Link Search Menu Expand Document

Syllabic Quinary

A goofy group of numeral systems where number names are the same as their numeral representation.

Posted: Feb 21st, 2023 - Modified: Mar 29th, 2023

Silly idea I just thought of while look at hex codes: A numeral system where numerals in even positions are consonants and odd positions vowels. Then the name of each number is the same as its numeral representation.

Base-5 and Base-6 versions are described below.

Syllabic Quinary (Base-5²)

In this base-5 system, even numeral positions use the consonants {j,k,l,m,n} in place of {0,1,2,3,4} and odd positions use the vowels {a,e,i,o,u}.

Leading js and as are optional. So 0-4 can be a,e,i,o,u or ja,je,ji,jo,ju.

I’m calling this a “syllabic” numeral system because each pair of numerals can be represented by a distinct syllable.

Base-5² Examples

0 is a or ja. The next 150 numbers are as follows:

1-10:       e,    i,    o,    u,   ka,   ke,   ki,   ko,   ku,   la, 
11-20:     le,   li,   lo,   lu,   ma,   me,   mi,   mo,   mu,   na, 
21-30:     ne,   ni,   no,   nu,  eja,  eje,  eji,  ejo,  eju,  eka, 
31-40:    eke,  eki,  eko,  eku,  ela,  ele,  eli,  elo,  elu,  ema, 
41-50:    eme,  emi,  emo,  emu,  ena,  ene,  eni,  eno,  enu,  ija, 
51-60:    ije,  iji,  ijo,  iju,  ika,  ike,  iki,  iko,  iku,  ila, 
61-70:    ile,  ili,  ilo,  ilu,  ima,  ime,  imi,  imo,  imu,  ina, 
71-80:    ine,  ini,  ino,  inu,  oja,  oje,  oji,  ojo,  oju,  oka, 
81-90:    oke,  oki,  oko,  oku,  ola,  ole,  oli,  olo,  olu,  oma, 
91-100:   ome,  omi,  omo,  omu,  ona,  one,  oni,  ono,  onu,  uja, 
101-110:  uje,  uji,  ujo,  uju,  uka,  uke,  uki,  uko,  uku,  ula, 
111-120:  ule,  uli,  ulo,  ulu,  uma,  ume,  umi,  umo,  umu,  una, 
121-130:  une,  uni,  uno,  unu, kaja, kaje, kaji, kajo, kaju, kaka, 
131-140: kake, kaki, kako, kaku, kala, kale, kali, kalo, kalu, kama, 
141-150: kame, kami, kamo, kamu, kana, kane, kani, kano, kanu, keja

(Pronounce each vowel in its own syllable. I suggest using the Spanish pronunciation of each vowel, which coincide with the IPA pronunciations. For the pronunciation of j, just follow your heart.)

Base-5² Converter

Decimal to Syllabic Quinary Decimal:
Normal Quinary:
Syllabic Quinary²:
Syllabic Quinary to Decimal Syllabic Quinary²:
Normal Quinary:

Syllabic Senary (Base-6²)

For the senary version, use {a,e,i,o,u,y} for even numeral positions, and {s,w,t,h,r,f} for odd numeral positions.

Why These Letters?

To do this thing in base-6, we need a sixth vowel. English has semivowels y and w, so let’s use the ol’ “Sometimes y” as vowel number 6. To make the sounds less ambiguous, it may help to pronounce y as it is pronounced in the IPA. In IPA, y represents a sort of “ew” sound, as in “few”. (In Pinyin, the same sound is written as ü or v.) Alternately, it could be pronounced , as in “fry”. That might be a bit easier on the tongue.

In the base-5 version, I used the first sequence of 5 back-to-back consonants in the alphabet.

This time, I chose a consonant set which can be used to make many common english words. The best option which didn’t overlap with {jklmn} was {swthrf}.1

I’ve mapped them to the digits like so: s is mapped to zero (because s and z sound similar), w to one (“wan”), t two, h three, r four, f five.

Base-6² Examples

0 is a or sa.

The next 150 numbers are as follows:

