This is twoth in the sense of 'second', rhyming with tooth; not the combination of twee and Goth, rhyming with moth.
A correspondent writes to say she heard someone say 'a thirty-twoth of an inch' rather than the expected 'thirty-second', and wonders whether I know this usage, as it's the first time she's encountered it.
As a playful alternative to second it's been around a while, though the OED has no file on it. I can recall playing with this word as a child, and saying such things as twenty-oneth and twenty-twoth. Certainly, the force of analogy from the usual -th ending has had an impact on the irregular first, second, and third, so we do find oneth and threeth as well.
There's plenty of playfulness online. I've just done a quick search and found chapter the twoth, the twoth of July, part the twoth, and many more, as well as quite a wide range of jocular expressions relying upon it. One person bought a second toothbrush and called it a twothbrush. US columnist Larry Levy has a piece on two-player games headed The twoth, the whole twoth, and nothing but the twoth.
The word has a minimalist entry in Wiktionary, so plainly it is widely recognized. It's labelled 'nonstandard', and that's correct. But is there any evidence of a usage in standard English? Yes, in mathematics and computing, where such forms as nth and zeroth are also found. We find such expressions as 'the twoth-complement number'. I don't think this use of twoth is especially frequent, but it exists.
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Cf the printing terms 32mo (thirty-twomo) & 64mo (sixty-fourmo). This series starts out bravely in Latin (quarto, octavo), but begins to falter a bit when it gets to 16mo (sextodecimo/sixteenmo), & finally tails off into English.
You note that twoth is used in mathematics and computing, and you mention the terms nth and zeroth.
I frequently encounter the -th suffix in a slightly different usage - coolth (how cold something is; cf.'warmth', how warm something is). This term is often used in the field of construction research, and I first encountered it in a paper written by an Australian. In Australia, of course, building designers are far more concerned about coolth (keeping the building cool) than our European engineers who worry about warmth (although climate change might mean coolth becomes an issue here too!).
I wonder whether adding the -th comes more easily to scientists/technicians, as in 'a thirty-twoth of an inch'?
Interesting - but note that this is etymologically a different suffix (see the OED entries at -th, where the two types are distinguished). Incidentally, there's nothing new about coolth. The OED first citation is 1547.
Well, you already have 'fourth', so all you need is to rationalise the series with 'threeth' and 'fiveth' and you've more or less done everyone a favour! *grin*
An analogous situation arises in chemistry, where the hydrocarbons begin with methane, ethane, propane and butane (for those with 1, 2, 3 and 4 carbons). They then adopt a more rational approach for the rest, with pentane, hexane, heptane, octane and onwards in Greek.
As a child I once asked my father, "What is the 'th' number for twenty-one?", and utterly failed to make myself understood. I wasn't able to adequetely express the question back then...
I'm dubious about 'the twoth-complement number'. I never encountered it while studying maths or working as a software engineer, and a Google search doesn't turn up anything much (there are a couple of hits, but I think they are errors for the much commoner two's complement).
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