I. Introduction
Over the past decade or so, the concept of melody seems to have changed from what it was for Rock or Big Band melodies. There are songs being written with the traditional concept of melody and I have provided some examples below. However, the most prominent interpretation of melody is what Iím calling contemporary melody.

In the past melodies were an important component of the marketability of the song. However, today melodies seem more like an afterthought. As I will demonstrate in this paper, it is possible to statistically measure the difference in variation between traditional and contemporary melodies. Moreover, traditional melodies exhibit a larger range of pitch whereas the contemporary melodies are confined to a narrow set of notes.

II. Traditional Melody

The notes in a good melody have a direction up or down. Overall the notes may have many up and down movements. However, they donít just randomly jump around or on the other hand remain in a very narrow range. Here are a set of guidelines for a traditional melody:

A good melody has movement.
A good melody is familiar Ė yet unexpected.
A good melody has a center.
A good melody repeats itself.
A good melody has form.
A good melody creates and resolves tension.
A good melody has repetition and structure.
Finally, the best melodies combine both the familiar with elements of surprise.

This melody written for Lady Gaga is a good example of a traditional melody. As you can see in the first verse the melody builds on a theme. This excerpt from the lyrics expresses the theme:

The melody for the verses reinforces the theme in the lyrics.

Bad Romance Sheet Music

Contemporary melody by and large ignores the guidelines that I described for traditional melody. Instead contemporary melodies move up and down by every single note for much of the song. Every so often the melody will include a high note to emphasize a particular point. These melodies are not very much different than rap. A good example of this type of melody is Love You Like a Love Song performed by Selena Gomez. This song is a different type of love song, as you can see from this sample of the lyrics of the first verse:

It's been said and done
Every beautiful thought's been already sung
And I guess right now here's another one
So your melody will play on and on, with the best of 'em
You are beautiful, like a dream come alive, incredible
A sinful, miracle, lyrical
You've saved my life again

The difference is that whereas the melody for Bad Romance reinforces the lyrics, the melody for Love You Like a Love Song is fairly monotonic.

Love You Like a Love Song

IV. Variance Methodology
If what I have just described about the difference between contemporary melodies and traditional melodies is true, the variation of the pitch in contemporary melodies will be significantly less than the variation of traditional melodies. There is a way to demonstrate this statistically. We can compute what is known as the coefficient of variation. This in turn requires us to compute the average pitch and the pitch variance. While these terms are meaningless musically they do provide a useful way to demonstrate my hypothesis. The average pitch is the sum of all the note pitches divided by the number of notes. To calculate the variance, subtract the average pitch from each individual pitch and square the result. The coefficient of variation is the variance divided by the average pitch. Itís not correct simply to use the variance because, for example, the variance of the same song at a higher pitch would be higher than the variance of the lower pitch. However, the coefficient of variation would be the same.

V. Results
Admittedly this is a small sample. As you can see from Figure 1, the average coefficient of variation for traditional songs is significantly higher than the coefficient of variation for contemporary songs.

Variance Comparison Summary

The statistics of each of these songs reflects the principles that I have discussed for each melody. Take a look at these histograms for each song. The melody for Bad Romance is primarily distributed over nine different notes which account for 99% of the notes in this song. The range of these notes and is 12 semitones. On the other hand in the melody for Love You Like a Love song a single note is used 43% of the time and only four notes account for 86% of the melody. The range of these notes is only five semitones.

Bad Romance Variance Analysis

Love You Like a Love Song