Post v6.2.2 (Markarth PTS)

Note that the DLC pledges don't give more, every amount rewarded to the player is now a fixed amount rather than random RNG amounts between 2 to 10 Transmute Crystals, PvP sources except Battlegrounds supposedly remain unaffected. We're also seeing a more clear tier list of Transmute Geodes:

White giving 1 Crystal

Green giving 3 Crystals

Blue giving 5 Crystals

Purple giving 10 Crystals

Sources of Crystals (PvE)

Source
Amount / Geode Type
All Pledges (Hard Mode)
5 Crystals / Blue Geode
Pledges (Non-Hard Mode/Maj al-Ragath)
1 Crystal / White Geode
Pledges (Non-Hard Mode/Gilrion)
3 Crystals / Green Geode
Pledges (Non-Hard Mode DLC)
Unknown
Random Normal/Veteran Dungeon
10 Crystals / Purple Geode
Random Normal/Veteran (after 1st)
1 Crystal / White Geode
Normal Trial Coffer
5 Crystals
Weekly Trial Reward Mail
10 Crystals / Purple Geode
Vateshran Hollows (Veteran)
5 Crystals
Blackrose Prison (Veteran)
5 Crystals
Maelstrom Arena (Veteran)
4 Crystals
Normal Arenas
Unknown
Daily Overland Quest (Undaunted, CWC, etc)
Nothing