Can anyone chant the Gāyatrī mantra?
traditionally it was given at upanayana; today many teachers and movements openly teach it to all, and families follow their own lineage.
The Gāyatrī is a verse of the Ṛgveda (3.62.10), a prayer to Savitṛ, the divine light, to inspire our intellect. In the classical system it was received from the guru at upanayana (the sacred-thread ceremony) and recited daily at sandhyā. Orthodox Vedic lineages still keep it within that framework, out of respect for the discipline of Vedic recitation.
From the nineteenth and twentieth centuries, reform movements such as the Ārya Samāj and later the Gāyatrī Parivār taught the Gāyatrī openly to everyone, and many respected teachers today encourage all sincere seekers to chant it. Countless people chant it daily with devotion.
Both views come from love of the mantra. If your family or guru follows a particular rule, honour it; otherwise, learning the correct pronunciation and chanting it with reverence is widely accepted.
Source: Ṛgveda 3.62.10 · Traditionally given at upanayana
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