Division of one Veda into four and development of many S’akas or branches.

Veda Vyasa collected, consolidated, and classified the Vedas into the 4 Samhitas, the Brahmanas, the Aranyakas and the Upanishads.

• Different brahmans had different functions in a yajna (yaj: means to worship, yajna is worship. I think many people inaccurately translate the word yajna as sacrifice).

Vyasa taught each of these functionaries a different set of Veda Mantrams and asked them to perform the Yajnams together. So for a complete understanding, we need to study the Vedas all together with the gestures and the actions to be performed along with the yajnam.

I also think that since other gurus such as Gauthama also taught the Vedas prior to Vyasa, their students, may have preserved a different order or classification of the Veda Mantras. We need to know where to find these versions. Different branches of these Vedas evolved over time.

As per the Vishnu Puranam, Vyasa taught :

1. Rig Veda to Paila
2. Yajur Veda to Vaisampayana
3. Sama Veda to Jaimini
4. Atharva Veda to Sumanthu
5. Puranas and Itihasas to Romaharshana.

Here is the description from the Srimad Bhagavatham:

Source : 1.4.15 to 1.4.23

Vyasadeva purified himself in the Sarasvati River and sat by her banks and meditated at sun-rise. He thought about the Dharma in the different Yugas. He observed the fall in Dharma, the decreased longevities and competencies of the people. He divided the Single Veda into 4 Vedas : ṛg-yajuḥ-sāma-atharva as well as the puranas and the itihasas and taught them as follows. The Sakas are branches of the Vedas grew as each student acquired disciples and grand-disciples of his own.

1. Rig Veda to Paila
2. Yajur Veda to Vaisampayana
3. Sama Veda to Jaimini
4. Atharva Veda to Angirasa also known as Sumanthu (1.4.22)
5. Puranas and Itihasas to Romaharshana, the father of Ugrasrava.

(Note : Max Mueller theorised that the Vedas were written one after the other at arbitrary and equally spaced intervals and treated the Rg Veda as the oldest. (This also explains the western obsession with the Rg Veda alone. My study, so far, shows that this theory of Max Mueller was not only wrong but also baseless, as per his own admission. There are Veda Mantrams in all the 4 Vedas that are composed at different points in time as revealed by astronomic dating and by the age and time of the rshis who composed/received them.  See : Date of Veda Mantras.)

The Shakalya branch is what I found online here, so I shall go along with this, at least for now.

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