Unit Power Prefixes

While it is possible to talk about dozenal numbers entirely in the English language without having to invent any new words, and I do not believe that a new language in the style of arbitrary natural languages should be fabricated as a replacement for English or other natural languages when discussing numbers in base twelve in ordinary conversation or written discourse, in terms of how many words and letters would be required to represent a number, the natural English language would not always be concise enough to compete with the international metric system of prefixes for powers of base ten. If any dozenal metrological system is being proposed in competition with decimal metric, it should at least be not worse in any respect than the decimal scheme. It seems to me that as far as concision is concerned, dozenal proposals of others have been inferior to the decimal metric system, which would be discouraging for the advocacy of a dozenal metrological system nomenclature claiming to be better that the existing international standard.

Relative Boons Of Decimal Metric Nomenclature
In the international decimal metric system of prefixes for powers of ten, the prefixes each have for convenience of phonetics:

• two syllables and no more
  
• no more than two consonantal phones in consonantal clusters
  
• consonantal clusters appear only intervocalically, allowing them to be divided into single consonants ending one syllable or starting the other between the two syllables
  

and for ease of orthographic spelling:

• no more than five letters
  
• letters of the English extension of the Roman alphabet only, easily accessible on the simplest of alphanumeric keyboards, with the exception of the Greek letter μ as the literal abbreviation for the prefix micro
  

There are languages, such as some Asian languages, in which the natural phonology does not encounter consonantal clusters within a syllable. If the nomenclature proposal is to be acceptable internationally, it ought to be accommodating to native speakers of all natural languages or as many as practically possible. The Chinese language, for example, tends to remove terminal consonants from syllables in the decimal metric prefixes, reducing them to syllables that appear in the native language and can be written with pre-existing characters.

The ratified standard for binary power prefixes in information technology reduces the syllables to monophonemic consonants followed by single vowels without terminal consonants or clusters, with the exception of the syllable ex, and each syllable is represented by only two letters. In the development of a nomenclature for prefixes of dozenal powers, this optimum should be the goal. Otherwise it would not be possible to say for certain that a dozenal nomenclature is better than the decimal ones.

Design of a Dozenal Numerical Nomenclature
Phonetic Considerations

• Articulatorily, the phonemic inventory is to be accessible in pronunciation to most native speakers of natural languages.
  
• Auditorily, between different words for numbers, the phonetic differences ought to be enough to prevent the different words being confused with each other.
  
• Words for numbers are to resemble those in natural languages to increase their recognition.
  

Regarding the accessibility of articulatory pronunciation and auditory contrast, phonetic contrasts between phonemes that do not exist in typical languages are likely to be difficult for novices of those phonemes to pronounce. The distinction between the liquids l of the lateral kind and r of the rhotic kind among speakers of Asian languages is a known example. However, constraints to be explained in more detail below arising from the available orthography may impel phonetic contrasts that do not exist conveniently in all common languages. To address conflict in such cases, it is sufficient to introduce further differences of the phonemes that compose the words for the numbers. Where words may to some native languages have similar consonants, their vowels are to be made very noticeably different.

Notwithstanding the phonetically contrastive redundancy in the words for numbers, they may be more easily recognised by being based on the words happening for numbers that are similar in as many natural languages and spoken by as many speakers over as wide an area as possible. Globally, the reach of the Indo-European group of languages and their words for numbers best satisfies an international aim. The main spoken languages of the American continents are now Indo-European in origin; most languages of Europe are, with the exception of the Uralic kind and isolated languages such as Basque; the official language of Northern Asia is an Indo-European language; in Australia the Indo-European language English is spoken; a lingua franca also known in other continents is likely to be an Indo-European language.

I therefore base the names for the counting numbers from zero to twelve on the words for such numbers in Indo-European languages, and preferably on reconstructed Proto-Indo-European, though simplified. As Indo-European numbers appear nowadays to be based on ten, there will not in every natural language be words for the numbers eleven and twelve. Nevertheless, I base names for these on words for them in Indo-European languages.

Some notes about these follow.

• Of the name for the number ten, in reconstructed Proto-Indo-European, this ends with a dorsal consonant here represented by k, but in many modern Indo-European languages the terminal consonant is more coronal such that s instead may be chosen.
  
• For eleven, an unvoiced terminal consonant f is preferable to a voiced one v, for the reasons of apposition and assimilation with a following unvoiced consonant.
  
• For twelve, I base the name on the English words inch and ounce related to twelve.
  
• For zero, the word is based on the two kinds, appearing in English as zero and null, and also the English word zilch taken to mean "no twelves" and a backformation from zillion taken to mean an unlimited number, interpreted as the reciprocal of zero.
  

Long Form Names
The simplification starts with reduction to single syllables, containing the phonemes most characteristic and distinctive of the words. In this manner, the words contain no more than four letters. The word-form names proposed to be used when referring to the numbers themselves or their numerals are, from zero to twelve:

zil
uon
duo
trei
kuor
penc
siks
sept
okt
nen
dek
lef
cei

I call these the long forms of the names for the numbers, which may be used for counting in the context of the use of any particular natural language being considered to be not internationally neutral enough. After the count of the number twelve, the names may be combined by concatenation with choice according to the customs of the natural languages or according to the names of the numerals in positional notation. For example, the name for twelve may be cei, uoncei, or uon zil, and that for the number following twelve may be cei-uon; two dozen would be duocei. A hyphen indicates addition, a space indicates positional listing of the numerals, and lack of space indicates multiplication.

