Which consonants the scribes of the Pyramid Texts could leave out

Jochem Kahl showed thirty years ago that in the earliest Egyptian writing — the first three dynasties and the Pyramid Texts — only six consonants are regularly left unwritten inside word stems. Counted afresh from the Pyramid Texts in the TLA, the six form one phonological class — and the reed leaf 𓇋 sits in the middle of it, next to 𓅱.

Egyptian spelling writes consonants, and it does not always write all of them. A word like bꞽk “falcon”, 𓃀𓇋𓎡𓐱𓅃, can appear as 𓃀𓎡𓐱𓅃, with the reed leaf 𓇋 missing; snsn “to fraternise” can be written 𓋴𓌢𓐰𓈖, with the reduplication left out. Jochem Kahl went through the inscriptions of the first three dynasties¹ and, in a separate article, through the Pyramid Texts,² and in both corpora the consonants that go unwritten inside a stem are the same six: 𓅱 w, 𓇋 ꞽ, 𓄿 ꜣ, 𓅓 m, 𓈖 n, 𓂋 r. Other consonants go unwritten only in isolated cases, which Kahl, following Sethe, takes for slips of the pen, and in a few particular words, such as ḥtp and ḏd-mdw.

Kahl himself read the reed leaf as a glottal stop, and he named, among the principles behind the omissions, “the special status of the semivowel w, of the glottal stop ꞽ and of the liquids”.³ In a footnote he passes on an observation by Frank Kammerzell: the omissions raise the question whether ꞽ, at least in the word forms in which it can go unwritten, is really a glottal stop at all — read as a palatal glide, it would line up with the other optionally written sounds w, m, n, r, ꜣ under the feature [+sonorant], where a stop would be [−sonorant].⁴ That is the idea this post puts to the test.

The class holds only if all six are sonorants. w, m, n and r are — consonants produced with the vocal tract open enough that they can carry a vowel’s load — and ꜣ is a liquid, as Otto Rössler showed when he identified it with Semitic r and dismissed the “old wives’ tale” of an Egyptian aleph.⁵ The one member whose sound value is still argued about is the reed leaf 𓇋. Carsten Peust’s survey of the question⁶ sorts the literature into three camps: a glide /j/ (among others Loprieno 1995 and Peust himself in 1999), a glottal stop /ʔ/ or a vocalic onset (from Brugsch 1864 to Allen 2013 and Peust 2016), or both from the start (Sethe, Edel and Gardiner among them). A fourth reading has gained ground since: Jim Allen (2020, 78) takes the sign to mark a vowel — an initial or final one, or two in sequence inside the word — rather than a consonant at all, and Daniel Werning has made the same case for the glides of the grammatical endings.⁷ If the six are a phonological class, the reed leaf must belong to it, and that leaves no room for a stop. This post counts the omissions again, from the Thesaurus Linguae Aegyptiae rather than by hand, and puts Kammerzell’s question in three steps: whether the six are really the only ones, whether one distinctive feature sets them apart from all the rest, and whether the rates at which they are left out fit that feature.

What the TLA already encodes

The TLA’s transcriptions distinguish, as editions do, the consonant that a spelling leaves unwritten, ms(ꞽ)ꜣ:t, from the one the editors restore as a scribal slip, 〈n〉ṯr. Both can be counted separately, and the slips then serve as a control group: if omission were nothing but carelessness, unwritten and forgotten consonants would show the same distribution.

The material is the eight pyramids that the TLA (corpus issue v20) groups as the Pyramid Texts: the five of Kahl’s 1992 table and of Sethe’s edition — Unas, Teti, Pepi I, Merenre, Pepi II — and those of Neith, Ibi and Ankhenespepi II. Together they come to 114,130 word tokens. Only content words are counted — nouns, verbs, adjectives, names, numerals, titles. The pronouns, prepositions and particles that make up the rest are written by rote, and most of them consist of nothing but the consonants in question — m, n, r, ꞽw, ꞽn — so that counting them would measure the spelling of a handful of function words rather than of word stems; that leaves 67,100 tokens. Counting follows Kahl: the unit is the word-form type, that is, a lemma in a given spelling, so that a word written the same way a hundred times counts once and a word with three spellings counts three times. Compounds are split at the hyphen. Components in square brackets — damaged, restored by the editors — are left out, since nobody can say what was written there; that removes 9,613 components. What remains are 4,345 word-form types, each contributing one observation per stem consonant, 12,267 observations in all. The three pyramids outside Kahl’s corpus add less than their size suggests: they are largely the same spells in other hands, four in five of their word-form types occur in the five as well, and the rates of the six lie within half a percentage point whether the five are counted or all eight.