1-10:        e,    i,    o,    u,    y,   wa,   we,   wi,   wo,   wu,
11-20:      wy,   ta,   te,   ti,   to,   tu,   ty,   ha,   he,   hi,
21-30:      ho,   hu,   hy,   ra,   re,   ri,   ro,   ru,   ry,   fa,
31-40:      fe,   fi,   fo,   fu,   fy,  esa,  ese,  esi,  eso,  esu,
41-50:     esy,  ewa,  ewe,  ewi,  ewo,  ewu,  ewy,  eta,  ete,  eti,
51-60:     eto,  etu,  ety,  eha,  ehe,  ehi,  eho,  ehu,  ehy,  era,
61-70:     ere,  eri,  ero,  eru,  ery,  efa,  efe,  efi,  efo,  efu,
71-80:     efy,  isa,  ise,  isi,  iso,  isu,  isy,  iwa,  iwe,  iwi,
81-90:     iwo,  iwu,  iwy,  ita,  ite,  iti,  ito,  itu,  ity,  iha,
91-100:    ihe,  ihi,  iho,  ihu,  ihy,  ira,  ire,  iri,  iro,  iru,
101-110:   iry,  ifa,  ife,  ifi,  ifo,  ifu,  ify,  osa,  ose,  osi,
111-120:   oso,  osu,  osy,  owa,  owe,  owi,  owo,  owu,  owy,  ota,
121-130:   ote,  oti,  oto,  otu,  oty,  oha,  ohe,  ohi,  oho,  ohu,
131-140:   ohy,  ora,  ore,  ori,  oro,  oru,  ory,  ofa,  ofe,  ofi,
141-150:   ofo,  ofu,  ofy,  usa,  use,  usi,  uso,  usu,  usy,  uwa,
151-160:   uwe,  uwi,  uwo,  uwu,  uwy,  uta,  ute,  uti,  uto,  utu,
161-170:   uty,  uha,  uhe,  uhi,  uho,  uhu,  uhy,  ura,  ure,  uri,
171-180:   uro,  uru,  ury,  ufa,  ufe,  ufi,  ufo,  ufu,  ufy,  ysa,
181-190:   yse,  ysi,  yso,  ysu,  ysy,  ywa,  ywe,  ywi,  ywo,  ywu,
191-200:   ywy,  yta,  yte,  yti,  yto,  ytu,  yty,  yha,  yhe,  yhi,
201-210:   yho,  yhu,  yhy,  yra,  yre,  yri,  yro,  yru,  yry,  yfa,
211-220:   yfe,  yfi,  yfo,  yfu,  yfy, wasa, wase, wasi, waso, wasu,
221-230:  wasy, wawa, wawe, wawi, wawo, wawu, wawy, wata, wate, wati,
231-240:  wato, watu, waty, waha, wahe, wahi, waho, wahu, wahy, wara,
241-250:  ware, wari, waro, waru, wary, wafa, wafe, wafi, wafo, wafu,
251-260:  wafy, wesa, wese, wesi, weso, wesu, wesy, wewa, wewe, wewi,
261-270:  wewo, wewu, wewy, weta, wete, weti, weto, wetu, wety, weha,
271-280:  wehe, wehi, weho, wehu, wehy, wera, were, weri, wero, weru,
281-290:  wery, wefa, wefe, wefi, wefo, wefu, wefy, wisa, wise, wisi,
291-300:  wiso, wisu, wisy, wiwa, wiwe, wiwi, wiwo, wiwu, wiwy, wita,

Base-6² Converter

Decimal to Syllabic Senary Decimal:
Normal Senary:
Syllabic Senary²:
Syllabic Senary to Decimal Syllabic Senary²:
Normal Senary:

Even Sillier: A Base-120 Version

Syllabic Senary is, in some sense, implicitly a base-36 system with 36 syllables for its numerals.

Let’s run with that idea and make a base-120 system using 120 different syllables.

I’ll be using the kind of mixed radix system described here which means I’ll need 10 initial consonants and 12 final ‘vowels’ to form my syllables.

For the consonants, I’ll just use {jklmpqrstv}. I may think of something more clever later. Pronouce the qs as a ch sound.

To get the extra ‘vowels’, I’ll double them up by using n. 0-9 will be a,e,i,o,u,y,an,en,in,on. Then ten will be un and eleven will be yn. (This does mean that each syllabic numeral can be either 2 or 3 characters long.)

I won’t go into further detail about the syllable mapping. The following chart will be more clear than a written explanation:

0-9:         ja,    je,    ji,    jo,    ju,    jy,   jan,   jen,   jin,   jon, 
10-19:      jun,   jyn,    ka,    ke,    ki,    ko,    ku,    ky,   kan,   ken, 
20-29:      kin,   kon,   kun,   kyn,    la,    le,    li,    lo,    lu,    ly, 
30-39:      lan,   len,   lin,   lon,   lun,   lyn,    ma,    me,    mi,    mo, 
40-49:       mu,    my,   man,   men,   min,   mon,   mun,   myn,    pa,    pe, 
50-59:       pi,    po,    pu,    py,   pan,   pen,   pin,   pon,   pun,   pyn, 
60-69:       qa,    qe,    qi,    qo,    qu,    qy,   qan,   qen,   qin,   qon, 
70-79:      qun,   qyn,    ra,    re,    ri,    ro,    ru,    ry,   ran,   ren, 
80-89:      rin,   ron,   run,   ryn,    sa,    se,    si,    so,    su,    sy, 
90-99:      san,   sen,   sin,   son,   sun,   syn,    ta,    te,    ti,    to, 
100-109:     tu,    ty,   tan,   ten,   tin,   ton,   tun,   tyn,    va,    ve, 
110-119:     vi,    vo,    vu,    vy,   van,   ven,   vin,   von,   vun,   vyn, 
120-129:   jeja,  jeje,  jeji,  jejo,  jeju,  jejy, jejan, jejen, jejin, jejon, 
130-139:  jejun, jejyn,  jeka,  jeke,  jeki,  jeko,  jeku,  jeky, jekan, jeken, 
140-149:  jekin, jekon, jekun, jekyn,  jela,  jele,  jeli,  jelo,  jelu,  jely, 

For example, decimal 308,745,538 (the US population according to the 2010 Census) would be expressed in this system as jepunrinrenpun.

  1. I looked at words appearing in the Brown Corpus (W. N. Francis and H. Kucera, 1979), as distributed in the Natural Language Toolkit (nltk) library for python. For each set of 6 consonants, I looked at the total count of words in the corpus which contain only those consonants (along with vowels, including y). Excluding any of {jklmn} from consideration, the consonant set {fhrstw} results in the highest total word count.

    Looking only at words which alternate between consonant and vowel, the result is the same: {fhrstw} Looking only at words which alternate between consonant and vowel and which begin or end with a vowel, the highest scoring set is {bfhrst}

Comments or questions about this page? Please send a message to RobertMartinWinslow at gmail dot com. Feedback is welcomed.