Myon Dozenal Nomenclature

This system of names for powers of twelve is inspired from the Duodecimal Myriad System nomenclature proposed by Takashi, 1st March 2019, http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/revised.pdf and the derivative Dozenal Mylliad Nomenclature, https://dozenal.forumotion.com/t8-dozenal-mylliad-nomenclature.

Positive exponents indicated by dozenal "digits" to the left of the fractional point or dozenal zot produce a suffix -on.
Negative exponents indicated by numerical figure characters to the right of the dozenal zot lead to a suffix -ino.
The -on or -ino suffixes for whether the exponents are positive or negative are suggestive of the names of particles such as the neutron and the comparatively small neutrino.

Dozenal numerical characters are grouped in fours.

The number of groups of four numerical characters from the same sign of exponent is indicated by a prefix standing for a counting number derived from Greek. These prefixes are as tabulated.

Table of number prefixes

Number	Prefix
one	my-
two	dy-
three	tri-
four	tetr-
five	pent-
six	hex-
seven	hept-
eight	oct-
nine	enn-
ten	dec-
eleven	enkomi-
twelve/zero	z-/zi-

If the prefix already ends with the vowel letter i, then when that prefix is joined to the suffix -ino, the i of one of those affixes is removed so that the vowels i do not appear twice and side-by-side in the middle of the formed word. For example, the prefix tri- joined to the suffix -ino becomes trino, not tri-ino.

The vowel letter i in the suffix -ino is removed when it appears after the letter y of the prefixes my- or dy-.

The prefixes for numbers of groups of four digits that are multiples of twelve up to the dozenth multiple of twelve groups of four and beyond are formed by combination of a prefix for the number of twelve groups of four characters followed by the prefix for the twelve of the groups of four. For example, the prefix for two dozen groups of four numerical characters on the same side of the dozenal zot would be dyz-.

A vowel letter -a- may be added between consonants of the two joined prefix components. For example, tetrzon becomes tetrazon. The letter -y- is not treated as a consonant for this procedure.

Table of words for dozenal powers

Positive exponent power of twelve	Nomenclature	In dozenal figures	Negative exponent power of twelve	Nomenclature	In dozenal figures
①⓪^④	myon	①,⓪⓪⓪⓪;	①⓪^-④	myno	⓪;⓪⓪⓪①
①⓪^⑧	dyon	①,⓪⓪⓪⓪,⓪⓪⓪⓪;	①⓪^-⑧	dyno	⓪;⓪⓪⓪⓪,⓪⓪⓪①
①⓪^①⓪	trion	①,⓪⓪⓪⓪,⓪⓪⓪⓪,⓪⓪⓪⓪;	①⓪^-①⓪	trino	⓪;⓪⓪⓪⓪,⓪⓪⓪⓪,⓪⓪⓪①
①⓪^①④	tetron	①,⓪⓪⓪⓪,⓪⓪⓪⓪,⓪⓪⓪⓪,⓪⓪⓪⓪;	①⓪^-①④	tetrino	⓪;⓪⓪⓪⓪,⓪⓪⓪⓪,⓪⓪⓪⓪,⓪⓪⓪①
①⓪^(⑤*④)	penton	①,⓪⓪⓪⓪,⓪⓪⓪⓪,⓪⓪⓪⓪,⓪⓪⓪⓪,⓪⓪⓪⓪;	①⓪^(-⑤*④)	pentino
①⓪^(⑥*④)	hexon	①,⓪⓪⓪⓪,⓪⓪⓪⓪,⓪⓪⓪⓪,⓪⓪⓪⓪,⓪⓪⓪⓪,⓪⓪⓪⓪;	①⓪^(-⑥*④)	hexino
①⓪^(⑦*④)	hepton		①⓪^(-⑦*④)	heptino
①⓪^(⑧*④)	octon		①⓪^(-⑧*④)	octino
①⓪^(⑨*④)	ennon		①⓪^(-⑨*④)	ennino
①⓪^(⑩*④)	decon		①⓪^(-⑩*④)	decino
①⓪^(⑪*④)	enkomion		①⓪^(-⑪*④)	enkomino
①⓪^(①⓪*④)	zon		①⓪^(-①⓪*④)	zino
①⓪^(②⓪*④)	dyzon		①⓪^(-②⓪*④)	dyzino
①⓪^(③⓪*④)	trizon		①⓪^(-③⓪*④)	trizino
①⓪^(④⓪*④)	tetrazon		①⓪^(-④⓪*④)	tetrazino
①⓪^(⑤⓪*④)	pentazon		①⓪^(-⑤⓪*④)	pentazino
①⓪^(⑥⓪*④)	hexazon		①⓪^(-⑥⓪*④)	hexazino
①⓪^(⑦⓪*④)	heptazon		①⓪^(-⑦⓪*④)	heptazino
①⓪^(⑧⓪*④)	octazon		①⓪^(-⑧⓪*④)	octazino
①⓪^(⑨⓪*④)	ennazon		①⓪^(-⑨⓪*④)	ennazino
①⓪^(⑩⓪*④)	decazon		①⓪^(-⑩⓪*④)	decazino
①⓪^(⑪⓪*④)	enkomizon		①⓪^(-⑪⓪*④)	enkomizino
①⓪^(①⓪⓪*④)	zizon		①⓪^(-①⓪⓪*④)	zizino

It is expected that a nomenclature of prefixes representing powers of the base would only be used in a technical context, for example, in science or technology.

