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 Systematic Dozenal Nomenclature, Intro/FAQ/wiki/spec/discussion...
Kodegadulo
Posted: Oct 16 2011, 09:06 PM


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NOTE: This thread represents a continuation of the discussion begun in the Clearer TGM Prefix Suffixes thread, in which SDN was developed. This post and others it links to attempt to provide a wiki about SDN summarizing the most up to date thinking, but realize that other posts here represent the ongoing discussion that lead to what you see here. For an actual wiki about SDN, see here.

Systematic Dozenal Nomenclature


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.

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:

[z] Default to dozenal
(See my index post to find out about base-neutral base qualifiers.)

N Digit String Multiplier (N ×) Reciprocal (N−1) Positive Power (10N) Negative Power (10−N)
Root Abbrev Prefix Abbrev Prefix Abbrev Prefix Abbrev Prefix Abbrev
1 un u uni u u* uninfra u\ u\ unqua u↑ u@ uncia u↓ u#
2 bi b bina b b* bininfra b\ b\ biqua b↑ b@ bicia b↓ b#
3 tri t trina t t* trininfra t\ t\ triqua t↑ t@ tricia t↓ t#
4 quad q quadra q q* quadinfra q\ q\ quadqua q↑ q@ quadcia q↓ q#
5 pent p penta p p* pentinfra p\ p\ pentqua p↑ p@ pentcia p↓ p#
6 hex h hexa h h* hexinfra h\ h\ hexqua h↑ h@ hexcia h↓ h#
7 sept s septa s s* septinfra s\ s\ septqua s↑ s@ septcia s↓ s#
8 oct octa o* octinfra \ o\ octqua o@ octcia o#
9 enn e ennea e e* enninfra e\ e\ ennqua e↑ e@ enncia e↓ e#
Ӿ dec d deca d d* decinfra d\ d\ decqua d↑ d@ deccia d↓ d#
Ɛ lev leva L* levinfra ℓ\ L\ levqua ℓ↑ L@ levcia ℓ↓ L#
10 unnil un unnili un un* unnilinfra un\ un\ unnilqua un↑ un@ unnilcia un↓ un#
11 unun uu ununi uu uu* ununinfra uu\ uu\ ununqua uu↑ uu@ ununcia uu↓ uu#
12 unbi ub unbina ub ub* unbininfra ub\ ub\ unbiqua ub ub@ unbicia ub↓ ub#
. . .
20 binil bn binil bn bn* binilinfra bn\ bn\ binilqua bn↑ bn@ binilcia bn↓ bn#
21 biun bu biuni bu bu* biuninfra bu\ bu\ biunqua bu↑ bu@ biuncia bu↓ bu#
22 bibi bb bibina bb bb* bibininfra bb bb\ bibiqua bb↑ bb@ bibicia bb↓ bb#
. . .


(For each of the forms, the abbreviations on the left use special Unicode characters; these should be favored in enhanced environments where Unicode is supported. The abbreviations on the right are alternatives using only the basic ASCII character set; these can be used in disadvantaged environments.)

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 zero 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 (see Reciprocal Prefixes)
  • power-markers which are appended onto the numeral strings to generate power prefixes (see Power Prefixes)
  • rules for combining multiplier prefixes, reciprocal prefixes, and power prefixes, with each other as well as with the words they modify (for instance, units of measure).
  • A 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.
Examples:This post will serve as the jumping-off point for the whole topic of systematic nomenclature. Subsequent posts will cover subtopics, and will be hyperlinked here as they are developed. This thread is still under construction, so please be patient.
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m1n1f1g
  Posted: Oct 16 2011, 09:55 PM


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I have thought of a rational way of describing why the -qua or -ua suffixes fit certain purposes, to do with euphony rather than magnitude. If the root ends in a consonant cluster (including 'x' = /ks/, but not 'nn' = /n/), '-ua' should be used; if not, '-qua' should be used. That gives:
nilqua
unqua
biqua
triqua
quadqua
pentua
hexua
septua
octua
ennqua
decqua
levqua

Otherwise, maybe if the root ends in a /k/, /s/, /t/ or /d/ sound, '-ua' should be used. I think these are called non-sonorant consonants. Helpfully, Wikipedia lists the sonorant consonants of English (with my annotations):
/l/, /m/, /n/, /ŋ/ = sing, /ɹ/ = borrow, /w/, /j/ = yellow
So, sonorant consonants and vowels have '-qua', and everything else has '-ua'. Let's see:
nilqua
unqua
biqua
triqua
quadua
pentua
hexua
septua
octua
ennqua
decua
levua

That's much closer to what I aimed for. Note that I looked all of this up on-the-spot. This is possibly wrong, I'm not an expert of these things. Effectively, the only difference is having "ennqua", and only having "quadua". That was the idea.