The reed leaf is counted on its own: 𓇋 ꞽ (Gardiner M17), the double reed leaf 𓇌 y, and the weak final radical ꞽ̯ of verbs like mrꞽ̯ are kept apart, since the last is conventionally unwritten for a different reason and would otherwise swamp the figures for the final position.

The six, and only the six

Figure 1 shows, for each consonant, the share of word-form types in which it is left unwritten (blue) and the share the editors treat as a scribal error and restore (red).

Figure 1: Omission rate per consonant in the Pyramid Texts. Blue: the consonant is left unwritten in that word form (round brackets in the TLA transcription); the grey top of a bar is the part of that which falls in the four words whose defective spelling Kahl lists as regular, ḏd-mdw, ḥtp, ḥꜥpꞽ and ṯrp. Red: restored by the editors (angle brackets). Whiskers are 95 per cent Wilson intervals of the blue and red parts; the small figure under each consonant is the number of word-form types containing it.

The blue bars are Kahl’s result, independently obtained: w 14.3 per cent, ꞽ 12.6, ꜣ 7.4, m and r 4.5, n 1.5 — and then nothing. No obstruent reaches 2.5 per cent, and the few obstruent cases there are can be listed. d owes its eight to a single word, the formula ḏd-mdw “recitation”, written with the logogram, 𓆓𓐳𓌃, and transcribed ḏ(d)-mdw. ꜥ has five, from ḥꜥpꞽ “inundation”, 𓎛𓊪𓐰𓈘, ꞽꜥnꜥ “baboon”, 𓇋𓂝𓐰𓈖, and ḏꜥm, a sceptre. p has five, among them ḥt(p), 𓊵𓐰𓏏. Most of the rest are abbreviated reduplications — bꜣ(bꜣ), sn(sn), zn(zn) — which is a different device altogether. These are lexical exceptions, not a weaker version of the same thing, and Kahl already drew the line: the omission of p in ṯrp and in words written with the logogram ḥtp, of ꜥ in ḥꜥpꞽ⁸ and of d in ḏd-mdw is regular, found in witness after witness, while the other obstruent cases are isolated and, with Sethe, slips of the pen.⁹ In the figures those four words are greyed out, in every consonant they affect,¹⁰ and what is left of the obstruents is a scatter of ones and twos — ꞽꜥn(ꜥ), ḏ(ꜥ)m, ꜥ(b)š, sḫ(p).t, the reduplications — with no consonant above 0.5 per cent, against 1.5 for n, the least omitted of the six.

Kahl’s two counts already agree with each other: the six fall in nearly the same order in the early-dynastic inscriptions and in the Pyramid Texts (Spearman’s ρ = 0.90).¹¹ Counted on Kahl’s five pyramids alone and set against his hand counts, the ranking of the six agrees (Spearman’s ρ = 0.81 over the six consonants, 0.73 over the eighteen consonant-by-position cells). The absolute numbers are higher here — Kahl lists twenty omitted types for w, the TLA gives 119 — which has an obvious cause: the TLA brackets every conventionally unwritten consonant, whether or not it is “stem-internal” in Kahl’s narrower sense. The ordering is what matters, and the ordering is the same.

The red bars are the control, and they are flat. Editorial restorations run between three and seven per cent for every consonant, sonorant or not, with no tendency whatever towards the six (a rank-sum test gives p = 0.95 against p = 0.0002 for the blue bars). Scribes slipped on every consonant equally. What they could leave out was a different and much smaller set. The old worry that Kahl’s list might reflect his own decisions about what counts as an error rather than a property of the writing system can be put aside. The separation used here is the editors’, made word by word without the class in mind; had their error category been salted with omissions that are really of the conventional kind, the red bars would rise over the six, and they do not.

