Each time I was taught music history (on various levels) the syllabus began with Plato and the Greek modes. Unfortunately, there is almost no extant music of ancient Greece, so there was nothing to which the modes could be applied. There were only Greek words and technical details that had to be memorized. No teacher ever applied the Greek modes to Medieval music, because the issue was the techniques of counterpoint. Besides, the Medieval musicians had misunderstood the Greek theory books and named the modes differently. Later, composers evaded the modes by adding sharps and flats. Although they called this musica ficta [fictitious music] it was actually incipient major and minor, their real music.

Each time I was taught music theory (on various levels) the syllabus began with Pythagoras and the overtone series. No teacher ever applied overtones to chords and harmonic progressions, because the issue was the circle of fifths, and roots and inversions and functions.

I wondered why the syllabus always began with the Greeks and their inapplicable doctrines. Now I think I see the reason, but I know that my point of view is nonconformist. Nevertheless. I shall present my opinions on the subject.

There is a common delusion, that a discussion of any subject must begin by proving its pedigree with a reference to its ancient Greek credentials. Perhaps this is justifiable for mathematics, but not everything is mathematics. If the subject is physics, it begins with a bow to the atomic theories of Anaxagoras or Democritus. If the subject is chemistry, it will be Aristotle's four elements. If it is the solar system, Aristotle's ideas about perfect spheres and circular orbits will be cited. If it is meteorology, it will be Vulcan forging lightning bolts and Zeus hurling them. If it is medicine, it will be the four humors and the Hippocratic oath. If it is the theater, it will be the tragos and the satyr plays. Similarly, if it is music, it will be Plato and the modes, and Pythagoras and the overtones.

I suppose Greek music theory must have been as meaningful in its context as our theory is in ours. I cannot, however, share Plato's misgivings about the supposedly noxious effect of certain modes on the listener. Likewise, the discovery of the overtone series was surely a major breakthrough in acoustics, but I cannot see why it was thought to constitute a proof that the ultimate reality of the cosmos is whole numbers. On the contrary, every avenue of exploration brought the Pythagoreans face to face with a constant that is not a whole number. Plane geometry led directly to pi; the theorem about the right triangle led directly to the square root of 2; the golden section led directly to the golden ratio, and the tuning of musical instruments led directly to the Pythagorean comma. When Hippasus of Metapontum discovered this inconvenient truth, he was quickly silenced. It is not clear whether he was merely exiled, or actually assassinated.

Western music theory too often mistakenly invokes the authority of ancient Greece. We have borrowed Greek terms -- chorus, orchestra, rhythm. mode, harmony, symphony -- but we have perversely given them different meanings. The Florentine camerata were sure that they were bringing the theater of ancient Greece back to life, improved by the addition of functional harmony. Wagner believed something similar, in his case with the added improvement of the symphony orchestra.

I suspect that the appeal to the modes in the music theory of the West has always been just a pose. As remarked above, Medieval composers misnamed the modes, and later used sharps and flats to circumvent them. Even as late as Bach, there are things like the Confiteor fugue in the B Minor Mass, which is in B minor but with a key signature of three sharps (as if it were Dorian) followed by a Vivace section in real D major with two sharps.

Many Western theorists have assumed that triadic harmony is ultimately based on the overtone series. Rameau in his Traite de L'harmonie (1722) asserted that the major triad is the "perfect chord" because it consists of overtones numbers 4, 5, and 6. Helmholz stated the same thing in his Tonempfindungen (1863) and so did Hindemith in The Craft of Musical Composition (1937). The most obvious objection is, that this does not explain why the minor triad is equally able to serve as a tonic, even though its lowered third is overtone number 19 (approximately). Another objection is, that tempered tuning makes nonsense of such theories. Furthermore, when we hear ragtime played on a purposely out-of-tune "honky-tonk" piano we still hear the roots of the chords.

Perhaps the whole thing follows from the view that Western civilization is a continuation of the classical Greco-Roman civilization. I subscribe to a different view: that the classical Greco-Roman civilization, after its demise, was replaced by Western civilization. The frontier between the Roman empire and the barbarians, approximately congruent with the Rhine and Danube valleys, became the backbone of the new civilization.

I believe, for example, that the theater of the West is not the direct descendant of the classical Greek theater. It is thought that Greek tragedy originated in the rites of Dionysus, from a ritual dialogue with the tragos [goat]. Why not grant European drama a similar dignity, and admit that it originated in the rites of the Christian church, from ninth-century dialogue tropes whose text was the ritual dialogue between the angel at the empty tomb of Christ and the three Marias. These developed into liturgical drama, and miracle plays, and mystery plays, and passion plays, and so on.

Similarly, I believe that Western music does not derive directly from Greek, but constitutes a distinct culture. The fact that Medieval schoolmen tried to appear erudite, and misused Greek terminology, is irrelevant. From its very beginnings, Western civilization had its own unique kind of music, based on chains of thirds and not on diatonic scales. I am not alone in this belief. Kurt Sachs, in The Rise of Music in the Ancient World, page 296, wrote:

          The author has tried to look at medieval music with an unbiased mind. As a result, he has 
          found that... there has been an all-embracing European style, neither modal nor 
          pentatonic... This style... ignores the interval of the fourth, indeed the octave itself. Its 
          melodies, rather, fall into patterns of thirds.

This Western perception of the third-relationship between tones, which is not derived from Greece, eventually developed into the perception of the chord. As a result, the additional dimension of harmony, with roots of chords and harmonic progression, is Western civilization's unique contribution to the music of mankind. Our perception of functional harmony is learned behavior, culturally determined. The uniqueness is now obscured by the fact that Western civilization is rapidly swallowing up all the other civilizations. But the uniqueness has nothing to do with objective facts of physics or acoustics. Therefore, there is no point in torturing beginning students with the Greek modes or the Pythagorean overtones.

Once upon a time, when I taught music theory at the Academy of Music in Jerusalem, I tried to convince the teachers of the first-year students to begin by building on the students' everyday perceptions of major and minor, and not to waste the first month nattering about Greek modes. Not only did they not agree; they looked upon me as a dangerous pervert, and got rid of me as quickly as they could.