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:
The following table summarizes the rules for generating prefixes: | |||
| Digit | Multiplier Markers | Reciprocal Marker |
Power Markers | |||
|---|---|---|---|---|---|---|
| Value | Root | Euphony Letter |
Final Vowel |
Positive | Negative | |
| 0 | nil | -i- | -nta- | -qua- | -cia- | |
| 1 | un | |||||
| 2 | bi | -n- | -a- [-i-] | |||
| 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.
- A numeral string may represent the mantissa of a multiplier prefix.
- A 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.
- A 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 String |
Multiplier Marker | Multiplier Prefix | ||||
|---|---|---|---|---|---|---|---|
| Euphony Letter |
Final Vowel |
Before Power Prefix |
Before Other | ||||
| Before Consonant |
Before Vowel |
Before Consonant |
Before Vowel | ||||
| 0 times | nil | -i- | nili- | nili- | nili- | nili- | |
| 1 times | un | uni- | uni- | uni- | uni- | ||
| 2 times | bi | -n- | -a- -i- |
bina- bini- |
bin- | bi- bina- |
bi- bin- |
| 3 times | tri | trina- trini- |
trin- | tri- trina- |
tri- trin- | ||
| 4 times | quad | -r- | quadra- quadri- |
quadr- | quadra- quadri- |
quadr- | |
| 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- | ||
Examples
- 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- |
Pendlebury Equivalent |
Uncial Negative Power Marker: -cia- |
Pendlebury Equivalent | |||||
|---|---|---|---|---|---|---|---|---|---|
| Value | String | Value | Prefix | Pronunciation* | Value | Prefix | Pronunciation* | ||
| 0; | nil | 10;0 | nilqua- | /'nɪl.kwə/ | nila- | 10;-0 | nilcia- | /'nɪl.ʃə/ /'nɪl.sɪ.ə/ |
nili- |
| 1; | un | 10;1 | unqua- | /'ʌŋ.kwə/ | zena- | 10;-1 | uncia- | /'ʌn.ʃə/ /'ʌn.sɪ.ə/ |
zeni- |
| 2; | bi | 10;2 | biqua- | /'baɪ.kwə/ | duna- | 10;-2 | bicia- | /'baɪ.ʃə/ /'baɪ.sɪ.ə/ |
duni- |
| 3; | tri | 10;3 | triqua- | /'traɪ.kwə/ | trina- | 10;-3 | tricia- | /'traɪ.ʃə/ /'traɪ.sɪ.ə/ |
trini- |
| 4; | quad | 10;4 | quadqua- | /'kwad.kwə/ | quedra- | 10;-4 | quadcia- | /'kwad.ʃə/ /'kwad.sɪ.ə/ |
quedri- |
| 5; | pent | 10;5 | pentqua- | /'pɛnt.kwə/ | quena- | 10;-5 | pentcia- | /'pɛnt.ʃə/ /'pɛnt.sɪ.ə/ |
queni- |
| 6; | hex | 10;6 | hexqua- | /'hɛks.kwə/ | hesa- | 10;-6 | hexcia- | /'hɛk.ʃə/ /'hɛks.sɪ.ə/ |
hesi- |
| 7; | sept | 10;7 | septqua- | /'sɛpt.kwə/ | seva- | 10;-7 | septcia- | /'sɛpt.ʃə/ /'sɛpt.sɪ.ə/ |
sevi- |
| 8; | oct | 10;8 | octqua- | /'akt.kwə/ | aka- | 10;-8 | octcia- | /'akt.ʃə/ /'akt.sɪ.ə/ |
aki- |
| 9; | enn | 10;9 | ennqua- | /'ɛn.kwə/ | neena- | 10;-9 | enncia- | /'ɛn.ʃə/ /'ɛn.sɪ.ə/ |
neeni- |
