Final answer:
Friedrich's ataxia is the genetically inherited neurological disorder that is not acquired by autosomal dominant heredity; it is inherited via an autosomal recessive pattern.
Step-by-step explanation:
The question asks which genetically inherited neurological disorder is not acquired through autosomal dominant heredity. Among the options, Friedrich's ataxia is the one that is inherited through an autosomal recessive pattern, meaning a person must inherit two copies of the defective gene, one from each parent, to express the disease. Disorders like Huntington's disease, myotonic dystrophy, tuberous sclerosis, and neurofibromatosis, by contrast, are inherited in an autosomal dominant pattern, where only one copy of the faulty gene is sufficient for the disease to manifest.