Most of the music that we hear today is written in major and minor keys, or comprises mainly major and minor triads with extensions, or both. Like it or lump it, "major-minor tonality" is the most widespread approach to structuring pitch relationships in music. Why?
 
To answer this question, we must understand where the system of major and minor keys came from originally. To what extent is it culturally arbitrary? To what extent is it based on universal acoustical, perceptual or physiological principles? These are age-old questions in music theory, and have more recently become central questions in music psychology. But the literature in these two disciplines still does not provide clear answers. Humanities scholars tend to assume the system of major and minor keys is largely arbitrary - the product of unpredictable social, cultural and political developments in Medieval and Renaissance Europe. Scientists tend to assume it is determined, directly or indirectly, by some kind of general natural principles. Scientists write a lot about acoustics, psychology and physiology, but ignore or skim over the historical and music-theoretical aspects. Music historians and music theorists write a lot about history and theory, but ignore or skim over the acoustical, psychological and physiological aspects. 

I recently published a long and detailed contribution to the journal Music Perception on this topic (Parncutt, 2011). My theory of the origin of major-minor tonality brings together and balances four relevant disciplines: music history, the history of music theory, music psychology and psychoacoustics. My basic arguments are as follows.
 
Consonance. Since the Medieval beginnings of polyphony in three or more voices, the sonorities that we now know as major and minor triads tended to predominate because of their consonance, which has three psychological aspects: smoothness (lack of roughness, origin: inner ear), harmonicity (similarity of the spectrum to the harmonic series, which may be associated with fusion, i.e. blending or "sounding as one"), and familiarity (sounds that are heard more often in music tend to be perceived as more consonant). The major and minor triads are the most consonant sonorities of three pitch classes because they include perfect fifths (harmonicity, fusion) but no seconds (roughness); and they became familiar to Western ears over an extended historical period (familiarity) (Parncutt & Hair, 2011).

Chord-scale relationships. Major and minor triads include missing fundamentals at intervals of a 4th and 6th above the conventional root: CEG has missing fundamentals at A and F (also at D, but weaker), and CEbG at F and Ab. Rameau referred to these as basses fondamentales, and the same principle applies to missing roots in jazz chords (bebop harmony). We do not normally perceive these pitches consciously, but psychoacoustical evidence (both empirical data and model predictions) confirms that they affect our perception of tonal music. These pitches can explain why major triads are associated with the first six tones of the major scale (Ionian mode) and minor triads with the first six tones of the (natural) minor scale (Aeolian mode). These chord-scale relationships emerged in the Renaissance as major and minor triads became commonplace and subsequently functioned as psychological points of reference (tonic triads). The seventh scale degree or leading tone has an older, Medieval origin in the mi-fa relationship. In chant, fa tends to be more stable (salient, prevalent) than mi, because the harmonic series above fa better fits the diatonic context. The difference in stability between fa and mi was reinforced in Renaissance and Baroque polyphony as mi was increasingly the third of the dominant triad and fa the root of the tonic triad. These ideas, which are consistent with Heinrich's Schenker's (1906) concept of  a tonal passage or work as a prolongation of the tonic triad, are explored in more detail in my recent paper in Music Perception. 
 
Chord progression. Musical chords follow each other well if they have perceived pitches in common. These pitches may be either notated ("real") or missing fundamentals ("implied"). For example the chords C major and D minor follow each other well, because CEG has implied pitches at D, F and A, and DFA has implied pitches at G and Bb. So the two chords have pitches D, F, G and A in common. The word "progression" also implies moving forward. In the music of the 17th-19th centuries, falling fifths and thirds between the roots of successive chords (regardless of inversion or tonal context) were generally more common than rising fifths and thirds (e.g. C-F > C-G; C-a > C-e). These asymmetries can be explained by considering implied pitches. When an implied pitch in a chord coincides with a real pitch in the following chord, we may speak of an implication-realisation relationship. For example in a chord progression from G major to C major (again, regardless of inversion or tonal context), the first chord implies C and E as missing fundamentals, which are then realised in the second chord. This is one of many levels at which implication-realisation relations can happen in tonal music; in every case they produce temporal asymmetries. (These claims apply to primarily polyphonic music in which a different musician sings or plays each part. Intonation is facilitated if each tone in each part is preceded by a missing fundamental at the same pitch. The implication-realisation theory of chord progression does not apply to rock music in which chord progressions are composed by ear and played on piano or guitar.) I have addressed these ideas in various places, and a paper devoted to them is in progress.
 

