Double, triple, quadruple, …

I recently needed a word for “multiply by 13” that was parallel to quadruple for “multiply by 4”, so I made up triskadekaduple by analogy with triskadecaphobia. That got me to wondering how you make words for multiples higher than four.

The best answer is probably “don’t.” Your chances of being understood drop sharply after quadruple. But despite the warning sign saying “hic sunt dracones” we forge ahead.

Double, triple, and quadruple are based on Latin names for numbers, so we should keep using Latin prefixes. Next would be quintuple, but I expect you would likely be understood if you said pentuple based on Greek penta-.

Next would be sextuple, septuple, and octuple. These terms are understandable, particularly in the context of multiple births: sextuplets, septuplets, and octuplets.

But now we hit a brick wall. The Latin prefix for nine is novem-, and it’s unlikely anyone would understand novemple or anything like that. The Greek prefix ennea– is no better. Enneauple? Enneaduple?

(The Latin prefix novem– is recognizable from November, which is the 11th month, so does that mean novem– stands for 11? No, November really is the ninth month, or at least it was when the year started in March.

The only example I can think of for a word starting with ennea– is the enneagram personality classification system.)

The prefixes after novem– are equally obscure. But if we jump to 13, some people will have heard of triskadecaphobia. This comes from tris kai deka (three and ten) from Greek. But I would only use triskadecaduple tongue-in-cheek.

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10 thoughts on “Double, triple, quadruple, …

  1. “Nonuplets” appears to be the accepted word for nine children in the same birth, but “dectuplet” is apparently preferred over “decuplet” for ten, so nonuple, dectuple and tredectuple would appear to be the right multiplier words for 9, 10 and 13.

    One alternative is “increase n-fold” where n is either a numeral or number name, e.g. 9-fold, ten-fold, thirteen-fold, etc.

  2. Interesting. Just a personal perspective here: reading this, when you got to quintuple and sextuple, my reaction was “those are just words”. Not very frequently used words, and not ones I go out of my way to use, but not anything that needed inventing. Past that I assume it’s been figured out at some point, but I agree they won’t be clear to most audiences.

    About 13: To me, “triskadectuple” sounds better. I have no idea whether this is more etymologically sound however.

  3. 7-tuple, 13-tuple it.

    I enjoy coining the occasional neologism[*], showing off to an unappreciative world how clever I am by assembling new dracones or chimeres (ha, pedantically Greek feminine plural there). Yet sometimes simple clarity lets us duck how thin our classical Latin and Greek can be when we only picked it all up through osmosis instead of study. Also, it saves the coiner the embarrassment of stitching up a chimera of a Latin root with a Greek one. Like, we say quintuple and not pentuple, pentagon and not quintagon.

    [*] Once I was studying the behavior of Bresnahan’s circle algorithm, working with integers, no antialiasing, black&white pixels. To draw a filled circle of radius r, nest outline circles of all radii from 0 to r. But if you’re drawing with XOR, it is necessary to draw each pixel exactly once — no gaps, obviously, but no overlaps either. What word describes unfilled circles that nest perfectly? After some etymological research, I called them “adjacerable annuli”. In fact: above, instead of “stitching up a chimera” I first wrote “adjacerating” the roots. Sometimes in straining for wit, one gets exactly halfway there.

  4. Not sure how reliable it is as a source, but wiktionary.org has an entry for “tredecuple” which defines it as meaning a tuple of thirteen thing. If it’s legitimate, then lagomoof seems to have been basically right.

  5. I looked in the Oxford English Dictionary and it does have an entry for “tredecuple”, however the only reference to its usage is by Sir Henry Billingsley in his first English version of Euclid’s Elements published in 1570, so I don’t think the OED are wrong when they call the word obsolete and rare! The details given are “Elements Geom. xvi. f. 453 To proue that an octohedron geuen, is tredecuple sesquialter to a trilater equilater pyramis inscribed in it”.

  6. I guess when you have a multiplicity of tuples we just use the word multi-ple?

    (my benighted contribution to the 1/2-wit category…)

  7. Simplex, duplex, triplex, et sic et semper.
    So: Latin, certainly not Greek, and the general rule for going from Latin to (Latinate) English is an extremely simple one: drop the ‘x’.
    I do not have enough Latin to know what, by regular formation, is the successor to octuplex.
    Meanwhile, fourfold, ninefold, thirteenfold, etc. are English — and they are literal cognates, which are the class of words in which the case for employing Latinate English is weakest.

