Sorry, too 
What we have as denominator values:
(1), 2, 4, 8, 16, (32)
So you´re missing 3 or 6 or 9 for example? Use triplets or i.e. 3/8 time signature!
You´re missing 5 or 7 or 10? Use quintuplets or septuplets or i.e. 5/8 or 7/8 time signatures!
All this can be done already. You don´t have to make changes to the way music is notated. You don´t have to invent “new” mesures.
Classical composers with far out ideas were and are able to deal with that system.
Your example “11/12 having 3 full triplets + 2/12”
can be written as || 3/8 | 3/8 | 3/8 | 2/8 || or || 6/8 | 5/8 || depending where the “beat” shall be.
Composer Peter Maxwell Davies did exactly this in his opera “The Lighthouse”, for which I had the opportunity the play guitar this year. Get the score and see how he does it. This opera is full of the most far out rhythms imaginable, all notated with usual meters, x-tuplets and polyrhythms.