An overview of Bamum phonology and orthography, with an additional focus on character and word frequencies in recent poetry

1 Introduction

Bamum language (ISO 639-3 code: bax) is a Bantoid language spoken in the Western province of Cameroon. It is classified as Bamum < Nun < Grassfield < Bantoid < Benue-Congo < Volta-Congo < Atlantic-Congo within the Niger-Congo macrofamily. The language is also known as Bamoum, Bamun, or Bamoun and is called shüpaməm in vernacular. The number of speakers was estimated as 420,000 in 2005 (Ethnologue 2024) and given the average yearly Cameroon population growth of 2.5 per cent (Census data 2005) can be estimated as over 600,000 people in 2022.

The Bamum people live predominantly in the Noun department with the capital in Foumban being the historical capital of the Bamum kingdom; see the map in Figure 1. The territory is situated between 10°30′ and 11°10′ East longitude and between 5° and 6° North latitude (Dugast and Jeffreys 1950: 1). Natural borders include the Vi River in the north, the Mbam River in the east, and the Noun River in the west and south-west (cf. Galitzine-Loumpet 2011). The Bamendjing Reservoir is located about thirty kilometers west of Foumban.

Figure 1:

Approximate location of the Bamum people in Cameroon.

The Bamum language is best known from the indigenous writing system created in 1896–1918 by the local leader (mfɔn) Ibrahim Njoya (c. 1860–1933) often referred to as King or Sultan Njoya. The writing system underwent a rapid evolution from a pictographic script to a nearly alphabetic one within a rather short period of time (Dugast and Jeffreys 1950; Schmitt 1963). Characters from the last development stage are shown in Table 1. This script is known as A ka u ku mfɛmfɛ ‘new a-ka-u-ku’, from the names of the first four syllabic signs (Dugast and Jeffreys 1950). The first stage is known as lewa ‘book’ (about 500 signs), the second one is mbima ‘mixed’ (437 symbols, ca. 1900), subsequent stages were named by the first syllables: nyi nyi nʃa mfɯʔ (381 symbols, before 1906), rii nyi nʃa mfɯʔ (295 symbols, ca. 1907–1908), rii nyi mfɯʔ mɛn (205 symbols, ca. 1907–1908), a ka u ku (80 symbols, after 1910). These stages are traditionally referred to by the Roman letters A to F, with the final, A ka u ku mfɛmfɛ, known as stage G (Dugast and Jeffreys 1950; Schmitt 1963). In this last version from 1918, the shapes of the 80 symbols from stage F were simplified (Dugast and Jeffreys 1950: 30). The first accounts on the script were published in 1907 by Göhring (1907a, 1907b), a Swiss missionary from Basel. For readers’ convenience, we list the sources about the Bamum writing system in the Appendix. The role of the script is analyzed in the Cameroonian (Schumann 2019; Zang Zang 2012) and a wider African context (Mazrui and Mazrui 1992; Nganang 2015; Tuchscherer 2007; Unseth 2011). The script is considered an important component of the Bamum identity (Battestini 2004). In October 2009, the modern Bamum script (i. e., A ka u ku mfɛmfɛ) became part of the Unicode standard (version 5.2) and historical logograms were added to Unicode in October 2010 (version 6.0).

Table 1:

Characters of the modern Bamum script A ka u ku mfɛmfɛ.

Beyond the studies devoted to Njoya’s writing system, especially those by Dugast and Jeffreys (1950) and a three-volume magnum opus by Schmitt (1963), the materials on the Bamum language are rather scarce. To our knowledge, the situation has not changed significantly compared to 2012 when Abdoulaye Nchare wrote that “Shupamem is one of the least studied of the Grassfields Bantu languages at least in terms of studies explicitly dealing with syntactic phenomena” (Nchare 2012: 15). The Bamum language was included in Sigismund Koelle’s Polyglotta Africana (1854) as IX.A.8. Bámom. The phonology of Bamum was analyzed in detail by Ward (1938). The present-day status of the language is reflected in the book by Matateyou (2002) from the Parlons series, in Abdoulaye Nchare’s works including his PhD dissertation (see Nchare 2012 and references therein), and in Solange Pawou Molu’s PhD dissertation (Pawou Molu 2018). Note that as of today we have not been able to locate a Bamum dictionary of any significant size beyond word lists given by Koelle (1854), Schmitt (1963), and Matateyou (2002). A parallel list of more than 400 words in French, Bamum, and Shümom (a secret language invented by Njoya) is given by Dugast (1950). The Bibliography of Cameroonian languages merely listed a score of titles about the Bamum language as of 1993 (Barreteau et al. 1993).

We hope our modest analysis presented here will be a contribution towards studies of the Bamum language and hope that it triggers interest in the language with prospects of further larger-scale research in this direction. We begin with a discussion on the Bamum phonology in Section 2 including in particular some historical accounts, then proceed to a detailed analysis of the writing system in Section 3 and report some observations relevant to orthographic principles reflecting modern practices of the Bamum script usage. In Section 4, we analyze the frequency distribution of characters and the most frequent words, based on a recently published collection of poems by Samuel Calvin Gbetnkom, a modern Bamum poet (Gbetnkom 2022). Conclusions are given in Section 5.