Words for numbers of dozenal characters that are not multiples of four may be specified by multiplying these technical terms by ordinary words in local natural languages for twelve raised to smaller powers, such as the words twelve or dozen for the first power of twelve in English.

It is thought not to be courteous to use special terms for all possible powers of twelve, just as in the decimal metric system of prefixes only powers of a thousand have special prefixes, with the exception of terms for ten raised to integer exponents closer to zero. This is because when units of measurement have different numerical prefixes, they have different orders of magnitude which need to be converted to be the same in order to be used in calculations. If the number of different orders of magnitude be limited or restricted, the chance of requirement for the additional complexity from adjustment for order of magnitude in calculations is reduced. Also, in natural languages, orders of magnitude are formed by multiplication of terms for powers of the base closer to one rather than having a new term for every possible power.

Compounding
Prefixes can be multiplied by each other by being set next to each other. For example, a myon myon is the same as a dyon, a myon dyon is the same as a trion, and a dyon dyon is the same as a tetron.

Because of the redundancy, this process of compounding of prefixes is mainly useful where the exponent of the fourth power of twelve is larger than twelve. For example, a myon to the power of the sum of twelve and one is a myon zon. The two prefixes myon and zon may be joined together into a single compound prefix as myonzon.

Thus, all the whole powers of myon between zon and dyzon can be formed. Similarly, after dyzon, all the powers to trizon can be formed, as in myon dyzon, dyon dyzon, trion dyzon, and so on.

Optionally, a vowel letter -a- may be infixed between the consonants, as in myona zon or myonazon, which may suit better some languages, such as Italian, which tend not to end the pronunciation of words on consonants, or syllabic languages the phonotactics of which do not admit consonantal clusters of the sort, although for English this is unnecessary.

Prefixes for negative exponents can also be compounded, as in mynozino meaning a myon to the power of minus the sum of twelve and one.

Prefixes for positive and negative exponents can be combined in compounds. For example, the meaning of myon zino, or myonzino, or myonazino, is a myon to the power of the sum of negative twelve and positive one, so the compound myonzino means the same as enkomino. Similarly, a mynozon means the same as enkomion. Notice that the prefix component myno, especially when followed by a component beginning with z-, evokes the English word minus for subtraction, or related words signifying smallness such as minor.

Pronunciation
The letter y in the prefixes my- and dy- is to be pronounced as a diphthong in English. In other languages, a different pronunciation may be preferred, such as a front rounded vowel. These differences are to be allowed and considered to be no more than regional variations, just as in different dialects of a single language such a English there may be different ways of pronouncing the same word, or in science there may be alternative forms and spellings of technical terms depending on the local or national language.

Prefixes of two syllables, such as myon or myno, are to be stressed on the first syllable.

In the suffix -on of the prefixes for positive exponents, the vowel o is to be unstressed and short, and as near to the quality of the Greek letter omicron as the local language will allow.

In the suffix -ino of the prefixes for negative exponents, the terminal vowel o is to be unstressed but long, with the quality of the Greek letter omega. This vowel may be diphthongalised in English.

In prefixes of three syllables, such as tetrino, in English the stress is usually to appear on the second syllable, except where an infixing vowel letter -a- between consonants has been added to prevent their apposition. Such an infixing -a- is to be unstressed and short, perhaps even a schwa. Terms of three syllables, such as tetrazon, containing this short unstressed infixing vowel should be stressed on their first syllable in English. However, a term such as dyzizon should be stressed primarily on the first syllable, secondarily on the last syllable, and unstressed on the middle syllable.

The terminal vowel i- of enkomi- followed by the suffix -on may be pronounced either vocalically or consonantally according to preference, affecting the number of syllables.

Regardless of its number of syllables, enkomion should be stressed on the second syllable. Enkomino, on the other hand, may in English be stressed primarily on the penultimate syllable, and secondarily on the first syllable.

Simpler forms elon and elino may be contemplated for these terms.

The vowel i in the suffix -ino should be stressed and long in all circumstances.

