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 it isn't a particularly useful base,1 it happens to be our favorite number, and we thought it'd be fun to make some kinda implementation of it.

## the numbers

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

name | 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 | derived from the Huli word "hgui" (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 for us to read, so we're going with those.

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

name | 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, just more generalized: 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 | power | sub.# | dec.# |

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 decimal 420,691,337. the standard separator is a (nonbreaking) space, sorta inherited from how hex is represented, tho if you prefer you can use a comma, period, semicolon, or other symbol of your choice.

## fractions

fractions are the aspect of suboptimal where it really shines in being incredibly unsuable. as a prime, 17 is only evenly divisible by itself (and 1), which means most fractions you could expect to encounter regularly are unwieldy and have infinitely repeating decimals. said repeating decimals are represented with an underline instead of an overline, because it's a lot more convenient to add an underline than an overline digitally (which is also why we're just putting an underline on the decimal numbers as well).

the first set-two fractions (one half through one set-third, or decimal one half through one twentieth) are:

ratio name | ratio | sub.# | dec.# |

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 |

one set-first | 1/11 | 0.0G | 0.05 |

one set-second | 1/12 | 0.0F39E5648 | 0.052631578947368421 |

one set-third | 1/13 | 0.0E7B | 0.05 |

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

## bonus

while we 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 we liked the idea too much to not include it here.

name | 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 (decimal 17) is "tone" /toʊn/, TOHN. the multiples of tone are formed by affixing: 20 is two-tone, D0 is sol-tone, etc. the powers of tone are:

name | sub.# | dec.# | |

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 decimal 420,691,337).