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I wonder if this practice, very simple and needs nothing but the breath and
voice, is a way of purifying the body through vibration.

Hi RT,
That sounds very good indeed. I love the way you are aware of all the physical sensations throughout your body whilst reciting the mantra. 'Awareness of body' is crucial as Buddha Dharma is sometimes treated as a head trip.
The beautiful thing is that your mind is dropping its usual stuff and your awareness is becoming unbounded. This process itself is real purification.
namaste
Kris