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:
and for ease of orthographic spelling:
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
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.
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:
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.
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
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
Mon Apr 15, 2024 12:08 am by Phaethon
» Dozenal Number Words from Metric Prefixes
Sat Apr 13, 2024 3:38 pm by Phaethon
» Dozenalizing Metric
Fri Apr 05, 2024 12:23 pm by Phaethon
» Myon Dozenal Nomenclature
Sat Feb 17, 2024 3:18 pm by Phaethon
» Information per Area of Numerical Forms
Mon Jan 29, 2024 10:50 am by Phaethon
» Denominational Dozenal Numerals
Sun Jan 28, 2024 9:25 pm by Phaethon
» Proto-Indo-European Numbers
Fri Jan 12, 2024 4:25 pm by Phaethon
» Radix Economy for Alternating Bases
Sun Dec 24, 2023 5:41 pm by Phaethon
» Graduation Subdivisions
Sat Dec 02, 2023 12:58 pm by Phaethon