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.

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 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.).

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).