The same holds for the negative power prefixes: "-cia" in place of "-qua" and "-ia" in place of "-ua".
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Kodegadulo
Posted: Oct 17 2011, 03:13 AM


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QUOTE (m1n1f1g @ Oct 16 2011, 09:55 PM)
I have thought of a rational way of describing why the -qua or -ua suffixes fit certain purposes, to do with euphony rather than magnitude. If the root ends in a consonant cluster (including 'x' = /ks/, but not 'nn' = /n/), '-ua' should be used; if not, '-qua' should be used. That gives:
...

Otherwise, maybe if the root ends in a /k/, /s/, /t/ or /d/ sound, '-ua' should be used. I think these are called non-sonorant consonants. Helpfully, Wikipedia lists the sonorant consonants of English (with my annotations):
/l/, /m/, /n/, /ŋ/ = sing, /ɹ/ = borrow, /w/, /j/ = yellow...

Those are interesting rationales, but I would prefer to keep the ninth powers as ennua/ennia, simply because the root enn was distilled from the original Greek ennea. Given this origin, it seems natural to follow enn with a vowel rather than a consonant. Also, I think there ought to be a clear contrast between ennua/ennia versus unqua/uncia, to make it unlikely people will confuse the first and ninth powers, if for no other reason. EDIT: On further consideration, I reversed my position on these points. See this post.)

We justify putting qua/cia on un because we want to capitalize on the ancient Latin uncia. We justify putting those on bi and tri because they end in a vowel so we need to interpose a consonant before we append more vowels. We justify putting those endings on quad because ... well, because dgoodmaniii insisted on the fourth powers being pronounceable in two syllables.

I admit though, the rationale for using qua/cia on nil is more problematic. I suppose they would work equally well as nilua/nilia. If there's a consensus for this, I can recast the rule either to make the q/c optional (like for quad) or place nil in the vowel-only group.
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dgoodmaniii
Posted: Oct 17 2011, 03:21 AM


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QUOTE (Kodegadulo @ Oct 17 2011, 03:13 AM)
I admit though, the rationale for using qua/cia on nil is more problematic. I suppose they would work equally well as nilua/nilia. If there's a consensus for this, I can recast the rule either to make the q/c optional (like for quad) or place nil in the vowel-only group.

Really? I find "nilqua" much easier to handle than "nilua."
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Kodegadulo
Posted: Oct 18 2011, 01:12 AM


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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 the digit 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:

[z] Default to dozenal
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 tres/tra "three"
4 quad Latin quadri-, quadra-, quadru-, quadr-, combining form of quattuor "four"
5 pent Greek penta-, pent-, combining form of pntē "five"
6 hex Greek hexa-, hex-, combining form of hx "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 enna"nine"
X dec Greek deka-, combining form of dka "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)
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Kodegadulo
Posted: Oct 18 2011, 01:14 AM


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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:

[z] Default to dozenal
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 103 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 89 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

The following table shows numeral strings representing the first few powers of dozen:

Value String
100 un
101 unnil
102 unnilnil
103 un-nilnilnil
104 unnil-nilnilnil
105 unnilnil-nilnilnil
106 un-nilnilnil-nilnilnil

Even though theoretically you can represent any natural number using these numeral strings, this last table demonstrates that, practically speaking, they are not scalable to very large numbers. But that is where power prefixes come in.
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Kodegadulo
Posted: Oct 18 2011, 03:12 AM


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user posted image user posted image

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.

[z] Default to dozenal

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

biennium = 2-year period
triennium = 3-year period
quadrennium = 4-year period
octennium = 8-year period
unnilennium = unquennium = 10-year period
unquadrennium = 14-year period
bioctennium = 28-year period
pentquadrennium = 54-year period
decoctennium = X8-year period
unnilnilennium = biquennium = 100-year period
unennquadrennium = 194-year period
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Kodegadulo
Posted: Oct 18 2011, 06:13 AM


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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 the multiplier 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.