Pronunciation may be altered in compounding. For example, while myon of two syllables is stressed on the first syllable, in the compounding myona of three syllables, it is rather the second syllable that is stressed, and its quality may also be changed to long, like the Greek letter omega, or diphthongalised in English. This particular guideline is not very strict however, and without the infixing -a- vowel the stress may remain on the first syllable despite compounding.

Some of the values of the myon system, so described, are more similar to the decimal short scale than long scale system of names, using the words million, billion, and trillion, for powers of ten.

The myon is near to twice ten thousand, the fourth power of ten, making the myon bigger than the thousand or mille, but less than a decimal "large thousand" or million. The dyon is not far from the ninth decimal power, called a billion in the decimal short scale. The trion is relatively a bit bigger than the twelfth decimal power, called a trillion in the decimal short scale.

This myon system based on the fourth power of twelve can be regarded as a kind of longer dozenal scale, because a shorter dozenal scale is based on the first power of twelve, and can represent all powers.

The nomenclature for this dozenal shorter scale is the same as for the longer myon scale, except that in the shorter scale the o vowels in the suffixes -on and -ino for the positive and negative exponents in the longer scale are changed to the vowel a, so the shorter scale suffixes are -an and -ina.

The terms of the shorter scale, or myan system, can be combined or compounded with the longer scale terms to give intermediate powers to the longer scale, instead of using such words as dozen or gross from a local language. This makes the system potentially more international.

The shorter scale allows the third power of twelve to be represented by a single and briefer word trian instead of dozen gross.

The shorter and longer dozenal scale nomenclatures have their terms spelt and pronounced differently, so there is no need to be frightened about them producing ambiguity in the way that the decimal short and long scales do.

I have not been a real fan of 'z' for dozenal powers. It sounds awkid. Something that is not voiced would be better, such as ch or p might work. In twelfty, the need exists to express numbers in dozens in contrast to the decimal form, such as when you multiply 53 by 10, you get 4.5 (four-dozen five). The current working word here is a norse word 'tulf' (which is twelve imploded), so fourtulf five. But i fear it is not distinct enough.

The scheme that I use is to suppose PIE numbers are counts of four, and 'nine' is the new one of the third quad. This could lead to the following middle and old, but the working set is 'mel' and 'lif'.

The column-names can then remain unchanged. In practice, the smallest names are used to name the rows of the count-table, and the larger names for the columns. Decimal uses only a single-row, and so the names ten, hundred, thousand, ... stand for columns to the left of the unit. On the other hand, twelfty uses two rows, and ten stands for the high row, and the columns are numbered hundred, thousand, etc.

This is in keeping with the number-changes in the XIV century, where the number was comprised of numerals in columns.

The higher order over a thousand follow the notion of the greek 'order of number', this means a hundred-thousand is a cent-ion or cention (hundred-big), and a thousand-thousand is a mill-ion a million (thousand-big).

wendy.krieger wrote:Something that is not voiced would be better, such as ch

This is an interesting suggestion, because it can be thought of as backformed from Latin uncia followed by Anglicization. In this case, the following vowel ought to be more fronted than the o or a. Consequently, the suffix that was -on should become -en. There is no need to change the vowel from i in the forms for negative exponents, because it is already sufficiently fronted. We thus have myen, dyen, trien, and so on for positive exponents. A disadvantage is that the forms decen and dychen might be confused for similar sound when spoken and heard. Separation of long and short scales may also be lost for want of different front vowels. The suffix for negative exponents could be -ini. For twelve the prefix che would be used rather than zi. Then, there would be chini instead of chino, a type of cotton fabric. Hence, myenchini would mean the same as enkomini, while mynichen would mean the same as enkomien.

Reference
https://de.wikipedia.org/wiki/Enkomion

This week, I found on the DozensOnline website forum the following instance of a suffix -izzon proposed for base twelve, whereas I proposed the suffix zon for the twelfth power of the fourth power of twelve:

Dan wrote:"10 = dozen
100 = gross
1000 = trizzon (or grand)
1@+4 = quatrizzon
1@+5 = cinizzon
1@+6 = sesizzon
1@+7 = setizzon
1@+8 = octizzon
1@+9 = nenizzon
1@+Χ = decizzon
1@+Ɛ = elncizzon
1@+10 = unzerizzon
1@+11 = ununizzon
1@+12 = unduizzon
1@+13 = untrizzon
1@+14 = unquatrizzon
...
1@+20 = duzerizzon
1@+30 = trezerizzon"

I do not like the representation of double-digit exponents in positional form by syllables, such as "unun-". In my system, multiplication of prefixes or powers is used instead, as in natural language.

The prefix "cin-" for five would not be very recognisable in English. The prefix "elnc-" for eleven is terrible. The use of the prefix "nen-" for nine is notable.

Reference:

• https://www.tapatalk.com/groups/dozensonline/another-proposal-for-number-names-t219.html
  Opening post date: "Jul 20, 2007#1".