One feature

Six consonants that can be left out are not yet a class. Whether they are one is the question the Prague School taught phonology to ask of any set of sounds that behave alike: is there a distinctive feature that all of them share and none of the others has? The test can be run without deciding the reed leaf’s sound value in advance. Every consonant of the Old Kingdom inventory is given a value, plus or minus, for fifteen features — syllabic, consonantal, sonorant, approximant, continuant, nasal, lateral, voiced, constricted and spread glottis, and the places labial, coronal, dorsal, pharyngeal and laryngeal.¹² The disputed signs get one row for each reading: the reed leaf as the glide /j/ and as the glottal stop /ʔ/, ꜣ as a liquid and as a glottal stop, ꜥ as the stop /d/ it was before the Third Dynasty and as the pharyngeal /ʕ/ it became. For every feature and every combination of readings one then counts how many consonants end up on the wrong side if “plus” is equated with “can be left out”. Figure 2 shows the grid with the disputed signs in the readings that make the six a class, and underneath each feature that count.

Figure 2: The feature grid. Rows: the 24 consonants, the six omittable ones on top, and below the line the other reading of each disputed sign; columns: 15 distinctive features, dark for plus, light for minus. The figure under each column is the number of consonants the feature puts on the wrong side of the omittable/not-omittable divide.

Table 1: Readings of the disputed signs and the consonants that [+sonorant] then puts on the wrong side.

ꞽ	ꜣ	ꜥ	consonants misplaced by [+sonorant]
glide	liquid	stop	none
glide	liquid	pharyngeal sonorant	ꜥ
glide	glottal stop	stop	ꜣ
glide	glottal stop	pharyngeal sonorant	ꜣ, ꜥ
glottal stop	liquid	stop	ꞽ
glottal stop	liquid	pharyngeal sonorant	ꞽ, ꜥ
glottal stop	glottal stop	stop	ꞽ, ꜣ
glottal stop	glottal stop	pharyngeal sonorant	ꞽ, ꜣ, ꜥ

One feature draws the line exactly, [+sonorant], and only in one combination: the reed leaf a glide, ꜣ a liquid, ꜥ not a sonorant (Figure 2, Table 1). The runners-up fail at points that can be named. [+approximant] takes in the glides and liquids but leaves out m and n, which are omitted too; [+voiced] takes in all six but brings with it b, g, ꜥ and ḫ, which never are; every other feature misplaces four consonants or more. Read the reed leaf as a glottal stop, and no feature does better than one error, the reed leaf itself: a stop that is left out while b, d, g and q never are. Read it as a vowel sign, and it does not belong in a table of consonants at all; the feature test cannot tell that reading from the glide, and the place to look is where in the word the omissions fall (below).

The same reasoning applies to ꜥ, which is not in the set. Had it been a sonorant in the Pyramid Texts — a pharyngeal approximant, as /ʕ/ often is — it should be left out like the six, and it is not: two scattered types in 394 once Kahl’s ḥꜥpꞽ is set aside. Whatever ꜥ sounded like by then, it behaved as an obstruent.

The test has two limits. It is only as good as the feature values, and those are a reconstruction: it shows which readings make the six a class, not that the reconstruction is right. And it treats “can be left out” as yes or no. That is where the counts come back in. The red bars and the grey ones are what make the yes or no defensible, and the rates say more than yes or no.

Three readings, four models

The feature test says which consonants can be left out. It does not say how often, and the counts can answer that too; they let the readings of the reed leaf be compared on the numbers rather than on a yes or no. Each reading of the reed leaf predicts how often every consonant should go unwritten in every position, and the readings can be compared by how well they predict the table. Four models, each a regression of the omission rate on the consonant’s class and its position in the stem, fitted in a Bayesian framework with weakly informative priors:

• Glide. Two classes, sonorant and obstruent, the reed leaf among the sonorants.
• Glottal stop. The same two classes, the reed leaf among the obstruents.
• Position split. The reed leaf gets terms of its own, one for the middle of the stem and one for the edges; the other consonants as in the second model. In the earlier version of this analysis it stood in for the vowel-sign reading, which predicts the edges to behave differently; the next section will show why it is better called what it is, a split by position.
• Graded sonority. Not two classes but a scale: glides, liquids, nasals, obstruents, each step allowed the same change in rate.