2 Remarks on phonology

The first detailed study of the Bamum phonology was made back in 1938 by Ida Ward. Later on, the relevant analysis was included in works by Dugast and Jeffreys (1950) and Schmitt (1963). Separate discussions on this issue are found in studies from the last two decades (e.g., Matateyou 2002; Nchare 2012; Pawou Molu 2018).

There is a significant discrepancy on the vowel inventory in Bamum according to different authors. Ward (1938) considers eight vowels /a, ɛ, ə, i, ɔ, o, ø, ɯ/, with a remark that /ø/ represents “a front rounded vowel between close and half-close: it was often heard as ü” and that /o/ “is about half-way between Cardinal o and u”. Dugast and Jeffreys (1950) and Schmitt (1963) list nine vowels and the set is slightly different: /a, ɛ, e, ə, i, ɔ, u, ü, ɯ/. Additionally, Schmitt (1963: 49) notes that phoneme /o/ is foreign to Bamum. Matateyou (2002: 47) reports seven vowels only /a, ɛ, ə, i, ɔ, u, ʉ/, with the latter standing for [ɯ] (i.e., close back unrounded and not IPA close central rounded vowel) in accordance with the General Alphabet of Cameroon Languages (Tadadjeu and Sadembouo 1979). However, in the book itself a set of ten vowels /a, ɛ, e, ə, i, ɔ, o, u, ü, ʉ/ is used in text written in Bamum (Matateyou 2002: 37–38). The same set of ten vowels is listed by Nchare (2012: 39) as /a, ɛ, e, ə, i, ɔ, o, u, y, ɯ/. The close front rounded vowel [y] is transcribed further in the present article using a more traditional notation /ü/ leaving the notation /y/ for the palatal approximant IPA [j]. To round out the complexity, we note that Solange Pawou Molu (2018) in her PhD thesis uses the same set of ten vowels but with ʉ for ü/y and preserving ɯ with its traditional value.

The summary of vowels and their notation used in the present work is presented in Table 2.^[1]

Vowels in Bamum can be short and long and can also form diphthongs. Diphthongs of iV and uV kinds result in palatalization and labialization of the preceding onset consonants, respectively (Nchare 2012: 42). The latter can be reflected in writing as wV: puə̀ or pwó ‘arm, hand’.

Similarly to other related Grassfield languages, Bamum has a complex tonal system, in which the following four tones can be identified (Nchare 2012: 63): high (H), low (L), rising (LH), and falling (HL). Of those, high and low tones might be considered the two principal tones (Matateyou 2002: 39; Schmitt 1963: 39). The role of tones in the Bamum grammar was recently analyzed by Magdalena Markowska in her M.A. thesis (Markowska 2020). Details on tone marking are discussed below in this section.

Bamum is rich in consonants. Three major groups are plosives /p, b, t, d, k, g, kp, gb, ʔ/ (with /ʔ/ denoting the glottal stop), fricatives /f, v, s, z, ʃ, ʒ, ɣ/, and nasal consonants /m, n, ɲ, ŋ/. The graphic representation of /ɲ/ is traditionally ny. Other consonants are a lateral /l/, a rolled /r/, and semivowels /w, y/. Matateyou (2002: 37–38) uses gh for /ɣ/ and sh for /ʃ/ and additionally lists ɓ for /β/ being the first consonant in Spanish vaca ‘cow’. Nchare (2012: 44) includes /β/ and adds a labiodental nasal /ɱ/. There are also prenasalized consonants /mb, mf, mv, nd, nt, ns, nz, nʃ, nʒ, nw, ny, ŋk, ŋg, ŋkp, ŋgb, ŋm/ (cf. Nchare 2012: 45).

It should be noted that word-finally “a light velar fricative” [x] was reported to follow back close vowels (Ward 1938). This feature was reproduced in writing and was later adopted by Dugast and Jeffreys (1950). It is not followed though either by Schmitt (1963) or later authors (Matateyou 2002; Nchare 2012; Pawou Molu 2018).

Palatalization can occur in /k/ before the front vowels /e, ɛ, i/ that is reproduced as ky in writing (Ward 1938). The rules for the palatalization are not straightforward though, cf. kyɛ́t ‘arrow’ and kɛ́t ‘barrel’ (Matateyou 2002: 159). This might be related to word etymology: Ward (1938: 425) provides an example of ŋkyɛ ‘water’ versus ɣakɛri ‘big’ derived from kɛri, a form of kɯt.

Although the sounds above have been indicated as phonemic, there is a chance that some of these may be allophones rather than independent phonemes.

