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A researcher in, say, mathematics, conducts research in the form of proving theorems, laying out foundations for new theories, etc. But what do, for example, PhD candidates do in music theory? Split into several questions:

  • Is music theory complete, or is there still ongoing "research"?
  • Do PhD candidates build upon theory/technique, or do they simply compose and recite pieces to demonstrate their mastery of the subject?

I apologize if this question is ill-posed or simply doesn't make sense. I'm more of a science person and was wondering what people who choose to specialize in music do.

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My PhD is in Music Composition, but it was a heavily theory-focused program. I also have many theorist colleagues.

Your question is interesting, and difficult to answer in total detail without writing a book, so I won't try to be exhaustive. Let me first say that the understanding of "Music Theory" is most definitely not complete, and that there absolutely is continuing research.

A lot of people use the phrase "Music Theory" as synonymous with "Theory of Common-Practice Tonal music of the 17th–19th Centuries in Europe," but it the actual field is vastly larger than that. There are so many different genres and types of music throughout all human eras and virtually everywhere on the globe. Even a study of just the music happening throughout the world right now on September 10th would be a massive study requiring a huge number of sub-disciplines of theory, composition, musicology, history, ethnomusicology etc. Historical research involving fragments of music notation from Ancient Greece and from Assyria and Babylon is ongoing and complex. Academic study of the musical structures and cultural impacts of pop, rock, hip-hop and other recorded forms of music is a fairly new and exciting field (for example, although my primary compositional world is centered on various kinds of "atonal" chamber music, my dissertation was a close analytical reading of several albums by a band called Nine Inch Nails). Ethnomusicological studies of Brazilian music and Hindustani music are being taught at my school, and new insights are being made constantly.

But even if we restrict ourselves to notated music more-or-less within the lineage of European "classical" music, theory is far from complete. Composers at the turn of the 20th-century in Europe and America began exploring new harmonic and melodic pitch combinations that are almost totally different than those favored during the common-practice era. They weren't just throwing random notes together, however (until later composers like John Cage occasionally experimented with that too!), they were developing new ideas about how to construct music with its own internal logic. For many composers of a theoretical bent, such as Arnold Schoenberg, this lead to definitions of entirely new theoretical systems. They were primarily interested in composing, but this was simultaneously "research" in new music-theoretical areas. For example, a new theoretical system called "set theory" developed as a way to, among other things, classify and catalog every possible combination of pitches in the 12-TET system. And although that set-theoretical cataloging process is complete, research into the effects of different set combinations, and the musical impact of different set choices, and the ways that one set can be transformed into another set (a sub-branch called Transformation theory) are very much open areas. In fact, I'm almost certain that research along these lines and others is a fundamentally open field that will never be truly exhausted.

But even if we restrict ourselves to only common-practice music of the 18th-century and Europe, there is plenty of ongoing research both historical and theoretical. I think it's fair to say that the underlying basics of common-practice music theory are essentially set and complete by now. The genome has been sequenced, if you will. But research into the specifics of how a particular composer realized those theoretical defaults in particular pieces is essentially inexhaustible. Just because the majority of, say, Beethoven's music has been analyzed, doesn't mean that people aren't finding new ways of looking at his musical choices or previously unexplored measures every year.

I'll try a mathematical analogy. In a sense, the field of polynomial algebra is complete once we've expanded the concept of "number" to include the complex numbers. We can say precisely how many solutions any given polynomial equation will have and confidently state that all of those solutions exist within the complex numbers. However, actually finding the solutions to, for example, a 12th-order polynomial is an entirely different matter. And even if we discover a full-proof, finite method for solving all polynomials of every possible degree, that still doesn't mean anything about whether further research in numbers beyond the complex numbers such as Quaternions and Octonions is worthwhile. And even if it did, that still wouldn't mean there wasn't more research to be done in calculus, or field theory, or statistics, or any other field of mathematics.

Research in a field as vast as Music Theory will never be complete, because we can always discover or create new vistas to explore.

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    I find it of greater importance than you placed on it that your dissertation was on NIN. It stands to prove your point almost more strongly than the rest of the answer (but obviously not entirely). The fact that you were able to do that in the world of Classical studies speaks not only to the changing times of academia but to the large difference between modern music and Classical. In a similar example, though not to the point of PhD, a friend of mine attended a Classical school with turntables as his primary instrument. Real point being that the NIN aspect is valuable here. – Basstickler Sep 10 '15 at 16:05
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In the interest of offering a brief answer:

  1. Music theory research is still "ongoing"
  2. As with all other academic domains, the research of PhD students is supposed to contribute the greater field of ongoing music theory research.

If you're interested in finding out specifically what people are looking into at the academic level, I would suggest reading the abstracts of the Society for Music Theory (SMT) presentations, or those of the American Musicological Society (AMS). Or any number academic journals such as the Journal of Music Theory (JMT), the Journal of Music Theory Pedagogy (JMTP), the Journal of the American Musicological Society (JAMS).

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The ideas of Musical Theory are certainly fluid. With each new broad era of western music new ideas and thoughts on music theories are developed. Each bringing with it a great amount of new thoughts on tonality.

For instance the Baroque era was integral in the way in which the church modes was replaced with Major and minor tonalities.

The classical era introduced Sonata form and gave the beginning to the piano. More homophony and the style galant.

