Piraha is hardly the only language which has a pure-tonal mode; such things are relatively common throughout the tropics, as I understand it. However, as I understand it the tonal modes of these languages tend to be pretty restricted compared to the full modes, since they lose too much information, and can only effectively communicate a limited suite of phrases and messages composed from those phrases.
Note that much of the research involving Pirahã is dubious.
Piraha is hardly the only language which has a pure-tonal mode; such things are relatively common throughout the tropics, as I understand it. However, as I understand it the tonal modes of these languages tend to be pretty restricted compared to the full modes, since they lose too much information, and can only effectively communicate a limited suite of phrases and messages composed from those phrases.