from The Century Dictionary.
- noun The quality or state of being grammatical, or according to the rules of grammar.
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- noun of language The
stateor attributeof obeyingthe rules of grammar; grammatical correctness.
Sorry, no etymologies found.
This suggests that the notion of level of grammaticalness is not to be considered in determining an abstract underlying order.