Mantraśastra or the ‘science of mantra’ is a very developed and intricate part of the Veda and Vedāñga.
It begins with the most basic learning, namely the Tantra or literally ‘science’ texts, which give the student the initial and most basic understanding of Mantras.
Herein are included the topics of choosing the right mantra, proper invocation and imbibing the mantra, ensuring it will not cause harm, right time for starting and ending the mantra practice, and the means to ensure the mantra gives fruits.
The student then evolves further to read the Purāṇa, the Upaniṣad and finally the Veda as part of their study.
Each tradition has some main Tantras that they depend on for their study, e.g. in the Uttara Kaliñga Vaiṣṇava Parampara and many others, the tantras studied are those of Śarada Tilakam and Prapañcasara Tantra.
In Tantra not all mantras are given clearly, and are instead hidden or require derivation. This has several purposes, namely on one hand to avoid the necessity of the author repeating the mantra, and secondly and far more important, to ensure only those competent and having learned the subject can derive the mantra. The simplest derivation is found in the kavacha-stotra where the mantra is split into its various syllables, and the mantra can be put together one syllable at a time. Two such examples are the Madhusudana Stotra or Shiva Panchakshari Stotra. Herein the purpose of the stotra is to give automatic initiation into the specific mantra, thereby enabling the practitioner to practice the mantra after having sung the stotra.
The more advanced portions of the tantra hide the mantra behind code-words. The proces of deriving the meaning of such mantra, or seed-syllables of the mantra, is termed Bīja bhedana. Fortunately Tantras such as Bhuta Damana Tantra, Kubjika Tantra and a few select others, give ready tables to learn the names of each sound. A selection of thes are given herein from Bhuta Damana Tantra.
ह्रीं hrīṁ – māya lajā parā samvit triguṇa bhuvaneśvari hrileka śambuvanita śakti devi iśveri mahamāya parvati samsthanakrtarupīni parameśvari bhuvanadatri jeevanamadyaga
ह्लीं hlīṁ – vahni endri yugamāya sthiramāya
श्रीं śrīṁ – śri lakṣmi viśnuvanita rāma śirasamudraja sāgni śanti vindu nāda lakṣmipraṇava
स्त्रीं strīṁ – śodasa vyanjanavarna vadhubīja vamekṣana yoṣiṭa ekākśi strī kāminī
ऐं aiṁ – bhaga yoni sarasvati adhara vagbhava vak
हूं hūṁ – sabdha dīrgakavaca tarapraṇava
क्रीं krīṁ – kālibīja ratibīja
क्लीं klīṁ – guhyakālibīja gopalabīja kāmabīja kameśvari parāśaktibīja
हौं hauṁ – śivabīja
An example of the usage is here given.
In the Bhuvaneśvarī Kavacham it is stated:
māyā padmāvatī svāhā saptārṇā parikīrtitā || 13||
Here the word ‘māyā’ refers to the sound ‘hrīṁ’ and to make the seven (sapta) syllable (arṇa) mantra we write:
hrīṁ padmāvatī svāhā
To be sure we can count that hrīṁ (1), padmāvatī (4), svāhā (2) equates to 7 syllables.
Another example from the same states:
tāraṁ durge yugaṁ rakṣiṇī svāheti daśākṣarā || 9||
Here the word ‘tāra’ refers to the sound oṁ which causes us to cross the bridge of life. The others names for this sound is tāraṇa or praṇava. The mantra needs to precede with this sound e.g. oṁ followed by durge and with yuga and rakṣiṇī and ended (iti) by svāhā giving us a ten syllable mantra. To be sure we can count: oṁ (1), durge (2), yuga (2), rakṣiṇī (3), svāhā (2) which adds up to 10.
A more complicated example:
tāraṁ māyā ca kavacaṁ khe rakṣetsatataṁ vadhūḥ || 16||
hūṁ kṣeṁ hrīṁ phaṭ mahāvidyā dvādaśārṇākhilapradā |
tāra is oṁ, māya is hrīṁ, kavaca is huṁ followed by rakṣetsatataṁ and hūṁ kṣeṁ hrīṁ phaṭ giving a 12 syllable Mahāvidya mantra.
om hrīṁ huṁ rakṣetsatataṁ hūṁ kṣeṁ hrīṁ phaṭ|
Notably the mantra give above may look somewhat different if we include the sound khe and consider vadhu as the sound strīṁ.
om hrīṁ huṁ khe – – – hūṁ kṣeṁ hrīṁ phaṭ –> herein three sounds are missing and we find that different sources give different versions for various protections:
om hrīṁ huṁ khe ca che kṣaḥ strīṁ hūṁ kṣeṁ hrīṁ phaṭ – Tvaritā Mantra [Paraśurāma Kalpa Sūtra, TāraBhakti Sudharnava & Svacchandapaddhati]
om hrīṁ huṁ keṁ keṁ kṣeṁ kṣeṁ śrīṁ hrīṁ kṣaṁ hrīṁ phaṭ – Lakṣmī Mantra [Meru Tantra]
Even the syllables of Sanskrit can be coded into other sounds where the combination of all the sounds can form a bīja. One such example is given from Bṛhat Tantra Sara:
nakulīśo’gnimārūḍho vāmanetrārddhacandravān |
bījaṃ tasyāḥ samākhyātaṃ sevitaṃ siddhikāṃkṣibhiḥ |
This would be hard to derive without some prior understanding, but we can infer that the mantra or bīja consists of nakulīśa, agni, ārūḍha, vāmanetra, arddha-chandra. Fortunately the same work lists a few lines later:
nakulīśo hakāraḥ, agnī rephaḥ, vāmanetramīkāraḥ, arddhacandro’nusvāraḥ || 23 ||
nakulīśa is ‘h’, agni is ‘r’, vāmanetra is the long i ‘ī’, arddha-chandra or half-moon is anusvāra or ‘ṁ’. Putting these together we get: hrīṁ