For me:
f(x)="Quality of the song"
f(x)="Do my ears find it pleasurable"?
There is no variable "t=time" in that function.
I'm not sure if this is a response to me or not, but I will continue anyway.
For my mock equations, the quality had nothing to do with the length of the song. The equations gave the instantaneous quality at a certain time stamp. The resulting "quality" (or rather, Quality-minutes) was then divided by the length of the song to find the average quality. My post was more of a response to previous posts saying things along the lines of, "the songs both score a 9, 9/6 > 9/20, so the 6 minute song is better", than a statement correlating song length and quality.
Now, obviously the perceived quality of a song is more complex than a simple average of all its parts. The flow, structure, and other macro-level elements play a huge role here. As 6 minute and 20 minute songs have different advantages in these areas, neither is inherently better than the other.
Fair point, and I'm with you on that to some degree ("We Can't Dance", anyone?). I was more looking at it from the perspective of the length of the song or album as a measure of quality.
What I mean is, when Flying Colors was first being talked about, they released the song list with the times, and there were a number of posts at Mike's site that were along the lines of "Infinite Fire is going to be EPIC!! And Blue Ocean is going to RULE! The rest I'm sure I can take or leave." And I'm scratching my head about how that can even be remotely accurate and not a complete crap shoot.
I definitely agree with all of this. I understand the heightened anticipation for longer songs, but judging quality by length alone is just ridiculous. To pick two extreme examples, neither Reign in Blood nor Six Degrees of Inner Turbulence feel any less complete than the other, despite the fact that one is 28 minutes and the other 98.