Bell's extensive knowledge of the nature of sound and his understanding of music enabled him to conjecture the possibility

Enabled – Past Indefinite Active Voice. In the first sentence we can observe a well-known fact happened in a certain moment of time in the past.

had been – Past Perfect Active Voice. In the dependent clause of the complex sentence action has been completed before the action in the independent clause.

offered – Past Indefinite Active Voice. Action in the main clause of the complex sentence represents ordinary well-known fact in the past.

was based – Past Indefinite Passive Voice. Past Indefinite is used to show simple action happened in the past. Passive Voice is used because the subject “harmonic telegraph” receives the action of the verb. We can understand that Bell based his telegraph on the certain principle.