Many connections can be found between the praṇava oṃ and the mantra “haṃsa” (sohaṃ). The symbol of the swan, like a bird, is found in the Nādabindūpaniṣad. This image and the connection with praṇava are described there as following:
अकारो दक्षिणः पक्ष उकारस्तूत्तरः स्मृतः।
मकारं पुच्छमित्याहुरर्धमात्रा तु मस्तकम् ॥मस्तकम् १॥
akāro dakṣiṇaḥ pakṣa ukārastūttaraḥ smṛtaḥ।
makāraṃ pucchamityāhurardhamātrā tu mastakam ॥mastakam 1॥
It is believed (smṛtaḥ) the mātrā “A” (akāraḥ) is in the right wing (dakṣinaḥ-pakṣaḥ), the mātrā “U”(ukāraḥ) in the north (uttaraḥ – “north” is “in the left” wing). Thus (iti), in his tail (puccham) is the mātrā “Ma” (makāraṃ), also (tu) they say (āhuḥ), ia half the mātrā, (ardhamātrā) is in his head (mastakam), i.e. nasalized vibration.
This mantra comes from the dhātu of the first verbal group – अव् / av, which means – रक्षण / rakṣaṇa – ‘protection’ (receiving from God, Ishvara). The semi-vowel labial व् / v is transformed into labial उ / u, then it is transformed into ओ / ou with the addition of labial and मन् / man, where only the nasalized म् / m remains, that can turn into a bindu.
This famous mantra is also called प्रणव / praṇava, from the prefix प्र / pra and the root णु / ṇu, which means ‘adoration’. But in this case, the vowel उ / u goes into a strengthened अव / ava, that gives णव / ṇava with the prefix प्रणव / praṇava. In a word, all together this can mean ‘the primary, initial adoration’ from which all forms of worship come from.
There are many other esoteric interpretations of praṇava. The most famous is its splitting into three mātras (अ – उ – म्), to which many traditions give very different meanings.
On the Bhuvaneśwari jayantī I want to write something about her famous and very significant mantra ह्रीँ (hrīm̐), which is sometimes called Mahāmāya–bīja (the seed syllable that includes all dimensions). According to the Vedas, the first sound of the original yajña and creation was the famous praṇava Om. Out of it three mātras (अ – उ – म) three worlds arose, it is also a form of anāhata–nāda creating or absorbing the creation. The practice of nāda is very significant for laya–yoga. However, each tradition has its own forms of praṇava, for example, in the Śаiva–sampradāya it is the bīja हुं (huṃ), in the Kaula–sampradāya it is the bīja ऐँ (aim̐), in the Trika tradition it is the bīja सौः (sauḥ), and for the Śаktas the praṇava will be ह्रीँ (hrīm̐). Since so many do not at all distinguish the concept of tantra with śakti–upāsanā, in India praṇava is often associated with tantrism. Thus, the Goddess Bhuvaneśwari is the Mother of all worlds, of different dimensions (bhuvanas) and is very significant for Śaktism in general.