What is Vitakka, Avitakka and Savitakka according to Sutta?

Q & A
1

What is Vitakka, Avitakka and Savitakka according to Sutta?
And what is their relation to Jhana?
I appreciate if you can explain this in both Sutta jhana (four fold) and Abhidhamm (five fold) formula.

2

AN 8.63 is the most clear of the EBT on this topic. (thereā€™s not much else, other than MN 128)
Here, the case for metta is given. The other 7 cases use the same formula (4bv brahmavihara, 4 sp (satipatthana)).

3 very interesting features to note:

  1. The 4sp and 4bv are all explicitly called ā€œsamadhiā€.
  2. sāta (satisfaction) is the equivalent of sukha in the 4j classification. Then you see how this 3 way samadhi maps into the 4 jhanas.
  3. later in the sutta, the Buddha says to do these 8 practices in all four postures for comfortable (phasu) abiding. This is a code phrase for saying, 4 jhanas can be done in all four postures, agreeing with AN 3.63, which coincidentally almost exactly the same number. The number three (3) is almost the same graphic image as the number (8) with a haircut.

(1. 4Bv #1: mettā me ceto-vimutti)

tato te,bhikkhu, evaį¹ƒ sikkhitabbaį¹ƒ:
 ā€œThen you should train yourself thus:
ā€˜mettā me ceto-vimutti bhāvitā
 ā€˜Good-will, as my awareness-release development,
bhavissati
 (will be) developed,
bahulī-katā yānī-katā
 Much-pursued, given a means of transport,
vatthu-katā anuį¹­-į¹­hitā
 given a grounding, steadied,
paricitā su-samāraddhāā€™ti.
 consolidated, & well-undertaken.ā€™
EvaƱhi te,bhikkhu, sikkhitabbaį¹ƒ.
 Thatā€™s how you should train yourself.
Yato kho te,bhikkhu, ayaį¹ƒ samādhi evaį¹ƒ bhāvito hoti bahulÄ«kato,
 When you have developed this concentration in this way,
tato tvaį¹ƒ,bhikkhu,
 then

(combine that with 3-way samādhi)

(1) imaį¹ƒ samādhiį¹ƒ sa-vi-takkampi sa-vicāraį¹ƒ bhāveyyāsi,
 (1) this concentration with-directed-thought & with-evaluation (you should) develop,
(2) a-vi-takkampi vicāra-mattaį¹ƒ bhāveyyāsi,
 (2) Without-directed-thought & a-modicum-of-evaluation (you should) develop,
(3) a-vi-takkampi a-vicāraį¹ƒ bhāveyyāsi,
 (3) Without-directed-thought & wiithout-evaluation (you should) develop,
Sap-pīti-kampi bhāveyyāsi,
 With-rapture (you should) develop,
nip-pīti-kampi bhāveyyāsi,
 Without-rapture (you should) develop,
sāta-sahagatampi bhāveyyāsi,
 Endowed-with-satisfaction (you should) develop,
upekkhā-sahagatampi bhāveyyāsi.
 Endowed-with-equanimity (you should) develop,
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3

A very popular monk (Walasmulle Abhaya) in Sri Lanka teaches like this.
Is this incorrect?
It appears wrong. How do you rectify it?

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First Jhana = Savitakka (Vitakka), Savicara (vicara),Pithy,Sukaha,Ekagata
Second Jhana = Savitakka (avitakka), Savicara (avicara),Pithy,Sukaha,Ekagata
Third Jhana = Savitakka (avitakka), Savicara (avicara),Sukaha,Ekagata
Fourth Jhana = Savitakka (avitakka), Savicara (avicara),Ekagata

4

I found the following:

http://the-wanderling.com/jhana_factors.html

5

@frank
Can I say Savitakka and Vitakka are the same thing?