Short Form Names
The long form names may be used additively and multiplicatively as suggested. For representation of powers of the base twelve, shorter forms of no more than three letters are suggested as prefixes. Suggested short forms are:

zi-
on-
do-
ter-
kor-
pen-
six-
sep-
ok-
nen-
dek-
lef-
ci-

For exponents in power prefixes, the short forms are used according to the numerals positionally, but without the necessity of spaces between them, because of the context of them being followed by a suffix that indicates the base of the power.

Power Suffixes
Where the base is twelve, this suffix can be -cea. I also considered -icea, -iche, -ica, -ca, and -za. Reduction of the suffix to just two letters as -ca while retaining the consonant c but followed by the non-fronted vowel "a" makes it too dorsal, and it would be better to use -za. However, z has the disadvantage of being voiced rather than unvoiced. I would reserve -ci for non-positional contexts.

Where the base is the reciprocal of twelve, the suffix is -cio. I also considered -iceo, -icho, -ico, -co, and -zo. It is important to bear in mind that these suffixes represent the base of a power.

Reciprocals
If rather the reciprocal is being used in the exponent or to state a fractional part, the suffix -an can be applied. Thus, a twelfth part would be ceian, which can be simplified to cean or cian. In many cases, oncean would mean the same as oncio, but this might not be true of bases other than that of the dozenal positional notation. For example, duoan simplified to doan would be a half, but there is no proposed suffix to indicate a base of two raised to a negative exponent in general. The international standard suffix for the base two raised to certain positive exponents is -bi. Kuoran would be a quarter. Zilan becomes a word for infinity.

Ordinals
For ordinal numbers, the usual English suffix -th may be appended. Thus, uonceith or onceath mean the twelfth counted in a list. Duoth would mean the second. Kuorth would be fourth.

It is possible to combine the reciprocal and ordinal suffixes. These would be rare, but there is zilanth meaning infinitieth.

Orthographic Spelling Considerations
Though the long and short word forms have only one syllable each, there is an aim to reduce their spellings to just two letters each. Furthermore, for their abbreviation in units of measurement, single consonantal letters in uppercase for power exponents and lowercase for negative exponents are sought. Vowels as single letter abbreviations ought not to be used in combination with consonants or else unintended words could result. We have these impositions for the syllable of each positional number:

• Two letters for the spelling of the pronounced form
  
• a consonant followed by a vowel
  
• a consonant that is sufficiently different in its uppercase from its lowercase for them to be distinct from each other in handwriting
  

In accordance with phonetic considerations, I base the consonants on the groups that I listed for dozenal mnemonics. Digraphic consonants must be rejected. Some notes specific to individual numbers follow.

• As the consonantal literal pair for the number two, I prefer D and d over B and b, even though both pairs are distinct between upper and lower cases, because the word for the number two in Indo-European languages has a non-labial rather than labial consonant.
  
• P and p are not distinct enough between the cases, so F and f must be used for five.
  
• For six, Kk and Qq could be confused with a sound in a word for eight, x is too similar to a multiplication symbol and variable, leaving Hh. C and c are not distinct enough between the cases.
  
• S and s are not distinct enough between the cases. For the negative exponent, y may be used. The proposal of this latter letter for seven was suggested before by David Kennedy and by L. C. Seelbach. It is not ideal, but there is not much better left.
  
• For ten, as D and d are reserved for the number two, J and j are suggested. In Indo-European languages, the numbers two and ten are usually distinguished by the latter being more palatalised, as the letter J should portray. J also happens to be the tenth letter of the English alphabet.
  
• For eleven, L and l are sufficiently distinct from each other, but if in certain fonts l is not distinct enough from other common characters such as the vowel capital I or digit 1, the Greek letter lambda λ could be used. I would rather reserve the character ℓ for a unit of length.
  

It is interesting that the effect of this proposal of digraphic syllables is similar to a proposal of L. C. Seelbach, to which there are correspondences among the consonants for the numbers zero, four, five, seven, eight, and eleven. However, Seelbach differed substantially in the consonants for most of the other numbers.

The vowels for the digraphic syllables are not as important as the consonants, and are chosen to resemble the vowels in the Indo-European numbers.

(To be continued …)

References

• https://en.wikipedia.org/wiki/Binary_prefix
  
• https://dozenal.forumotion.com/t26-proto-indo-european-numbers
  
• https://dozenal.forumotion.com/t20-dozenal-nomenclature-of-geometrical-figures
  
• https://dozenal.forumotion.com/t27-mnemonics
  
• https://www.tapatalk.com/groups/dozensonline/uncial-nomenclature-t1570.html#p40009563
  
• http://www.dozenalsociety.org.uk/archives/DN/DuodecimalNewscast032-web.pdf
  
• https://en.wikipedia.org/wiki/Numeral_(linguistics)
  Has "See also
  Numerals in various languages
  Main article: List of numbers in various languages",
  but the link there does not lead to the page, as though it no longer exists.
  
