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Question: Please see the title.

Assumption: The conductor cannot imitate or rely on previous recordings, especially if a musical work has never been performed or recorded before.

Argument:

  1. Any musician can master only ≤ 2 instruments virtuosically.

  2. Conductors operate with many more instruments, and so need more musicology and music theory, than soloists.

  3. The complexity of Western orchestral music necessitates research-level music theory and musicology for (improved) analysis and interpretation.

  4. Musicologists dissent about or fail to comprehend objectively some musical works.

  5. 4 implies that conductors must understand, at least, academic research-level musicology for constructing an informed opinion of a musical work.

  6. Only a small number of conductors graduated with Doctorate degrees in music, e.g. African-Americans as listed here and such females as JoAnn Falletta, Jane Glover, and Xian Zhang; most famous conductors have not studied beyond an undergraduate degree in music and so would not have studied research-level musicology: e.g. none of the 10 opined by Bachtrack as the world's best in 2015 and per Wikipedia:

A small number of conductors become professionals without formal training in conducting. These individuals often have achieved renown as an instrumental or vocal performer, and they have often undertaken a great deal of training in their area of expertise (instrumental performance or singing). Another way that a small number of conductors become professionals without formal training in conducting is by learning on the job by conducting amateur orchestras, school orchestras, and community orchestras (or the equivalent choral ensembles).

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  1. No. The number of instruments mastered by virtuosi is going to follow a power law curve, with the largest number of performers playing one instrument, and a tiny number playing many. Paul Hindemith was a very well-known example of the latter.
  2. Maybe, but not so much theory on how the instruments work as how the music fits together. In other words, it's not the number of performers that might require thought, it's the complexity of the musical structure, and that doesn't necessarily scale with size of the ensemble. (It's often true that orchestral music is painted in broader strokes than chamber music. Its function is more public.)
  3. Following (2), no more than any other kind.
  4. That's going to be the case for any kind of music. Music is an art, not a science (and even scientists disagree on their topics of interest).
  5. Whatever for? Conductors need some familiarity with the instruments they lead, they need to be to able read the score well, they need enough analytical skills to handle the music's structure, they need to "play their instrument" well. This isn't significantly different from what is required of any other performer.
  6. Most performers of any sort possess no more than an undergraduate degree. Fields that are primarily concerned with praxis rarely require more than that - medicine might be the exception. Some practitioners may wish to research to a greater depth the music that interests them - the HIP movement comes to mind - but that too doesn't require a degree, it just requires self-discipline and persistence. (Note too that musicologically influenced performance practices like HIP are not the only valid way to do things. Music is a living art.)

Answer: They don't have them because they aren't necessary.

Edit regarding "no recordings":

Partly I'd go with what @endorph said about consulting the composer for new works. This is something we composers tend to encourage, because the feedback works both ways: the conductors get our input on the interpretation; we get to pick their brains to ensure that our writing for the ensemble is practical and optimal. It is normal for a work to be revised after a rehearsal (hopefully there is a rehearsal) or, at least, after consultation with the conductor.

Partly I would point out that, if the idea is to encourage the use of musicology by conductors, then this is going about it backwards: recordings are primary documents regarding the history of performance practice in musicology.

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If I were feeling inflammatory, I'd say that is because research level musicology has very little to do with actually playing music, and leave it there. But given that's not exactly fair, let's flesh the question out a bit more.

Start with your first pair of assumptions. I'm not going to strongly disagree with 1, because I don't think it's highly relevant to the question, but I would say that 'virtuoso' is hard to define, and generalisations are dangerous. Number 2 is more interesting. Conductors do need to know about each instrument they conduct, but in far less detail than the instrumentalist themselves. They're likely to have a wider theoretical knowledge, but not deeper (particularly regarding the finer details of technique for each instrument). Do they need more theory, or just different bits of theory?

Assumptions 3 and 4 are curious. Sure, music can be deep and complex, but I don't think you need 'research-level theory/musicology' to interpret it. For a start, you can always just read the analysis of the specific piece, if you really need to. Or, you could listen to an existing interpretation, and emulate it. Also, as a side note, it's quite difficult to objectively rank anything musical, because it's so subjective. So disagreement is almost the norm, not the exception.

As a result of these comments, I disagree with 5. Sure, they can be useful, but I don't think an understanding of the academic literature on a piece is strictly necessary for interpretation. As I mentioned earlier, emulating a recording is probably going to be just as valuable.

Which leads me to 6. I'm not going to verify the numbers; they seem reasonable. I would argue that this is the strongest evidence that conductors do not need this type of extended academic training.

As a postscript, I have nothing against the work that researchers do in this area. I am just not convinced that deep knowledge of this work is necessary for conducting, and I think the numbers raised in assumption 6 reflect that.

Edit You've just added an additional assumption that the conductor cannot rely on existing recordings. That's a pretty unlikely scenario, unless the work is new. In which case, you can talk to the composer. If that's not an option, it's pretty unlikely that anyone has analysed it anyway. So, in general, I think it's a pretty artificial restriction.

Regardless, I don't think a doctorate would be a big advantage in that situation. Wide experience would be much more useful.

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    To summarize this: Usain Bolt has a running coach, Glen Mills (en.wikipedia.org/wiki/Glen_Mills). How many Olympic medals has Mills won, and how many world records does he hold? The most important skill of a musical conductor is "coaching" the people being conducted. The fact that there are different musicological opinions about a work is irrelevant, because any performance can only perform one version of it on any particular occasion, and choosing that version is the job of the performer(s), not a bunch of academics arguing from their armchairs. – user19146 Dec 25 '16 at 21:22
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Why do carpenters not need research-level arbology to succeed? Why doesn't it take an Electrical Engineer to use a TV set? Well, it might if the actual Electrical Engineers did their job sloppily or just went in the "the customer will know best how he wants to finish this box" mind frame (if you try matching the scores of, say, Astor Piazzolla to his actual ensemble performances, you'll see that the score does not tell all the story, and the parts it tells use musical language in their own way).

But usually a conductor does not need to rearrange stuff. And even when his available instruments don't fit the score, he will generally develop a solution with the actual players.

The conductor does not need the mind set required to recreate the music, but rather the mindset to cast the music in a form accessible to the listener. So he needs to work with a listener's mind rather than a composer's mind.

There are a few exceptions, like when dabbling in things like "historically informed performances" which are quite hip these days. But like with artisanal food, this is more a historically inspired performance than a historically accurate one (which would in several aspects be blunter), so the level of required in-depth knowledge does not need to rise to the level of actual reproduction.

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