Dozenal Wiki

Systematic Dozenal Nomenclature (SDN) is, primarily, a system of metric prefixes derived from familiar numeric word-roots from classical Greek and Latin, with dozenal extensions. It is inspired by (and subsumes as a subset) the Systematic Element Name scheme devised by the International Union of Pure and Applied Chemistry (IUPAC). It is also inspired by (and is offered as a replacement for (Why?)) the dozenal metric prefix system devised by Tom Pendlebury as an adjunct to his TGM System of measurement units. The system is used by some systems of measures such as IDUS.

Power Prefixes[]

Of chief importance are the power prefixes generated by the SDN rules. They are expected to be the most frequently used parts of this system, acting as metric-style scaling prefixes on units of measurement. The table below summarizes these prefixes and the quantities they represent:

Unqual Positive Powers Uncial Negative Powers
Value Prefix Value Prefix
10;1 unqua- 10;-1 uncia-
10;2 biqua- 10;-2 bicia-
10;3 triqua- 10;-3 tricia-
10;4 quadqua- 10;-4 quadcia-
10;5 pentqua- 10;-5 pentcia-
10;6 hexqua- 10;-6 hexcia-
10;7 septqua- 10;-7 septcia-
10;8 octqua- 10;-8 octcia-
10;9 ennqua- 10;-9 enncia-
10;X; decqua- 10;-X; deccia-
10;E; levqua- 10;-E; levcia-
10;10; unnilqua- 10;-10; unnilcia-
10;11; ununqua- 10;-11; ununcia-
10;12; unbiqua- 10;-12; unbicia-
10;20; binilqua- 10;-20; binilcia-
10;21; biunqua- 10;-21; biuncia-
10;22; bibiqua- 10;-22; bibicia-


Rules for Generating Prefixes[]

SDN uses the following elements to generate dozenal metric prefixes:

  • a set of digit roots derived from classical Latin and Greek, representing the dozenal digits one through eleven (see Digit Roots)
  • rules for combining a sequence of digit roots into a place-valued numeral string (see Numeral Strings)
  • multiplier-markers which are appended onto the numeral strings to generate multiplier prefixes (see Multiplier Prefixes)
  • an optional reciprocal-marker which may be appended onto any multiplier prefix to turn it into its reciprocal prefix (seeReciprocal Prefixes)
  • power-markers which are appended onto the numeral strings to generate power prefixes (see Power Prefixes)
  • rules for combining multiplier prefixesreciprocal prefixes, and power prefixes, with each other as well as with the words they modify (for instance, units of measure).
  • systematic dozenal prefix consists of an optional multiplier prefix, followed by an optional reciprocal prefix, followed by an optional power prefix. (This is known as the Compact Rational Scientific scheme, because it accomplishes with words something analogous to what scientific notation does with numerals, but also allows the mantissa part to be expressed as either an integer, a "ditted" floating-point value, or as a rational fraction.)
  • The power prefixes can also be repurposed as standalone English words, providing possible solutions for the Dozenal English problem.

The following table summarizes the rules for generating prefixes:

Digit Multiplier Markers Reciprocal
Power Markers
Value Root Euphony
Positive Negative
0 nil -i- -nta- -qua- -cia-
1 un
2 bi -n- -a-
3 tri
4 quad -r-
5 pent -a-
6 hex
7 sept
8 oct
9 enn -e-
X; dec
E; lev

Digit Roots[]

  • SDN uses a set of digit roots derived from classical Latin and Greek.
  • The roots for the digits one through nine are identical with those chosen by IUPAC for its (decimal) Systematic Element Names.
  • SDN extends these dozenally with roots for transdecimal digits ten and eleven.
  • The root dec is the obvious choice for digit ten
  • The root lev is a coinage derived by contracting English eleven -- but it can also be derived from Latin! (See below.)
  • Digit roots are concatenated to form numeral strings. (See Numeral Strings.)
  • SDN multiplier prefixes are designed to be close approximations of the Latin or Greek combining forms from which thedigit roots themselves are derived. The intent is to mimic forms already in current use by scientists and lay people, since those forms act as simple numeric multipliers. (See Multiplier Prefixes.)
  • SDN power prefixes, on the other hand, are designed to be clearly distinct from those pre-existing combining forms, yet still recognizably derivative from them, and at least plausible as Latinate word-forms. (See Power Prefixes.)