• https://wiki2.org/en/List_of_numbers_in_various_languages
  
• https://handwiki.org/wiki/List_of_numbers_in_various_languages#Indo-European_languages
  
• https://dozenal.forumotion.com/t23-pendulum-system
  

Monoliteral Abbreviations
The international decimal metric system uses single letter abbreviations for the power prefixes. Mainly they are uppercase or capital letters for positive exponents, with the exceptions of those for kilo, hecto, and deka, and lowercase or minuscule letters for the negative exponents. I likewise appoint uppercase letters for positive exponents and lowercase letters for negative exponents. The following is my proposal, as explained in the previous opening post in this topic:

Numeral	+Exponent	-Exponent
⓪	Z	z
①	M	m
②	D	d
③	T	t
④	R	r
⑤	F	f
⑥	H	h
⑦	S	y
⑧	G	g
⑨	N	n
⑩	J	j
⑪	L	l
①⓪	C	c

Some notes about the individual monoliteral abbreviations follow:

• The insufficient distinguishability of capital Z and minuscule z in handwriting does not matter because positive zero is the same as negative zero. Capital Z would nevertheless be used among positive exponents, while lowercase z would be used among negative exponents.
  
• B and b instead of D and d could be options for the abbreviations of the number two.
  
• Abbreviations C and c for twelve are probably not needed.
  

Digraphic Monosyllables
Similarly to the international standard prefixes for certain powers of binary having just one digraphic syllable preceeding the syllable of the base, my proposals for digraphic monosyllables for the numbers consequent from the monoliteral consonantal abbreviations and mnemonic vowels, to be used positionally in exponents for example are:

Number	Digraphic Syllabic Prefix
Zero	zi-
One	mo-
Two	dy-
Three	te-
Four	ro-
Five	fy-
Six	he-
Seven	sa-
Eight	go-
Nine	ny-
Ten	je-
Eleven	le-
Twelve	ci-

It may also be possible to use bi- for two instead of dy-. D. A. George has also proposed short monosyllabic words for numbers as single consonants followed by vowels, and his proposals resemble those here for some of the numbers, including the consonant F for the number five and G for the number eight, in agreement with Lewis Carl Seelbach.

Notes about Short Forms

• The short forms of three letters for the numbers nine, ten, and eleven were not different from their long forms. The context would often provide their interpretation, but if word form prefixes are to be unambigously multiplicative, then they can be succeeded by the infixing vowel -a- between them and the following number affix. In the multiplicative sense, the numbers are considered to be behaving as adjectives, and take a grammatical form accordingly.
  
• In English, adjectives do not have a special form, but multiples by a number other than the unit would produce plurals, which in the style of English may be appended as the sibilant suffixes -s or -es.
  

Concise Dozenal Longer Scale Suffixes
The suffixes -cea and -cio in combination with the numerical prefixes as outlined above allow all powers of twelve with integer exponents to be representable. However, permission of all powers of the base for prefixes to units of measurement ought to be discouraged, as it is in the decimal metric system, by restriction of the nomenclature to a larger power of the base. In the case of the decimal metric system, power prefixes are limited to the first three powers of ten with positive or negative exponents and thereafter to only powers of a thousand or its reciprocal. Even though prefixes are provided officially for the first power of ten and its reciprocal, these prefixes, namely deka and deci are rarely used as though they were abrogated, even though there is no rule preventing their use. The reason is that using different power prefixes on the units acts as though different units are being created that need to be interconverted, which is a nuisance. It is quite common for the ordinary person not to know how to convert between the units with different prefixes when those units are squared or cubed, for example; I would suspect that a large proportion of people would not be able to say with ease how many cubic millimetres there are in a cubic decimetre. The conversion is not difficult when understood, but the reality is that many people do not have that knowledge. This may be partly worsened by the prefixes deka and deci being so rare, which is because they are too close in size to the other prefixes and are therefore not needed. The units of a measurement or quantity only need to be changed to have the next prefix as the size of the number increases to more than three significant digits in front of the decimal point (or to a lesser extent decreases to more than three zeros after the decimal point). Three or four digits are quite subitizable, and as well as causing an inconvenience of excessive proliferation of different scales of units and their interconversion, it would be wasteful of the words for powers in positional notation through confinement to scientific notation all the time. People tend to count units up to larger powers rather than subdivide to smaller and smaller powers. It is an advantage of the decimal metric system not to have prefixes for all powers of ten to integer exponents.

So that a dozenal proposal for power prefixes of units will not be worse than the decimal metric standard, I encourage that the base used for dozenal powers be the fourth power of twelve or twelve to the power of four, similarly to the Dozenal Mylliad and Myon nomenclatures that I suggested earlier. Today, based on simplification of the -lliad suffix from my Mylliad proposal, I suggest the suffix -lia for the fourth power of twelve and the suffix -lio for the reciprocal of that power. They can be further simplified to the digraphic suffixes -la and -lo respectively.

