Pronouncing Base 6 Numbers

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What's the best way to pronounce heximal numbers?

One could just read them out like they're decimal: "21" being pronounced "twenty one", etc. But that leads to some confusion when mixing heximal and decimal numbers in conversation, and more generally just confuses people who are currently used to only using decimal numbers. It also makes phrases like "base ten" confusing/ambiguous - which base is that 10 in???

Instead I'll propose two simple possibilities, both of which I like for different reasons. One sticks close to decimal while remaining distinguishable; the other is much more foreign but has fun and interesting numerical and syntactic qualities.

How To Pronounce It Like Decimal

(Several aspects of this are inspired by jan Misali's method, but I don't like all the details of their proposal.)

All the individual digits are pronounced normally, as in decimal English: zero, one, two, three, four, five.

All the "teens" (two-digit numbers with a 1 in the tens digit) are also pronounced like in decimal English: 10 is "six", 11 is "seven", 12 is "eight", 13 is "nine", 14 is "ten", and 15 is "eleven".

Higher numbers are pronounced akin to how decimal does it, just with a different suffix. Rather than appending -ty, append -sy: 20 is "twosy", 21 is "twosy one", 32 is "threesy two", etc with "foursy" and "fivesy". (Note: English phonotactics dictates that all of these S's become voiced, pronouncing as "z".)

After two digits, use "quat" to indicate the third digit: 123 is "one quat twosy three".

Always group quats into two digits: 1234 is "eight quat threesy four".

Then use thousand/million/billion/etc for larger numbers, grouping by 4 digits (rather than by 3 like in decimal; 4 heximal digits are roughly equal to 3 decimal digits): 1,2345 is "one thousand twosy-three quat foursy-five"; 1,0203,0405 is "one million, two quat three thousand, four quat and five".

Justification

Keeping the single digits same as in decimal is obvious; all bases do that already.

Pronouncing 10₆ as "six" isn't too unusual, from what I understand of other base-pronunciation schemes. Having a unique word for your 10 value helps in talking about it, so you don't constantly have to mutter "base six" after every mention of "ten".

For the rest of the 1X values, continuing to use the decimal names makes them simple and easy to remember. Also, the 1X's don't yet have the ability to do the unifying suffix pattern that the higher values do (which I'll get to in a sec), so they've gotta be weird somehow anyway; this is why decimal has the unique "X-teen" variant (shortened from "X and ten"). As a bonus, decimal has unique weird words for all the values we need; it doesn't start systematizing them (which would feel weird carrying over into heximal) until thirteen.

For 2X and after, I use a naming scheme distinguishable from but obviously inspired by decimal. 20⏨ in decimal was originally "two tens"; English shortened the "tens" to a -ty suffix (and lightly modifies "two" and "three" to sound better with the suffix). If we follow the same pattern in heximal, 20₆ is "two sixes", shortening to "twosy".

An accidental nice feature of this over decimal is that it lacks the "thirteen/thirty"/etc confusion that decimal has; a final "n" is hard to hear in some circumstances. In heximal, "nine" and "thirty" are totally different-sounding.

For higher values, "quat" was chosen because (a) it sounds good and unique, not easily confusable with any other numbers, and (b) it's a shortening of "quarter gross", because 100₆ is indeed one quarter of 144⏨.

For even higher values, I'm just reusing thousand/etc because it's not that important; if you're actually saying values that large you're probably already in a context where base 6 is assumed.

How To Pronounce It Not Like Decimal

(This system was suggested to me by @berenryan, apparently cribbed from their old notes talking to fellow conlang nerds. )

The previous method has the nice benefit of being familiar; everyone will understand you with an absolute minimum of confusion or required teaching. But it inherits the arbitrary historical structure of English numbering, which is OK but not great for several reasons.

If you're willing to get a little weird and deal with the fact that nobody will understand your numbers (but have the satisfaction that in a theoretical world where everyone learned it as kids, it would be better than the first method), here's a much better system.

First, the digits. 0 is "pa" (like in "papa"), 1 is "be" (like "bay"), 2 is "ti" (like "tea"), 3 is "do" (like "d'oh!"), 4 is "ku" (like "coup"), and 5 is "gr" (like "grrrr" but not drawn out). Note that all of the vowels are Spanish-style, not English-style.

When speaking numbers larger than a single digit, group them into pairs and pronounce each pair as follows:

+0+1+2+3+4+5
00pamabefativadonakusagaza
10peŋebimetofeduvekanegese
20piziboŋitumidafikevigini
30posobuzotaŋodemokifogovo
40punubasutezudiŋukomugufu
50pavrbenrtisrdozrkuŋrgamr

(ŋ is pronounced "ng")

So the basic patterns:

  • the first letter corresponds to the ones digit; anything with a 0 ones digit starts with a "p", etc.
  • the last letter corresponds to the tens digit; all the 1_ values end in an "e", etc.
  • the second and third letters cycle between five vowels and seven consonants, respectively, so they correspond to the value of the number modulo 5 or 7.

