Morphology is the study of the formation and inflection of words. It studies how morphemes (the smallest units of meaning) are combined to form words from components such as roots and affixes. For example, the word dogs contains two morphemes dog and the plural s.
Morpheme is the smallest meaningful unit of language. A vocal-auditory morpheme is composed of phonemes, the smallest units of sound. A written morpheme is composed of graphemes, the smallest units of a written language (e.g. alphabetical letters). A visual-manual morpheme is composed of parameters (and their primes).
E.g. "dog", "un-", and "-able" in English. E.g. #DOG and APPLE in ASL.
Free morpheme is when it can stand alone as a word. Free morphemes in English, for example, are: dog, stop, smile, etc. ASL: again, love, see, your, etc.
Bound morpheme is the smallest meaningful unit that cannot stand alone. These bound morphemes are the affixes attached to words. E.g. -s, -er, -ed, un-, -able, etc.
The English word dogs has two morphemes (dog and s); unstoppable (three morphemes: un, stop, able); abnormal (two morphemes: ab, normal).
On the other hand, the ASL sign teacher has two morphemes: teach and agent (person). Another example is a numeral handshape which is affixed to a ASL word. E.g. seven-day, two-week, six-month and so on. This process is known as called numeral incorporation .
 Numeral incorporation are described in works by Scott Liddell and Robert E. Johnson.
Clayton Valli, et al. "Linguistics of American Sign Language: An Introduction." Washington, D.C.: Gallaudet University Press. 2005. Pp 17.
Charlotte Haker-Shenk and Dennis Cokely. "American Sign Language: A Teacher's Resource Text on Grammar and Culture." Washington, D.C.: Gallaudet Press. 1980.
word formation (compounding and blending) in sign language linguistics.
You may also be interested in phonology.
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