I think that the trigraphic suffixes are short enough when the digraphic prefixes are used, and the combined results resemble words in English for decimal powers.

• In this case, it would be better to use the prefix mo- rather than on- for the number one, to produce a prefix that evokes the English word million and the related word in other languages.
  
• Similarly, the prefix bi- for the square power can be used.
  

It would also be stylish to use the shorter prefixes for numbers that I suggested, which have no more than three letters each. The aim would be for the combined prefixes of exponents and the base to not have more than five letters, which can often be achieved in more than one way.

• For the third power of the quartic dozen, the short trigraphic prefix ter- may be more recognisable than the digraphic one te-. So, terla- and terlo- may be better than telia- and telio-, the latter of which may be too similar to the Greek prefix teleo- meaning "end".
  
• The prefix helio- would be in conflict with that of the Greek prefix meaning "Sun". The prefix sixla- could be used instead.
  

References

• https://dozenal.forumotion.com/t8-dozenal-mylliad-nomenclature
  
• https://dozenal.forumotion.com/t25-myon-dozenal-nomenclature
  

Yesterday, I considered combined prefixes of either five or four letters for the powers of the fourth power of twelve. The prefixes of five letters are more readily recognised as being derived from Indo-European words for numbers. However, they produce consonantal cluster in the middle of the prefixes that might be unfavourable to some natural languages. Furthermore, their initial letters do not always agree with the monoliteral abbreviations developed for the units as described above. For these reasons, I prefer the shorter combined prefixes of just four letters each.

• I change the trigraphic prefix of the number six to hex- in order to agree with the monoliteral abbreviation and mnemonic vowel. This makes the triliteral prefix more similar to the Greek word for the number six.
  
• Likewise, the triliteral prefix dek- for ten is more similar to Greek than many other Indo-European languages, which probably ought to produce the letter s instead of k.

Multilingual Word Numbers		Unit Prefixes
Positive Exponents	Negative Exponents	Positive Exponents	Negative Exponents
zilia-	zilio-	zila-	zilo-
molia-	molio-	mola-	molo-
bilia-	bilio-	bila-	bilo-
terla-	terlo-	tela-	telo-
korla-	korlo-	rola-	rolo-
penla-	penlo-	fyla-	fylo-
hexla-	hexlo-	hela-	helo-
sepla-	seplo-	sula-	sulo-
oktla-	oktlo-	gala-	galo-
nenla-	nenlo-	nyla-	nylo-
dekla-	deklo-	jala-	jalo-
lefla-	leflo-	lula-	lulo-
ceila-	ceilo-	cila-	cilo-

For the digraphic prefixes for the numbers in the combined prefixes of just four letters, I altered the vowels in order to make those with similar consonants more distinct. Consonants with a similar place of articulation ought to have different vowels. For this reason:

• the prefixes for the numbers three and ten ought to not have the same vowel, as both had non-labial coronal plosion;
  
• the prefixes for the numbers seven and ten ought to not have the same vowel, as both were strident or had sibilant frication in their consonants; and
  
• the prefixes for the numbers four and eleven ought to have different vowels, because their consonants were liquids.
  

To achieve these differences and yet balance the distinguishability with similarity to the Indo-European words and the mnemonic contrasts, I chose to reduce the vowels from the mnemonics for the numbers seven and eleven to the vowel u, allowing the vowel for the number ten to be changed so that it would be different from that for the number three without being the same as that for the number seven. These changes also allow the vowel of the number eight to be less backed and less rounded, as it is in some natural languages. The prefixes for the numbers zero and twelve do not have to have different vowels, as they are unlikely to be used together, since one of them is not used as a numeral in positional notation, while the other is not used as a numeral in non-positional notation. More benefits of this scheme are that:

• The chosen system of vowels has optimum contrast when there are only six different vowel letters available to be used for twelve numbers, as each monoliteral vowel is used twice or in two numbers.
  
• Consonants of similar place of articulation are nevertheless contrasted by more than one difference of articulation. Where one is voiced, the other is unvoiced, and at the same time where one is a stop, the other has frication or where one is a fricative the other is a plosive. Thus, the pairs F and B, T and J, S and J, and H and G differ in these ways. Whereas Z and J have the same voicing, they differ enough in place of articulation and their vowels are more different now too. Although S and Z differ in voicing but not place of articulation, their vowels are more different now than before, and in any case Z for zero is unlikely to occur in a prefix in itself.
  
• The consonantal groups based on the mnemonics involve at least one phoneme that is common among a wide variety of languages. There are no very unusual kinds of articulation in the groups as a whole.
  

Nevertheless, for better contrast between the numbers for four and eleven, the original prefix le- for eleven could be used instead of lu-, without causing conflict with another consonant. The vowel u is acceptable because it is a reduction of the letter v in the word eleven.

All of these contrasts and differences would make the system suitable for audible distinction in noisy environments, such as over radio or telephone communications when there may be interference or poor signal reception. In this manner, the numbers would be able to compete with the so-called NATO "Phonetic" Alphabet or International Radiotelephony Spelling Alphabet word names.