In the remainder of this section, we present an analysis of historical changes in vowels inspired by Nchare’s observations (2012: 16–23). We select twenty words having a single-character representation in the A ka u ku mfɛmfɛ script, see Table 3. Their pronunciation is given according to Koelle (1854), Delafosse (1922), Ward (1938), Dugast and Jeffreys (1950), Schmitt (1963), Matateyou (2002), and Nchare (2012). The two latter sources can be considered modern Bamum. The data by Dugast and Jeffreys (1950) and Schmitt (1963) differ only slightly and mostly in tones.

Table 3:

Historical changes in some Bamum words represented by a single character in A ka u ku mfɛmfɛ.

1. *The last phonetic value corresponds to modern Bamum as evidenced by Matateyou (2002) and Nchare (2012).

Being historically dispersed and therefore written in different linguistic models, all the quoted sources are rather inconsistent in the notation of vowels. Koelle (1854: vi) uses ẹ for /ɛ/, ọ for /ɔ/, and n· for /ŋ/. The macron ( ˉ ) indicates long vowels and the acute ( ˊ ) is used to mark ‘accent’, though whether Koelle was referring to stress or tone is unclear.

Delafosse (1922) uses è for /ɛ/, ò for /ɔ/, é for /e/, and ṅ for /ŋ/. Differences between ou and où are unclear: both correspond to modern /u/ and /ɯ/. Examples include choù for the modern character ʃu and chou for modern ʃɯ but soù for modern suu and sou for modern sɯ as well as lou for lu and nou for nu but yoù for yuʔ. In one instance, poù corresponds to modern /ü/ as in pü ‘we’.

The notations by Ward (1938) mostly correspond to modern practices, except for the previously mentioned /o/ versus /u/ and /ø/ versus /ü/. Schmitt (1963: 50–51) suggested that the chosen values /o/ and /ø/ could be due to peculiarities of the informant’s pronunciation. Nchare (2012: 22) suggests that Ward’s data might represent a specific dialect while a dozen pages earlier no dialectal variations are mentioned (Nchare 2012: 10); no known dialect is independently reported by the Ethnologue data (2024). In what follows, we assume the phonetic values to be /u/ for Ward’s o and /ü/ for Ward’s ø.

Dugast and Jeffreys (1950) and Schmitt (1963) follow the convention of using the set of nine vowels /a, ɛ, e, ə, i, ɔ, u, ü, ɯ/ and additionally mark tones inserting after the respective words [.] for the low tone, [˙] for the high tone, and the combinations of these marks for more complicated tonal contours.

Matateyou (2002) and Nchare (2012) use ten vowels /a, ɛ, e, ə, i, ɔ, o, u, ü, ɯ/ but the notation differs for the latter two, as reported above: ʉ for /ɯ/ (Matateyou 2002) and y for /ü/ (Nchare 2012). Both sources use the grave accent ( ˋ ) for the low tone, the acute ( ˊ ) for the high tone, and the combinations of these marks in the form of a caron ( ˇ ) for the rising tone and a circumflex ( ˆ ) for the falling tone. Note that the issue of tone marking in practical orthography is rather complicated (cf. Bird 1999, 2001; Bernard et al. 2002; Lüpke 2011). In indigenous African scripts created since the 19^th century, tones are mostly unmarked (cf. Rovenchak and Buk 2020; Daniels 2023), with prominent exceptions exemplified by the Bassa Vah and Nko alphabets.

Rows 11 and especially 12 in Table 3 suggest that the reading of Ward’s o should indeed be identified with /u/ rather than /o/. Additional examples include ń·gub – ŋgop – ŋgùp ‘skin’ and mbó – ŋgox – ŋgù ‘town, country’, where the first word stands for Koelle’s data, the middle corresponds to Ward’s data, and the last one is the modern phonetic value.

Certain examples demonstrate stable phonetic values: /a/ in rows 4, 7, and 8 (first vowel); /o/ in row 1; /i/ in row 13; /u/ in rows 6 and 8.

From Nchare’s data (2012: 21) we can draw the following vowel shifts:

[ɔ] → [u], [o]/[u] → [ü], [a] → [ɛ]

All of them correspond to vowel raising (movement “up” according to Table 2 considering that [ɛ] and [ɔ] are actually open-mid vowels). Additionally to these shifts we have also discovered an [e] → [i] transition with the same direction. It is also exemplified by the word Ɲiɲi ‘God’ given as nyḗnye by Koelle (1854).

Some other potential vowel shifts based on historical data as shown in Table 3 are listed in Table 4. The time given corresponds to the recorded data and suggests the upper estimation. Delafosse’s records often quote also Bamum character readings from 1907, so they likely represent the situation with the Bamum language at the turn of the 20th century.