The models are compared by how well each predicts cells it was not fitted to, in a currency where higher is better and a difference is to be read against its standard error.¹³ The glottal-stop model comes last, at −410 ± 101. The glide model is better by about 170, at −240 ± 52. The position split is better still, at −199 ± 50, and the graded scale is best of all, at −122 ± 20, with the fewest parameters. Figure 3 shows why.

Figure 3: Top: observed omission rate per consonant (black) and the rate predicted by three of the models, with 90 per cent intervals — the reed leaf as glottal stop (red), as glide (blue), and the graded sonority scale (dark). Bottom: the reed leaf by position, predicted by a model fitted to the other 23 consonants, once as a sonorant and once as an obstruent.

The red marks say what a glottal stop would have to look like: the reed leaf at about 2 per cent, among d, p and b. It is at 13. The blue marks put every sonorant on one level near 7 per cent, and the data do not do that either: w and the reed leaf sit well above, m and n well below. The dark marks follow the slope — glides first, liquids next, nasals last — and that is the model the table prefers. Kahl himself had described the six as a zone of transition between the consonants that are always written and the vowels that never are;¹⁴ the graded model gives that transition a slope, and [+sonorant] marks where it begins. What the position split adds over the plain glide model is not an edge effect of the vowel-sign kind: its two terms put the medial reed leaf at 4.1 [3.6; 4.5] on the log-odds scale and the edges at 3.4 [3.1; 3.8], both above the other sonorants at 2.5 [2.2; 2.8]. The reed leaf is allowed to be more omittable than m, n, r and ꜣ, and it uses the allowance.

The lower panel makes the same point without the reed leaf in the fit at all. A model trained on the other 23 consonants predicts, for a sonorant, 1.6 per cent of omissions initially, 6.8 medially and 8.9 finally; for an obstruent, 0.1, 0.6 and 0.8. Observed for the reed leaf: 5.6, 26.0 and 18.1. It is not merely on the sonorant side of the line; it is beyond the average sonorant in every position, where w is.

The same comparison can be run over the readings that have actually been proposed. Table 2 puts each through the feature test and through the graded rate model; the last column gives how far each falls behind the best, with its standard error; Figure 4 draws that column.

Table 2: Readings of the disputed signs in the literature, by the feature test and by how well the graded rate model predicts the omissions under each.

reading	ꞽ	ꜣ	ꜥ	[+sonorant] misplaces	behind the best
Peust 1999; Loprieno 1995; Kammerzell for the Old Kingdom	/j/	liquid	/d/ or fricative /ʕ/	nothing	0
Kammerzell 1995	/j/	liquid	sonorant	ꜥ	9 ± 9
Allen 2020	vowel sign	/l/	approximant /ʕ/	ꜥ	11 ± 9
Edel; Vergote	/j/ or /ʔ/	/ʔ/	/ʕ/	ꜣ, and ꞽ read as /ʔ/	102 ± 46
Peust 2016; Kahl 1992; Rössler 1971	/ʔ/ or a palatal stop	liquid	/d/ or /ʕ/	ꞽ	239 ± 100

Figure 4: The last column of Table 2: how far each reading falls behind the best model, with one standard error. Blue: within reach of the best; red: not.

Every reading that takes the reed leaf or ꜣ for a stop falls far behind, by a hundred and more, over twice the uncertainty. Between the glide and Allen’s vowel sign the counts cannot decide: a model that lets the reed leaf go its own way does no better than one that makes it a glide (2 ± 3), which is what the feature test led one to expect. The sonorant ꜥ of Kammerzell 1995 and Allen 2020 is excluded by the feature test, but the rates only lean against it, by about one standard error; a single consonant that is almost never left out weighs little against twenty-three others.¹⁵

Where in the word

The omissions themselves have been used as evidence on the other side. Allen lists ꞽt ~ t “father” and bꞽk ~ bk “falcon” and concludes that “the frequent omission of j also suits a vocalic mater lectionis better than a phonemic consonant”;¹⁶ a vowel sign, the reasoning goes, is dispensable in a way a consonant is not. Peust adds a distributional point:¹⁷ 𓇋 is far commoner at the beginning of a word than anywhere else, which he reads as favouring a glottal stop or vocalic onset. Both arguments look at the reed leaf on its own. Figure 5 puts it next to w and ꜣ.