The very concise unit prefixes are only proposed as prefixes to metrological units or for other technical purposes and it is not suggested that they be introduced into natural languages as words to be used when doing ordinary counting. The longer words can be used in the context of counting or conversation.

Reference

• https://www.worldometers.info/languages/nato-phonetic-alphabet/
  
• https://en.wikipedia.org/wiki/NATO_phonetic_alphabet

So that prefixes would be as suitable as possible for the two major modes of communication through light and sound, it is proposed that they be designed with graphic and phonetic considerations in mind, each of which has a mode of production and a mode of reception. Of the graphic modes to which the prefixes should be well adapted there are

• Writing, and
  
• Reading
  

while of the phonetic modes there are:

• Pronunciation, and
  
• Audible contrast
  

Graphic Considerations
Writing
For suitability to the graphic production mode of writing, it is proposed that the prefixes conform to the following aims:

• Keyboard Accessibility: The prefixes can be spelt using characters that are easily accessible on a typical keyboard.
  
• This means that the characters composing the prefixes should be letters of the Roman alphabet extended to the modern English version. Letters of the Greek alphabet or other alphabets are ordinarily less accessible in this way. Logographic systems of writing have too many characters to fit on a standard keyboard.
  
• There ought to be no special character "brand marks" required.
  
• There ought to be no annotations with special formatting such as superscripts or subscripts required.
  

Reading
For adaptation to the graphic reception mode of reading, it is proposed that the prefixes conform to the following aims:

• The prefixes are as short as possible in terms of numbers of letters. There ought to be no more than four letters per prefix uncompounded.
  
• The single letter abbreviations for the prefixes ought to be distinguishable between upper and lower cases in handwriting and at any scale or size of font. Letters not distinguishable enough between upper and lowers cases and better left unused as monoliteral abbreviations for the prefixes are:
  Cc
  Oo
  Pp
  Ss
  Vv
  Ww
  Xx
  Zz
  
• The single letter abbreviations when combined by compounding should by their sequences of letters avoid being misinterpreted as words. To achieve this most easily, vowels as monoliteral abbreviations for the prefixes should not be allowed. This removes the availability of the following letters as monoliteral abbreviations:
  Aa
  Ee
  Ii
  Oo
  Uu
  and probably also Yy.
  

Phonetic Considerations
Pronunciation
For suitability to the phonetic production or articulatory mode, it is proposed that the prefixes conform to the following conditions:

• The phonemes composing the prefixes ought to be commonly and easily articulated among major languages of the world. The most typical systems of vowels are said to consist of five vowels that are capable of being represented by the letters A, E, I, O, and U, to which Y may be added. The most widespread consonants may be classified into kinds as follows:
  
  OBSTRUENTS:
  
  Plosive stops:
  Unvoiced: p t k
  Voiced: b d g
  
  Fricatives: f s h
  
  SONORANTS:
  Nasals: m n ŋ
  Liquids:   l (r)
  Semivowels: w j (r)
  
  Here, the phoneme j has the glide or vocoid sound and not the affricate sound that it has in English.
  
  
• Phonologies for the structures of syllables that do not suit many speakers of some languages ought to be avoided. This may limit consonantal clusters by discouraging terminal consonantal clusters altogether and severely limiting consonantal clusters initially and medially too.
  
• The word form uncompounded prefixes ought to contain no more than two syllables.
  

Audible Contrast
For the receptive phonetic mode by acoustic distinguishability, the following aims for the prefixes ought to be adhered to:

• The phonemes composing the prefixes should be distinct enough to avoid being confused in noisy environments. It is supposed that in noisy environments, the less sonorous consonants are less easy to perceive. By making words be disyllabic of two different vowels without the same permutation of vowels among any of the words, it is likely that the words will remain distinguishable across noisy channels. This is a basis of typical radiotelephony spelling alphabets. Diphthongalisation as a contrast for monosyllables is likely to be less distinct than different pairs of vowels separated by consonants in disyllables.
  
• Where consonants of different prefixes are similar in sound, the vowels of the prefixes are to differ markedly.
  

Design of Prefixes
Combining the limitations on consonants from the graphic executive keyboard accessibility, perceptive reading distinguishability between upper and lower cases, and phonetic productive and receptive conditions of widespread phonemic distribution among languages of the world, the following consonants are less favourable:

Cc
Pp
Qq
Ss
Vv
Ww
Xx
Zz

any of which could be used as an abbreviation for zero, which does not differ by a positive or negative sign, or twelve, leaving the following consonants as more favoured for the intervening numbers:

Bb
Dd
Ff
Gg
Hh
Jj (as a vocoid or glide)
Kk
Ll
Mm
Nn
Rr
Tt

It is interesting that there are exactly twelve consonant phonemes in this list, of which eleven are needed to match the number of numbers. They are almost all the same as those proposed for the single letter prefix abbreviations in earlier posts here.

• Since Jj as a vocoid, glide, or semivowel might not be clearly distinguishable acoustically from a high front vowel in certain allophonic environments, it may be better to use the affricate quality of the English pronunciation.
  