[z] Default to dozenal

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 100 nilqua- /'nɪl.kwə/ nila- 10-0 nilcia- /'nɪl.ʃə/
/'nɪl.sɪ.ə/
nili-
1 un 101 unqua- /'ʌŋ.kwə/ zena- 10-1 uncia- /'ʌn.ʃə/
/'ʌn.sɪ.ə/
zeni-
2 bi 102 biqua- /'baɪ.kwə/ duna- 10-2 bicia- /'baɪ.ʃə/
/'baɪ.sɪ.ə/
duni-
3 tri 103 triqua- /'traɪ.kwə/ trina- 10-3 tricia- /'traɪ.ʃə/
/'traɪ.sɪ.ə/
trini-
4 quad 104 quadqua- /'kwad.kwə/ quedra- 10-4 quadcia- /'kwad.ʃə/
/'kwad.sɪ.ə/
quedri-
5 pent 105 pentqua- /'pɛnt.kwə/ quena- 10-5 pentcia- /'pɛnt.ʃə/
/'pɛnt.sɪ.ə/
queni-
6 hex 106 hexqua- /'hɛks.kwə/ hesa- 10-6 hexcia- /'hɛk.ʃə/
/'hɛks.sɪ.ə/
hesi-
7 sept 107 septqua- /'sɛpt.kwə/ seva- 10-7 septcia- /'sɛpt.ʃə/
/'sɛpt.sɪ.ə/
sevi-
8 oct 108 octqua- /'akt.kwə/ aka- 10-8 octcia- /'akt.ʃə/
/'akt.sɪ.ə/
aki-
9 enn 109 ennqua- /'ɛn.kwə/ neena- 10-9 enncia- /'ɛn.ʃə/
/'ɛn.sɪ.ə/
neeni-
X dec 10X decqua- /'dɛk.kwə/ dexa- 10-X deccia- /'dɛk.ʃə/
/'dɛk.sɪ.ə/
dexi-
E lev 10E levqua- /'lɛv.kwə/ lefa- 10-E levcia- /'lɛv.ʃə/
/'lɛv.sɪ.ə/
lefi-
10 unnil 1010 unnilqua- /,ʌn.'nɪl.kwə/ zennila- 10-10 unnilcia- /,ʌn.'nɪl.ʃə/
/,ʌn.'nɪl.sɪ.ə/
zennili-
11 unun 1011 ununqua- /,ʌn.'ʌŋ.kwə/ zenzena- 10-11 ununcia- /,ʌn.'ʌn.ʃə/
/,ʌn.'ʌn.sɪ.ə/
zenzeni-
12 unbi 1012 unbiqua- /,ʌn.'baɪ.kwə/ zenduna- 10-12 unbicia- /,ʌn.'baɪ.ʃə/
/,ʌn.'baɪ.sɪ.ə/
zenduni-
13 untri 1013 untriqua- /,ʌn.'traɪ.kwə/ zentrina- 10-13 untricia- /,ʌn.'traɪ.ʃə/
/,ʌn.'traɪ.sɪ.ə/
zentrini-
14 unquad 1014 unquadqua- /,ʌn.'kwad.kwə/ zenquedra- 10-14 unquadcia- /,ʌn.'kwad.ʃə/
/,ʌn.'kwad.sɪ.ə/
zenquedri-
15 unpent 1015 unpentqua- /,ʌn.'pɛnt.kwə/ zenquena- 10-15 unpentia- /,ʌn.'pɛnt.ʃə/
/,ʌn.'pɛnt.sɪ.ə/
zenqueni-
16 unhex 1016 unhexqua- /,ʌn.'hɛks.kwə/ zenhesa- 10-16 unhexia- /,ʌn.'hɛk.ʃə/
/,ʌn.'hɛk.sɪ.ə/
zenhesi-
17 unsept 1017 unseptqua- /,ʌn.'sɛpt.kwə/ zenseva- 10-17 unseptia- /,ʌn.'sɛpt.ʃə/
/,ʌn.'sɛpt.sɪ.ə/
zensevi-
18 unoct 1018 unoctqua- /,ʌn.'akt.kwə/ zenaka- 10-18 unoctcia- /,ʌn.'akt.ʃə/
/,ʌn.'akt.sɪ.ə/
zenaki-
19 unenn 1019 unennqua- /,ʌn.'ɛn.kwə/ zenneena- 10-19 unenncia- /,ʌn.'ɛn.ʃə/
/,ʌn.'ɛn.sɪ.ə/
zenneeni-
1X undec 101X undecqua- /,ʌn.'dɛk.kwə/ zendexa- 10-1X undeccia- /,ʌn.'dɛk.ʃə/
/,ʌn.'dɛk.sɪ.ə/
zendexi-
1E unlev 101E unlevqua- /,ʌn.'lɛv.kwə/ zenlefa- 10-1E unlevcia- /,ʌn.'lɛv.ʃə/
/,ʌn.'lɛv.sɪ.ə/
zenlefi-
20 binil 1020 binilqua- /,baɪ.'nɪl.kwə/ dunnila- 10-20 binilcia- /,baɪ.'nɪl.ʃə/
/,baɪ.'nɪl.sɪ.ə/
dunnili-
21 biun 1021 biunqua- /,baɪ.'ʌŋ.kwə/ dunzena- 10-21 biuncia- /,baɪ.'ʌn.ʃə/
/,baɪ.'ʌn.sɪ.ə/
dunzeni-
22 bibi 1022 bibiqua- /,baɪ.'baɪ.kwə/ dunduna- 10-22 bibicia- /,baɪ.'baɪ.ʃə/
/,baɪ.'baɪ.sɪ.ə/
dunduni-
23 bitri 1023 bitriqua- /,baɪ.'traɪ.kwə/ duntrina- 10-23 bitricia- /,baɪ.'traɪ.ʃə/
/,baɪ.'traɪ.sɪ.ə/
duntrini-
24 biquad 1024 biquadqua- /,baɪ.'kwad.kwə/ dunquedra- 10-24 biquadcia- /,baɪ.'kwad.ʃə/
/,baɪ.'kwad.sɪ.ə/
dunquedri-