The Romantic era in its turn gave rise to the art song. It also had the effect of compositions being deeply personal and the great fast development of the piano.

In its turn the modern era. Like a forgotten youngest child was desperate to break the shackles of the four centuries of musical development. With this in effect there was a great search for new styles.

The Impressionism school championed by Claude Debussy (And also its German cousins the Expressionists) was a remarkable deviation of the classic ideals of music. The use of the whole tone scale and the Pentatonic scale brought forth new sonic possibilities.

The omission of thirds from chords and the lack of leading tones brought a vague tonality to the music of the Impressionists that gave it a surreal quality that was wonderfully new.

Also with the invention of Jazz a great rethinking of chordal theory was introduced. Here taking from the African American Influences that had a large effect on the music of New Orleans the idea of music build almost solely on four note chords was developed.

And even in the 20th century since the creation of many electric instruments even more new sonic possibilities was created.

Just in the mere 50 years since the electric guitar was invented we have come from the Elvis Presley / Blues-influenced Rock'n'Roll to an more heavy sound championed by the Godfathers of Metal Black Sabbath into an eighties metal sound characterized by long epic solos and even a neo-metal scene brought into existence in the early 2000's.

So in closing yes there is a lot of new ideas of music theory. It certainly is not solved or stagnant. With the invention of new instruments and the general development of technology it has to adapt to the fads and fashions of the day.

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    A lot of historical and factual errors here. The Baroque Period had sonatas, the piano was invented in 1700, fifty years before JS Bach died, which is largely seen as the end of the period. Art Songs have been around since the Renaissance, so, several hundred years before the Romantic Era. Debussy never considered himself an "Impressionist" and rather disliked the term, actually. You also left out the 2nd Viennese School, Set Theory, and most of what happened during the 20th Century. – jjmusicnotes Sep 10 '15 at 12:46
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    The sonata form was largely a feature of the classical era. Baroque era had the harpsichord which was not entirely a piano and yes the art song was most definitely a key characteristic of Romanticism. – Neil Meyer Sep 10 '15 at 13:16
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    This reads more like "a short history of music" than "a description of what music theory is". Here's an open-access, peer-reviewed journal to see for yourself the sort of research that music theorists are doing: mtosmt.org/index.php – user19146 Sep 10 '15 at 15:05
  • To echo the previous comment, this describes the evolution of music practice rather than that of music theory. – phoog Mar 11 at 4:12
  • @jjmusicnotes sonata form is not the same as the sonata; it is the form that arose in the classical period to dominate all kinds of music, including symphonies and masses. Earlier pieces called sonatas (also in the renaissance) were not in sonata form. The piano was indeed invented in 1700 but was not widely used before the classical period. One can define "art song" so as to include the songs written in the renaissance or to limit it to those from the 19th century and later, but I can't think of a definition that includes renaissance songs while excluding medieval songs. – phoog Mar 11 at 4:16
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Conventional music theory seems oriented toward practice methods. Evolution and wider extrapolations would result from research extending beyond musical styles, techniques and methods. Perhaps future music theoretical systems and research will extend into fields of auditory related science, technology, and psychology.

One fascinating area of research involves micro-pitch music and perception. Technology continues to facilitate the rapid development of new exploratory vistas far beyond the limits of mechanical-era musical instruments. The research process holds the potential of expanding our awareness and understanding of sound, pitch perception, and the discovery of new aesthetic possibilities in music.

At the same time, this modern research is revealing many limitations of an antiquated music theory developed in a modal era. One persistent difficulty relates to updating the symbology of a music theoretical system based on modal (7 notes per octave) scales. This traditional system of numbering intervals reflects an increasing incongruity not only with advances in the sound related sciences, but also with more contemporary musical methods (chromatic 12 notes per octave, microtonal >12 notes per octave). Importantly, it also impedes the development of any system of integration between music theory and quantitative scientific theories in sonic phenomena and auditory perception research.

Another theoretical limitation involves the use of flat (b) and sharp (#) symbols as both pitch-definitions (Db, C#) and pitch-modifiers (accidentals: b, #). This inconsistency has created a situation in microtonal music where each scale derivation method has its own pitch-modifier symbol system. The lack of any foundational system creates a theoretical roadblock to wider exploration and implementation of microtonal music (i.e. the use of multiple micro-pitch scales in a single composition - in series or simultaneously).

Difficulties like these, in the practice of music, inspire the creation of new music theories and an evolution of conventional symbolic representations in nomenclature. Optimally, new music theoretical systems may represent a closer ‘harmony’ with modern quantitative methods of understanding sound phenomena - i.e. acoustics, psychophysics, audiology and otoneurology.

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A researcher in, say, mathematics, conducts research in the form of proving theorems, laying out foundations for new theories, etc.

Uh, no? That's not research, like putting up bricks is not architecture.

Research is foremost a survey and organization of the field. While it may involve working on missing links, the main focus of research is more working towards the identification and classification of such links.

That's not all that much different from music research.

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    You seem to be wrong regarding mathematics research, see our sister site: math.stackexchange.com/questions/301763/… – Todd Wilcox Sep 10 '15 at 14:10
  • No, what you described is what Rutherford dismissed in his well known quote "All science is either physics or stamp collecting". "Stamp collecting" may be a precursor to doing research in a new field, but music theory is not a new field! – user19146 Sep 10 '15 at 14:43

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