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my teacher pointed something out today... he said its probably just a coincidence... and I think it is... but cool none the less... the sequence goes 1 2 3 5 8 13 21 etc -from C to C, there is 13 keys (including the high C) -there are 8 white keys (including the high C) -there are 5 black keys -they are in groups of 3, and 2 :-) notice anything? |
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who knows it might not be a coincidence, considering alotta things follow the fibinocci sequence that you wouldnts expect, like the spikey things on a pineapple |
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You are holding up 1 finger in your avatar, and you are 21 years old. Next year. |
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ok |
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0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 |
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Starting at C and proceeding to the next C gives us an octave. In this octave you will find two black keys grouped together and then three black keys grouped together. Surrounding the two black keys are three white keys and surrounding the three black keys are five white keys. In the octave are eight white keys. Counting the white and black keys, you have 13 notes. These thirteen notes are known as a chromatic scale. |
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Students can go on to research (at the previously mentioned Web sites) the vibrations per second of the notes in the chromatic scale beginning with middle C on the keyboard. Middle C vibrates at 264 vibrations per second, while A (the sixth) vibrates at 440 vibrations per second. This ratio reduces to 3/5, a Fibonacci ratio. |
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This hardly seems like a pattern to me |
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BT - Fibonacci Sequence !!! AWESOME TRACK |
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I wish I had my Golden Ratio book to hand as theres quite a bit in there about music...(I'll grab it at work today and see what I can find..) Maths & Music have alway been closely interwtined throughout history, & the Fib sequence (& it's relation to Phi, the golden ratio) crops up seemingly everywhere, so I'm not that suprised to see it on the design of a piano keyboard... |
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Nice page here, Zeus...and Fib & Musical Harmony... ... |
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Indeed, I was just going to post something about his track. |
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bookmarked, thanks! Oh, and my teacher was talking about how people studied bachs work, and found that a huge portion of it, can be related to the F.S. Like, modulations occur at certain ratios to each other, or this or that. It was freaky. Thats what got us into the conversation actually... we were looking at a Bach Fugue, and someone commented on how amazing it all fit together, and then my teacher went of on like a 45 min discussion on the FS But yeah... he said he doesnt know if bach did it on purpose... or if it is a coincidence... he said on theory is that, since this number is found around us in nature so much, that perhaps it has some deeper meaning... and that the fact that Bach wrote his peices, with the FS all through out, (apparently by coincidence) that perhaps he was just so in tune with the universe... and also why his music is so amazing. Or something. I dont know... I tend not to take that kind of stuff seriously... the universe fitting altogether etc... it becomes to close to a religious type ideal... but it is an interesting thing to ponder... "what if...?" |
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Agreed...I'm not too fond of that whole GR is the secret of the universe thing when people get numerology & mathematics confused... I'll post a link to the GR book I've got when I get to work; it dispels a lot of the myths about it.... |
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cool yeah, I think he was just playing devils advocate though |
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no i think number theory (which i am currently studying in school)does not pertain to no ;""answer of the universe" humans think toomuch, and live too less njoy |
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The 'golden section' which was brought up in a recent thread can also be derived from the fibonnaci sequence. If in the sequence each term is "F,n" then F,n = F,n-1 + F,n-2. That just says you add the previous two together to get the next term in the sequence. But if you take the limit of the sequence:{(F,n+1)/F,n} as n goes to infinity it approaches what is called the 'golden ratio' or the 'golden section' which is the ratio 1.61803 which was mentioned recently in another thread. Both the fibonacci sequence and the golden ratio are found in nature, like the ratio of the length of the bones in your finger, flowers, seashells, pinecones, plants, etc. But what is crazy is this jigsaw puzzle below, which is related to the fibonacci sequence. The 8x8 blue square is cut into the two triangles and two trapezoids, then rearranged to form the 5x13 rectangle. 8x8=64, 5x13=65? Try it for yourself with some cut and pasting. You can also rearrange them to form a shape that has an area of 63 also. |
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is anyone's head going to explode yet? c'mon c'mon |
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if you keep the numbers involved low enough you'll find all sorts of coincides fabinocci numbers do occur in nature quite often though. but that is cause they are solutions to some minimizing problems |
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The reason that that rearrangement puzzle works is because the slopes of the two slanted parts are actually slightly different. Slope of the slanted part of the trapezoid = 5/2 = 2.5 Slope of the hypotenuse of the triangle = 8/3 = 2.666666.... This means that the pieces actually don't fit together perfectly when rearranged. There is a small gap, which happens to have an area of one square unit. 'Tis simple. |
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... the book I mentioned above...The Golden Ratio: The Story of Phi, the World's Most Astonishing Number by Mario Livio HIGHLY recommended.... Theres some sample pages ta that site.... (typical it's now out in PB, my love of Hrdabacks made me buy it full rpice...but like I say, well well worth it...)... Will discuss more in the morning...just got back froma E fueled night and feeling somehwat woooooozy!!!:)... |
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