  8. Some thoughts: In classical Latin, septemplex and septuplus were used; since we have septuple in English, nonuple would be appropriate. A parallel can be drawn between the names from triple onwards and those from trillion onwards (quintuplequintillion etc.; replace -iple/-uple by -illion). In Italian, there is vigecuplo (20-fold), on the other hand, we have vigintillion (though Hahnemann wrote vigesillionfache Verdünnungvigesillion-fold dilution) and I have seen vigintuple mentioned in English.

    Overall, the naming may seem inconsistent, but perhaps we can make sense of it from an aesthetic point of view: If the ordinal stem ends in -t, take it (sextus ‘sixth’ → sextuple); after all, the ending -tuple in words such as quintuple gave us the term tuple (this does not lead to tertuplex since the inflectional stem of the ordinal tertius ‘third’ is terti-, not tert-). Otherwise, take the cardinal numeral, but use the familiar form quadr- instead of quattuor and the form non- for 9 (as found in the ordinal nonus, from *novenos, derived from the cardinal *noven which became novem through the influence of decem); nov-, in contrast, might seem like meaning ‘new’. Henkle took the standard zillion names up to duodecillion as a basis and thought that analogy demands the use of ordinals. This is dubious because -im is part of the inflectional stem of septimus and decimus and -av belongs to the inflectional stem of octavus. After striking these out, we are still left with three exceptions. He even wrote Vigillions, Trigillions etc. (thus striking out -es). Rudolf Ondrejka was more consistent in his use of additive elements (employing septimo and octavo while Henkle used septo and octo, but on the other hand decimo, vigesimo etc.) but retained the dictionary word vigintillion and still used additive elements derived from ordinals with it – e.g., primo-vigintillion, mixing an ordinal with a cardinal (the cardinal coming last!) in the same word. I reject that.

    In a Latin grammar from 1575, I have found vigecuplex simplex ‘21-fold’. This is analogous to two-word constructions such as vigesimus primus ‘21st’, but in English, we presumably want a single word. It would be grammatically correct to say one thousand vigintillion, one million vigintillion etc., but how are we going to call a 21-tuple? We say twenty-first (there is even unetvicesimus in Latin, literally one-and-twentieth), so trigintisextuple (found in the OED!) may come across as a reasonable analogy (I would prefer triginta to the combining form triginti-, compare with Italian trentasettesimo; on the other hand, we have centimillionaire, but one might misinterpret centi- to mean ‘one hundredth’). Latinists might prefer putting two ordinal numerals together (trigesimussextuple), but this would make the system more complicated. Since million does not actually contain a constituent m-, I do prefer vigintiunillion to vigintimillion for the 21st power of 1000 after 1000.

    The Nasdaq.com Glossary contains words such as septenvigintillion (as if they were used in FINANCE, ha!) where the numerals before the multiples of 10 are the same as in undecillion, duodecillion etc. A problem with this is that the septem is assimilated to septen in septendecillion while this change is uncalled for before viginti. The dictionary word novemdecillion is not consistent with septendecillion either (-n vs. -m), but at least there is no wrong assimilation here. Also note that while one may say unus et viginti (besides viginti unus), this order is not used above 100 (e.g., centum viginti unus) and it is not used in English numerals like twenty-one either. In post-classical Latin, one also finds duocenti, trescenti and the like instead of ducenti, trecenti etc., so duocentuple (instead of centumduple) for a 102-tuple would be misleading.

    For one million, the Romans said decies centena mil(l)ia, but let us agree on mille millia, which leads to millemilluple. We might also employ the modern Latin word millio (thus, millionuple), but duodecillionillion would be structurally ambiguous – is it the two decillionth zillion or the duodecillionth zillion? A further issue is whether the Latin zillion words from which English tuple and zillion words are formed are to be understood according to the short scale simply because the words are formed in English or rather according to the long scale as in French and Italian. To say billillion for one millillion millillion by analogy to billion is artificial to me. Digits are written in groups of 3, we do not use a grouping that would correspond to the schema n-illillion!

    Regarding triskadecaduple, what is the second d doing here? Also note that an i is missing. Triskaidecuple, if you want to mix in ancient Greek.

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