> I beg to differ. The Golden Mean exists outside of time. You observe the > golden mean as a whole. Music exists in time. You don't know how much >music > is ahead (i.e., how much of the ratio is left) until you get to the end. >You > don't observe music as a whole until it's over. I've listened to some of > Bartok's pieces which are written around the Golden Mean, and I don't >hear > it. I like the music, but I don't hear it. Bartok is one of my favorites! > But tell me, what songs use the Golden Mean? Maybe if I listen more, I'll > begin to notice it. Well, I can't even remember the exact ratio -- it is around 61% -- just under two-thirds. This suggests that for a work that lasts say, three minutes, the climactic passage (or "the payoff" if you will) would occur around the two minute point. Generally, I expect that climax of my music to occur well... around 2/3 into the work. Perhaps a jam-session can be used to provide a simple explanation. Back in my teenage years, sometimes a few friends and I would get together to make some music in the basement. And what did we do? Well... we did what a lot of kids do... we did a 12-bar blues jam. And, true to teenage form, we all poured incredible energy into the music however by the fourth repetition, there was nowhere left to go! With experience comes a notion of "holding back" ... start out slow and let the music gain momentum... build to a climax over a longer period of time... then let it wind down naturally. Composers, too, often build works along these lines just doing what "clicked" for them. At some point in academia, someone came up with the "Golden Section" idea -- would this ratio somehow correspond to the buildup of formal compositions? And, well... many musical examples corresponded (more or less) to this ratio. It has been applied to work from all musical periods. As far as a specific example... well, I have never measured it with a stopwatch but the final movement from Mahler's 9th has a huge climax that is roughly 2/3 of the way through. A lot of times, when the music just seems to "flow" we are unaware of the underlying form, proportion, or whatever. I have yet to hear someone exclaim upon hear a new work, "Wow. The Golden Section was really cool!". When music doesn't quite "click" ... then we may become aware of something that is out of proportion (too long, too short, too much of this, not enough of that). Often the "not clicking" is due to some underlying technicality and may not always just be due to a lack of passion, inspiration, or whatever from the composer. I wholeheartedly agree with the notion of creating music that "sounds good and feels good". However, when I create something that "just doesn't quite work" I tend to want to dig in a find out what I did that caused the situation. Thus, the Golden Section is a suggestion for the placement of a climax. At least for me, it isn't cast in stone. It is a little like the "Law of nine squares" in photography which serves as a suggestion for the placement of the main subject of a photo. Consider a movie -- if the climactic moment happens near the beginning, then the balance of the film may seem kind of bland. If the climax occurs in the final scene -- followed by the credits -- the audience may feel kind of "ripped off" (heaven knows, there were a lot of late 60's/early 70's movies that just ENDED... always left me feeling empty). The choice of where to place the BIG CLIMACTIC moment is an artistic one. The Golden Section is one possible position for the climax that tends to "work" most of the time. Thus, it is not a hard and fast rule.