What is the origin of major-minor tonality? A good theory must plausibly explain how major-minor tonality emerged historically, and it must do so more convincingly than competing theories. The theory's basic underlying principles must be generalisable to phenomena outside the theory (here, outside the perception of major-minor tonality, or of musical pitch) - otherwise they would be arbitrary. The theory must be consistent with the known social and psychological constraints within which major-minor tonality emerged historically, but also with the way major-minor tonality is perceived today. The theory should be able to predict which chord progressions occur most commonly in major-minor music, and its predictions should change as the constraints change in a way that can account for different tonal styles (e.g. baroque, romantic, impressionist or bebop harmony). Given a tonal passage, the theory should be able to predict the changing tonality of a modulating passage as determined by music theorists or perceived by listeners, and the points in time at which there are shifts to different tonal areas. The above arguments provide a framework within which these goals can  be approached more closely than before, but much further work needs to be done.

It is interesting to consider the history of music theory from this perspective. Many generations of music theorists have grappled with questions of this kind. In a nutshell, Pythagoras pointed to the role of number ratios (later frequency ratios), Rameau and Stumpf to the role of the harmonic series, Helmholtz to the role of beats and roughness, Terhardt to the role of pitch perception, Cazden and Krumhansl to the role of familiarity and learning. But none of these theorists, and no other theorist to my knowledge (one could easily list a hundred of them), came up with simple, plausible, testable answers to simple basic questions such as: Why did major and minor triads emerge in the 13th-15th centuries? Why did the major and minor key systems emerge in the 15th-17th centuries? Why did both come to dominate Western tonal music?

Schenker was surely the greatest music theorist of the 20th century, but his attempts to answer these questions were embarrassing by today's standards. He rightly criticised the failed attempts of his predecessors and contemporaries, but could not come up with anything better. For example, he theorised that the seventh harmonic is not part of the Western tonal system, but failed to subject the question itself to analytic scrutiny (what exactly does this question mean?). It is more realistic to ask why certain specific chords became common in tonal Western music while others remained uncommon, and then to develop a theory of consonance to explain that. The problem with the mistuning of the seventh harmonic by comparison to the equally tempered scale or commonly heard musical tunings cannot be addressed by listening and performing music and merely reflecting on one's experience. It is necessary to collect empirical data on tuning in real music and on the sensitivity of the ear to mistunings in different musical and non-musical contexts. If music theorists want to answer these questions, they need basic training not only in traditional music theory but also in acoustics, psychology and psychoacoustics.

Schenker went on to claim (in agreement with many others) that the major mode is more "natural" while the minor mode is more "artificial", but of course both are artificial: it took hundreds of years of musical development for them to emerge and become accepted in Western culture. His discussion of the music of "primitive peoples" in conjunctions with this question is completely misguided by modern standards and is barely worth criticizing.

To be fair, Schenker not only made the greatest contribution to music theory and analysis of any 20th-century theorist, he also stressed that he was primarily an artist and not a researcher or theorist. Moreover, his explanations have the advantage that they are grounded in analyses of real music. But from a modern scientific viewpoint we cannot learn much from his attempts to explain major/minor triads and keys.

Today, we need a fresh approach to these basic questions that is grounded in careful empirical investigations and careful testing of predictive models. Given that music is happening right here on earth as part of human culture, we need to adopt the empirical approach of Aristoxenus and not the idealistic attitude of Pythagoras. That is what I am trying to do in this research. I am not rejecting study of the history of music theory, and in fact I am sure that there are many important insights to be gained from it that have largely been ignored by music psychologists; but I am also not afraid to point out (as Schenker himself did) that most of the conclusions drawn by music theorists of the past about basic musical questions were incorrect by modern standards. This statement, incidentally, is not confined to music theory, but applies quite generally to the history of science (Bryson, 2004).


Current research projects

Current research at the Centre for Systematic Musicology in Graz about the perceived structure of tonal music is going in two contrasting directions:

1. Statistical analysis of a database of medieval and Renaissance sacred polyphonic music. How often did specific vertical pitch-class sets occur in different periods and styles? Can prevalence profiles, and historical changes in such profiles, be explained in terms of psychological theories of consonance and dissonance?

2. The perception of pitch in complex tonal sonorities such western chords and Indonesian gamelan sounds. In both cases we are studying the effect of musically typical acoustic manipulations and individual differences between listeners with different expertise and listening styles. On that basis, we will  study perceived pitch-based relationships between successive chords in western chord progressions.

A few references

Bryson, B. (2004). A short history of nearly everything. London: Transworld.
Parncutt, R. (2011). The tonic as triad: Key profiles as pitch salience profiles of tonic triads. Music Perception, 28, 333-365. pdf
Parncutt, R., & Hair, G. (2011). Consonance and dissonance in theory and psychology: Disentangling dissonant dichotomies. Journal of Interdisciplinary Music Studies, 5 (2), 119-166. pdf
Schenker, H. (1906). Neue musikalische Theorien und Fantasien. 1. Band: Harmonielehre. Stuttgart: Cotta.