• The pair Kk was not used in the previous proposal as a result of the Indo-European forms and English mnemonics.
  

In the order based on the natural Indo-European languages, the pairs of consonants would be:

1. Mm
   
2. Bb or Dd
   
3. Tt
   
4. Rr
   
5. Ff
   
6. Hh
   
7. ??
   
8. Gg
   
9. Nn
   
10. Jj (as an affricate), though some dozenists proposed Dd
    
11. Ll
    

suggesting Kk as a possibility instead of Rr for four, or instead of Hh for six, leaving Hh for seven instead, etymologised as from the Greek hept, or perhaps instead of Jj for ten, etymologised as dek. The possibility of using Kk for ten and Jj for seven is not ruled out. If we consider Yy to be consonantal in an initial position, then it could be used instead of Jj for seven.

References/See also:

• https://www.quora.com/What-are-the-most-common-phonemes-among-all-language
  "The most common vowel system consists of the five vowels /i/, /e/, /a/, /o/, /u/. The most common consonants are /p/, /t/, /k/, /m/, /n/."
  
• https://knowledgeburrow.com/what-are-the-most-common-phonemes/
  "The most common consonants: /m, k, j, p, w, n, s, t, b, l, h, ɡ, ŋ, d/ – these sounds occur in more than 50% of all languages, in this order"
  
• https://www.quora.com/What-phonemes-are-common-to-all-human-languages
  
• https://en.wikipedia.org/wiki/Liquid_consonant
  "Many languages [...] have a single liquid phoneme that has both lateral and rhotic allophones."
  "Many [...] European languages have one lateral and one rhotic phoneme."
  "Elsewhere in the world, two liquids of the types mentioned above remains the most common attribute of a language's consonant inventory except in North America and Australia."
  
• https://en.wikipedia.org/wiki/Spelling_alphabet
  

The rule of preventing the compounds of monoliteral abbreviations accidentally forming words of natural languages by disallowing vowels as single letter abbreviations for prefixes and the rule of enabling distinction between upper and lower cases of handwriting are considered to be really necessary rules.

Listing the letters of phonemes allowed by these constraints produces the following pattern:
OBSTRUENTS
Plosive stops:
Unvoiced:
Tt Kk
Voiced:
Bb Dd Gg
Fricative:
Ff Hh
SONORANTS
Nasals:
Mm Nn
Liquids:
Ll
Rr
Semivowels:
Jj

Diphonic Sibilants and Palatalised Consonants
According to how long the list of the most common phonemes from languages of the world is chosen to be, a series of consonantal phonemes from a postalveolar or palatal place of articulation could be included in the list. However, such phonemes, with the exception of the palatalising semivowel or approximant, would be poorly distinguishable phonetically from diphones. In English for example they do not exist as independent phonemes. It may be nevertheless possible to indicate some of these consonants by single letters that are readily available from the Roman alphabet, such as Cc or Jj.

Distinction of Consonants by More than One Phonetic Feature
A less stringent though beneficial rule mentioned earlier above is that any two consonants used for the monoliteral abbreviations should differ from each other by more than one phonetic trait or feature to increase their distinguishability. Under such a rule, if a voiced plosive is used, the unvoiced plosive in the corresponding place of articulation should not be used, and if an unvoiced fricative is used, the corresponding unvoiced plosive should not. The allowed consonants by the more stringent rules above indicate that:

• since the fricative for the dorsal or guttural place is unvoiced, the unvoiced plosive Kk phoneme should not be used.
  
• For the dental or alveolar place, unvoiced or voiced plosives are available. If the unvoiced plosive phoneme is chosen to be allowed, the fricative should be voiced. This voiced fricative phoneme could be approximately the phoneme Zz, which however is not allowed for the monoliteral abbreviations of numbers between one and eleven inclusively by the constraint of distinguishability between upper and lower cases. Alternatively, the letters Jj may be used for a voiced affricate. This is the preferable solution. It also means that the phoneme Dd should not be used.
  
  On the other hand, if rather the voiced dental or alveolar plosive were to be the one allowed, then the fricative should be unvoiced, and could be the fricative phoneme indicated by the letters Ss or affricate by the letters Cc. This is a less favorable option, not just because of the poor distinguishability between the upper and lower cases of the letters, but also because it would mean that the unvoiced plosive phoneme indicated by Tt would not be used, though it is most suitable as the initial for the number three.
  

Avoidance of Vowels as Monoliteral Abbreviations
The letters Yy should not be treated as a consonant phoneme because they are too readily interpreted as vowels. For example, in the spelling of the English language, some fairly recognisable examples of words with this vowel and no other include the following:

(cry
crypt
cyst)
dry
fly
fry
(glyph
gypsy)
hymn
(jynx
lymph
lynch)
my
myth
(nymph
pry
psych
pygmy)
rhythm
(scry)
shy
(sky
spy)
sty
(sylph
sync)
thy
try
(why
wry)

Those in parentheses are not of concern if certain of the letters that are poorly distinguishable between upper and lower cases are not used. The words are not parenthesised solely be virtue of the letters s, since this may have to be used for the number seven in the absence of a better option. Nevertheless, some fairly common and short words could result in confusion in ordinary contexts, such as my, dry, fly, and try. Therefore, it is better not to use the letters Yy or the semivocalic palatal phoneme as a consonant for monoliteral abbreviations. This does not mean that semivowels are not to be treated as consonants in phonological theory.

