 1000 and central Sweden towards the end of the eleventh century (Wessén 1968, pp. 32 f., after Marklund 2018, p. 12). Magnus Källström (2014) has read the spelling sten, with a dotted i-rune, as a sign that æi had become [e:] in Västmanland, around Uppsala, in western Uppland and at two places in Södermanland, and he frames the question as one of written norm and dialect (after Marklund 2018, p. 13). That the carvers spelled differently, and that spelling can be used to tell them apart, has long been known (Thompson 1975).

We have found no study that measures how the share of monophthong spellings changes over time with place and carver held constant. If the spelling followed the pronunciation, the share should rise in the Mälaren region during the eleventh century. The aim here is to measure the change and to test whether it holds.

No analysis plan was locked for this question before the results were known. The finding is therefore not pre-registered, and it should be read as a discovery in a systematic survey.

The survey was a general method applied at once to 14 traits in the spelling and content of the runestones: the same model, the same measure of time, the same correction over the traits and the same division of the material into two halves for every trait, fixed in the program code before the survey was run. The trait in this report was added to the survey on 11 October 2026. On the same day, after the pattern had been seen, twelve checks of the measurement were added to test the objections a runologist would reasonably raise; all are reported in section 5.4, including those that do not hold.

The p-value is corrected for the 14 traits tested and for all 48 associations the project reports, and the halves were fixed independently of the patterns. Section 5.5 on the carvers and the ways of spelling is exploratory: it was computed after the pattern was known and is reported with p-values that are not adjusted. The check of the coding in 5.4 was made on 31 October 2026, while the report was being written.

• Source. The Scandinavian Runic-text Database (Rundata), Department of Scandinavian Languages, Uppsala University: transliteration, normalisation, province, parish, carver and style group for each inscription. The material was frozen for the analysis on 29 October 2026.
• The stones. Viking-Age runestones in the Swedish provinces. Runestones only; other objects with runes are not included. Skåne and Blekinge are counted as Denmark in Rundata and are not included.
• The words. Words with æi in Rundata's normalisation (ræisa, stæinn, þæiR, bæði and others), compared word by word with the transliteration, only when the two texts have the same number of words; proper names and uncertain readings are not counted. A word is spelled with a diphthong when the transliteration has ai, ia, ei or ae, otherwise with a monophthong. stæinn makes up 48 percent of the 1,278 words.
• The trait. A stone has a monophthong spelling when at least one of its æi words is spelled with a monophthong. The trait can be determined on 1,091 stones; 649 of them are dated, and 363 have a monophthong spelling.
• Time. The midpoint of the style group in Gräslund's chronology of the ornament (Gräslund 2006): RAK 998, Fp 1030, Pr1 1030, Pr2 1035, Pr3 1065, Pr4 1085, Pr5 1115. The style groups rest on the ornament, not on the spelling.
• The carver. The carver Rundata gives without a question mark. Stones without a secure carver are grouped by parish.

4.1 The model. Logistic regression (the R package mgcv, R 4.6.1; Wood 2017) with the trait against the style-group midpoint as a smooth curve, the stone's location as a spatial smooth and the carver as a random effect, so that a prolific carver's habit is not counted as a change. The curve is shown as the adjusted share for a typical carver, with 95 % intervals from 300 draws of the model's coefficients. The uncertainty of the dating is tested by drawing each stone's year evenly within its style group's interval, ten times.

4.2 Correction and replication. Holm correction (Holm 1979) over the 14 traits whose change was tested. Internal replication: the material was divided once, for all the project's analyses, into two halves parish by parish, and the change must hold in each half on its own.

4.3 Sensitivity analyses. The same fixed series as for every association the project reports, with time in steps of 50 years and the odds ratio for one such step: the raw model; adjusted for province; the carver as a random effect; the parish as a random effect; the stone's location as a spatial surface (only stones that stand in place); each half on its own; and without one province at a time (provinces with at least 30 stones). An analysis holds when p is below 0.05 and the direction is the same as in the adjusted model; without a province, significance is required only where at least two thirds of the stones remain. The p-values are also adjusted together for all 48 associations reported (Benjamini & Hochberg 1995); the adjusted value is called q. The model's assumptions are checked with simulated residuals (DHARMa; Hartig 2022).

4.4 Checks of the measurement. Twelve variants of the same straight trend in time, with location and carver as in 4.1 unless stated (listed in 5.4), and a check of the coding with a stricter rule.