Figure 5: Share of word-form types in which the consonant is left unwritten, by position in the stem. Whiskers are 95 per cent Wilson intervals; the figures give omitted over total types.

Peust’s distribution is confirmed, up to a point: 481 word-form types have 𓇋 stem-initially, 310 finally, only 127 in the middle. The initial weighting itself is not unusual — s, ḥ, h and ẖ are more initial-heavy still, and š is close behind — and part of it is an artefact of lemmatisation, since the TLA does not separate the causative s- or the verbal ꞽ- prefix from the stem. What is unusual is the middle: 14 per cent of the occurrences of 𓇋 are medial, less than for any other consonant. But a distribution of signs is not a distribution of sounds when the sign is omittable. A consonant that goes unwritten in a quarter of the medial types where lexicography knows it to be present will be missing from the record wherever lexicography does not, and those words contribute nothing to anyone’s count of medial reed leaves. The scarcity Peust observes is, in part, Kahl’s omission seen from the other side. The rate model is not affected by this, because its denominator contains only words whose reed leaf is known; a distributional argument is.

And the omissions run the other way. Initially, where 𓇋 is commonest, it is left out least, 6 per cent; medially, where it is rarest, most, 26 per cent; finally 18 per cent, and the difference between the medial and the edge positions is not noise (Fisher’s exact test, p < 0.0001). w — a consonant on every account, Allen’s included — shows the same profile: 3, 18 and 21 per cent. The rates match, the positions match, and nothing in Figure 1 or Figure 5 singles the reed leaf out from the glide next to it. Omission is what the six do; that the reed leaf does it too is a fact about the class, not about the reed leaf. If the sign were a vowel marker, its row ought to look like nothing else in the table; instead it looks like w. The counts cannot rule out a vowel sign that happened to behave exactly like a glide in every respect that can be counted, but they give no reason to prefer one.

One detail should be stated rather than left for a reader to find. Initially, the reed leaf is omitted in 5.6 per cent of its types, which is low for the reed leaf but higher than for any other sonorant in that position (ꜣ 5 per cent, w 3, m 1, r and n below 1). The 27 cases are lexically clustered: the god’s name Ꞽtm:w in three spellings, ꞽḫ:t “thing” in five, the nisba ꞽm:ꞽ and its compounds, ꞽwꜥ “heir”, ꞽr:ꞽ, ꞽtꞽ “father” — about a dozen lemma families, among them precisely the nouns Allen cites. They are real, and they are the whole list.

Werning has given the mater-lectionis reading its most explicit form, and his criterion is frequency: where a word or morpheme is spelled much more often without a glide than with it, the occasional glide marks a vowel, not a consonant.¹⁸ The cases he has in mind are endings — the resultative, the posterior, the passive — and those are excluded here by design, since only stem consonants are counted. Applied to the stems, his criterion cuts the other way: stem-internal 𓇋 is written in nine types out of ten, and in the medial position still in three out of four, so by Werning’s own test it is a consonant. Where his account and the counts meet is his fifth hypothesis, that a phonological glide may be spoken as a consonant and written, or spoken as a vowel and left unwritten, depending on its place in the syllable.¹⁹ That is a mechanism for what Figure 1 shows: the two glides are left out most because they are the consonants that can turn into vowels, the liquids and nasals less because they can do so less readily, the obstruents never. Werning notes that his arguments work equally if the reed leaf is a glottal stop, the weak radical of verbs apart;²⁰ the counts do not. What looks like a point of friction cannot be settled yet. Werning takes it as axiomatic that intervocalic glides are usually written out,²¹ and the medial position is where 𓇋 and 𓅱 are left out most — but a medial consonant need not stand between vowels. For part of the material the vowels are known independently: from Wolfgang Schenkel’s reconstructions of deverbal nouns on the basis of Coptic, and from the nominal classes after Osing and Schenkel that the TLA records for 189 of the lemmata.²² The two ways of linking them do not yet agree: matched by root, glides between vowels are left out in two types out of forty-three; matched by lemma number, in four out of twelve, against one in five elsewhere. The numbers are too small to decide, and most of the omitted glides in that set are the w that III-inf. roots show before the feminine ending — ms(w):t, ḥz(w):t, wp(w):t — where the first question is whether the glide belongs to the root at all. That is the question the lemma-by-lemma review has to answer before the syllable can be asked.