* Pronunciations given are guides, not dictates. Your mileage may vary. smile.gif
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Kodegadulo
Posted: Oct 18 2011, 06:11 PM


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QUOTE (m1n1f1g @ Oct 16 2011, 09:55 PM)
I have thought of a rational way of describing why the -qua or -ua suffixes fit certain purposes, to do with euphony rather than magnitude. If the root ends in a consonant cluster (including 'x' = /ks/, but not 'nn' = /n/), '-ua' should be used; if not, '-qua' should be used.

You know, I'm persuaded by this now, m1n1f1g. Good job.

I'm in the middle of building up this thread as a definitive pinnable resource for people, so I'm forced to nail down all the details, and there's definitely devils in them. In particular I'm trying to resolve some goals:

(1) Make sure the positive and negative power prefixes, as well as the multiplier prefixes are all distinctive and clearly distinct from each other.

(2) Get the multiplier prefixes to resemble, as much as possible, the original Latin/Greek combination forms they're derived from and which are already used in English.

(3) Make sure it all fits together cleanly and compellingly.

So for example goal (2) means getting the multiplier prefix for nine to be ennea-. I can easily get there by saying that the middle -e- is a "euphony letter" and use the same final vowel -a- as for most of the other multipliers. The trouble is, I just can't hear any difference in pronunciation between ennea- as a multiplier and ennia- as a negative power.

So now I'm persuaded that the ninth powers should be ennqua- and enncia-. And I'm backing off my concern that those might get confused with unqua- and uncia-. The differences are in well-stressed vowels, so I shouldn't worry. I mean, a hundred years ago the Brits were mobilizing to go to war with "the Hun". If we can't tell the difference between that and going to war with "the Hen", I think we're in real trouble! smile.gif

In fact, I think you're right about the rest too. To meet goal (1), we should maximize the use of those distinctive -qua- and -cia- syllables. Put them everywhere we can get away with them. Only reduce them to -ua- and -ia- where we absolutely have to, after those difficult consonant clusters between pent and oct. That's a good, clear rationale that fits goal (3).

I'll adjust the tables in the other posts accordingly. Once I do, let me know what you think, folks.
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Kodegadulo
Posted: Oct 18 2011, 07:14 PM


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QUOTE (Kodegadulo @ Oct 18 2011, 06:11 PM)
I'll adjust the tables in the other posts accordingly. Once I do, let me know what you think, folks.

Done.
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Kodegadulo
Posted: Oct 19 2011, 03:57 AM


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Added pronunciation guides to the Power Prefixes post.
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Kodegadulo
Posted: Oct 19 2011, 04:09 AM


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[z] Default to dozenal

SDN Examples: Polygon Names

Sides Systematic Name Traditional Name
Pure Multiplier With Power
3 trigon triangle, 2-simplex
4 quadragon square, 2-orthoplex, 2-cross-polytope
5 pentagon pentagon
6 hexagon hexagon
7 septagon heptagon
8 octagon octagon
9 enneagon nonagon, enneagon
Ӿ decagon decagon
Ɛ levagon hendecagon
10 unniligon unquagon dodecagon
11 ununigon tridecagon, triskaidecagon
12 unbigon tetradecagon
13 untrigon pentadecagon
14 unquadragon hexadecagon
15 unpentagon heptadecagon
16 unhexagon octadecagon
17 unseptagon nonadecagon, enneadecagon
18 unoctagon icosagon
19 unenneagon henicosagon
undecagon docosagon
unlevagon tricosagon
20 biniligon binunquagon tetracosagon