Monoliteral Abbreviation for the Number Seven
Since the letters Yy should not be used as monoliteral abbreviations by the above arguments, I propose a mixture of letters representing different phonemes between the upper and lower cases, or else an exceptional letter not available on the keyboard. A possible solution would be the letters S and c, since c for twelve is unlikely to appear as a monoliteral abbreviation in compounds. Here, the letter c could be interpreted as a spelllng of an unvoiced postalveolar sibilant fricative. Another possibility for this is the elongated letter esh ʃ, with the letter c as a fallback accessible on the keyboard.

Thus, probably the best solution for the monoliteral abbreviations of positional numerals is:
0. Zz

1. Mm
   
2. Bb
   
3. Tt
   
4. Rr
   
5. Ff
   
6. Hh
   
7. Sc
   
8. Gg
   
9. Nn
   
10. Jj
    
11. Ll
    

It is unlikely that any better solution than this exists.

References

• http://web.phonetik.uni-frankfurt.de/upsid_info.html
  
• https://en.wikipedia.org/wiki/English_words_without_vowels
  

Digraphic Monosyllabic Prefixes
Where there are only six vowels available for twelve numbers, each vowel is to be used twice to maximise contrast in digraphic monosyllabic prefixes, as suggested below:

0. ZI

1. MO
   
2. BI
   
3. TE
   
4. RO
   
5. FY
   
6. HE
   
7. SA
   
8. GU
   
9. NY
   
10. JA
    
11. LU
    
12. CI
    

That list is the same as one in an earlier post above, except that I have swapped the vowels for seven and eight. There are other ways of assigning the vowels, but this is the version that I prefer at the moment.


Trigraphic Monosyllabic Prefixes Without Consonantal Clusters
If all twelve numbers are to have different vowels or diphthongs to increase distinguishability, then modelled on those proposed for mnemonics and based on the words for numbers in natural Indo-European languages, I propose the following words:

0. ZI

1. MOU
   
2. BYH
   
3. TEI
   
4. ROA
   
5. FAI
   
6. HEH
   
7. SAU
   
8. GUW
   
9. NOI
   
10. JAH
    
11. LEU
    
12. CI
    

The purposes of having three letters per numeral are firstly to Anglicise the spelling in such a way as to suggest pronunciations and secondly to increase graphic distinguishability by reducing the chance of confusion with other words in foreign languages.

Radiotelephony Numerical Words
For enhanced distinguishability in noisy channels, I suggest the following disyllabic words for the numerals:

0. zilnun

1. monuon
   
2. duobyh
   
3. tertri
   
4. kuorot
   
5. faifen
   
6. heksix
   
7. sauvta
   
8. ogteit
   
9. noinev
   
10. jeksen
    
11. leufin
    
12. chicei
    

It occurred to me today that another option for the monoliteral abbreviation of the negative seven exponent could be the dollar sign $ instead of the letters esh or c. The dollar sign would be useful because it obviously looks like a version of the letter S and is accessible on the keyboard, even on keyboards that do not have the euro currency sign. Since the dollar sign used in this way would only ever be followed by letters representing units of measurement or possibly other prefixes, it could not be confused as a monetary currency symbol, which would be followed by digits.

This frees up and restores the letter c for twelve. Although the letter c for twelve was originally derived as stated from the English words inch and ounce, it did not escape my attention that this letter in resulting prefixes such as ceila- and ceilo- evoke the Latin word caelo, caelum, or words related to ceiling or celestial referring to the heavens, which is appropriate for the number twelve being higher than and the end of the positional numerals in base twelve and because of its use in division or segmentation of the celestial sphere or ecliptic into twelve lunes in astronomy.

Prefixes with an exponent of positive or negative twelve could be the last prefixes, because when the base is the fourth power of twelve, the twelfth power and its reciprocal are so large and small and exceeding the range of the international decimal metric prefixes only going as far as the tenth positive and negative powers of a thousand that further prefixes are unlikely to be needed before scientific notation is used instead. For this reason, with the dozenal system of prefixes based on the fourth power of twelve, there may be no need to resort to compounding of prefixes to extend the range of powers represented, and therefore no need to contemplate whether compounding of prefixes should be done positionally or rather multiplicatively representing the number of dozenal numerical figures simply by summing the exponents of the compounded prefixes.

It could be possible to use the letters C and c for a base of twelve and its reciprocal in consonantal literal abbreviations of the prefixes to distinguish a system of prefixes based on twelve from a system based on the fourth power of twelve. For example, an abbreviation of GCg for the okceagram (the same unit as a biliagram or bilagram) could be distinguished from that of Gg for an oktlagram. Since the consonant letters L and l are used for prefixes indicating a positive or negative exponent of eleven, there is not a monoliteral abbreviation for a base of the fourth power of twelve, which is instead treated as a default for concision. It could be possible, however, to use the pound £ or lira symbol for this purpose, since it is graphically related to the letter L and easily accessible on the keyboard. This would make an abbreviation for an oktlagram be G£g. The abbreviation for the oktlogram would then have to be g£g.

