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Song Variance Comparison

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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 I’m 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.


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You're making a lot of assumptions about meaning both semantically and audibly which are never expanded upon. I mainly am arguing against your section as to what you think a good melody is, and what it means to "reinforce" lyrics. Your entire last section deals with variance = goodness, essentially, but a lot of early medieval/renaissance music use static pitch, especially in plainchant. Opera also commonly uses recitative on a single pitch, yes, often to exposit, but the composer is in charge of that decision; is the foundation of what made these trends a thing in the first place also bad?


A good melody has movement.
A good melody is familiar – 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.

The example you give for a "bad melody" in Love You Like a Love Song actually does most of the things you think a good melody does. Let's see how:
1. In the first portion of the first verse, the range spans an octave, with the tessitura at a comfortable minor seventh. 
2. The first portion of the same verse utilizes a very brief sequence with its repeated notes. In measure four, the repeated Bb is the minor seventh over the iv chord. Two measures later, the A is a major seventh over the III chord. The melody, in effect, is a simple walkdown utilizing the same approach figure. Measure 8 almost repeats the figure with G, but cuts itself short to change it at the last minute. This is a truncated sequence (ABAB'), in a classical sentence structure with the second half of the verse. Thus, familiar, yet unexpected. That's what the Gallant era did best.
3. You could easily argue that the tonic is very clearly defined throughout the melody of the verse. G is the tonic of the song, and you'll notice it returns to it frequently throughout the verse to ground it within the extended harmony the repeated notes use. In the chorus, it's ironically the minor third that becomes the static pitch, but if that's not a center, I don't know what is.
4. Definitely repeats. Read what I mean about sequence in section 2.
5. Read section 2.
6. The repeated notes in m. 4 form a minor 7th against the bass, which immediately resolve to a typical triadic structure in m. 5, where the singer forms a major third against the bass. It's not an atypical way of dealing with dissonance (resolution by escape tone), and does its job well. The A's in m. 6 form an even spicier major 7th against the bass and resolve to the same triadic structure in the next measure. The chord progression with extensions (from m. 3) are Gm - Cm7 - F - Bb∆7 - Eb. Notice that where an extension is used, it is immediately resolved in the next chord. 
Edit: In the chorus, the repeated use of the one phrase over and over also creates and resolves tension by having the minor third and perfect fourth vary in relevance to the tonic of that chord. 
7. See section 2. 


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