After compiling a set of empirical data of the billboard corpus list that our class has been presented, the data (included in the GitHub repository alongside the analytical scripts) showed interesting and musically significant results. These results include mean transitional probabilities, confidence interval transitional probabilities, and mean chord occurrence probabilities within a four bar phrase. Similar to much classical musical theory, the harmonic structure seems to follow a tonic-predominant-dominant structure; with the tonic being most prevalent. Tonic is defined as the one (I) chord, predominant functions as the four (IV) chord, and dominant functions as the five (V) chord. Popular music must always have a strong sense of grounding with the one chord to be as accessible as possible to the masses; this is likely why the one chord is most common in all four measures in the phrase, as shown by our data.
Not only does the data of the chord occurrences correspond with assumptions in music theory, but additionally so does the function of each chord in a phrase. In the first measure of a phrase, it is 18% likely for a I chord to go to a IV chord. This is highest probability of any following chord, other than I repeating itself. In all four measures, IV and V are both highly likely to return to I, since there is such a high percentage of the I chord occurring in the phrase. In the second measure of the phrase, IV is 22% likely to go to V; in the third measure this progression is also 22% likely. These are second most common, to IV-I. This corresponds with the tonic-predominant-dominant function that previously addressed. It is common in musical theory for IV to lead to V. It’s also likely for the four bar phrase to end on a V (21%) or a I (36%). These are also known cadences (or traditional phrase endings) in music theory.
While the chords addressed (I, IV, and V) have the strongest presence among the phrases within the corpus, other chords are present, but not as prevalent. The six (VI) and seven (VII) chords are the next most present, due to their fairly strong stepwise motion in leading back to the tonic. They represent a more interesting way to navigate through the basic harmonic structure and may appeal to audience members who would want to hear something a little different.
This study did not differentiate between major, minor, diminished, or augmented chords (chord qualities). Since it is believed by many that the quality of the chord alters its function, this is a logical next step in the study. For example, minor IV (iv) could possibly function as a different chord than major IV. It would be interesting to see what results this study could yield. Additionally, it may be interesting to address phrases of lengths other than four measures. This would possibly result in different chords functioning at different times. While we have gained data to back up many assumptions within music, there is still more that we can explore within this realm of phrase and harmony structure.