SDN Examples: Platonic Solids

Faces Systematic Name Traditional Name
Pure Multiplier With Power
4 quadrahedron tetrahedron, 3-simplex, 4-sided die
6 hexahedron cube, hexahedron, 6-sided die
8 octahedron octahedron, 3-orthoplex, 3-cross-polytope, 8-sided die
10 unnilihedron unquahedron dodecahedron, 10-sided die
18 unoctahedron icosahedron, 18-sided die

SDN& Examples: Platonic Hyper-Solids

Cells Systematic Name Traditional Name
Pure Multiplier With Power
5 pentachoron pentachoron, hyperpyramid, 4-simplex, 5-cell
8 octachoron octachoron, tesseract, 8-cell
14 unquadrachoron hexadecachoron, 4-orthoplex, 4-cross-polytope, 14-cell
20 binilichoron binunquachoron icositetrachoron, octaplex, 20-cell
Ӿ0 decnilichoron
 
decanunquachoron
unquaplex
hecatonicosachoron, Ӿ0-cell
dodecaplex
420 quadbinilichoron quadbinunquachoron hexacosichoron, 420-cell
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Kodegadulo
Posted: Oct 19 2011, 11:57 AM


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SDN Examples: Names for Numeric Bases

(Allowing -im- as a "euphony syllable" in some cases.)
Radix Systematic Name Traditional Name
[d] [z] Pure Multiplier With Power
d|2 z|2 binal
binary
binary
d|3 z|3 trinal
trinary
trinary, ternary
d|4 z|4 quadral quaternary
d|5 z|5 pental quinary
d|6 z|6 hexal senary
d|8 z|8 octal octal
d|9 z|9 enneal nonal
d|10 z|X decimal decimal
d|11 z|E leval undecimal
d|12 z|10 unnilimal unqual duodecimal, dozenal
d|13 z|11 ununimal tridecimal
d|14 z|12 unbinal quadradecimal
d|15 z|13 untrinal quindecimal
d|16 z|14 unquadral hexadecimal
d|18 z|16 unhexal octadecimal
d|20 z|18 unoctal vigesimal
d|21 z|19 unenneal unvigesimal
d|22 z|1X undecimal duovigesimal
d|24 z|20 binilimal binunqual quadravigesimal
d|25 z|21 biunimal quinvigesimal
d|60 z|50 pentnilimal pentanunqual sexagesimal
d|72 z|60 hexnilimal hexanunqual duoseptagesimal
d|84 z|70 septnilimal septanunqual quattuoroctagesimal
d|100 z|84 octquadral hundred
d|120 z|X0 decnilimal decanunqual long hundred
d|144 z|100 unnilnilimal biqual grossal
d|210 z|156 unpenthexal
d|240 z|180 unoctnilimal unoctanunqualdouble long hundred
d|360 z|260 bihexnilimal bihexanunqualtriple long hundred
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Kodegadulo
Posted: Oct 19 2011, 12:30 PM


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How do our British members feel about the palatalized monosyllabic /ʃə/ pronunciation I've given to the -cia- marker (and even to the -tia- in powers 5 through 8)? This may seem "Americanized", but on the other hand how do you pronounce words like "special" and "partial"? If anyone wants to offer a "British pronunciation" for any of these prefixes, I'd be happy to incorporate them into the chart.

QUOTE (Kodegadulo @ Oct 18 2011, 06:13 AM)
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 -[q]u- or the -[c]i-) remains intact.


I'm starting to second-guess this idea, at least for the negative powers. I think eliding the -a- might turn -cia- /ʃə/ into -ci- /sɪ/. Is this a problem? Opinions?


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m1n1f1g
Posted: Oct 19 2011, 07:36 PM


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QUOTE (Kodegadulo @ Oct 19 2011, 01:30 PM)
How do our British members feel about the palatalized monosyllabic /ʃə/ pronunciation I've given to the -cia- marker (and even to the -tia- in powers 5 through 8)? This may seem "Americanized", but on the other hand how do you pronounce words like "special" and "partial"? If anyone wants to offer a "British pronunciation" for any of these prefixes, I'd be happy to incorporate them into the chart.

Surely it's easy enough to offer the alternative of /ʃə/ or /sɪ.ə/. That said, we do say /spɛ.ʃəl/. However, "specia" is not the root, it comes from Latin "specialis". That also went through French. With "uncial" (and related terms) the root is "uncia", and that looks like /ʌn.sɪ.ə/. That came straight from Latin. It would be helpful if anyone could find a similar word matching these criteria to back up this point.

