A family of languages is called arithmetic if each infinite language in it is such that its length set contains an arithmetic progression. It is proved that there exists an ETOL language which is not an arithmetic substitution of any EDTOL language. This result shed some light on the question: How much more “complicated” are ETOL languages than EDTOL languages?
Ehrenfeucht, Andrzej and Rozenberg, Grzegorz, "On Arithmetic Substitutions of EDTOL Languages ; CU-CS-096-76" (1976). Computer Science Technical Reports. 94.