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#1 2006-08-01 00:17:59
- John E. Franklin
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6th root of 2 (whole tone scale)
I came across this approximation for the 6th root of 2.
55/49
It has some interest in the physics of music.
If 440Hz (Hertz) is a concert A, then 440 * 55/49 Hz is close to a "B concert".
Note that 55 - 49 is 6 and 36/6 = 6, hence near 6th root of 2, I noticed.
So following that idea.
56/48 should be the 4.5th root of 2 because 56-48 = 8 and 36/8 = 4.5, and it is pretty close!
And 54/50 should be close to the 9th root of 2.
I haven't graphed this relationship, just playing on a calculator.
Imagine for a moment that even an earthworm may possess a love of self and a love of others.
#2 2006-08-01 03:28:37
- Ricky
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Re: 6th root of 2 (whole tone scale)
Where does the 36 come from?
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
#3 2006-08-01 04:04:40
- Kurre
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Re: 6th root of 2 (whole tone scale)
was gonna test it but...doh my calculator died 
#4 2006-08-01 08:19:03
- John E. Franklin
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Re: 6th root of 2 (whole tone scale)
I don't know where the 36 comes from, I just made it up out of nowhere!
Imagine for a moment that even an earthworm may possess a love of self and a love of others.
#5 2006-08-01 10:55:01
- Ricky
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Re: 6th root of 2 (whole tone scale)
Holds pretty well till x is about 20, where it is 0.2 off. Then it gets exponetially worse.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
#6 2006-08-01 11:14:25
- mikau
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Re: 6th root of 2 (whole tone scale)
you know there are certain mathematical patterns to music, if thats true, there must be a way to randomly generate a song through math. Kind of creepy to think about.
A logarithm is just a misspelled algorithm.
#7 2006-08-01 11:52:16
- John E. Franklin
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Re: 6th root of 2 (whole tone scale)
Nice equation, Ricky. mikau, what is creepy to you is magical to me!
Imagine for a moment that even an earthworm may possess a love of self and a love of others.
#8 2006-08-01 12:02:22
- George,Y
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Re: 6th root of 2 (whole tone scale)
I still wonder how and why...
X'(y-Xβ)=0