The Misalian base-naming system is a system for naming various positional numbering bases in English created by jan Misali. The system, itself, is not positional, instead relying on the prime factorization of numbers.[1]

The first unexian base names are available as a webpage,[2] while the first biexian base names are available as a text file.[3]

Roots, prefixes and suffixes

  • Base 0 is "nullary".
  • Base 1 is "unary".
    • Prime bases without a root name are expressed as "one plus number"; for proper names of bases, the prefix is "un-", while for prefix forms, the circumfix is "hen-...-sna-".
  • Base 2 is "binary".
    • "bi-" is a prefix meaning "times two".
  • Base 3 is "trinary".
    • "tri-" is a prefix meaning "times three".
  • Base 4 is "quaternary".
    • "tetra-" is a prefix meaning "times four".
  • Base 5 is "quinary".
    • "penta-" is a prefix meaning "times five".
  • Base 6 is "seximal".
    • "hexa-" is a prefix meaning "times six".
  • Base 7 is "septimal".
    • "hepta-" is a prefix meaning "times seven".
  • Base 8 is "octal".
    • "octo-" is a prefix meaning "times eight".
  • Base 9 is "nonary".
    • "enna-" is a prefix meaning "times nine".
  • Base 10 is "decimal".
    • However, if this name is preceded by a prefix, it becomes "-gesimal".
    • "deca-" is a prefix meaning "times ten".
  • Base 11 is "elevenary".
    • "leva-" is a prefix meaning "times eleven".
  • Base 12 is "dozenal".
    • "doza-" is a prefix meaning "times twelve".
  • Base 13 is "baker's dozenal", a name credited to Kate of Tangerine's Neocities Page.[4]
    • However, if this name is preceded by a prefix, it becomes "-ker's dozenal".
    • "baker-" is a prefix meaning "times thirteen".
  • Base 16 is "hex".
    • "tesser-" is a prefix meaning "times sixteen".
  • Base 17 is "suboptimal". It is named for the fact that it has the worst representations of rational numbers of any base from 2 to 20.[5]
    • "mal-" is a prefix meaning "times seventeen".
  • Base 20 is "vigesimal".
    • "icosi-" is a prefix meaning "times twenty".
  • Base 36 is "niftimal". Derived from the seximal word "nif", niftimal has been proposed by jan Misali as a compression method for seximal.[6]
    • "feta-" is a prefix meaning "times thirty-six".
  • Base 100 is "centesimal".
    • "hecto-" is a prefix meaning "times one hundred".
  • "nega-" is a prefix negating the number following it; for example, "negadecimal" is base -10. This extends the system from all natural numbers to all integers.
  • "vot-" or "vöt-" is a prefix for the reciprocal of the number following it; for example, "votdecimal" is base 1/10. It is named after the conlang Vötgil, which, to name numbers, lists their decimal digits in reverse order, thus employing votdecimal. This extends the system to all rational numbers.
  • The final two suffixes, albeit not used together with the standard roots, prefixes and suffixes above, extend the system to all numbers that can be named.
    • "-nary" is a suffix which can be added to the English name of any number less than six to form a name for a system that uses that number as a base.
    • "-imal" is a suffix which can be added to the English name of any number greater than six to form a name for a system that uses that number as a base.

Forming compounds

For any base that is neither prime nor has a basic root form, the algorithm is to take the two closest factors of the number and write the smaller one in prefix form and the larger one in root/suffix form.

For example, 120 can be decomposed into two factors that are either prime or have root forms in two ways: 10 × 12 and 6 × 20. However, as 10 and 12 are closer to each other than 6 and 20, base 120 is known as decadozenal rather than "hexavigesimal".

Sources

less than unexian: six · twelve · thirsy · foursy · fifsy · nif · tarumba
-exians: unexian · biexian · triexian · quadexian · pentexian · unnilexian · ununexian · umbiexian · untriexian · unquadexian · umpentexian · binilexian
extended -exians: biunexian · bibiexian · bitriexian · biquadexian · bipentexian · trinilexian · quadanilexian · pentanilexian · unnilnilexian · binilnilexian · trinilnilexian · quadanilnilexian · pentanilnilexian · unnilnilnilexian · unnilnilnilnilexian
-eciams: uneciam · bieciam · trieciam · quadeciam · penteciam · unnileciam · ununeciam · umbieciam · untrieciam · unquadeciam · umpenteciam · binileciam · biuneciam · bibieciam · bitrieciam · biquadeciam · bipenteciam · trinileciam · quadanileciam · pentanileciam · untwaieciam · unthrieciam · umfedrueciam · umfimfeciam · unainoeciam · unainaineciam · unaintwaieciam · unainthrieciam · unaimfedrueciam · unaimfimfeciam · untwainoeciam · unthrinoeciam · umfedrunoeciam · umfimfanoeciam · unaindvieciam · unaintreyeciam · unainchatureciam · unaimpancheciam · unainekashunyeciam · unainekayilingeciam · unainekayisasmereciam · unainekayisasnabiniboeciam · unainekayisasnabiniboniboeciam
Other systems by jan Misali: Chronary system · Misalian decadozenal system · Misalian base-naming system

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