Researching "uncia", I've found that the snow leopard is called either "uncia uncia" or "Panthera uncia", probably the first one although it is disputed. Also, note that the plural of uncia is "unciae", in English as well as Latin.
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Shaun
Posted: Oct 19 2011, 07:48 PM


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The "ounce" is also an English name for the big cat.
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Kodegadulo
Posted: Oct 20 2011, 01:42 AM


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I added the alternate three-syllable /sɪ.ə/ pronunciation for the -cia- positive powers. Then to balance things, I figured the positive powers deserved to have an alternate three-syllable pronunciation too, but to do that I had to re-introduce the old -cua- marker as an variant spelling. Don't worry, I'll use the -qua- versions for all the examples.
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Kodegadulo
Posted: Oct 20 2011, 10:19 AM


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[z] Default to dozenal

SDN Examples: Units of Time Measurement


In the table below, we do some comparisons with different units of measure. First we show plain quantities of equivalent units, unscaled. Then we drop the trailing zeroes from the quantities and exchange them for power prefixes on the units. Then for good measure, we show how the mantissa digits could be turned into multiplier prefixes.

In the rightmost columns, we show an alternate scheme where multiplier prefixes include the syllable dit to indicate the presence of a radix point. That way, we can scale the power prefix up to the closest order of magnitude less than the quantity and place the mantissa between 1 and 10..

These demonstrate what we can theoretically do with the Compact Scientific prefix scheme, taken to extremes. In practice, however, we are unlikely to use the latter forms unless they are very simple, such as pentaMinute for unciaHour or septaDay for Week.

Unit Equivalent Scaled to Power Compact Scientific Fully Scaled "Ditted" Compact Scientific
 
1 Day = 2 Clocks
= 20 Hours
= A00 Minutes
= 42,000 Seconds
= 200,000 Tims
= 2 Clocks
= 2 unquaHours
= A biquaMinutes
= 42 triquaSeconds
= 2 pentquaTims
= 1 biClock
= 1 binunquaHour
= 1 decabiquaMinute
= 1 quadbinatriquaSecond
= 1 binapentquaTim
 
 
 
= 4.2 quadquaSeconds
 
 
 
 
= 1 quadditbinaquadquaSecond
 
 
1 Clock = 0.6 Days
= 10 Hours
= 500 Minutes
= 21,000 Seconds
= 100,000 Tims
= 6 unciaDays
= 1 unquaHour
= 5 biquaMinutes
= 21 triquaSeconds
= 1 pentquaTims
= 1 hexanunciaDay
= 1 unquaHour
= 1 pentabiquaMinute
= 1 biunitriquaSecond
= 1 pentquaTim
 
 
 
= 2.1 quadquaSeconds
 
 
 
 
= 1 bidituniquadquaSecond
 
 
1 Hour = 0.06 Days
= 0.1 Clocks
= 50 Minutes
= 2,100 Seconds
= 10,000 Tims
= 6 biciaDays
= 1 unciaClock
= 5 unquaMinutes
= 21 biquaSeconds
= 1 quadquaTim
= 1 hexabiciaDay
= 1 unciaClock
= 1 pentanunquaMinute
= 1 biunibiquaSecond
= 1 quadquaTim
 
 
 
= 2.1 triquaSeconds
 
 
 
 
= 1 biditunitriquaSecond
 
 
1 unciaHour = 0.006 Days
= 0.01 Clocks
= 5 Minutes
= 210 Seconds
= 1,000 Tims
= 6 triciaDays
= 1 biciaClock
= 5 Minutes
= 21 unquaSeconds
= 1 triquaTim
= 1 hexatriciaDay
= 1 biciaClock
= 1 pentaMinute
= 1 biuniunquaSecond
= 1 triquaTim
 
 
 
= 2.1 biquaSeconds
 
 
 
 
= 1 biditunibiquaSecond
 
 
1 biciaHour = 0.0006 Days
= 0.001 Clocks
= 0.5 Minutes
= 21 Seconds
= 100 Tims
= 6 quadciaDays
= 1 triciaClock
= 5 unciaunciaMinutes
= 21 Seconds
= 1 biquaTim
= 1 hexaquadciaDay
= 1 triciaClock
= 1 pentanunciaMinute
= 1 biuniSecond
= 1 biquaTim
 
 
 
= 2.1 unquaSeconds
 
 
 
