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The smallest building blocks of meaning in a language are called morphemes. Walk, for example, the basic form of the verb, is a morpheme. We can’t break it down any further in terms of meaning. Wal, for example, doesn’t mean anything in Modern English, and nor does alk. The basic form, walk, is what you’d look up in a dictionary, and it’s used when we say I walk, you walk, we walk, and they walk, and also when there’s no particular person attached to the verb, as in He prefers to walk. When we’re talking about someone other than you and me or you and us or several other people, we add -s to the basic form to produce he walks and she walks.
If we add –ed we can create the past tense, they walked. That ending also forms the past participle that allows us to say things like we have walked. Finally, we can add –ing and get walking, and that allows us to make constructions like we were walking. It also means we can say things like Walking is good for your health.
So walk can occur in four different forms. Because it can stand on its own it’s called a free morpheme. It contrasts with the morphemes -s, -ed and –ing which are of no use on their own. To make any sense they have to be tied, or bound, to a free morpheme, and so they’re known as bound morphemes.
Now, take a word like recalculation. That happens to be a noun, but at the heart of it there’s the verb calculate. We can’t break that down any further in terms of meaning, so we can conclude that calculate is a morpheme, and, because it makes sense on its own, it’s a free morpheme. But we can create a noun from it by dropping the –e and adding –ation to give us calculation. -ation cannot be further broken down in terms of meaning, so we can conclude that it, too, is a morpheme, and, because it cannot stand alone, it’s a bound morpheme. If the process of calculation happens more than once we can place re- , another bound morpheme, in front and get recalculation.
A final note on bound morphemes. The bound morphemes -s, -ed and -ing can be added to a verb to show how we want the verb to be understood, but they don’t change its basic meaning. They’re called suffixes because they come at the end of the verb, and because they merely modify the verb, they’re called inflectional suffixes. They contrast with a morpheme like –ation, which creates a new kind of word, a noun. Because they allow us to derive one word from another, suffixes like that are called derivational suffixes. When bound morphemes occur at the beginning of a word, like re-, they’re called derivational prefixes.
Caxton 
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Not sure I got that last sentence – is ‘re-‘ derivational or inflectional? Does it modify the verb, or change it more essentially?
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The prefix re- when added to calculation produces a new word, recalculation, with a different meaning. It is thus a derivational morpheme. Inflectional morphemes don’t change the meaning of a word, but rather indicate its grammatical function. There are in fact only eight inflectional morphemes in English. A noun can be modified by -’s (sometimes –s’), and –(e)s, a verb by –s, -ing, -(e)d and –en and an adjective by –est and –er.
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Thank you. Tiny steps for little feet.
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Two interesting special cases are (neo)classical compounds and cranberry morphs. The former are made entirely of bound morphemes, like biography = bio- ‘life’ and -graphy ‘writing’. The latter contain morpheme-like forms without an identifiable meaning because they appear only in one word, like mul-berry and rasp-berry against black-berry and blue-berry. (Cranberry is not actually a good example, because cran- is just a variant of crane; the independent word rasp has nothing to do with the rasp- in raspberry.)
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I had wondered whether the first part of ‘calculate’ was a morpheme in Latin, but apparently not.
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Oh yes. Calculatus is the past participle of calculare, from calculus ‘pebble’, which in turn is from calx ‘limestone’ and -ulus, a diminutive ending.
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Thank you. I dimly remember that, and a little further research in the OED would have reminded me.
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Did mul or rasp have independent meanings in earlier forms of English?
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The OED gives ‘mulberry’ as a Germanic word which is derived ultimately from ‘morum’, the Latin word for a mulberry tree.
The OED concludes that origin of ‘rasp’ in ‘raspberry’ is a mystery.
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Ouch. I wish you’d install the WordPress preview plugin.
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I’d need to be a customer of WordPress.com Enterprise to do that, which would presumably cost me money. Anyway, I’ve edited your comment, which is, as always, welcome.
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Thanks.
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“we can conclude that calculate is a morpheme, and, because it makes sense on its own, it’s a free morpheme. But we can create a noun from it by dropping the -e and adding -ation to give us calculation. -ation cannot be further broken down in terms of meaning, so we can conclude that it, too, is a morpheme, and, because it cannot stand alone, it’s a bound morpheme”
A little nit: All we add is -ion if we drop the -e from calculate (not -ation). I would say calcul- is the root morpheme, which is bound in English (if not in Latin, I don’t know). -at- is an affix, -e and -ion can be added to it, but I imagine calcul-us is the same root, no?
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‘-ation’ is what the OED gives as the suffix. ‘Calculate’ is from ‘calculat-’ , the participial stem of Latin ‘calculare’. ‘Calculate’ seems to be a morpheme in that it cannot be further broken down into any constituent English morphemes.
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I’d say that from a linguistic (but not necessarily a lexicographic) standpoint, the morphemes of calculation are calcul-ate-tion.
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