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suboptimal is a number system based around the number 17, in the same way decimal is based around the number 10. 17 is a kinda odd number and a bit of a mess to work with, so while this isn't a particularly useful base (hence the name suboptimal, coined by jan misali), i thought it'd be fun to make some kind of implementation of it.

the numbers

suboptimal uses 17 digits (the decimal numbers 0 through 16, with "10" equalling decimal 17). the first ten of these, 0 through 9, are the same as in decimal. the remaining are as follows:

name pronunciation sub.# dec.# name basis
ten /tɛn/, TEN A 10 same as decimal
eleven /ə.'lɛv.ən/, ə-LEV-ən B 11 same as decimal
doze /doʊz/, DOHZ C 12 derived from "dozen"
baker /'beɪ.kɚ/, BAY-kər D 13 taken from "baker's dozen"
echo /'ɛ.koʊ/, EH-koh E 14 taken from the IRSA letter for "e"
gui /'gu:.i/, GOO-ee F 15 dervied from the Huli word "ngui" (fifteen)
nibble /'nɪ.bəl/, NIH-bəl G 16 taken from the measure of data, which can be represented with one hex digit

while alternative/invented symbols might be more interesting, using the basic A through G set feels more intuitive to read, so i'm going with those.


the number 10 (decimal 17) is called "set" /sɛt/. the multiples of set are roughly constructed with the suffix "-(s)et", as follows:

name pronunciation sub.# dec.#
twoset /'tu.sɛt/, TOO-set 20 34
thriset /'θɹi.sɛt/, THREE-set 30 51
fourset /'fɔɹ.sɛt/, FOR-set 40 68
fifset /'fɪf.sɛt/, FIF-set 50 85
sixet /'sɪk.sɛt/, SIK-set 60 102
sevenset /'sɛ.vən.sɛt/, SE-vən-set 70 119
eitset /'eɪt.sɛt/, AYT-set 80 136
nineset /'naɪn.sɛt/, NYNE-set 90 153
tenset /'tɛn.sɛt/, TEN-set A0 170
elevet /ə.'lɛv.ɛt/, ə-LEV-et B0 187
dozet /'dʌz:ɛt/, DUH-zet C0 204
bakeset /'beɪk.sɛt/, BAYK-set D0 221
echset /'ɛk.sɛt/, EK-set E0 238
gooset /'gu:.sɛt/, GOO-set F0 255
nibset /'nɪb.sɛt/, NIB-set G0 272

other two-digit numbers are formed as compounds in the same way as decimal: 16 is set-six, 21 is twoset-one, 7E is sevenset-echo, GG is nibset-nibble, etc.


the names for the powers of set are as follows:

name pronunciation power suboptimal # decimal #
hundret /'hʌn.dɹrɛt/, HUN-dret 17^2
1 00
289
ten hundret /tɛn 'hʌn.dɹrɛt/, TEN HUN-dret 17^3
10 00
4,913
array /ə.'ɹeɪ/, ə-RAY 17^4
1 00 00
83,521
ten array /tɛn ə.'ɹeɪ/, TEN ə-RAY 17^5
10 00 00
1,419,857
grid /ɡɹɪd/, GRID 17^6
1 00 00 00
24,137,569
ten grid /tɛn ɡɹɪd/, TEN GRID 17^7
10 00 00 00
410,338,673
billid /'bɪ.lɪd/, BIH-lid 17^8
1 00 00 00 00
6,975,757,441
trillid /'tɹɪ.lɪd/, TRIH-lid 17^10
1 00 00 00 00 00
2,015,993,900,449
quadrillid /kwɑˈdɹɪ.lɪd/, kwah-DRIH-lid 17^12
1 00 00 00 00 00 00
582,622,237,229,761
etc.

these also form compounds in the same way: 10 74 G3 64 is ten grid, sevenset-four array, gooset-three hundret, sixet-four, or dec 420,691,337. the standard separator is a (nonbreaking) space, sorta inherited from how hex is represented, though if you prefer you can use a comma, period, semicolor, or other symbol of your choice.


fractions

fractions are the aspect of suboptimal where it really shines in being incredibly unusable. as a prime, 17 is only evenly divisible by itself (and 1), which means most fractions you could expect to encounter regularly are unwieldy.

infinitely repeating decimals (most of them) are represented with an underline instead of an overline, though that's mostly for formatting convenience.


the first G fractions (one half through one seteth) are:

ratio name ratio suboptimal rep. decimal rep.
one half 1/2 0.8 0.5
one third 1/3 0.5B 0.3
one fourth 1/4 0.4 0.25
one fifth 1/5 0.36DA 0.2
one sixth 1/6 0.2E 0.16
one seventh 1/7 0.274E9C 0.142857
one eighth 1/8 0.2 0.125
one ninth 1/9 0.1F 0.1
one tenth 1/A 0.1BF5 0.1
one eleventh 1/B 0.194ADF7C63 0.09
one dozeth 1/C 0.17 0.083
one baketh 1/D 0.153FBD 0.076923
one echoth 1/E 0.13AFD6 0.0714285
one gooeth 1/F 0.1249 0.06
one nibblth 1/G 0.1 0.0625
one seteth 1/10 0.1 0.0588235294117647

these work pretty much how you'd expect. the ordinals not listed are formed the same way, by affixing "-(e)th" (arrayeth, grideth, billith, trillith, etc.).


bonus

while i went with a somewhat incongruent set of new number terms for the bulk of this, the number of new base digits lends itself to using the solfège notes as number terms, and i like the idea too much to not include it here.

name pronunciation sub.# dec.#
do /doʊ/, DOH A 10
re /ɹeɪ/, RAY B 11
mi /mi/, MEE C 12
fa /fɑ:/, FAH D 13
sol /soʊl/, SOHL E 14
la /lɑ:/, LAH F 15
ti /ti:/, TEE G 16

10 (dec 17) is "tone" /toʊn/. the multiples of tone are formed by affixing: 20 is two-tone, D0 is sol-tone, etc.

the powers of tone are:

name pronunciation power suboptimal # decimal #
hundred /'hʌn.dɹrɛd/, HUN-dred 17^2
1 00
289
ten hundred /tɛn 'hʌn.dɹrɛd/, TEN HUN-dred 17^3
10 00
4,913
scale /skeɪl/, SKAYL 17^4
1 00 00
83,521
ten scale /tɛn skeɪl/, TEN SKAYL 17^5
10 00 00
1,419,857
aria /'ɑ:.ɹɪ.ə/, AH-ree-ə 17^6
1 00 00 00
24,137,569
ten aria /tɛn 'ɑ:.ɹɪ.ə/, TEN AH-ree-ə 17^7
10 00 00 00
410,338,673
billia /'bɪ.li.ə/, BIH-lee-ə 17^8
1 00 00 00 00
6,975,757,441
trillia /'tɹɪ.li.ə/, TRIH-lee-ə 17^10
1 00 00 00 00 00
2,015,993,900,449
quadrillia /kwɑˈdɹɪ.li.ə/, kwah-DRIH-lee-ə 17^12
1 00 00 00 00 00 00
582,622,237,229,761
etc.

this works the same as above: 10 74 G3 64 is ten aria, seven-tone-four scale, ti-tone-three hundred, six-tone-four (still dec 420,691,337).