If the GM is not deciding any destination, then what are they doing? How does one "find common ground" without either (a) reaching a compromise with someone else, such that both parties determine the end result and thus recognizing their independent agency, or (b) declaring what the result will be, which the other(s) must simply accept (or walk away from, but I assume people who want to keep playing)?
Let's take the example, P1 wants to say
my PC is in Townshire because my mentor told me that's where I can find the herbs that will let us brew the potion that will revive my cousin from the magical sleep the local warlock tyrant has placed him into?
But P2 has a different idea, they want to say that nothing can revise the cousin except for a sacrifice on their part of whatever they hold dearest. Is it down to who spoke first? GM helps players navigate such conflicts, applying the rules judiciously.
How does one "harmonize"? What does that mean? Because to me, the "harmonizing" is not at all like being a conductor. In fact, I find the analogy completely inapplicable and useless--to the point that I nearly responded to it backwards because I thought you were calling the players conductors. Conductors assist other people in their performance of a piece. GMs do not "assist" players at all, in the GM-authorship mode being discussed here. GMs are assisted by players. It is the GM actually doing the action; the players simply provide inputs.
Harmonize may not be the best word, but I mean this. Each player decided who their character was, what motivates them, etc. GM helps them create characters that belong in the same space, and that - in their interactions - enhance rather than disrupt each other's purposes.
Whose hands are on the metaphorical instrument--the player, or the GM? Because as far as I can tell, it's exclusively the GM. That's why every single time, someone asks something to the effect of, "Well, did you clear it with the GM well in advance?"
I took clearing in advance to mean something like this. Suppose we're playing RuneQuest: astronaut characters are unlikely to fit well, and it's more likely rune or spirit magic that has the cousin in the magical sleep. The herbs should be considered in terms of their connection with those things, and... the player has told the GM where they want to go and what they want to achieve. Practically begging them to add a twist... "and what problems await you in Townshire? Why did you leave?" Part of the GM's job is to help the player say things they otherwise wouldn't want to say, or say those things for them. They can't protagonise without antagony. Or in sim mode to encourage curiousity "Why would the tyrant need to do that to your cousin? Who is your cousin? How do they figure? What threat did your cousin pose to the warlock?"
It's quite insufficient just to have warlocks doping cousins. Tyrants need motives. Cousins need to be their subject, or have interfered somehow. It's GM's job to make sure those are known. The analogy of conductor is replete with resources for grasping this.
Conductors don't "clear" orchestra performers well in advance of the performance of a piece. They do nothing like "clearing" anything. If the performer won't perform the piece as intended, they won't be asked to perform the piece at all.
I very much think they do. They don't just let Jo Harmonica rock up to their classical piece. Not without considering the effect to the whole.
The analogy does not hold.
It holds nicely. That it doesn't seem that way might be down to taking some unsatisfactory version of trad GMing that one has experienced, and reading it into every description of trad GMing. One might as well say that players make proposals to the dice, which do all the actual initiating!
And, separately from all of the above; WHAT "player authorings"? Per the repeated questions from at least two different posters in this thread, everything must be (a) "cleared" through the GM well in advance, and (b) the GM must be allowed to draft up appropriate content. But the latter thing IS the authorship. There is no player involvement in it. Players can insert hoped-for notions into the GM-authorship black box, and potentially get the payoff out at the other side. They don't actually participate in the authorship process at all.
Another version of trad GMing is, as Eero put it "GM story hour"
What I would like to offer as a modest alternative to old-fashioned railroading theory is that the purpose of the GM story hour is not to cheat and create an illusion of freedom; it is to exquisitely prepare nuanced literary material for intimate consideration
A group may be blessed to have access to a narrator whose stories they love to immerse in. Who will serve as their lusory-means through which they satisfy their pre-lusory goals. Or, in trad forms of sim, they may be blessed to have a GM working to
expand their ludic-agency in the directions they show interest in, just as bedrockgames explained multiple times in another thread. And this really matters, because at any given moment, regardless of whatever set of ludic-agency I might think a player has, they can only avail of a few elements. (This is one reason why playbooks turn out to afford good ludic-agency: not because they are expansive (they are not) but because they contain the ludic-agency the player will want to employ in each moment of play, oriented to the situation and premises of the specific game.)