Verse 12

12.  The partless OM is Turiya,  the fourth.  Soundless,  fearless,  unutterable,  a quieting down of all relative manifestations,  blissful,  peaceful,  non-dual.  Thus,  OM is the Self,  verily.  He who knows thus,  merges his self in the Self - yea,  he who knows thus.

"The fourth is Turiya,  soundless,  fearless,  unutterable",

This fourth quarter is called  "Turiya"  which literally and only means "fourth".
This fourth quarter,  though named  (as state or quality etc.)  is none of these.  Not even a state of consciousness.  It is the Absolute Alone.  Without attributes it is the Being of pure Consciousness.  It is ever present and supports but transcends waking,  dreaming,  deep Sleep  and Creation itself.

"a quieting down of all relative manifestations".

Because the Absolute,  which is Absolute Consciousness,  alone Exists all else that is detectable  "all relative manifestations",  are  (were)  merely a projection of this Absolute Knowledge.

"blissful,  peaceful,  non-dual.  Thus,  OM is the Self"

The manifest  "AUM"  was merely a projection of the eternal knowledge of the Absolute    ("Thus,  OM is the Atman").  Therefore at the time of dissolution after all that was manifest    (OM)  returns to rest as the unmanifest Absolute,  the primal singularity of Truth,  Consciousness  and Bliss Alone exists.

"verily.  He who knows thus,  merges his self in the Self"

As stated in the scriptures he  "self"  who Realises the truth of the Non-Dual Absolute   "Self"  achieves  "merges his self in"  that Consciousness.

Indeed this Realisation is the one goal of all beings.

 

As stated earlier, The point is,

which quarter is the One quarter that knows all other quarters or states, but at the same time is unknown by those three states?
Which quarter is the One quarter that provides continuity or unity to the other three?
Which One quarter is it that through the very fact of its existence allows the other three quarters to "imagine" themselves as being a complete entity?
Which one quarter is it that allows the other states to rise and fall, come into apparent being and apparently to fade out of being?
Which one "Quarter" is Eternal?
What is it that Alone Truly Exists?