Caveats

The bracket convention is the TLA’s, and it is not applied with complete uniformity: ꞽꜥnꜥ appears both as ꞽꜥn(ꜥ) and as plain ꞽꜥn, and only the sign encoding, 𓇋𓂝𓐰𓈖 in both cases, shows that the same thing was written. The counts above are therefore a lower bound on the TLA’s own transcriptions, and the next step is to check the transcriptions against the sign encoding directly, which is available for 49 per cent of the tokens. Some medial reed leaves in TLA lemma forms — bꞽk, mꞽn:t, ꞽm:ꞽ — are there because of later vocalised forms rather than Old Kingdom spelling, and a lemma-by-lemma review of the bracketed sonorant cases is under way. The early-dynastic corpus of Kahl’s 1994 book is not in the TLA in this form, so the replication rests on the Pyramid Texts alone.

None of this touches the main result. Six consonants can be left out, six consonants are sonorants, and the reed leaf is one of them.

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Eight pyramids from TLA v20 — Unas, Teti, Pepi I, Merenre, Pepi II, Neith, Ibi, Ankhenespepi II: 114,130 word tokens, 67,100 of them content words, 4,345 word-form types after damaged components are excluded; the comparison with Kahl’s hand counts uses his five alone. Counts of bracketed consonants in the TLA transcriptions; four Bayesian binomial regressions of omission on consonant class and position, and twenty-four more for the readings of Table 2, compared by leave-one-out cross-validation (bambi/PyMC, four chains, no divergences); the feature test over fifteen features and sixteen combinations of readings for ꞽ, ꜣ, ꜥ and ḥ. Syllable positions from Schenkel 1983 and the nominal classes recorded in the TLA. Scripts, tables and the list of every bracketed case with its TLA sentence ID are in the project repository, https://scm.cms.hu-berlin.de/paultobi/defektivschreibungen. This is work in progress; the findings are provisional.

Footnotes

1. Kahl, Jochem. 1994. Das System der ägyptischen Hieroglyphenschrift in der 0.–3. Dynastie. Göttinger Orientforschungen IV/29. Wiesbaden: Harrassowitz.

2. Kahl, Jochem. 1992. Die Defektivschreibungen in den Pyramidentexten. Lingua Aegyptia 2, 99–116.

3. Kahl 1992, 105.

4. Kahl 1992, 105 n. 26, where the stop is also given as [−voiced], which follows from [−sonorant].

5. Rössler, Otto. 1971. Das Ägyptische als semitische Sprache. In: Franz Altheim and Ruth Stiehl (eds.), Christentum am Roten Meer 1, 263–326. Berlin: de Gruyter. § 37. The liquid reading is now the usual one: Loprieno, Antonio. 1995. Ancient Egyptian: A Linguistic Introduction. Cambridge: Cambridge University Press. P. 33 (/ʀ/); Peust, Carsten. 1999. Egyptian Phonology: An Introduction to the Phonology of a Dead Language. Göttingen: Peust & Gutschmidt. Pp. 127–129, following Schenkel and Kammerzell; Allen, James P. 2020. Ancient Egyptian Phonology. Cambridge: Cambridge University Press. P. 78 (/r/ or /l/).

6. Peust, Carsten. 2016. Der Lautwert der Schilfblatt-Hieroglyphe (M17). Lingua Aegyptia 24, 89–100.

7. Werning, Daniel A. 2016. Hypotheses on Glides and Matres Lectionis in Earlier Egyptian Orthographies. In: James P. Allen, Mark A. Collier and Andréas Stauder (eds.), Coping with Obscurity: The Brown Workshop on Earlier Egyptian Grammar (Wilbour Studies in Egyptology and Assyriology 4), 29–44. Atlanta: Lockwood Press.

