Low frequencies mask higher ones, and louder masks quieter- the higher notes will be there, but they will be masked by the lower pitched, louder tones. It's not phase cancellation, but the effect happens at your ears. If you're off axis to the speaker, this will strengthen the phenomena as low frequencies are more omni-directional, whilst higher frequencies are directional; if you're not in front of the speaker, you'll be hearing less of the high frequencies too.
:)