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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

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.

**igloo** **myrtilles** **fourmis**

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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..."

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**Kurre****Member**- Registered: 2006-07-18
- Posts: 280

was gonna test it but...doh my calculator died

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

I don't know where the 36 comes from, I just made it up out of nowhere!

**igloo** **myrtilles** **fourmis**

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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..."

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

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.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Nice equation, Ricky. mikau, what is creepy to you is magical to me!

**igloo** **myrtilles** **fourmis**

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,319

I still wonder how and why...

**X'(y-Xβ)=0**

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