We do not have sufficient evidence to discuss the evolution of /ɯ/. The reason is that such a phoneme is not distinguished by Koelle (1854) and neither is it possible to identify the respective notation properly in the data by Delafosse (1922). The following relevant lineages were discovered: ákōt – kwɯt – kùt ‘leg’, átot – tɯt – tɯ̀t ‘ear’, ndṣū́ – (yɯ) – njɯ́ ‘I eat’, ń·gọ – ŋgɯə – ŋgɯ́ə̀ ‘leopard’. In these examples, the first word corresponds to Koelle (1854), the second one is by Ward (1938), and the third one is the modern version from Matateyou (2002) or Nchare (2012).

3 The A ka u ku mfɛmfɛ script

In Bamum, words are mostly one or two syllables. The syllables have the structure (C)V(C), where the final consonant is either nasal /m, n, ŋ/ or voiceless /p, t/. A syllable can end in the glottal stop /ʔ/, which might originate from final /k/ (Schmitt 1963, p. 57; Nchare 2012, p. 48). As we have mentioned in the previous section, consonants can be prenasalized. Vowel-only words are not uncommon for the language and include in particular frequently used pronouns, see in particular Table 8.

Creating a writing system that would reproduce such a phonotactically complex structure is a tricky task. As shown in Table 1, the ultimate stage of the Bamum script might seem to be syllabic at first glance: of 80 characters in total, there is only one purely alphabetic character for /m/, a few characters for closed syllables and an overwhelming majority of open-syllable characters. It appears, however, that the system functioned quite efficiently given that it was governed by several general and specific rules as described below.

The most productive approach to extend a syllable inventory is to apply diacritical marks; just compare the dakuten (゛) and handakuten (゜) marks in the Japanese kana. One of the diacritics in the Bamum script is called kɔʔndɔn; it looks like a circumflex mark over characters. Its main function is to mark a final glottal stop but certain unpredictable syllable changes are also attested (see Tables 5 and A in the Appendix). In five cases, kɔʔndɔn differentiates between low and high tone, all are for Cɛn syllables: tɛ̀n / tɛ́n, kɛ̀n / kɛ́n, mɛ̀n / mɛ́n, rɛ̀n / rɛ́n.

The second diacritical mark is called tukwɛntis; it looks like a horizontal line over a character. It mostly functions as a “killer stroke” removing vowels from syllables (see Table 5). This is similar to the virāma mark ( ् ) in Brahmi-derived scripts or sukūn ( ـْـ ) in ḥarakāt (system of short vowel marks in the Arabic orthography). Note that, to our knowledge, symbols with such a function are not attested in known syllabaries.

Table 5:

Representation of syllables in A ka u ku mfɛmfɛ. Gbetnkom (2022) innovations are highlighted in red on the gray background in the respective cells.

It might seem that the diacritics suffice to represent the entire variety of Bamum syllables in an almost alphabetic manner, by combining consonants obtained via the killer stroke with stand-alone vowels (cf. Table 5). But kɔʔndɔn and tukwɛntis are just recent additions into the script. During previous development stages, other strategies were developed, and they survived to the current A ka u ku mfɛmfɛ writing system.

The complex nature of the Bamum script can be exemplified by principles governing representation of syllables not covered by the set of Table 1 (with additions provided by diacritical marks). The main way to represent such a syllable (of the shape C₁V₁) is to write it as a combination C₁V₂+C₂V₁. For instance, in a quite regular manner Cɯ syllables are written as Cu+ɣɯ. Often, the combinations Ci+ü are used to represent Cü.

According to Dugast and Jeffreys (1950: 32) and Schmitt (1963: 48), the vowels /ɔ/ and /ə/ were not differentiated in the Bamum script. Certain observed phonotactic restrictions might be helpful in guessing word readings. For instance, /ɛ/ and /wə/ do not occur in open syllables, /ɔ/ is always /ɔʔ/ in monosyllabic words, except ɔ ‘yes’, tɔɔ ‘to pierce’, ṁgbɔ ‘corn’ (Schmitt 1963: 57).

Diphthongs are mostly written as consecutive vowels: pɯən = pɯ+ə+n ‘people’, puaʔ = puə+aʔ ‘is’, ʃie = ʃii+i+e ‘name (verb)’. Some characters contain diphthongs in syllable nucleus: nue ‘drink’, rie ‘say’. Such reading is preserved in polysyllabic words, e.g., mbirien = m+pi+i+rie+n ‘antelope’.

Word-final /p/ is represented by pɯ: ndap = n+ndaa+pɯ ‘box, house’, nʒap = n+nʃa+pɯ ‘meat’, pap = pa+a+pɯ ‘wide’. One character with kɔʔndɔn reads mvɔp ‘dust, gunpowder’ (Dugast 1950). It is worth noting that the use of epenthetic (“dummy”) vowels to represent word- and syllable-final consonants is typical of syllabic scripts, e.g., -e in the Cypriot syllabary as in ka-re (read right-to-left) for the Ancient Greek γᾰ́ρ ‘for, since’ (cf. Gnanadesikan 2011) or the use of katakana symbols of the -u [-ɯ] series to represent foreign words in Japanese (デスク de-su-ku for ‘desk’ or ホテル ho-te-ru for ‘hotel’).

