A qname is composed of a sequence of roots. Each root has a numerical value, and the value of a qname is formed by multiplying together the values of the roots. Affixes are placed around roots or groups of roots to combine them into larger factors. qname is based on superior highly composite numbers (SHCNs). It is the successor to my earlier pname, which was inspired by Michael Thomas de Vlieger's argam.

qname has 17 consonants and 7 vowels:

Labial | Alveolar | Post-alveolar | Palatal | Velar | Glottal | ||
---|---|---|---|---|---|---|---|

Nasal | m | n | |||||

Stop | Voiceless | p | t | k | |||

Voiced | b | d | g | ||||

Fricative | Voiceless | f | s | x (/ʃ/) | h | ||

Voiced | v | z | j (/dʒ/) | ||||

Approximant | l | y (/j/) |

Front | Central | Back | ||
---|---|---|---|---|

Close | i | u | ||

Mid | Non-rhotic | e | ı (/ə/) | o |

Rhotic | r (/ɚ/) | |||

Open | a |

Each letter is pronounced like its IPA value unless otherwise noted. Additionally, 'z' can be pronounced /ts/, and 'v' can be pronounced /w/.

There are two additional consonant phonemes, 'ŷ' and 'ŵ'. 'ŷ' is pronounced and written as 'j', but when preceding a hyphenation point, it and its vowel combine into a single /i/ (spelled 'i'). Similarly, 'ŵ' followed by schwa is pronounced like /u/ and spelled 'u', whereas preceding other vowels, it is pronounced and written like 'v'. Both of these vowels can glide with the previous syllable to form the diphthongs 'ai', 'oi', and 'au'. An alternative pronunciation can exist where the schwa-containing syllables do not modify the way 'ŷ' and 'ŵ' are pronounced, and they become identical to 'j' and 'v'.

Every syllable is of the form CV, with the exception of the vocalic syllables 'a' and 'un' (0 and 1), and the combined 'i' and 'u' from above. The schwa can be elided out to form consonant clusters or word-final consonants, as long as it does not conflict with another consonant's prononciation (ex. eliding /təs/ into /ts/ is forbidden as it conflicts with 'z', but eliding /kəs/ into /ks/ is allowed.) The letter 'ı' may be omitted everywhere except before the final nasal of an SHCN suffix.

Every consonant (except 'y', 'j', and 'h') has a hardened form. These are always a cluster of two consonants. The schwa between them is always elisible.

Cons. | Hard | Cons. | Hard | Cons. | Hard |
---|---|---|---|---|---|

m | mp | n | ns | ||

p | ps | t | tx | k | ks |

b | bl | d | j | g | gl |

f | fk | s | sk | x | xk |

v | ft | z | st | ||

ŵ | ft | l | lk | ŷ | ŷk |

Weak roots are one syllable. Strong roots are two syllables with the final vowel omitted, with the form CVC. If no vowel is specified for a strong root, schwa is assumed. Every basic root with value less than or equal to 12 is weak, and those that are greater than 12 are strong.

The basic roots are of the following forms:

Small roots represent numbers from 2 to 60.

n | Root | n | Root | n | Root | n | Root | n | Root | n | Root |
---|---|---|---|---|---|---|---|---|---|---|---|

11 | ze | 21 | lex | 31 | nad | 41 | yal | 51 | tas | ||

2 | da | 12 | va | 22 | zad | 32 | dov | 42 | dag | 52 | kad |

3 | te | 13 | kal | 23 | ful | 33 | zed | 43 | sil | 53 | saf |

4 | ka | 14 | del | 24 | gam* | 34 | das | 44 | zag | 54 | daŷ |

5 | pe | 15 | fen | 25 | pin | 35 | pal | 45 | nob | 55 | pez |

6 | se | 16 | bov* | 26 | yaf | 36 | sin | 46 | fol | 56 | noŷ |

7 | la | 17 | gas | 27 | naŷ | 37 | mag | 47 | fox | 57 | god |

8 | yo | 18 | saŷ | 28 | lag | 38 | dex | 48 | boŷ | 58 | nan |

9 | no | 19 | xig | 29 | nen | 39 | min | 49 | lin | 59 | kul |

10 | xu | 20 | ven | 30 | faŷ | 40 | yob | 50 | pan | 60 | baŷ |

*When preceding a hyphenation point, 'bov' and 'gam' change to 'bo' and 'ga' respectively.

A prime root represents a prime from 2 to 659 (the 120th prime). Prime roots under 60 coincide with the small roots.