 
= 1 bidituniunquaSecond
 
 
1 triciaHour = 0.00006 Days
= 0.0001 Clocks
= 0.05 Minutes
= 2.1 Seconds
= 10 Tims
= 6 pentiaDays
= 1 quadciaClock
= 5 biciaMinutes
= 21 unciaSeconds
= 1 unquaTim
= 1 hexapentiaDay
= 1 quadciaClock
= 1 pentabiciaMinute
= 1 biuniunciaSecond
= 1 unquaTim
 
 
 
= 2.1 Seconds
 
 
 
 
= 1 bidituniSecond
 
 
1 quadciaHour = 0.000006 Days
= 0.00001 Clocks
= 0.005 Minutes
= 0.21 Seconds
= 1 Tim
= 6 hexciaDays
= 1 pentciaClock
= 5 triciaMinutes
= 21 biciaSeconds
= 1 Tim
= 1 hexahexciaDay
= 1 pentciaClock
= 1 pentatriciaMinute
= 1 biunibiciaSecond
= 1 Tim
 
 
 
= 0.21 Seconds
 
 
 
 
= 1 ditbiuniSecond
 


[Arggh! Lost a bunch of this post by accident! Serves me right for over-editing!]
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Heynonnymouse
Posted: Oct 20 2011, 10:41 AM


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These lists are fascinating - but will anybody actually use these long words? The ordinary person surely will prefer simple expressions. Words have to be made where they are not in the language - they will need to be short and simple if they are to be liked and used. These may be good with scientists but each language will prefer a word for the unit - maybe, for argument, "prima" for the first twelfth of the hour, "sekunda" for the next and so on.
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dgoodmaniii
Posted: Oct 20 2011, 12:07 PM


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QUOTE (Heynonnymouse @ Oct 20 2011, 10:41 AM)
These lists are fascinating - but will anybody actually use these long words? The ordinary person surely will prefer simple expressions. Words have to be made where they are not in the language - they will need to be short and simple if they are to be liked and used. These may be good with scientists but each language will prefer a word for the unit - maybe, for argument, "prima" for the first twelfth of the hour, "sekunda" for the next and so on.

No, I think Kode knows that people are unlikely to use these lengthy words except in extraordinary circumstances; they are just a demonstration of how the prefixes are used in more normal situations.

People are likely to go right on using hours; with TGM, the Tim is the smallest integral unit, and people will probably come up with some simple words for it. E.g., a twelfth of an hour might be a block, a twelfth of that might be a tock, and a twelfth of that a tick, until we get to a Tim (a twelfth of the last).

We really do need a name for units between an hour and a minute long. The dozenal system gives us convenient-sized units for such, including the ever-present five-minute period (a twelfth of an hour), and TGM is even based on one such (1 hour x 10-4, or 410), the Tim; all we need to do is fill in the names.
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icarus
Posted: Oct 20 2011, 01:42 PM


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Heynonnymouse, I remember back in 1976 reading that the Earth weighed "six sextillion tons". Being six, I thought that sextillion was a word much like thousand, million, and billion. Clearly the word had its use, i.e. weighing rocky inner planets. Much beyond that, there is very little use for the word, yet it can exist.

Today we read about "400 nanometer" wavelengths of light. (I think that's very deep blue, near ultraviolet). The word nanometer may not see everyday application for most of society. Yet in certain circles, it is in common use. A LED light salesman was talking to me a couple months ago about wavelengths in nanometers.

"Sextillion" might have caught on if SI weren't superior to US Customary for scientific purposes, as it is a scalable system of measure, i.e. based on the number base in play, not because it is decimal. (Additionally, the British and American systems for powers of ten larger than 108 differ significantly, this renders "sextillion" a provincial word. The American "billion" is also provincial, even in Italian it is milliardo, but it is ubiquitous, thanks to all the debt everywhere.) Such words would have fared better if the construction of the nomenclature of the powers of ten was better organized, like Kode's system is shaping up to be. (Tom Pendlebury also has a well-functioning system of number words).

I think this is what is going on in this thread; Kode is studying a systematic method for naming numbers of extreme scale. Not everyone will use them everyday, but some would rely on them, because of their special interests and work applications.

As a matter of fact, I am about to apply Kode's system to my next post. Let me see when the client needs this cathedral I'm working on, and you'll see it. (I am sure I am going to get it wrong.)
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Kodegadulo
Posted: Oct 20 2011, 01:51 PM


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QUOTE (dgoodmaniii @ Oct 20 2011, 12:07 PM)
QUOTE (Heynonnymouse @ Oct 20 2011, 10:41 AM)
These lists are fascinating - but will anybody actually use these long words? The ordinary person surely will prefer simple expressions. Words have to be made where they are not in the language - they will need to be short and simple if they are to be liked and used. These may be good with scientists but each language will prefer a word for the unit - maybe, for argument, "prima" for the first twelfth of the hour, "sekunda" for the next and so on.