Both syllable-final /m, n/ and syllable-initial /m, n/ followed by consonants (forming consonant clusters, which are treated as prenasalized consonants) are represented by and , respectively: mgbie = m+pi+i+e ‘woman’, nsɛn = n+si+e+n ‘forest’, lum = lu+m ‘year’. The character is also used for /ŋ/ before /k, g/: ŋkye = n+kye+e ‘salt’, ŋgup = n+ku+u+pɯ ‘skin’ (Dugast 1950). Final /m/ and /n/ are intrinsic to several Bamum characters, see the last column in Table 5.

There was also a rather curious approach to marking the final /t/ using rɯ, first attested during stage C and which became standard during stage F (Schmitt 1963: 151–155). It might originate from an implicit pronoun ‘your’, e.g., nʒɯt ‘sheep (sg.)’ versus nʒɯrɯ ‘your sheep (sg.)’. The version in the Bamum script would be ʃɯ+rɯ (Schmitt 1963: 155). This method can be occasionally applied also word-internally: mbuətnə = m+puə+ɔ+rɯ+na+ɔ ‘blessing’ (Dugast 1950: 246), fɯtmum = fɯ+ɣɯ+rɯ+mɔ+m ‘Tuesday’, yetnʒuə = i+e+rɯ+nʒuə ‘Friday’ (Dugast 1950: 250). In the list of words given by Dugast (1950), only two words use different strategy for word-final /t/: mbit = m+pi+i+ti ‘excrement’ and pit = pi+ti ‘war’ (cf. also Schmitt 1963: 155) but the same ending is again represented by rɯ in laʔpit = laʔ+pi+rɯ ‘the morning star’ (Dugast 1950: 244). Three characters possess intrinsic final /t/: kɛt used as a suffix, ŋuət ‘body’, and tɛt ‘three’.

As non-prenasalized voiced stops /b, d, g, gb/ are rarely found in syllable onsets in Bamum, no separate characters were invented to represent them. Instead, the respective voiceless counterparts are used: bɯa = pu+a ‘that (relative pronoun)’, gbayi = kpa+a+i ‘lion’, geloba = kye+lɔʔ+pa ‘camel’ (Dugast 1950); the latter word is given as keloba by Schmitt (1963: 695). From examples by Oumaru Nchare (c. 2005) and Matateyou (2015: 142) one can derive a principle to represent voiced consonants as follows: C_voicelessV₁+V₁ = C_voicedV₁, so that adding a vowel-only character to a syllable with the respective inherent vowel changes the syllable’s onset to the voiced consonant, e. g., ʃu / ʒu =  ʃu + u. It is not clear, however, to what extent this rule has a universal nature. In particular, numerous examples by Dugast and Jeffreys (1950) suggest that adding the inherent vowel character to a syllable is one of the approaches to distinguish homonyms.

There are also numerous irregular character combinations in the traditional A ka u ku mfɛmfɛ orthography: mfə = fu+ɔ, mfɔn = fu+ɔ+m, lɛt = lee+a+rɯ, etc. (Schmitt 1963: 168–169).

We have discovered several of Gbetnkom’s innovations in the representations of syllables. Some systematic approaches include:

1. combinations with ə for Cə syllables: bə = mbaa+ə, də = ndaa+ə, kə = kɔ+ə, mə = mɔ+ə, lə = li+ə, və = vü+ə, sə = sɯ+ə;

2. combinations with üʔ for Cü syllables: bü = pü+üʔ, tü = tə+üʔ, dü = ntuu+üʔ, nü = na+üʔ, lü = lɔʔ +üʔ, sü = sɯ+üʔ, yü = yɯ+üʔ;

3. some new combinations for Ci and Ce syllables: bi = pi+i, yi = ya+i, ne = na+e, ve = fe+e, ye = ya+e (note that bi and ve follow the voiceless–voiced representation rule mentioned above);

4. some new combinations with tukwentis to represent syllable-final consonants: -d (?). The latter two seem mostly applicable for the transcription of foreign words.

In Table 5, the characters and their combinations are listed. It is compiled mostly from Schmitt (1963) and Dugast and Jeffreys (1950) with some data by Delafosse (1922). Information from Nchare (c. 2005) and Matateyou (2015: 139–143) supplements representation of syllables with initial voiced consonants. Gbetnkom’s additions are highlighted in red and placed on the right side of the respective cells. We are aware that some of them might have been used before in other sources that may have slipped from our attention.

The first row in cells corresponds to syllables without the glottal stop in the coda; those with the glottal stop are given in the second row. Variants of representation are separated by the slash (/). Parentheses denote two possible representations, e.g., () for wi means that this syllable can be written both and and () for wu mean the and representations. Brackets […] mark characters usage not in their primary function.

