A vowel is a phoneme that is made through almost continual airflow through your mouth around your tongue in various ways. These are often caterogized as tense (using some mouth muscles) or lax (using few mouth muscles) vowels. For example [ah] is a tense vowel whereas [oh] is a lax one. You can feel the difference in your mouth when making the sounds.
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Writing System
Definition
A writing system is a method of visually representing spoken language, based on a script and a set of rules regulating its use