4.5 Deviations and errors. No plan existed, so no deviations from a plan can be reported. While the report was being written, a random sample of the words showed that the rule also counts words spelled with a alone or without a vowel as monophthongs. The result was therefore recomputed with a stricter coding (5.4); it does not change.

5.1 The main test. With location and carver constant the share falls from 69 percent around 998 to 22 percent around 1115, a change of 48 percentage points (95 % interval 22–66), p = 0.005, Holm-corrected p = 0.028. The curve does not fall evenly: it goes from 69 to 58 percent up to about 1030, hardly moves until about 1070 (55 percent) and then falls again. Half A: 343 stones, from 70 to 24 percent, p = 0.049. Half B: 306 stones, from 69 to 33 percent, p = 0.015. The change thus holds in both halves. In plain words: around 1000 about seven stones in ten had at least one word spelled with a monophthong, around 1115 about two in ten. The sensitivity analyses' odds ratio of about 0.5 per 50 years means that the odds of a monophthong spelling roughly halve in fifty years.

5.2 The uncertainty of the dating. When each stone's year is drawn within its style group's interval, the change is significant in 9 of 10 refits and has the same shape in all of them; it then becomes smaller, between 22 and 33 percentage points.

5.3 The sensitivity analyses (649 stones, 363 with a monophthong spelling; time in steps of 50 years). All 8 hold:

• Raw model: odds ratio 0.44 (0.35–0.56), p < 0.001.
• Adjusted for province: 0.55 (0.39–0.76), p < 0.001. That corresponds to 68 percent in 1000 against 42 percent in 1100, 25 percentage points (probably between 12 and 39).
• Carver as a random effect (315 carvers and parish groups): 0.52 (0.33–0.81), p = 0.004.
• Parish as a random effect (326 parishes): 0.49 (0.34–0.70), p < 0.001.
• The stone's location as a spatial surface (390 stones that stand in place): 0.54 (0.34–0.88), p = 0.014.
• Half A (340 stones): 0.60, p = 0.025. Half B (309 stones): 0.49, p = 0.005. The halves follow the same rule as in 5.1 but are computed separately, so that three stones fall in the other half.
• Without one province at a time (4 provinces tested): the direction holds without each of them. Weakest without Uppland, when 301 stones remain, fewer than two thirds: odds ratio 0.53 (0.24–1.17), p = 0.12.
• The model's assumptions: residual distribution p = 0.25, overdispersion p = 0.26, remaining spatial pattern p = 0.26; no deviations.
• Adjusted for all 48 associations the project reports: q < 0.001. The association is one of 15 that hold in every sensitivity analysis.

5.4 The checks of the measurement. The direction is the same in all twelve; nine are significant and three are not:

• Per stone: odds ratio per 50 years 0.55 (0.37–0.83), p = 0.005. Per word, so that a stone with many æi words does not weigh more: odds ratio per 50 years 0.54 (0.38–0.78), p < 0.001.
• stæinn only: odds ratio per 50 years 0.59 (0.38–0.92), p = 0.021 (569 stones). Other æi words only: odds ratio per 50 years 0.64 (0.41–0.99), p = 0.044 (531 stones). The change is thus not confined to the word for stone.
• Only stones with a secure carver: odds ratio per 50 years 0.46 (0.24–0.87), p = 0.018 (270 stones). Only stones without: odds ratio per 50 years 0.55 (0.35–0.87), p = 0.010 (379 stones). Without the carver in the model: odds ratio per 50 years 0.54 (0.43–0.68), p < 0.001.
• Uppland only: odds ratio per 50 years 0.42 (0.26–0.67), p < 0.001 (348 stones). Södermanland only: odds ratio per 50 years 0.31 (0.12–0.84), p = 0.020 (113 stones).
• Not significant: only signed stones, odds ratio per 50 years 0.91 (0.39–2.15), p = 0.83 (106 stones); within the same carver, odds ratio per 50 years 0.50 (0.23–1.10), p = 0.084 (11 carvers with stones in at least two style groups, 174 stones); without the earliest and the latest style group, odds ratio per 50 years 0.67 (0.42–1.08), p = 0.098 (481 stones).
• The coding. Of the 599 words the rule counts as monophthongs, 79 are spelled with a alone or without a vowel (most often stan, rasa and þaR); they show no monophthong. With a stricter rule, in which only i or e in the place of the diphthong counts as a monophthong and the other words as uncertain, 28 stones change group and 16 drop out. The odds ratio per 50 years becomes 0.53 adjusted for province (against 0.54 with the rule), 0.57 and 0.46 in the halves and 0.58 in Uppland only, all with p below 0.01.