Certain hints about the values of character combinations used by Gbetnkom can be obtained from a poem in French being transcribed using the A ka u ku mfɛmfɛ writing system, see examples (1)–(3). In the first line, the original French phrase is given followed by the A ka u ku mfɛmfɛ version (transcription) in the second line. The third line lists the values of individual characters (separated by hyphens within words). The fourth line contains provisional reading of the Bamum script text. Note in particular the use of nte to represent /te/.

(1)

Si l’amour était devenu la force dominante du monde actuel,

si-i la-mu-rɯ e-nte ndaa-ə-vü-ə-na-üʔ la fu-ɔ-rɯ-si ndaa-ɔ-mi-na-a-n-tə ntuu-üʔ mɔn-ndaa-ə a-kɯ-tə-üʔ-e-li

sii lamurɯ e(n)te dəvənü la fɔrɯsi dominaantə dü mɔndə akɯtüeli

(2)

Les pauvres et les faibles trouveraient forces et places dans le coeur des riches

lee pɯ-ɔ-vü-rə e lee fe-mbaa-l-ə tə-ru-fe-e-re fu-ɔ-rɯ-sɯ-ə e pɯ-la-sɯ-ɔ ndaa-a-n lɔ-ə kɔ-ə-ə-rɯ ndaa-e rii-ʃ

lee pɔvürə e lee feblə təruvere fɔrɯsə e pɯlasɔ dan lə kəərɯ de riiʃ

An interesting approach is used to reflect the liaison rule:

(3)

Dans l’âme des a ttristés

ndaa-a-n la-m ndaa-e z-a a-tə-rii-si-nte

dan lam de za a təriisi(n)te

The A ka u ku mfɛmfɛ writing system has a peculiar symbol called nʒəmli. It is used as a determinative and its role on the previous stages of the Bamum script development was to mark proper names (Schmitt 1963: 200). It is likely though that this symbol also had an additional role of distinguishing homonyms. Dugast and Jeffreys (1950: 7) suggest that nʒəmli is placed before words situated “higher” on some native scale of values. Schmitt (1963: 202–203) gives a slightly different interpretation and provides several examples where nʒəmli is used to distinguish homonyms without reference to hierarchies: i reads as yi ‘know’ while means yi ‘nose’, stands for nyi ‘enter’ versus nyi ‘knife’, etc.

In the book we analyze (Gbetnkom 2022), the first occurrence of nʒəmli is on the cover in the author’s name rendered as Gbetnkom Samuel Calvin = det+Mbaa+kpa+e+ti+kɔ+ɔ+m sa+mi+üʔ+e+li ka+li+fe+e+n. Note that the determinative is placed only before the first word. The most frequent word with nʒəmli is Ɲiɲi ‘God’. The following geographical names are found with nʒəmli: ‘Africa’, ‘Kilimanjaro’, ‘Himalaya’, ‘Everest’, ‘Mississippi’, ‘America’, ‘Europe’, as well as the name ‘Manu Dibango’, a Cameroonian musician. It does not seem that the determinative is used in another role in the texts of Gbetnkom that we analyzed, i.e., to distinguish homonyms. Also, no names without the determinative are attested in any available texts.

4 Frequency distribution of the Bamum characters and words

We have compiled three frequency lists based on the texts of the nine poems by Samuel Calvin Gbetnkom (2022). The tenth poem in this book is in French, so it was excluded from the analysis. In the first list, a character with the kɔʔndɔn or tukwɛntis diacritical marks is considered a single token different from the respective base character (without diacritics). For the second list, the diacritical marks were removed, and the frequencies of the basic characters were counted. Finally, the third list corresponds to words in the analyzed Bamum texts. In modern practice, an ordinary space character is used to separate words. All the lists were then sorted with respect to frequencies in the descending order yielding the so-called rank–frequency lists. The first (most frequent) item has rank 1, the next word has rank 2 and so on.

There are N = 3798 running characters (tokens) in the analyzed texts. The first list contains 114 distinct characters (types) and the second list has 72 types. The latter means that not all the A ka u ku mfɛmfɛ symbols had been used in the poems: the entire set should contain 80 (semi-)syllabic characters plus one nʒəmli symbol. Note that we did not count punctuation marks and did not consider diacritical marks as separate tokens.

In fact, the following nine characters are not attested in the analyzed material:  mee, yɔʔ, lu, rɯ, kɛn, fɔm, mbɛn, mɛn, and ɣɔm. Another two occur only with diacritical marks: z and yuən. Results are shown in Table 6 and Figures 2, 3.

Table 6:

Absolute frequencies of the A ka u ku mfɛmfɛ symbols. “Symbol-1” and “Frequency-1” columns correspond to characters with diacritics while “Symbol-2” and “Frequency-2” columns stand for characters with diacritics stripped off.

Figure 2:

Rank–frequency distribution for list 1 (characters with diacritics) along with fitting functions. The values of absolute frequencies (vertical axis) are calculated as f _r  = NP _r , where N is the sample size (total number of characters) and P _r corresponds to the respective model, in particular, given by Equation (4). The variable r on the horizontal axis is rank.