The following table shows etymological derivations for the digit roots:

Value Digit Root Derivation
0 nil Latin nīl, nīlum, variant of nihīlum "nothing"
1 un Latin ūni-, combining form of ūnus "one"
2 bi Latin bi-, combining form of bis "twice"
Latin bin-, combining form of bīnī "two each, by twos"
3 tri Latin tri-, combining form of trēs/tria "three"
Latin trīnī, trīn, variant of ternī "three each, by threes"
Greek treîs/tría "three"
4 quad Latin quadri-, quadra-, quadru-, quadr-, combining form of quattuor "four"
5 pent Greek penta-, pent-, combining form of péntē "five"
6 hex Greek hexa-, hex-, combining form of héx "six"
7 sept Latin septi-, sept-, combining form of septem "seven"
8 oct Latin octa-, octo-, oct-, combining form of octo "eight"
Greek okta-, combining form of oktṓ "eight"
9 enn Greek ennea-, combining form of ennéa"nine"
X; dec Greek deka-, combining form of déka "ten"
Latin deci-, combining form of decem "ten"
E; lev contraction of English eleven, from Old High German einlif "one left (after counting 10)"
Latin laevo-, levo-, lev-, combining form of laevus "to the left" (apt since eleven is to the left of dozen on the number line)

Numeral Strings[]

  • SDN concatenates digit roots to form place-valued numeral strings.
  • Normally, numeral strings do not appear in isolation but instead are embedded within a prefix.
  • numeral string may represent the mantissa of a multiplier prefix.
  • numeral string may represent the exponent of a power prefix.
  • The second -n- in enn is elided if followed by nil, yielding ennil rather than ennnil.
  • Except for dozenal interpretation, and the presence of transdecimal digit roots, these numeral strings are the same as those generated for IUPAC's (decimal) Systematic Element Names.

The following table shows the first one gross two dozen numeral strings generated according to SDN rules:

Value String   Value String   Value String   Value String   Value String   Value String   Value String
0; nil 20; binil 40; quadnil 60; hexnil 80; octnil X0; decnil 100; unnilnil
1; un 21; biun 41; quadun 61; hexun 81; octun X1; decun 101; unnilun
2; bi 22; bibi 42; quadbi 62; hexbi 82; octbi X2; decbi 102; unnilbi
3; tri 23; bitri 43; quadtri 63; hextri 83; octtri X3; dectri 100; unniltri
4; quad 24; biquad 44; quadquad 64; hexquad 84; octquad X4; decquad 104; unnilquad
5; pent 25; bipent 45; quadpent 65; hexpent 85; octpent X5; decpent 105; unnilpent
6; hex 26; bihex 46; quadhex 66; hexhex 86; octhex X6; dechex 106; unnilhex
7; sept 27; bisept 47; quadsept 67; hexsept 87; octsept X7; decsept 107; unnilsept
8; oct 28; bioct 48; quadoct 68; hexoct 88; octoct X8; decoct 108; unniloct
9; enn 29; bienn 49; quadenn 69; hexenn 89; octenn X9; decenn 109; unnilenn
X; dec 2X; bidec 4X; quaddec 6X; hexdec 8X; octdec XX; decdec 10X; unnildec
E; lev 2E; bilev 4E; quadlev 6E; hexlev 8E; octlev XE; declev 10E; unnillev
10; unnil 30; trinil 50; pentnil 70; septnil 90; ennil E0; levnil 110; ununnil
11; unun 21; triun 51; pentun 71; septun 91; ennun E1; levun 111; ununun
12; unbi 22; tribi 52; pentbi 72; septbi 92; ennbi E2; levbi 112; ununbi
13; untri 33; tritri 53; penttri 73; septtri 93; enntri E3; levtri 113; ununtri
14; unquad 34; triquad 54; pentquad 74; septquad 94; ennquad E4; levquad 114; ununquad
15; unpent 35; tripent 55; pentpent 75; septpent 95; ennpent E5; levpent 115; ununpent
16; unhex 36; trihex 56; penthex 76; septhex 96; ennhex E6; levhex 116; ununhex
17; unsept 37; trisept 57; pentsept 77; septsept 97; ennsept E7; levsept 117; ununsept
18; unoct 38; trioct 58; pentoct 78; septoct 98; ennoct E8; levoct 118; ununoct
19; unenn 39; trienn 59; pentenn 79; septenn 99; ennenn E9; levenn 119; ununenn
1X; undec 3X; tridec 5X; pentdec 7X; septdec 9X; enndec EX; levdec 11X; unundec
1E; unlev 3E; trilev 5E; pentlev 7E; septlev 9E; ennlev EE; levlev 11E; ununlev

Multiplier Prefixes[]