Larger numbers work the same as in the previous system; use "quat" after two digits and then thousand/million/etc after 4/8/etc digits.

So, 1,2345 is "befa thousand, dafi quat gufu".

Justification

This is actually a pretty brilliant setup for several reasons.

  • First, the digit names are obviously chosen to just use the Nth first/last letter; they also (aside from gr/gaza) are the first syllable of the 0_ numbers, since the second and last letters cycle thru the same vowels for the first five values.

  • Second, the sounds are well-chosen to be regular but distinguishable. The first consonants are all plosives, alternating between unvoiced and voiced; the second consonants are a collection of nasals and fricatives. Choosing consonants this way gives each word a sharp, distinguishable start that won't blend into other words, and then softens into a blending sound in the middle that carries stress well.

  • Third, the words all have significant redundancy, which helps with hearing. It's common for invented systems like this to be minimally redundant; it would have been easy to just produce two-letter words from the first and last letters of these words. They'd all be unique, so that technically works, right? In real conversation tho, where people might mumble, or the room might be noisy, or a radio might be crackling, distinguishing between some of those sounds can be quite difficult; this is why military jargon pronounces 5 and 9 as "fiver" and "niner", because "five" and "nine" sound remarkably similar over a low-bandwidth radio and the addition of the "er" sound forces us to emphasize the "v" versus "n" and makes them more distinct.

    In here, the first and fourth letters cover 6×6 unique combinations, for the 36 possible values, but the second and third letters cover 5×7, or 35, possible values, meaning they're also almost completely unique across the set of numbers. (Only 0₆ and 55₆, pama and gamr, share their center letters.) As well, the two sets tile their combinations in different ways, so if two sounds are kinda similar they won't show up together multiple times. If someone is shouting across the room and you're not sure if they said "pizi" or "bizi", well, only one of those is the name of a number. If you can correctly hear any two letters in the word, you can almost always tell which number it was; you've got to fuck up really bad to mishear it.

    (Of the six possible pairs of letters you could hear, three of the pairs uniquely identify a number in every instance; one (the center two letters) has a single collision, between 0₆ (pama) and 55₆ (gama); and two (the first and second letter, or the second and fourth letter) have six collisions, as each 0₆/_5₆ or 0₆/5_₆ number collides.)

  • Fourth, it puts divisibility right into the name of the number: numbers divisible by 2 start with "p", "t", or "k"; numbers divisible by 3 start with "p" or "d"; divisible by 5 has an "a" in the second position; divisible by 7 (11₆) has an m in the third position.

    This scales above two-digit numbers, using the divisibility trick for values one above a base: if you add together all the digit pairs, the original number is divisible by 11₆ if the result is. So 1,2345 becomes 1+23+45, or 113, which is 1+13, or 14; that's kane, which is |5 (due to the second letter being "a") but not |7 (since the third letter isn't "m"), so 1,2345 is |5 but not |7. (The trick happens to work for the value one below the base, too; it's an elaboration of the simpler "add all the digits" trick that works for only the value one below the base.)

    (This ties into the ease of identifying primes in base 6; all the primes past 6 start with "b" or "g", and among the two-digit numbers, every single b- or g- word is prime with only two exceptions, 41₆ and 55₆. In this system those are basu and gamr, both of which are obviously (to someone raised in this system) divisible by five because of the "a" sound.)

  • Fifth, some studies have shown an inverse correlation between the number of syllables in the names for numbers and the amount of numbers a person can remember at once. That is, in languages where digits are shorter to say (like Chinese, where they're all single-syllable), people can remember longer numbers than in languages with longer digit names (like English, with "seven" being two-syllable and several of the digits being four or five letters, and almost of the names for the tens digits being two or three syllables). In this system, each digit is a single syllable; all two-digit numbers are two syllables; writing out a pronounced number requires exactly twice as many letters as writing it out in digits. That's about as small as you can get things!

  • Sixth, having a dedicated and very short system for pronouncing all the two-digit values is convenient for "senary compression", the act of grouping heximal digits into pairs and treating them as units. Since base 6 is a little on the small side, this can be useful when talking about or remembering long numbers (this is the same reason octal and hexadecimal are useful, as compression methods for reading/discussing long binary numbers).

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I'm pretty sure it's a marvelous way to fuck things up in a child's brain. We already have to deal with language irregularities. It's not "nine-ten-to" it's "ninety-two". In french, it's not "neuf-dix-deux" it's "quatre-ving-douze" which is "four-twenty-twelve". Try to gain a child's trust in calculus with that... it selects only the ones focusing on the graphical writing of numbers, and leave all others on the side of the road. So i suggest you take these fancy ideas about numbers and languages and put them in a bin, and then go to golf, or billiard, or bowling. Hell, even play violin.

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Re #1: Congrats on missing the entirety of the point! This is about a world in which we're already using base 6, not imposing a bizarre base-36 naming system on top of the existing base-10 numbering system.

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