Figure 3:

Rank–frequency distribution for list 2 (characters without diacritics) along with fitting functions. The values of absolute frequencies (vertical axis) are calculated as f _r  = NP _r , where N is the sample size (total number of characters) and P _r corresponds to the respective model, in particular, given by Equation (4). The variable r on the horizontal axis is rank.

Previous studies of character distribution in various writing systems have demonstrated that the respective rank–frequency dependencies follow certain mathematical models being rather uniform at least for alphabetic scripts (Grzybek 2007; Grzybek and Kelih 2005; Li and Miramontes 2011; Wilson 2013) later extended to an abugida exemplified by Devanagari (Pande and Dhami 2015) and a syllabary exemplified by Vai (Rovenchak et al. 2018). This means in particular that mathematical patterns governing the relationship between character frequencies and their ranks in various writing systems do not significantly depend on the genre or authorship of texts. This pattern, observed to be particularly uniform in some scripts, indicates a structured and predictable distribution of characters within texts in the respective languages. Similar models can also describe distributions of syllables at least in some languages (Rovenchak and Vydrin 2020). The universal nature of such models is yet to be checked for additional abugidas and syllabaries.

Here, we focus on discrete models paying special attention to a possibility of parameter interpretation. In this respect, the so-called (1-displaced) negative hypergeometric distribution given by

is of special interest. In the above formula, (…) are the so-called binomial coefficients (Binomial coefficient 2020; Weisstein 2024), r is the rank of the symbol in the rank–frequency list, real numbers K and M are fitting parameters with no special interpretation so far; they might depend, for instance, on author or genre of a particular text. The parameter n is interpreted as the grapheme inventory size (with a unity subtracted since the minimum values for both inventory and rank are 1). Equation (4) has proven to describe well the distribution of graphemes in alphabets for Slavonic (Grzybek and Kelih 2005), German (Grzybek 2007), Irish and Manx (Wilson 2013) languages, as well as for characters in the Vai syllabary (Rovenchak et al. 2018).

We have applied the Altmann-Fitter software (Altmann 2000) to analyze the first (characters with diacritics) and second (characters without diacritics) rank–frequency lists. This tool analyses the data over a few hundreds of discrete distributions and enables finding the best fits with respect to several criteria. Without delving into mathematical details of other distributions (Wimmer and Altmann 1999), we present in Table 7 a summary of those with the best accuracy. Due to cumbersome expressions, we do not present the other two distributions explicitly. The quality of fits is demonstrated using the so-called determination coefficient R² (the closer is its value to 1 the better fit) and the discrepancy coefficient C = χ²/N that is calculated using the Pearson χ² goodness-of-fit test (Mačutek and Wimmer 2013). A fit is considered satisfactory if C < 0.02, which is an empirical “rule of thumb” (Antić et al. 2006; Mačutek 2008). The results are also illustrated by Figures 2 and 3.

The first immediate observation from Table 7 is that the negative hypergeometric distribution [Equation (4)] does not produce a good fit: for both lists, C > 0.02 and is almost twice as high as the desired maximum value for a proper fit. Another interesting result is that the value of the n parameter in this distribution does not reflect the inventory size of the script. For the first list, n = 124 is rather far from the expected 175 corresponding to 80 characters with and without kɔʔndɔn, 15 characters with tukwɛntis (this includes original 13 plus two being Gbetnkom’s innovations), and nʒəmli. For the second list, the inventory size corresponds to n = 80 while the fitting yields n = 74. Note that the quality of fitting improves if the value of n is fixed appropriately; still, the discrepancy coefficient C remains too high in these cases. The behavior of graphs in Figures 2 and 3 might be misleading as all the curves seem to follow the observed data in a satisfactory manner. This impression is due to the logarithmic vertical scale, which compresses the actual values closer together. To get an idea about the quality of the fitting, one should consult the C and R² values.

The two-fold nature of the A ka u ku mfɛmfɛ script, i.e., the presence of both syllabic and alphabetic features, might be to blame for the character distribution not following the expected negative hypergeometric law with good precision. Distribution yielding better fitting characteristics require additional studies as the interpretations of their parameters is not well-established. Note that the Jain–Poisson distribution was shown to be a proper model for syllable distribution in Bamana and Maninka (Rovenchak and Vydrin 2020). The failure of the negative hypergeometric distribution to achieve a desired accuracy could mean, in particular, that in the A ka u ku mfɛmfɛ writing system proper units to analyze in this regard are not characters but certain of their combinations.

In Table 8, the most frequent words in the analyzed poems are listed. Since the A ka u ku mfɛmfɛ script lacks tone marking, it is not possible to tell apart homographs differing in tone only. Obviously, complete homonyms (words with the same tone) cannot be differentiated as well without deeper analysis of the respective word occurrences in sentences. A glossed text is required in order to deal with such situations. At the moment, no tools to analyze this level of the Bamum languages are available.

Table 8:

Most frequent words in the poems by Samuel Gbetnkom.

