The Sequence and Nature
The Fibonacci Numbers consist of the infinite sequence of numbers where Fn = Fn-1 + Fn-2. Ratios between consecutive Fibonacci Numbers approach Phi, 1.618, the Golden Ratio (Meisner, 2012). This ratio is readily apparent in nature through seed heads, pinecone spirals, pineapples, cauliflower, growth points of flowers and branches, honeybee colonies, and human anatomy, for instance (Lamb, 2008).
A432 Music
Although it is common practice today to tune to A440, classical composers used a tuning system based on A432, that is tuning the pitch A above middle C to 432 Hz. After performing cymatic experiments and determining which frequencies yield the strongest results, the following table has been created based on musical frequencies and colour values calculated from Fibonacci Ratios when tuning to A432 (Meisner, 2012).
Aural and Visual Ratios
The frequencies and the colours are based on the same Fibonacci ratios. To achieve the Fibonacci colour, the ratio was applied between the red and green values of the RGB colour model and multiplied by a factor of 31 (since 8 is the highest number in the ratios to keep the greatest multiple below 255, 8 * 31 = 248). Blue remains 255 throughout to lend an oceanic ambience to the palette. The only exception to this rule is if there are two ratios per frequency, in which case it embodies the third number, also multiplied by 31.
Table of Fibonacci Frequencies and Colours
Fibonacci Ratio(s) | Frequencies | Note | Colours (RGB) | Colours (HEX) |
---|---|---|---|---|
3/8 | 81 Hz | E | rgb(93,248,255) | #5DF8FF |
2/5 | 86.4 Hz | F | rgb(62,155,255) | #3E9BFF |
3/5 | 129.6 Hz | C | rgb(93,155,255) | #5D9BFF |
5/8 | 135 Hz | C# | rgb(155,248,255) | #9BF8FF |
2/3 | 144 Hz | D | rgb(62,93,255) | #3E5DFF |
3/8 | 162 (Phi) Hz | E | rgb(93,248,255) | #5DF8FF |
2/5 | 172.8 Hz | F | rgb(62,155,255) | #3E9BFF |
1/1 | 216 Hz | A | rgb(31,31,255) | #1F1FFF |
3/5 | 259.2 Hz | C | rgb(93,155,255) | #5D9BFF |
5/8 | 270 Hz | C# | rgb(155,248,255) | #9BF8FF |
2/3 | 288 Hz | D | rgb(62,93,255) | #3E5DFF |
3/2, 3/8 | 324 Hz | E | rgb(93,62,248) | #5D3EF8 |
2/5, 8/5 | 345.6 Hz | F | rgb(62,155,248) | #3E9BF8 |
5/3 | 360 Hz | F# | rgb(155,93,255) | #9B5DFF |
1/1 | 432 Hz | A | rgb(248,248,255) | #1F1FFF |
3/5 | 518.4 Hz | C | rgb(93,155,255) | #5D9BFF |
5/2, 5/8 | 540 Hz | C# | rgb(155,62,248) | #9B3EF8 |
2/3, 8/3 | 576 Hz | D | rgb(62,93,248) | #3E5DF8 |
3/2 | 648 Hz | E | rgb(93,62,255) | #5D3EFF |
8/5 | 691.2 Hz | F | rgb(248,155,255) | #F89BFF |
5/3 | 720 Hz | F# | rgb(155,93,255) | #9B5DFF |
Note. Adapted from “Music and the Fibonacci Series and Phi,” by G. Meisner, 2012, Phi 1.618 The Golden Number.
References
Chandra, P., & Weisstein, E. W. (n.d.). Fibonacci Number. Wolfram MathWorld.
Retrieved February 10, 2014, from http://mathworld.wolfram.com/FibonacciNumber.html
Lamb, R. (2008, June 24). How are Fibonacci numbers expressed in nature?. HowStuffWorks.
Retrieved February 9, 2014,
from http://science.howstuffworks.com/life/evolution/fibonacci-nature1.htm
Meisner, G. (2012, May 4). Music and the Fibonacci Series and Phi. Phi 1.618 The Golden Number.
Retrieved February 3, 2014, from http://www.goldennumber.net/music/