The question of terminology
The study of handwriting, or rather writing systems, is practiced by a lot of different kinds of people, and each kind have tended to devise their own terminology, which have hardened by use and custom. These terminologies have been produced to meet the ad hoc day to day needs of the particular discipline involved, whether medieval paleography or modern graphology or modern forensic handwriting analysis, without perhaps too much thought to a theoretical base that would cover all writing systems and all aspects of writing, rather than the script or aspect of writing under consideration. I suggest that we should try and to base our terminology on this more general view, though we should of course respect the use and custom of those who are going to use our material (because otherwise they are likely to be upset).
This theoretical work has already been done. The work of Haas and Sampson sets out the terminological base for the study of any writing system, from the point of view of the linguistics of writing system, and in what follows I am largely paraphrasing their work; I also use the OED to determine use and custom.
Clashes between the view put forward by linguists and those of other kinds of writer about writing abound. For instance, I would like to say that the fundamental unit of any writing system is the graph. Here the OED is unhelpful:
n.3Philol. ... A visual symbol representing a phoneme or a segment or feature of speech; esp., a letter, or one of its occurrent forms, or a combination of letters.
Writing systems do not represent speech. Quotation marks, for instance, have no speech counterpart, which is why speakers make odd hand gestures when they want to say them. The relationship between spoken and written language is that they are each dialects of the same (originally spoken) language.
I think the best way to proceed is to work by analogy with the study of spoken language, which for historical reasons is much more developed than that of written language. So I will first sketch out the way in which spoken language is described.
the analogy with spoken language
In phonetics, one would say that the fundamental unit of spoken language is the phone, which is
1. An elementary sound of spoken language; a simple vowel or consonant sound.
A phone is the actual minimal signifying noise made in any actual real life speech act. If I say class, I am producing four phones.
Any phone is an allophone of a phoneme. In other words, when the Queen says class and when I say it different sounds will be heard: in particular, her /a/ and mine are completely different. But not so different as to make any native speaker of English think I am saying a different word to the one she is saying. The difference between those two /a/s is allophonic, and both versions (allophones) of /a/ are members of the phoneme /a/, which contains all the noises that English speakers would tolerate as acceptable realizations of the /a/ noise.
These of course vary from language to language. So in French the vowel in tu and that in tous are phonemically different, because are heard as distinguishing two different words; whereas in English the same two sounds are not phonemically different: if we heard someone say the English word you, which usually has something like the tous vowel, with the tu sound instead, we wouldnt think they were saying a different word, we would just say they had a Scottish accent.
If we translate that terminology over to written language, we have the following. I would suggest that the fundamental unit of written language is a graph: an elementary graphic shape in any writing system that will express the kind of minimal unit that that system uses, whether it is phonetic (expressing sounds) or logographic (expressing words or morphemes (for which, see below). A graph is, strictly, the actual minimal signifying shape produced by any writer in the act of writing, though it is usual and acceptable to use graph more generally as for instance <a> is a graph in the roman alphabetic system. If I write class, I am producing five graphs.
Any graph is an allograph of a grapheme. If I see
then I am seeing very different graphic shapes, but I know I am seeing the same word each time: each of the five graphs are allographs of the graphemes <c> <l> <a> <s> <s>.
Now, when I write <class> and when someone else does the allographic differences between the graphs may be idiographic. That is, characteristics of the writing may demonstrate that I wrote it and not anyone else. Idiographic aspects of handwriting have the following characteristics.
Firstly, they are cumulative. You cannot establish identity on the basis of a few idiographs, though obviously the more idiosyncratic the writing, the more this is possible. Secondly, idiographic characteristics have several levels: they indicate membership of a sub-class of the general class of writers of that script, but there may be many sub-classes which any individual can be a member of, and which can show up in the writing: a generation, a gender, an emotional or physiological state (terrified, or drunk), and so on; one of these sub-classes is the sub-class of one that only that individual is a member of.
Here are some more terms that are relevant to the cuneiform material.
word and morpheme
A fundamental unit of any language is a word. Our writing system designates words very clearly by putting a space before and after them, though I believe linguists find it very difficult to define the word word in a rigorous manner. Words can be further split into morphemes.
1973 Sci. Amer. Feb. 57/2 Every language has a stock of several thousand morphemes: the bearers of the basic semantic and grammatical content. An expression such as can openers comprises four morphemes: can, open, -er and -s.
A morpheme is a minimal unit of meaning. This is quite different from a syllable, which is a unit of sound: a morpheme may have several syllables, for instance catamaran.
Any system of writing may be logographic or phonographic. Phonographic writing indicates (more or less efficiently) how it is to be spoken; logographic writing expresses a word or morpheme without necessarily showing how that word is pronounced. So for instance the numeral <1> is a logograph, and refers to the word one, or un, or ein, and so on.
Logographs may or may not have a pictorial component. If they do, they are said to be motivated; if not, they are arbitrary. The numerals <1> and <0> can be said to be motivated (and could, it occurs to me, be read in as Freudian a way as any cuneiform sign) but the numeral <8> is not (as far as I can see) motivated: its shape is arbitrary.
The highest level we refer to is the script. This is presumably in OED sense 3:
3. A kind of writing, a system of alphabetical or other written characters.
I think this is appropriate as a general term, though the more precise expression writing system is better. You can use the same script to express different languages, though usually there will be variations in the script as applied to those different languages: French and German and English writers use the same writing system, but French people need the cedilla and Germans the umlaut.
Here are two words which it is advisable to avoid. They both derive from Western misconceptions of Chinese writing.
Pictographic refers to the pictorial content of motivated logographic writing, but suggests that the writing system is readable simply by looking at the pictures. No known logographic system is thus interpretable. Ezra Pound claimed to be able to read Chinese without any previous knowledge of the language. He could only make that claim because he had no knowledge of Chinese.
Ideographic is also used of motivated logographic writing, and derives from the view that there could be an ideal writing system where you have one symbol for every concept in the intellectual universe. It was thought (in England, in the late seventeenth century) that this would put a stop to languages unfortunate innate creativity and prolixity, thus making the world a much tidier and safer place. Fortunately there can be no such script. <10> does not express ten-ness, it expresses the word ten (or dix or zehn). It was thought that Chinese was such a writing system. It isnt.