1. The following standard glosses are used for personal pronouns: 1SG – 1st person singular, 1PL – 1 person plural, 2SG – 2nd person singular; 3SG – 3rd person singular; 3PL – 3rd person plural.

   *Schmitt (1963: 682, 689, 696) gives naa ‘mother’. **Schmitt (1963: 691) suggests a possible reading yii ‘this’.

In the third frequency list, there are 587 distinct words (types) while the total number of running words in the analyzed poems is 1622. More than two thirds of the types (396) occur only once in the texts. Such types are known as hapax legomena and their share can indeed be that high for rather short texts (cf. Kornai 2002). Note that the first ten most frequent words occupy more than 25 per cent of the text (407 of 1622 running words), while the first 15 words correspond to more that 30 per cent of text (494 of 1622). Slightly more than 50 words are required to cover a half of text and almost 190 suffice for 75 per cent.

The structure of the high-frequency vocabulary is quite regular. As we can see from Table 8, the majority of words there are function words (conjunctions, prepositions). Every third word of 15 is a personal pronoun and body parts are the only nouns within the top-frequent words. The appearance of body parts in high-frequency vocabulary was observed across various languages and text genres (see, e. g., Buk and Rovenchak 2007; Pattillo 2021).

There are a couple of interesting remarks here. First, the modification to represent -ə syllables that might seem secondary from Table 5 is in fact one of the most productive in the running text: it appears in four out of 15 most frequent words. Another observation is that nda ‘true, good’ and mbə ‘to be’ from the top-frequent words have an “alphabetic” (three-symbol) representation. With a variety of approaches to form syllables in the Bamum script, it remains unclear why such a complicated approach was used in those cases, e.g., why not * or * to render mbə.

5 Conclusions

In the first part of the paper, we have summarized the information about the phonology of Bamum and demonstrated certain discrepancies across various authors, especially with respect to the vowel inventory. We have been able to confirm previous suggestions by Nchare (2012) regarding historical changes of vowels, with the additional [e]→[i] shift discovered.

We have analyzed orthographic principles of the last version of the Bamum script known as A ka u ku mfɛmfɛ. An attempt was made to summarize variants of syllable representation based on various sources. The study of texts by Samuel Calvin Gbetnkom, a modern Bamum author, suggests certain regularization of syllable representation in modern practice. We might be witnessing a gradual establishment of a new orthographic norm in A ka u ku mfɛmfɛ. To corroborate these observations, further studies are required with more texts in the script by various authors, especially modern ones. It should be noted in particular that existing variability in syllable representations provides potential possibilities to distinguish homonyms and even to mark tones on a regular basis.

The analysis performed on the rank–frequency distributions of characters in the A ka u ku mfɛmfɛ script failed to achieve the desired accuracy with a mathematical model known as the negative geometric distribution, where one of the fitting parameters corresponds to the character inventory size. This result suggests that in complex orthographies, proper units aligning with this model are not characters but some of their combinations, even though, e.g., letter frequencies in English follow the mentioned distribution (Pande 2021). A recently proposed model (Özbey 2023) is worth attention in the future, as it was applied to describe character frequencies in over 100 languages, including those using non-alphabetic scripts like Amharic, Devanagari, Ojibwe, as well as Chinese and Japanese. Last but not least, ancient writing systems with both alphabetic and syllabic features, namely, Old Persian cuneiform (cf. Kent 1989) or Paleohispanic scripts (cf. Ferrer and Moncunill 2019), should be studied to discover a proper mathematical model for character frequency distribution, although the available material for quantitative analysis is rather limited.

While the fraction of alphabetic characters in Bamum is much lower than in the Old Persian script, there is at least one common feature in both writing systems: pleonastic representation of some syllables. Repeating the inherent vowel is typical of Old Persian, for instance, di+i stands for di (see Testen 1996). In Bamum, however, this approach mostly serves a different purpose—voicing the onset—and most probably historically it was also used to discriminate homonyms, as we have mentioned in Section 3 (cf. also Coulmas 2004, p. 38).

We have performed an analysis of the Bamum character frequency data using distributions considered by Özbey (2023) and have not obtained a good fit for both rank–frequency lists (with and without diacritics). In particular, the parameter responsible for the character inventory size appeared significantly different from the real values (about 50 % and over 200 %, depending on the model). It is worth mentioning that a quick analysis of the Old Persian based on partial frequency data from the Behistun inscription (Hallock 1970) proved the negative hypergeometric distribution as the best fit, with the proper value of the parameter corresponding to the inventory size of 36 symbols (Testen 1996).

Finally, we would like to stress that for any widescale analysis of Bamum, electronic form of texts is essential. Some texts (by Abdoulaye Mbouombouo, another modern Cameroonian poet) available in Shümom, a secret language invented by Njoya, are another source for studies of the script. Moreover, it would be informative to conduct some analysis for Shümom itself. Corpus-based studies of the Bamum language are yet to be done and tools for processing this language yet await their creation and implementation.