  • SDN appends multiplier markers onto numeral strings to generate multiplier prefixes. The numeral string in a multiplier prefix represents its mantissa.
  • SDN multiplier prefixes are designed to be close approximations of the Latin or Greek combining forms which the digit roots themselves are derived from. The intent is to mimic forms already in current use by scientists and lay people, since those forms act as simple numeric multipliers.
  • multiplier marker consists of a final -a- or -i-, depending on the immediately-preceding digit root, possibly with an intervening letter added for euphony depending on the preceding digit root.
  • Where both -a- and -i- are allowed, they do not change the meaning of the prefix.
  • The euphony letters are derived from the original etymologies of their respective digit roots.
  • Elision is allowed where it produces no ambiguity: Some or all of the multiplier marker may be dropped depending on whether the multiplier prefix is followed by a power prefix or something else; and also on whether the follower begins with a consonant or a vowel (see table below). In some cases, when the follower is a power prefix beginning with a vowel, an -n- is inserted for euphony.
  • One dit syllable may be included between digit roots to indicate the position of the radix point in the mantissa. If none is included, the mantissa represents a whole number.
Value Mantissa
Multiplier Marker Multiplier Prefix
Power Prefix
0 times nil -i- nili- nili- nili- nili-
1 times un uni- uni- uni- uni-
2 times bi -n- -a-
bin- bi-
3 times tri trina-
trin- tri-
4 times quad -r- quadra-
quadr- quadra-
5 times pent -a- penta- pentan- penta- pent-
6 times hex hexa- hexan- hexa- hex-
7 times sept septa- septan- septa- sept-
8 times oct octa- octan- octa- oct-
9 times enn -e- ennea- ennean- ennea- enne-
X; times dec deca- decan- deca- dec-
E; times lev leva- levan- leva- lev-
10; times unnil -i- unnili- unnili- unnili- unnili-
11; times unun ununi- ununi- ununi- ununi-


  • bi

ennium = 2-year period

  • tri

ennium = 3-year period

  • quadr

ennium = 4-year period

  • oct

ennium = 8-year period

  • unnil

ennium = unquennium = 10′-year perio

  • unquadr

ennium = 14′-year period

  • bioct

ennium = 28′-year period

  • pentquadr

ennium = 54′-year period

  • decoct

ennium = X8′-year period

  • unnilnil

ennium = biquennium = 100′-year period

  • unennquadr

ennium = 194′-year period

Power Prefixes[]