5.5 The ends and the carvers (exploratory, descriptive).

• In Uppland 19 of the 23 RAK stones have a monophthong spelling, and 16 of the 23 were carved by Gunnar, who writes a monophthong on 19 of his 20 stones. Of the 20 Pr5 stones, 2 have a monophthong spelling, and 16 of the 20 are Öpir's. In between, the share lies between 34 and 64 percent in every style group.
• Öpir himself writes a monophthong on 11 of 21 stones in style group Pr4 but on 1 of 16 in Pr5 (Fisher's exact test, p = 0.004, not adjusted). It is the clearest change within one and the same carver in the material.
• The monophthong is spelled in two ways: with a plain i-rune (stin) or with a dotted i-rune (sten). It is the i-spelling that disappears, from 63.1 percent of the æi words on the RAK stones to 3.3 percent on the Pr5 stones. The e-spelling is rare in every style group, between 2.0 and 9.9 percent, and most common on the Pr4 stones. Dotted runes become more common during the period, so the e-spelling was not available everywhere from the start.

What the finding says. On the runestones the monophthong spelling becomes rarer over time. This holds with location and carver constant, in both halves, in Uppland and in Södermanland, word by word and for both stæinn and other words. If the spelling followed the pronunciation, it would mean that the Mälaren region had the monophthong early and lost it, and nobody assumes that: Old Swedish has the monophthong. The most reasonable reading is that the spelling did not follow the pronunciation. The early carvers often wrote a single rune for the diphthong, and the late Upplandic carvers almost always wrote ai. That looks like a written norm that took hold, carried by carvers such as Öpir, rather than a change in speech.

Against earlier research. Wessén dated the sound change from the spelling of the runestones. Our result says that in the Mälaren region this spelling moves in the wrong direction to bear such a dating: the late stones write the diphthong more often than the early ones. It supports Källström's (2014) way of putting the question, in which the written norm and the dialect have to be kept apart, and it fits with the fact that it is the i-spelling that disappears, while the e-spelling, which Källström reads as a monophthong, remains and is most common on the Pr4 stones. It does not say when the monophthongisation reached the Mälaren region. It says that the runestones' stin and stain cannot show that on their own.

Weaknesses, in order of weight.

1. The ends carry the decline. Between about 1030 and 1070 the share hardly moves, and without the earliest and the latest style group the trend is not significant (p = 0.098). Pr5 has only 20 stones.
2. In Uppland the ends are two carvers. Gunnar accounts for 16 of 23 RAK stones and Öpir for 16 of 20 Pr5 stones. Within the same carver the trend goes the same way but is not significant (p = 0.084). The finding can therefore be read as a difference between carving traditions rather than a gradual change in everyone. That fits a written norm, but it means the result rests on few workshops.
3. The dating. The style groups are a relative chronology with uncertain years. RAK is a broad, early group whose stones stand mostly in Götaland; the model holds location constant, and Uppland on its own shows the same direction, but there RAK is largely Gunnar. With years drawn within the style groups' intervals the change becomes 22–33 percentage points instead of 48.
4. The measurement. The trait rests on Rundata's normalisation and transliteration, word by word. The coding check changes nothing, but signed stones alone give no significant result (106 stones).
5. What the spelling means. Whether stin denotes a monophthong or is a shortened way of writing the diphthong is the very question the result touches. The result shows that the spelling does not follow the sound change in the expected direction, but it cannot by itself decide what the spelling denotes.

What would overturn the finding. A dating that does not rest on the ornament, in which the late stones of the Mälaren region had a monophthong spelling as often as the early ones; or if Öpir's Pr5 stones turned out to stand in a district where every carver wrote the diphthong, so that the difference is one of place and not of time.

The monophthong spelling becomes rarer on the runestones, from 69 to 22 percent with location and carver constant, and the change withstands every sensitivity analysis. It runs against the sound change the spelling has been used to date. The late Upplandic spelling stain probably reflects a written norm. The next step is to test the change within carving schools across generations and against a dating independent of the ornament.