In plain words
All four Vedas came forth from the Gāyatrī mantra itself!
The air we breathe in is the principle of Prakṛti, whose svarūpa is form and name. That is ‘So’. Through this sound we draw in the air of Prakṛti. ‘Haṃ’ is letting it out; that is recaka. The point between this pūraka and recaka is kumbhaka. ‘So…haṃ’: that is, because we keep drawing it in with the very sound haṃsa, they called it ‘Haṃsa Gāyatrī’. Gāyatrī means what has thirty-six letters. That is why in these seven cakras, the Mūlādhāra, the Svādhiṣṭhāna, the Maṇipūraka, Anāhata, Viśuddha, Ājñā and Sahasrāra, there are thirty-six letter-petals. That is why it came to be named ‘Gāyatrī’. What is this Gāyatrī? Who is She? ‘Gāyatrīṃ chandasāṃ mātā.’ The Mother of the Vedas, She whose form is all the deities. The Ṛg Veda, the Sāma Veda, the Atharva Veda, the Yajur Veda: all these four Vedas came forth from this Gāyatrī mantra itself! Wherever we sing, there Gāyatrī is. ‘Gāyan’ means living beings. What protects living beings is Gāyatrī. Only because prāṇa, joined with the vital air, moves through all the limbs and all the nāḍīs of the body, from this Mūlādhāra up to the Sahasrāra, is a living being able to live. Because it protects living beings they called it ‘Gāyatrī’: ‘Gāyantāṃ trāyate iti gāyatrī.’ When we constantly remember and worship such a Gāyatrī principle, it goes on taking shape as a tāraka mantra.
All sounds come forth from the Praṇava alone
When we remember this mantra at all times and in all states, and in all places, it takes shape in the form of tāraka. That is, whatever work we are doing, whatever we are thinking, wherever we may be, to act with the feeling ‘Sarvakarma bhagavatprītyarthaṃ’ is the right meaning of this tāraka mantra.