The Academic Papers section of my website includes a PDF scan of a paper that I delivered at the Music Theory Southeast conference on March 16-17, 1996. The paper was titled “Toward an Epistemology-Based Theory of Meter.” My central argument was that our perception of meter derives from musical cues integrated in the subconscious in accordance with epistemological principles. One of the most important of these cues is harmonic change. From the paper: “The beginning of a new harmony is of great structural significance and preferably should coincide with a new metric unit…. If the harmony is complicated by a suspension, then that harmony can be more readily grasped if the suspension is resolved within that same metric unit — that is, on a metrically weaker beat.”
The illustration below shows a simple suspension as we might see it in a freshman theory class, exemplifying harmonic practice in the common practice era. (The common practice era comprises roughly the Baroque, Classical, and Romantic periods of music history.)
The suspension itself appears on the metrically strong first beat of the second measure. It is prepared on a relatively weak third beat, and also resolved on a weak third beat. Consequently, the harmonic change from tonic to dominant occurs on a downbeat, and the return to tonic is also on a downbeat. Thus the meter and harmony are naturally aligned, so that the harmony makes the meter easy to grasp, the meter makes the harmony easy to grasp, and it easy to perceive which tones belong to the chords and which are nonharmonic tones.
In the next example, the pattern is expanded into a long chain of suspensions.
The suspensions are contained in alternate chords, all on downbeats. Each intervening chord contains the resolution tone for the previous suspension, which also serves as the preparation tone for the next one. Here again the meter and harmony support one another, with harmonic changes occurring at metrically strong points. The natural alignment is reflected in our Roman-numeral analysis, where each new harmony (i. e., each new Roman numeral) begins on the downbeat of a measure.
Now imagine if the last example were shifted over by two beats, so that the suspensions appeared on relatively weak beats. The harmonic changes would then no longer be aligned with the meter, and the Roman numerals would appear in the middle of each measure instead of on the downbeat. But most importantly, the musical structure would be obscured for the listener. Depending on the surrounding context, the listener might become confused either about the points of harmonic change or else about the metrical boundaries. Thus there is a sound reason behind the rule that suspensions appear on relatively strong beats: This rule helps to ensure that the music will make sense to the listener.
The final two measures in the above example illustrate a typical “cadential six-four” pattern. According to the rules of common-practice harmony, the six-four chord in such patterns should appear at a stronger metrical beat and resolve on a weaker one. In this case, the six-four appears on a downbeat and resolves on the weaker third beat. In freshman theory classes, such a six-four is often referred to as a “tonic six-four,” but in reality it is part of a dominant harmony in which the third and fifth are embellished by their upper neighbors. In the Roman-numeral analysis, I have shown the chord as dominant, with 6 resolving to 5, and 4 resolving to 3. Underneath, in parentheses, I have indicated the misleading and less sophisticated notation typically used in freshman theory classes.
Once we recognize that the cadential six-four is really a form of dominant harmony, we can see why it appears on a strong beat. Just as in the case of suspensions, the changes of harmony need to be aligned with the meter. The dominant harmony — which includes the six-four together with its resolution — occupies a single metrical unit (the penultimate measure), and the following tonic occupies the next one.
There are also other kinds of six-four chords, some of which can appear on weak beats.
The six-four in this case occurs on a weaker second beat and is resolved on the third beat. This six-four is generated by an upper-neighbor pattern in the soprano and tenor voices and is really not a separate chord, but rather an embellishment of the surrounding tonic harmony. Once again, the harmonic changes appear on relatively strong beats. (As often happens, the harmonic rhythm accelerates toward the end of the phrase, which is why ii and V7 are compressed into a single measure.) In the Roman numerals taught in freshman theory, this six-four is often notated as a form of IV, and this less correct interpretation is again indicated underneath in parentheses.
So it turns out that the basic rules about meter and harmony that you learned in freshman theory are not arbitrary or conventional, although they may have seemed such if you were using oversimplified Roman-numeral conventions — or other chord-naming systems (very prevalent these days) that muddy the distinction between harmonic and nonharmonic tones. In the cases we have examined here, at least, the rules are ultimately based on how human perception and cognition work. They also reflect the musical aesthetic of the common-practice period, according to which music should be structured so as to be comprehensible to the listener. (That aesthetic itself can be seen as an expression of the Enlightment view that the universe is intelligible to the human mind.) Yes, such the harmonic and other features of such music may sometimes be adventurous, provocative, and even challenging, but fundamentally that music is not intended to be confuse or obfuscate. The same cannot be said of all the music of other eras, including in particular a substantial portion of twentieth-century music.