No, I think Kode knows that people are unlikely to use these lengthy words except in extraordinary circumstances; they are just a demonstration of how the prefixes are used in more normal situations.


In fact, I mentioned that myself in introducing those examples. The point really is to demonstrate that the multiplier prefixes and the power prefixes aren't two completely separate and competing systems, but rather two parts of an integrated system that you can combine and dovetail to whatever extent you please. I'm demonstrating that you can really push these word-formation rules to extremes without them breaking down. In practice, though, we're likely to use only a simple multiplier or a simple power by itself at any given time, but if there's an application for gluing them together, there's no barrier to doing that.

QUOTE
People are likely to go right on using hours; with TGM, the Tim is the smallest integral unit, and people will probably come up with some simple words for it.  E.g., a twelfth of an hour might be a block, a twelfth of that might be a tock, and a twelfth of that a tick, until we get to a Tim (a twelfth of the last).


What these examples allow you to do is make definitional statements like:

"An Hour is a quadquaTim, or a pentniliMinute. A Tim is a quadciaHour."

"A Clock is a pentquaTim, or an unquaHour, or a pentabiquaMinute. A Day is a biClock, an Hour is an unciaClock, and a Tim is a pentciaClock."

"A Block is a triquaTim, or an unciaHour, or a pentaMinute." I rather like this as a colloquialism. It conveys the sense of a "5-minute period" as a minimal "block of time" on the clock. And together with "Clock" it makes a nice frame around "Hour": "Two Clocks in a Day, twelve Hours in a Clock, twelve Blocks in an Hour."

"A Tock is a biquaTim, or a biciaHour, or a biuniSecond. A Tick is an unquaTim, or a triciaHour, or a bidituniSecond." I don't like these as much, because "tick" and "tock" don't really convey any sense of how long these periods are, at least to me. I don't imagine a clock ticking every two-and-one-twelfth seconds, and tocking every two-dozen-one seconds. I expect if a clock is going to tick, it would do so on its finest time resolution, which can quite reasonably be the Tim. (See my UncialClock.) That's why I've suggested some form of the word "Tick" as a colloquialism for Tim.
In which case:

"An Unctic (/'ʌŋk.tɪk/, rhymes with "hectic") is an unquaTim, or a bidituniSecond. A Bictic (/'bɪk.tɪk/, rhymes with "hectic", sort of rhymes with "minute") is a biquaTim, or a biciaHour, or a biuniSecond." Given that "bi" features so prominently in the definition of TGM's "quasi-minute" period, I figure the colloquialism for it should incorporate that.

QUOTE
We really do need a name for units between an hour and a minute long.  The dozenal system gives us convenient-sized units for such, including the ever-present five-minute period (a twelfth of an hour), and TGM is even based on one such (1 hour x 10-4, or 410), the Tim; all we need to do is fill in the names.


Pssst:
1 hour x 10-4 = 4Hr
410 = 31

wink.gif
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dgoodmaniii
Posted: Oct 20 2011, 03:30 PM


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QUOTE (Kodegadulo @ Oct 20 2011, 01:51 PM)
Pssst:
1 hour x 10-4 = 4Hr
410 = 31

wink.gif

He got me! Yes, what Kode said. A Tim is a quadciaHour (4Hr). There should not be a zero in there.

So possible colloquialisms are a block for an unciaHour(1Hr)/triquaTim(3Tm), a bictic for a biciaHour(2Hr)/biquaTim(2Tm), and an unctic for an triciaHour(3Hr)/unquaTim(1Tm), and perhaps even "tick" for a Tim.

Similarly, people sometimes say "click" for "kilometer."

Also, you forgot a "c" in "unctic," didn't you?
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m1n1f1g
Posted: Oct 20 2011, 09:28 PM


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Presumably that's "unctic", not "untic"; and why /ŋ/ instead of /n/? Surely that would be "ungctic", which is not it.

Other than that, I've been wondering recently about the power prefixes used on your constructed numeral (IUPAC) prefixes. Would it be better to specify the magnitude of the most significant digit, rather than the least significant? I was thinking this because then firstly you know the magnitude without having to hear all of the digits and also rounding is a simple matter of taking off the digits. It would mean that the day is a quadbinaquaduaSecond, as opposed to ...triquaSecond. It's a bit like scientific notation, and would also bring nilqua into use if we went into fractionals. Basic digit lists (like on unbipentizium) could be kept, with power inferred.

It's okay if you don't agree - I'm not sure if I agree - but I wanted to put another idea forward.
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