A syllabary is a set of written symbols that represent the syllables or (more frequently) moras which make up words. A symbol in a syllabary, called a syllabogram, typically represents an (optional) consonant sound (simple onset) followed by a vowel sound (nucleus)—that is, a CV or V syllable—but other phonographic mappings such as CVC, CV- tone, and C (normally nasals at the end of syllables) are also found in syllabaries.
A writing system using a syllabary is complete when it covers all syllables in the corresponding spoken language without requiring complex orthographic / graphemic rules, like implicit codas (⟨C1V⟩ ⇒ /C1VC2/) silent vowels (⟨C1V1+C2V2⟩ ⇒ /C1V1C2/) or echo vowels (⟨C1V1+C2V1⟩ ⇒ /C1V1C2/). This loosely corresponds to shallow orthographies in alphabetic writing systems.
True syllabograms are those that encompass all parts of a syllable, i.e. initial onset, medial nucleus and final coda, but since onset and coda are optional in at least some languages, there are middle (nucleus), start (onset-nucleus), end (nucleus-coda) and full (onset-nucleus-coda) true syllabograms. Most syllabaries only feature one or two kinds of syllabograms and form other syllables by graphemic rules.
Syllabograms, hence syllabaries, are pure, analytic or arbitrary if they do not share graphic similarities that correspond to phonic similarities, e.g. the symbol for ka does not resemble in any predictable way the symbol for ki, nor the symbol for a. Otherwise they are synthetic, if they vary by onset, rime, nucleus or coda, or systematic, if they vary by all of them. Some scholars, e.g. Daniels, reserve the general term for analytic syllabaries and invent other terms (abugida, abjad) as necessary. Some system provides katakana language conversion.