Incidently, while the -la and -lo components of prefixes for the fourth power of twelve or its reciprocal as base were derived from the Dozenal Mylliad Nomenclature, I had thought that they can also be considered as evoking the English words "large" and "low" respectively.

It could be possible to extend the system of abbreviations to the representation of other bases by choosing suitable consonants for them. The unused consonants that are not distinct enough between upper and lower cases could be used for this purpose, as would the letters C and c be. For example, the letters V and v could be used for a binary base. However, use of the letter C or c might conflict with a unit of electrical charge, unless that is instead represented by another letter such as Q or q. The potential for extension to other bases is quite limited, as it should be for practicality.

Extension to Nomenclature for General Bases
Monoliteral Abbreviations
Immediately after my previous post above, I realised that a nomenclature could be extended to bases other than twelve or powers of twelve. For each number from zero to twelve, there is a different consonant single letter, available in upper and lower cases depending on whether that number is in a positive or negative exponent. To represent any of these numbers as a base rather than as an exponent by single letters, the monoliteral symbol can be a currency symbol corresponding to the same consonant. Most letters have a currency symbol version or can be converted into suitable symbols by a strikethrough singly or doubly vertically, horizontally, or obliquely by formatting or by combining diacritic line characters.

However, most small bases would not be practical bases for power prefixes because they are too small. For example, in the case of the base twelve itself, a larger power of twelve such as its fourth power is more beneficial as a base of the prefixes. For each power of the base being used as the basis for prefixes, a different monoliteral abbreviation would be required, or else the literal abbreviation would have to be more complicated than single letters or letter forms. Thus, even with the availability of currency symbols as abbreviations, there would not be enough single character letters available in a systematic way for the larger bases that are required for systems of prefixes for units of measurement.

Power Infix Monosyllables
In the dozenal nomenclature, for each number from zero to twelve, there was a unique consonant and also a unique vocalic nucleus, some of which were monophthongs while others were diphthongal. In the cases of the diphthongs for the number monosyllables to be used as prefixes, they were formed by combination of the monophthongs and codal high vocoidal targets.

This system left available for other purposes than prefixes the combinations of onset vocoids followed by monophthongal vowels. Examples of combinations of this sort were proposed for the power infixes -cea- for twelve and -cio- for the reciprocal of twelve as bases. For generalisation to infixes for other bases, I thought of appending the digraphic combination of letters -ea- to the monoliteral consonant of the number for the base to be represented where its exponents are positive, while the letters -io- would be appended to the same consonant for that base raised to negative indices.

Where the base for the prefixes is to be not the first power of one of the smaller bases but rather one of the larger powers of a smaller base, the power to which the smaller base is raised to give the larger bases could be indicated by following the power prefix of the smaller base by the consonant of the power to which it is raised. For example, if the base is to be the third power of four, then the power infix would be -reat-. It may be necessary to increase the length of the power infix to two syllables to make it more obvious what base it represents. For example, -reat- may be lengthened to -reate-, -reater-, or -reatrei-. which would mean the same as -beahe-, -beahex-, -beasix-, -beasiks-, -geabi-, -geado-, or -geaduo-. These larger base infixes would be preceded by monosyllabic prefixes of their exponents in the usual way. For example, for the second power of the square of eight, a prefix to units could be bigeado-. Since our base is twelve, prefixes for other bases such as these are unlikely to be desired. In any case, their use should be restricted to power prefixes to units of measurement and they should not be replacements for expression of powers in bases by ordinary language such as the example of "second power of the square of eight" that I used above.

Syllabic Length Purposes and Etymology
For a practical system of nomenclature for power prefixes to units of measurement in metrology, concision is more important than recognisability of the component morphemes. Several different bases and nomenclatures for them are not expected to be used and the use of many bases requiring interconversion is not recommended. The short form and long form monosyllables are intended in different circumstances. In prefixes to units of measurement where concision is paramount, the short form digraphic or trigraphic syllables are preferred. For words of numbers in isolation to be recognised internationally without being confused with other words in different languages, greater differentiation of the words is encouraged by the longer form numerical words more closely resembling protolanguage numerical root words. The digraphic monosyllablc prefixes are mainly intended for combination with the infixes -la- or -lo- for the fourth power of twelve or its reciprocal and not with the infixes -cea- or -cio- for powers of twelve, where the short form syllables of no more than three letters and closer to the Indo-European roots would be intended.

Most Indo-European languages do not use a word like bi from Latin beginning with a labial consonant for the cardinal number two in counting. For this reason, a word beginning with the letter d is preferred in the word form of the number as duo. Similarly, the beginning of the word for six as the consonant h is peculiar to Greek, whereas most Indo-European languages and speakers would have the basic word for the number six starting with a sibilant, which is why siks is preferred as a word. Likewise, the terminal letter t of pent from Greek is less usual among the languages than a less coronal phone, for example in Slavic or Eastern European languages.