π(n) | n | Root | π(n) | n | Root | π(n) | n | Root | π(n) | n | Root | π(n) | n | Root | π(n) | n | Root |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | da | 21 | 73 | sag | 41 | 179 | nib | 61 | 283 | pom | 81 | 419 | tal | 101 | 547 | men |

2 | 3 | te | 22 | 79 | tid | 42 | 181 | mob | 62 | 293 | sam | 82 | 421 | pub | 102 | 557 | nol |

3 | 5 | pe | 23 | 83 | van | 43 | 191 | teg | 63 | 307 | yub | 83 | 431 | biz | 103 | 563 | lol |

4 | 7 | la | 24 | 89 | kom | 44 | 193 | lus | 64 | 311 | gad | 84 | 433 | pon | 104 | 569 | luz |

5 | 11 | ze | 25 | 97 | man | 45 | 197 | lod | 65 | 313 | teb | 85 | 439 | sad | 105 | 571 | dub |

6 | 13 | kal | 26 | 101 | fel | 46 | 199 | pad | 66 | 317 | dis | 86 | 443 | lad | 106 | 577 | sig |

7 | 17 | gas | 27 | 103 | kob | 47 | 211 | siv | 67 | 331 | hol | 87 | 449 | fan | 107 | 587 | nil |

8 | 19 | xig | 28 | 107 | nix | 48 | 223 | kam | 68 | 337 | bel | 88 | 457 | laŷ | 108 | 593 | has |

9 | 23 | ful | 29 | 109 | kub | 49 | 227 | yen | 69 | 347 | tul | 89 | 461 | kid | 109 | 599 | maŷ |

10 | 29 | nen | 30 | 113 | zin | 50 | 229 | san | 70 | 349 | yeb | 90 | 463 | tol | 110 | 601 | dam |

11 | 31 | nad | 31 | 127 | gal | 51 | 233 | sib | 71 | 353 | lud | 91 | 467 | pod | 111 | 607 | lon |

12 | 37 | mag | 32 | 131 | yel | 52 | 239 | tel | 72 | 359 | haf | 92 | 479 | yul | 112 | 613 | kog |

13 | 41 | yal | 33 | 137 | las | 53 | 241 | yod | 73 | 367 | tan | 93 | 487 | neb | 113 | 617 | yan |

14 | 43 | sil | 34 | 139 | sel | 54 | 251 | xen | 74 | 373 | vol | 94 | 491 | pud | 114 | 619 | fov |

15 | 47 | fox | 35 | 149 | bol | 55 | 257 | xiz | 75 | 379 | len | 95 | 499 | mal | 115 | 631 | mov |

16 | 53 | saf | 36 | 151 | kib | 56 | 263 | bal | 76 | 383 | som | 96 | 503 | kum | 116 | 641 | liv |

17 | 59 | kul | 37 | 157 | lub | 57 | 269 | lan | 77 | 389 | lid | 97 | 509 | bag | 117 | 643 | ten |

18 | 61 | log | 38 | 163 | sol | 58 | 271 | xil | 78 | 397 | pul | 98 | 521 | kaf | 118 | 647 | gon |

19 | 67 | kaŷ | 39 | 167 | yed | 59 | 277 | pas | 79 | 401 | vaŵ | 99 | 523 | vaŷ | 119 | 653 | lig |

20 | 71 | kas | 40 | 173 | zil | 60 | 281 | nid | 80 | 409 | hag | 100 | 541 | fal | 120 | 659 | xin |

The first nine SHCNs, up to 55440, have basic root forms. SHCNs under 60 coincide with small roots.

n | Root | n | Root |
---|---|---|---|

2 | da | 360 | kol |

6 | se | 2520 | saŵ |

12 | va | 5040 | pol |

60 | baŷ | 55440 | den |

120 | han |

Compound roots, roots that are composed of multiple other roots, can be either single or multiple. A single root is defined to be either a single basic root or any compound root which does not have an exponent at the outermost level. Numerically, single roots represent numbers less than or equal to 60, primes, primorials, and SHCNs, but not their powers. Compound roots which are not single roots (they are products of powers of single roots) are multiple roots. A constituent root is a single root, or a single root with an exponent prefix.

A compound root is considered strong if it ends in a strong basic root, prime '-k' or '-t', or an SHCN suffix. A compound root is considered weak if it ends in a weak basic root or the primorial '-vi', '-bi', or '-po'.

A hyphenation point is a point in the word where a hyphen can be inserted. Hyphenation points occur at every point that is directly between the end of a numerical root or suffix and the beginning of another numerical root or 'su-'. There are also hyphenation points at the beginning and end of the word.

There are two separate affixes to produce primes larger than 659. The first is '-k'. This is appended to any single root with value n, and it produces the nth prime. The second prime suffix is the circumfix 'su-t'. When surrounding a multiple root with value n, it produces the nth prime. In the root is strong and ends with 'd', 'k', 'l', 'v', or 'ŵ', the vowel 'o' is inserted between it and the prime suffix. Any other strong root has an 'a' inserted between it and the suffix.

