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Changed By: jjjtttggg
Change Date: July 30, 2017 10:51AM
Re: circle of fifths construction and use
I can't say that the 60 and 12 thing is definitely not related, but I don see how it would be either musically or mathematically.
It really isn't terribly complicated. Two sounds having frequencies a factor of 3/2 apart sound good to the ear/brain because the beat frequency is an octave below the lower note. So, if we start with some frequency and go up by that factor, and divide by 2 whenever we go more than one octave above our starting note, we can produce a series of notes that are all within the same octave, and all different until we try to make the 13 note. When we try to make that 13th note, it comes out so close to our original note as to be effectively the same. We could keep going, but we'd just get notes that are very close to the first twelve we made.
The fact that the thirteen th note isn't EXACTLY the same as the starting point leads to lots and lots of more complicated discussion, but for all practical purposes it is the same, so the answer to the "Why 12?" question is really just that simple. "Up by 3/2" sounds good, and if you do it over and over you get exactly 12 truly distinct notes.
-J
Original Message
Author: jjjtttggg
Date: July 30, 2017 10:50AM
Re: circle of fifths construction and use
I can't say that the 60 and 12 thing is definitely not related, but I don see how it would be either musically or mathematically.
It really isn't terribly complicated. Two sounds having frequencies a factor of 3/2 apart sound good to the ear/brain because the beat frequency is an octave below the lower note. So, if we start with some frequency and go up by that factor, and divide by 2 whenever we go more than one octave above our starting note, we can produce a series of notes that are all within the same octave, and all different until we try to make the 13 note. When we try to make that 13th note, it comes out so close to our original note as to be effectively the same. We could keep going, but we'd just get notes that are very close to the first twelve we made.
The fact that the thirteen note isn't EXACTLY the same as the starting point leads to lots and lots of more complicated discussion, but for all practical purposes it is the same, so the answer to the "Why 12?" question is really just that simple. "Up by 3/2" sounds good, and if you do it over and over you get exactly 12 truly distinct notes.
-J