Continued:
The Brahma Sutra explains the same, in a sutra;
6.6 (Thus) consisting of breath, it is known by his sound (oṁ) and by its constancy, that these the powers—according to the description of them are in a place apart from that supreme one (breath).
6.7 But according to the scripture on the partition and by their diversity, there is the arrangement of the right names (Agni, Soma, Varuna etc.) and the right things (the fire, the soma juice, the water, etc.), by the three ways of performing (the three Vedas: Rik =chanting, Sāma=singing, Yajus=giving instructions).
The Upanishads are abundant with the explanations of the A, U, and M, which form the OM. I will give only some examples.
The Dhyana Bindu Upanishad explains the Vedic Pranava as:
The" Om," which is the Brahman, should always be meditated upon by those who desire release from bondage. In “A," the first part of the Pranava, the Earth, Fire, the Rg-veda, the world Bhur, and Pita-maha (Brahman) have found their repose.' In “U," the second part of the Pranava, the intermediate region, Yajur-veda, the Air, the world Bhuvar, Visnu and Janardana have found their repose. In “M," the third part of the Pranava, the celestial region, the Sun, the Sama-veda, the world Svar and Mahes'vara find their repose. “A” is of yellow colour un rhythmic in quality, “U” is rhythmic in quality and of white colour, and “M " is of black colour and inert quality. He who does not know the Pranava of eight Anga-s, having four feet, three seats (Sattva, Rajas and Tamas qualities, Past, Present and Future durations)and five deities (Brahman, Visnu, Rudra, Is'vara and Sadas'lva) he cannot be a Brahmana (Knower of Brahman).
It further alludes to the purpose of Aum.
Pranava is the bow, the Atman is the arrow and the Brahman is the target, If aim be taken with due care, as is the case with the arrow (the Aum and the Manas), will become merged in the target (of the Brahman and become one with it) When that which is far and near is but seen, all actions recede, All the gods take their origin from the Omkar. All the vowels take their origin from the Omkara All the three worlds, with everything, animate and inanimate therein, take their origin from the Omkara.
Then we have the Nada Bindu Upanishad, which gives more explanation of the A, U, M letters or more rightly personified as the Vairaja-pranava.
The letter “A " is the right wing (of that king of birds, the Vairaja -pranava). The letter “U “is considered to be the other wing. The letter “M” is its tail, they say. The Ardha-matra is its head. Its legs and the like are the Gunas (Sattva, Rajas and Tamas). Its body is said to be the Truth. Dharma is its right eye, and A-dharma is said to be the other (eye).
Then the Brahma Vidya Upanishad has this to say:
The body of the “A” (of the Pranava) has been explained by the expounders of the Vedanta as the Rg-veda, the Garha-patya (Fire), the Earth and Brahman. The “U “(of the Pranava) has been said to be the Yajur-veda, Antariksa, the Daksipa Fire, so also, and the Lord Vishnu. The “M “(of the Pranava) has been said to be the Sama-veda, and so the upper Ethereal region and so also the Shavaniya (Fire) and the Supreme Is'vara. The “A " has its seat in the middle of the forehead, in the middle of the region of the Sun. The “U “resembles the Moon and is well placed in the middle of it (the region of the Moon in the middle of the forehead). The “M " is like the Fire in appearance, is smokeless and resembles lightning. The three Matra-s (syllables) are similarly to be understood as of the form of the Moon, the Sun and the Fire. Even as the flame of a lamp stands over it, so also should the Ardha-matra (the half-syllable) be understood as standing over the Pranava.
And the YogaCudamany Upanishad provides more details, and somewhat confirms the other Upanishads.
Akara, Ukara and Makara; and thus the three Varna-s, the three Veda-s, the three worlds, the
Three Guna-s, the three letters. In this manner there shines the Pranava. The ' A ' is in, the
Waking state and in the eye of all beings. The ' U ' is in the throat in the dreaming state and the
‘M’ is in the heart, in the state of sleep. …………. The ' A ' is said to be Rajasic, red in colour, Brahman, and sentient. The ' U ' is said to be Sittvic, white in colour, and Visnu. The ' M ' is likewise said to be Tamasic, black in colour and Rudra. From the Pranava is generated Brahman, from the Pranava is generated Hansa (atman), from the Pranava is generated Rudra, the Pranava verily becomes the Para (the transcendent Atman). In “A” is dissolved Brahman, in “U ' is dissolved Hansa, in ' M ' is dissolved Rudra,—the Pranava alone is manifest.
To be continued.