The vast majority of my sources were able to agree on the classifications of:
- Consonantal alphabet or consonatary (e.g. Phoenician, Arabic, Hebrew)
- Alphabet or vococonsonantary (e.g. Greek, Latin, Cyrillic)
- Semanto-phonetic or logographic (e.g. Chinese, Egyptian, Mayan, Sumerian)
- Syllabary or syllabic alphabet (e.g. Cherokee, Kana, Yi)
So I've come to the conclusion that there are five broad classifications of writing systems: consonantary, alphabet, syllabary, alphasyllabary and semanto-phonetic, as well as defectives and mixes thereof. Alphabets and alphasyllabaries may or may not have inherent vowels, but this isn't part of their basic classification. Syllabaries consist of syllabograms that include the syllable nucleus but vary in how they accommodate different types of syllables, such as special orthographic rules or phonograms for initial or final consonants. Alphasyllabaries are similar to syllabaries but have devised a variety of ways to display individual phonemes such as diacritics, rotations, and syllable blocks.
This results in some previously ambiguous writing systems being reclassified as follows:
- Alphabet: Meroitic
- Alphasyllabary: Hangul, Aboriginal Syllabics
- Syllabary: Bamum, Old Persian cuneiform, Zhuyin fuhao, Khom script
- Mixed: Paleohispanic scripts
- Swank, Heidi (2008). It all hinges on the vowels: Reconsidering the alphasyllabary classification. Written Language & Literacy, 11(1), 73-89. doi:10.1075/wll.11.1.06swa
- Pae, Hye K. (2011). Is Korean a syllabic alphabet or an alphabetic syllabary. Writing Systems Research, 3(2), 103-115. doi:10.1093/wsr/wsr002
- Retrieved from http://www.iranicaonline.org/articles/cuneiform-script
- Valério, Miguel (2008): “Origin and Development of the Paleohispanic scripts: The Orthography and Phonology of the Southwestern Alphabet". Revista Portuguesa de Arqueologia 11-2, pp. 107–138.