8. Kahl himself reads the word as ḥ(r)p(ꞽ): following Rössler, ꜥ can arise as a by-product of the consonant /l/, which is written n, ꜣ or r, so that “Nile” may have developed from ḥrpꞽ to ḥꜥpꞽ rather than, as Sethe assumed, the other way round. The consonants left unwritten would then be a liquid and the reed leaf (Kahl 1992, 102, Anmerkung 1). On that reading the case is not an obstruent at all.

9. Kahl 1992, 102 with Anmerkungen 1–3; the d of ḏd-mdw as an acrophonic abbreviation.

10. Sonorants included: the r in ṯ(rp) and the reed leaf in ḥ(ꜥ)p(ꞽ), three cases against 410 sonorant omissions.

11. Kahl 1992, 103 Abb. 1; Kahl 1994, 86 Abb. 7; rank correlation over the numbers of omitted word-form types per consonant.

12. The values are taken from the literature one by one. Reed leaf: /j/ with Peust 1999, 49, Loprieno 1995, 33 and Kammerzell (after Peust 1999, 49); /ʔ/ with Peust 2016, 89–90 and Kahl 1992, 105. ꜣ: a liquid with Peust 1999, 127–128, following Schenkel and Kammerzell, and Loprieno 1995, 31, 33 (/ʀ/); /ʔ/ in the older view of Edel and Vergote (after Peust 1999, 128). ꜥ: /d/ with Rössler 1971, 276–277, Kammerzell 1998, 120 (Kammerzell, Frank. 1998. Sprachkontakte und Sprachwandel im Alten Ägypten. Habilitationsschrift, Göttingen) and Peust 1999, 99–102; /ʕ/ with Loprieno 1995, 31, 33 and Allen 2020, 71, 84. r /ɺ~ɾ/: Peust 1999, 128 (/l/); Allen 2020, 72 ([ɾ]). The glottalic series and the fricatives follow Kammerzell 1998, 120: d /tʼ/, ḏ /cʼ/, q /kʼ/, z /t͡s/, ẖ /x/, ḫ /ɣ/; the ejectives also in Loprieno 1995, 34, the voicing of ḫ against ẖ already in Rössler 1971, 274, 296–297 (after Peust 1999, 117), the affricate in Baer and Schenkel (after Peust 1999, 125–126). ḥ was run both as the pharyngeal /ħ/ (Peust 1999, 98; Loprieno 1995, 33; Allen 2020, 72) and as Kammerzell’s ejective /xʼ/ (1998, 120); both are obstruents, and nothing below changes. The table and the script are in the project repository.

13. Leave-one-out cross-validation, expected log predictive density (ELPD). Priors are bambi’s defaults, normal distributions centred on zero and scaled to the data; the models were fitted with bambi/PyMC, four chains of 2,000 draws, no divergences, all R-hat ≤ 1.002; WAIC gives the same ordering with the same gaps. Nor does the result depend on the priors: with the broader priors McElreath recommends for logistic regression — normal, standard deviation 1.5 for the intercept and 1 for the slopes (McElreath, Richard. 2020. Statistical Rethinking: A Bayesian Course with Examples in R and Stan. 2nd ed. Boca Raton: CRC Press. Ch. 11) — or with very wide ones (standard deviation 2.5 throughout), every figure given here moves by at most 5, against gaps between the models of 40 and more.

14. Kahl 1992, 103.

15. Each reading is coded by its values for the reed leaf, ꜣ and ꜥ, with the sources given above; Kammerzell 1995 after Peust 1999, 100, Kammerzell for the Old Kingdom: Kammerzell 1998, 120; Rössler’s palatal after Peust 2016, 89 n. 4. The vowel-sign and the ambiguous readings give the reed leaf a term of its own. Leave-one-out cross-validation as above; script and table in the project repository.

16. Allen 2020, 82.

17. Peust 2016, 90.

18. Werning 2016, 31 (Hypothesis 1).

19. Werning 2016, 43 (Hypothesis 5).

20. Werning 2016, 29 n. 4.

21. Werning 2016, 30.

22. Schenkel, Wolfgang. 1983. Zur Rekonstruktion der deverbalen Nominalbildung des Ägyptischen. Göttinger Orientforschungen IV/13. Wiesbaden: Harrassowitz. Appendix 4.2, 210–252; the syllable position of each radical is read off the structural formula of the class.