If there are several consecutive instances of the same prime suffix, the 'k' or 't' will change to 'y' in an alternating manner such that the outermost suffix does not change (for instance, in a run of four '-k' suffixes, the first and third change to 'y'.)

There are three affixes that produce primorials. The first, '-vi', appends to a prime root n, inserting a schwa if the prime is strong, and produces the primorial with highest factor n. The other two, '-bi' and 'su-po' act like prime '-k' and 'su-t'. '-bi' attaches to a single root n, and produces the primorial whose highest prime factor is the nth prime. 'su-po' produces the same by surrounding a multiple root. All three suffixes insert schwa if they attach to a strong root.

If the suffix '-vi' succeeds a strong root ending in 'v', the 'v' and '-vi' are combined into '-fi'. The point before the primorial suffix acts like a hyphenation point in that 'ŷ' and 'ŵ' are pronounced like 'i' and 'u' respectively, but otherwise cannot by hyphenated.

Ancillary | |||||
---|---|---|---|---|---|

π(n) | n | 0 | 1 | 2 | 3 |

6 | 13 | kalın | kaldın | kalsın | kalfın |

17 | 59 | kulın | kuldın | kulzın | |

34 | 139 | selın | seltın | selfın | |

36 | 151 | kibın | kipxın | kiblın | |

92 | 479 | yulın | yulmın | yulkın |

Larger known highest prime factors with ancillary 2 are n = 1709, 1907, 2753, 2939, 6301, 7229, 49433, 1117370759, with π(n) = 267, 292, 402, 424, 820, 924, 5080, 56496498.

If n is not listed in this table, it either has highest ancillary value 1 or is greater than 659. If the ancillary is 1, replace the consonant before the SHCN suffix with its hardened version. If the ancillary is 2, the single root n ends in the prime suffix '-k' or '-t'; replace them with 'p'. If the ancillary is 3, harden the 'p' into 'ps'. It is an open problem whether an ancillary of 3 ever occurs outside of n=13.

If the SHCN precedes a labial consonant, the final 'n' should be replaced by 'm'. Before the final nasal, the letter 'ı' should always be written. This vowel cannot be elided.

Any single root can have an exponent prefix, denoting a power of the value. If the exponent is less than 12, the prefix is derived from the small root of the number, by replacing the final vowel with 'i', or 'e' if the exponent is 12 ('va' becomes 've'). Additionally, the prefix for an exponent of 8 is 'ji' instead of 'yi'. If the exponent is a primorial, which ends in '-vi', '-bi', or '-po', then that suffix is replaced by '-vo', '-ba', or '-pa' respectively. If the exponent is otherwise a strong simple root, the prefix is the simple root with the vowel 'r' at the end. Otherwise, the exponent is a multiple root, in which case the circumfix 'su-pr' is applied, and the entire unit is prepended to the base of the power.

In certain situations, the prefix 'su-' can be removed. When 'su-' succeeds one of prime suffixes '-k' or '-t', optionally separated by a SHCN nasal suffix or a consonant added by hardening, which is ignored for the purpose of the following contractions, and the root preceding the prime suffix is strong and ends in 'p', 't', or 'z', the vowel preceding the prime suffix changes to 'u'. Otherwise, if the root is strong, the vowel preceding the prime suffix changes to 'e'. Finally, if the root ends in the primorial '-vi', '-bi', or '-po', the suffix is replaced by '-ji', '-gi', or '-ki' respectively. The '-fi' contraction is not applied, so '-fi' is replaced with '-vji'. In all of these cases, 'su-' is removed.

If the root preceding the prime suffix ends in a weak basic root, and the prime suffix is '-t', then 'su-' cannot be removed, but '-t' and 'su-' can combine into '-zu-'. The hyphenation point formerly between the '-t' and 'su-' is placed after the 'zu'.

If, after all other contractions, there are two 'su-' next to each other, the second one should be replaced with 'gu-'. This continues in an alternating manner, so for instance 'sususususu-' (five repetitions) becomes 'sugusugusu-'.

A valid word is any word that can be parsed into a number by the rules given above.

A subcanonical word is a valid word with the additional properties that the values of the constituent roots are in descending order, every constituent root of any subword that can be expressed with a basic root is expressed with a basic root, there are no compound prime roots with index 120 or less, and there are no exponents on perfect power roots (4, 8, 9, 16, 25, 32, 36, 49).

A quasicanonical word is a subcanonical word where every subword is expressed with the fewest constituent roots.

A canonical word is, given its value, the unique quasicanonical word with that value where, for every subword, the first constituent root's value is as high as possible. If there are multiple quasicanonical words with this property, the second constituent root's value must be as high as possible, and so on.