A bunch of duos

Question

My friend, disappointingly, just left to go somewhere without telling me. He was supposed to produce my classical techno-fusion jazz metal rap album! Instead, he left me four riddles, each with two-letter-long solutions, to piece together his whereabouts. He already gave me the solution to the last riddle, "NK."

1) I'm truly the first two in "go back to the start";
Obey me you must if you've mastered the art.
Halting's not smart;
It hasn't ended;
Please let me remind of the part I appended. _ _

2) I can show imagination, I can show you what's real;
Let me show you the unheard, it's what I reveal.
I frequently wander,
And pass time as you ponder;
How all that you've heard is only piecemeal. _ _

3) "Press" on those keys, oh "tug" on those strings;
Do both and you'll make a rise and tide out of things;
Now split them in half;
That's it, don't laugh;
Or flip "down" two-fold like it's a drum stick spinning. _ _

4) NK

Can you help me solve the first three and tell me where he went? It better have been worth it - studio recording time is expensive.

Hint 1:

1) A phrase's first two letters;
2) Initials;
3) Two letters borne out of splitting either of two words in half. Using either word should suffice.

Hint 2:

There's a vague theme across this entire riddle, including the non-highlighted text. Solving #3 first might engender ideas on what #1 and #2 may be.

Hint 3:

Riddle 2 is by far the hardest. I want to draw your attention to the idea that every sound you hear is almost never just one "sound". A pure sine wave is the exception. A mathematician, of all things, may be most qualified to solve this.

Answer 1

The duos that this puzzle clue all add up to reveal another duo:

DAFT PUNK

1. I'm truly the first two in "go back to the start"; Obey me you must if you've mastered the art. Halting's not smart; It hasn't ended; Please let me remind of the part I appended.

As @TCooper found, this clues the two letters 'DA', the first two letters of the musical phrase 'da capo', which means 'go back to the start'. It also begins the word 'DAFT' (more on that later), which means 'not smart' - so if that hasn't ended, we've got the first two letters 'DA' clued again...

2. I can show imagination, I can show you what's real; Let me show you the unheard, it's what I reveal. I frequently wander, And pass time as you ponder; How all that you've heard is only piecemeal:

This clues the letters 'FT'. My initial interpretation was by way of a reference to 'ft.', the abbreviation that often follows the main artist name attached to a record to credit a second performer who played a big part in its production, but might have been 'unheard' as a producer or musician (much like Mark Ronson is often credited).

Having only noticed later that the OP left a hint that this duo should represent initials for something mathematical, this is actually a reference to the 'Fourier Transform', a mathematical technique which decomposes a function into its constituent frequencies. This has big uses in signal processing, where you can break down a signal (like a sound) into its constituent parts, allowing you to pick out things that were previously 'unheard' and lurking beneath the overall effect. Delving into the technical aspects of Fourier Transforms (after a nudge from the OP), these are 'complex' in the mathematical sense and consist of two parts: one imaginary and one real (hence "I can show imagination, I can show you what's real"). It also converts from the time domain to the frequency domain (hence the clues hidden in "I frequently wander, And pass time as you ponder").

3. "Press" on those keys, oh "tug" on those strings; Do both and you'll make a rise and tide out of things; Now split them in half; That's it, don't laugh; Or flip "down" two-fold like it's a drum stick spinning.

This clues the letters 'PU'. Another phrase meaning 'press' and 'tug' is 'push and pull'. 'Split them in half' and you see that both begin with 'PU'. These two letters also spell 'UP' backwards, which is what you get if you 'flip "down" two-fold' - once in meaning, then once in letter order.

Put these all together with the known 'NK' fourth part and you have:

DAFT PUNK. And let's face it, if you're into 'classical techno-fusion jazz metal rap' you're probably into the fusion music this 'duo' cooks up too!

Answer 2

Trying a partial answer, maybe it'll help someone else get there.

1) I'm truly the first two in "go back to the start"; Obey me you must if you've mastered the art. Halting's not smart; It hasn't ended; Please let me remind of the part I appended. _ _

Da Capo - "an Italian musical term that means "from the beginning" https://en.wikipedia.org/wiki/Da_capo

2) I can show imagination, I can show you what's real; Let me show you the unheard, it's what I reveal. I frequently wander, And pass time as you ponder; How all that you've heard is only piecemeal. _ _

??

3) "Press" on those keys, oh "tug" on those strings; Do both and you'll make a rise and tide out of things; Now split them in half; That's it, don't laugh; Or flip "down" two-fold like it's a drum stick spinning. _ _

WA - WAx and WAne, while not exactly half for wax, as close as can be. Wasn't considering this until I thought about the don't laugh clue.

4) NK

That gives us:

DA??WANK