The 51 matrikas (letters of the Sanskrit alphabet) constitute the Goddess in the form of sound. This is why Kali wears a garland of 51 skulls and it is also why these letters are shown on the petals of the six chakras. The yantra above is called the Tortoise Chakra (source Gandharva Tantra) and is used to determine whether the area a practitioner is working in is inimical or not to his worship.
Below is the Matrika Chakra. This, says Ram Kumar Rai in his excellentEncyclopaedia of Yoga, is to be drawn with saffron (kesara) for Shakti worship and with ashes (bhasma) for Shiva worship. It contains all the 51 matrikas and is used in the first of the ten rites to purify a mantra (samskara) after it has been received from a guru. On the petals of the yantra are the consonants while the vowels are in the eight spokes. In the centre is the syllable Hsauh while in the cardinal directions is the Bam bija and in the intermediate directions the Tham bija mantra.
Perhaps one of the clearest expositions of the tantrik view of mantra is given in Sir John Woodroffe's collection of essays, Shakti and Shakta, chapter 24.
The supreme absolute (Parabrahman) exists in the human being (jivatma) as Shabda Brahman, the absolute as sound. Mantras are not prayers and the relationship of the letters of the Sanskrit alphabet, whether consonants or vowels, he says, point to the appearance of devata (divinity) in different forms. An uttered mantra is the manifestation of a more subtle sound while mantras themselves are forms of Kundalini. Mantras may be male, female or neutral. Female mantras are called Vidyas.
"By Mantra the sought for (Sadhya) Devata appears, and by Siddhi therein is had vision of the three worlds. As the Mantra is in fact Devata, by practice thereof this is known. Not merely do the rhythmical vibrations of its sound regulate the unsteady vibrations of the sheaths of the worshipper, but therefrom the image of the Devata appears." (op cit) Mantras are masculine (solar), feminine (lunar) or neuter. A female mantra is called a vidya, which means knowledge, while solar and neuter forms are called mantras. Mantras are only such if they were first revealed by a rishi or seer. Only then do they have life, according to the tradition. A mantra can only work if it is received from a guru who has, herself or himself, received it in an unbroken line from its first rishi. There are, however, exceptions to this, according to some tantras which prescribe methods of purification for mantras received in dream. And, according to Mahachinachara, the Kali mantra does not rely on the very elaborate rules usually found in the Tantras.
In describing mantras, the different tantrik texts always give their origin or rishi as well as the metre to pronounce them. While a mantra is divinity in sound form, a yantra is the same in geometrical form and an image the devata in gross form. Refer also to the page on Tattvas on the relationship between the consonants and the 36 tattvas.
Bija MantrasThe word Bija means a seed and describes a mantra which is usually of one syllable. There are many tantrik 'dictionaries' of the matrikas which indicate their significance as well as the meaning of the bija or seed mantras. This section below draws information from the Bhutadamara(BD); the Varnanighantu (VN), alleged to be part of the Rudrayamala; and the Uddharakosha (UK), ascribed to Dakshinamurti. Longer mantras are often formed from a concatenation of these bijas. The table below is not exhaustive, there are many more bijas.
The bija mantra Shrim is described as Vishnupriya - the beloved of Vishnu - that is Lakshmi, according to the UK. The syllable Hrim is called the Maya bija. It is also Raudri, according to the Bhutadamara. The UK describes it as the Para or supreme bija. The bija mantra Krim is described as the pitribhuvasini, that is the goddess who dwells in the ancestral or cremation ground, Kali. It is also the dravana and kledana bija.
Hum with the long letter 'u' is called the Kurcha bija and is the mantra of the Mother worshipped by heroes (viras). The Bhutadamara also describes it as the mantra of Mahakala. Aim is called Vagbhava bija and is the syllable of Sarasvati, according to the BD. Phat is the bija of the great fire at the end of time (Pralayagnirmahajvala).
Krom is called the Krodhisha bija. Svaha, otherwise known as Thah Thah, is Vahnijaya, representing the fire sacrifice.
Klim is the deluder of the three worlds bija, also known as Kama or Manmatha, the Hindu god of love, often identified with Krishna. It is the sexual desire bija, says the BD. Hum (with the short letter 'u') is called theKavacha or armour bija. It is the bija of Chandabhairavi. Hraim is the bija which destroys great sins (mahapataka), and is the light mantra. Drim is called the great Kinkini (small bell) bija, says the Bhutadamara.
Sphem is the Bhairava (Shiva) bija which comes at the end of a yuga. Plrem is the Vetala (vampire) bija, according to the Bhutadamara.
Klrim Svaha is called the bija which causes things to tremble. It is the Manohari and ends in Thah Thah (Svaha, see above). The mantra Prim is the crow bija, used in works of Indrajala (magic). The UK describes this bija as the Vagura. Tham Tham Thah Thah are the bijas in the worship of the greatly alluring Chandika, says the BD. Sphrim is the bija of the uncanny Dhumrabhairavi (smoky Bhairavi), also known as Phetkarini.
The bija Hrum (with long letter 'u') is the single syllable mantra of Kalaratri, the great night of time. The same bija, but with a short letter 'u', is the mantra of Vaivasvata.
Hskphrem, says the BD, is the bija mantra of Ananda Bhairava in the form of one's own guru.