A single note played on an acoustic instrument is itself (typically) a compound of multiple frequencies, usually (but not in e.g. a church bell) in a more or less harmonic relationship.
Furthermore, the overtone series for a nontonal instrument exists; you can tell which of two blocks is higher pitched. But, the overtone series is not the regular one we expect from (half)?open pipes. So it is not treated in the brain as a tone.
This is why bell choirs are either totally awful or completely amazing and never anything in between.