  • SDN appends power markers onto numeral strings to generate power prefixes.
  • The intent for the power prefixes is they be at least plausible as Latinate word forms, but at the same time clearly distinct from pre-existing Latin and Greek combining forms already used in English (which the multiplier prefixes are intended to mimic and which the digit roots themselves derive from).
  • The intent is also to make the positive and negative power prefixes clearly distinct from each other, without forcing speakers to put unnatural stress on otherwise unstressed syllables. One issue with Pendlebury's power prefixes is that the only difference between his positive and negative powers are the final vowels -a- and -i- in unstressed syllables, which are difficult to distinguish unless the speaker makes an unnatural effort to enunciate the -i- sound.
  • The -cia- marker was chosen for the negative powers because this makes uncia the first negative power (equal to one dozenth). This is exactly the same as the Latin word uncia "a twelfth-part", from which English derives both inch and ounce. The combination of the fronted glide from the -i- to the -a-, as well as the soft -c-, are distinctive and easily distinguished from the flat -a- or -i- sound heard in the multiplier markers.
  • The -qua- marker was chosen for the positive powers to provide a contrast with other forms. The labial glide from the -u-to the -a-, as well as the hard -q-, are distinctive and easily distinguished from the negative prefixes as well as themultiplier markers.
  • The final -a- on any of the power prefixes may be dropped, without loss of meaning, when the following word begins with a vowel. The natural tendency of English to do this elision causes no harm, so long as the distinctive part of these prefixes (the -qu- or the -ci-) remains intact.
  • Some may find the consonant clusters of pentqua-, septqua-, and octqua-, with the juxtaposition of a /n/, /p/, or /k/ sound immediately followed by a /t/ and then a /kw/, difficult to articulate. This can be alleviated by interjecting a slight pause or even a faint /ɪ/ syllable in between the /t/ and /k/, or by weakening the/t/ to a glottal stop /ʔ/.
  • Based on the resulting forms for their first powers, the positive and negative power prefixes are informally know as "Unqual" and "Uncial" prefixes, respectively.
Exponent Unqual Positive Power
Marker: -qua-
Uncial Negative Power
Marker: -cia-
Value String Value Prefix Pronunciation* Value Prefix Pronunciation*
0; nil 10;0 nilqua- /'nɪl.kwə/ nila- 10;-0 nilcia- /'nɪl.ʃə/
1; un 10;1 unqua- /'ʌŋ.kwə/ zena- 10;-1 uncia- /'ʌn.ʃə/
2; bi 10;2 biqua- /'baɪ.kwə/ duna- 10;-2 bicia- /'baɪ.ʃə/
3; tri 10;3 triqua- /'traɪ.kwə/ trina- 10;-3 tricia- /'traɪ.ʃə/
4; quad 10;4 quadqua- /'kwad.kwə/ quedra- 10;-4 quadcia- /'kwad.ʃə/
5; pent 10;5 pentqua- /'pɛnt.kwə/ quena- 10;-5 pentcia- /'pɛnt.ʃə/
6; hex 10;6 hexqua- /'hɛks.kwə/ hesa- 10;-6 hexcia- /'hɛk.ʃə/
7; sept 10;7 septqua- /'sɛpt.kwə/ seva- 10;-7 septcia- /'sɛpt.ʃə/
8; oct 10;8 octqua- /'akt.kwə/ aka- 10;-8 octcia- /'akt.ʃə/
9; enn 10;9 ennqua- /'ɛn.kwə/ neena- 10;-9 enncia- /'ɛn.ʃə/
X; dec 10;X; decqua- /'dɛk.kwə/ dexa- 10;-X; deccia- /'dɛk.ʃə/
E; lev 10;E; levqua- /'lɛv.kwə/ lefa- 10;-E; levcia- /'lɛv.ʃə/
10; unnil 10;10; unnilqua- /,ʌn.'nɪl.kwə/ zennila- 10;-10; unnilcia- /,ʌn.'nɪl.ʃə/
11; unun 10;11; ununqua- /,ʌn.'ʌŋ.kwə/ zenzena- 10;-11; ununcia- /,ʌn.'ʌn.ʃə/
12; unbi 10;12; unbiqua- /,ʌn.'baɪ.kwə/ zenduna- 10;-12; unbicia- /,ʌn.'baɪ.ʃə/
13; untri 10;13; untriqua- /,ʌn.'traɪ.kwə/ zentrina- 10;-13; untricia- /,ʌn.'traɪ.ʃə/
14; unquad 10;14; unquadqua- /,ʌn.'kwad.kwə/ zenquedra- 10;-14; unquadcia- /,ʌn.'kwad.ʃə/
15; unpent 10;15; unpentqua- /,ʌn.'pɛnt.kwə/ zenquena- 10;-15; unpentia- /,ʌn.'pɛnt.ʃə/
16; unhex 10;16; unhexqua- /,ʌn.'hɛks.kwə/ zenhesa- 10;-16; unhexia- /,ʌn.'hɛk.ʃə/
17; unsept 10;17; unseptqua- /,ʌn.'sɛpt.kwə/ zenseva- 10;-17; unseptia- /,ʌn.'sɛpt.ʃə/
18; unoct 10;18; unoctqua- /,ʌn.'akt.kwə/ zenaka- 10;-18; unoctcia- /,ʌn.'akt.ʃə/
19; unenn 10;19; unennqua- /,ʌn.'ɛn.kwə/ zenneena- 10;-19; unenncia- /,ʌn.'ɛn.ʃə/
1X; undec 10;1X; undecqua- /,ʌn.'dɛk.kwə/ zendexa- 10;-1X; undeccia- /,ʌn.'dɛk.ʃə/
1E; unlev 10;1E; unlevqua- /,ʌn.'lɛv.kwə/ zenlefa- 10;-1E; unlevcia- /,ʌn.'lɛv.ʃə/
20; binil 10;20; binilqua- /,baɪ.'nɪl.kwə/ dunnila- 10;-20; binilcia- /,baɪ.'nɪl.ʃə/
21; biun 10;21; biunqua- /,baɪ.'ʌŋ.kwə/ dunzena- 10;-21; biuncia- /,baɪ.'ʌn.ʃə/
22; bibi 10;22; bibiqua- /,baɪ.'baɪ.kwə/ dunduna- 10;-22; bibicia- /,baɪ.'baɪ.ʃə/
23; bitri 10;23; bitriqua- /,baɪ.'traɪ.kwə/ duntrina- 10;-23; bitricia- /,baɪ.'traɪ.ʃə/
24; biquad 10;24; biquadqua- /,baɪ.'kwad.kwə/ dunquedra- 10;-24; biquadcia- /,baɪ.'kwad.ʃə/


See Also[]