| X; | dec | 10;X; | decqua- | /'dɛk.kwə/ | dexa- | 10;-X; | deccia- | /'dɛk.ʃə/ /'dɛk.sɪ.ə/ |
dexi- |
| E; | lev | 10;E; | levqua- | /'lɛv.kwə/ | lefa- | 10;-E; | levcia- | /'lɛv.ʃə/ /'lɛv.sɪ.ə/ |
lefi- |
| 10; | unnil | 10;10; | unnilqua- | /,ʌn.'nɪl.kwə/ | zennila- | 10;-10; | unnilcia- | /,ʌn.'nɪl.ʃə/ /,ʌn.'nɪl.sɪ.ə/ |
zennili- |
| 11; | unun | 10;11; | ununqua- | /,ʌn.'ʌŋ.kwə/ | zenzena- | 10;-11; | ununcia- | /,ʌn.'ʌn.ʃə/ /,ʌn.'ʌn.sɪ.ə/ |
zenzeni- |
| 12; | unbi | 10;12; | unbiqua- | /,ʌn.'baɪ.kwə/ | zenduna- | 10;-12; | unbicia- | /,ʌn.'baɪ.ʃə/ /,ʌn.'baɪ.sɪ.ə/ |
zenduni- |
| 13; | untri | 10;13; | untriqua- | /,ʌn.'traɪ.kwə/ | zentrina- | 10;-13; | untricia- | /,ʌn.'traɪ.ʃə/ /,ʌn.'traɪ.sɪ.ə/ |
zentrini- |
| 14; | unquad | 10;14; | unquadqua- | /,ʌn.'kwad.kwə/ | zenquedra- | 10;-14; | unquadcia- | /,ʌn.'kwad.ʃə/ /,ʌn.'kwad.sɪ.ə/ |
zenquedri- |
| 15; | unpent | 10;15; | unpentqua- | /,ʌn.'pɛnt.kwə/ | zenquena- | 10;-15; | unpentia- | /,ʌn.'pɛnt.ʃə/ /,ʌn.'pɛnt.sɪ.ə/ |
zenqueni- |
| 16; | unhex | 10;16; | unhexqua- | /,ʌn.'hɛks.kwə/ | zenhesa- | 10;-16; | unhexia- | /,ʌn.'hɛk.ʃə/ /,ʌn.'hɛk.sɪ.ə/ |
zenhesi- |
| 17; | unsept | 10;17; | unseptqua- | /,ʌn.'sɛpt.kwə/ | zenseva- | 10;-17; | unseptia- | /,ʌn.'sɛpt.ʃə/ /,ʌn.'sɛpt.sɪ.ə/ |
zensevi- |
| 18; | unoct | 10;18; | unoctqua- | /,ʌn.'akt.kwə/ | zenaka- | 10;-18; | unoctcia- | /,ʌn.'akt.ʃə/ /,ʌn.'akt.sɪ.ə/ |
zenaki- |
| 19; | unenn | 10;19; | unennqua- | /,ʌn.'ɛn.kwə/ | zenneena- | 10;-19; | unenncia- | /,ʌn.'ɛn.ʃə/ /,ʌn.'ɛn.sɪ.ə/ |
zenneeni- |
| 1X; | undec | 10;1X; | undecqua- | /,ʌn.'dɛk.kwə/ | zendexa- | 10;-1X; | undeccia- | /,ʌn.'dɛk.ʃə/ /,ʌn.'dɛk.sɪ.ə/ |
zendexi- |
| 1E; | unlev | 10;1E; | unlevqua- | /,ʌn.'lɛv.kwə/ | zenlefa- | 10;-1E; | unlevcia- | /,ʌn.'lɛv.ʃə/ /,ʌn.'lɛv.sɪ.ə/ |
zenlefi- |
| 20; | binil | 10;20; | binilqua- | /,baɪ.'nɪl.kwə/ | dunnila- | 10;-20; | binilcia- | /,baɪ.'nɪl.ʃə/ /,baɪ.'nɪl.sɪ.ə/ |
dunnili- |
| 21; | biun | 10;21; | biunqua- | /,baɪ.'ʌŋ.kwə/ | dunzena- | 10;-21; | biuncia- | /,baɪ.'ʌn.ʃə/ /,baɪ.'ʌn.sɪ.ə/ |
dunzeni- |
| 22; | bibi | 10;22; | bibiqua- | /,baɪ.'baɪ.kwə/ | dunduna- | 10;-22; | bibicia- | /,baɪ.'baɪ.ʃə/ /,baɪ.'baɪ.sɪ.ə/ |
dunduni- |
| 23; | bitri | 10;23; | bitriqua- | /,baɪ.'traɪ.kwə/ | duntrina- | 10;-23; | bitricia- | /,baɪ.'traɪ.ʃə/ /,baɪ.'traɪ.sɪ.ə/ |
duntrini- |
| 24; | biquad | 10;24; | biquadqua- | /,baɪ.'kwad.kwə/ | dunquedra- | 10;-24; | biquadcia- | /,baɪ.'kwad.ʃə/ /,baɪ.'kwad.sɪ.ə/ |
dunquedri- |
Examples[]
- Time Units, and Suggested Colloquialisms.
- Length/Distance Units: Suggested Colloquialisms.
- Volume Units: Suggested Colloquialisms.
- Polytopes
- Numeric Bases