A Mathematical Guide to Musical Vibrations

___ I would like to share a magical book with you. https://steemitimages.com/DQmYFCGWVdvKkaXjgNnKGUmbDgP2jGoDW7MAPsdMGKUyhho/IMG_3762.JPG Harmonograph: A Visual Guide To The Mathematics of Music By Anthony Ashton Published by [Wooden Books](http://woodenbooks.com) ___ ___ A __harmonograph__ is a curious device that looks like this: https://steemitimages.com/DQmRaDrLvdrFxVM2YSehbFZM4U1ogM44UsBcqr9arvuvq3u/Harmonograph.jpg (*Image found on [Pinterest](https://www.pinterest.com/daralette/harmonograph-yall/?lp=true)*) It uses weights and pendulums to draw fancy shapes. We can see the shapes musical notes create because we can apply musical ratios to the weights as they guide the pendulums. Allow me to explain…. ___ ___

Story Time!

___ ___ As the legend goes, Pythagoras noticed the ringing of a blacksmith’s hammer changed when a larger or smaller hammer was used. Through experimentation he concluded that **simple fractions** produced **pleasing sound**. A hammer half as large produced a higher sound, a ratio of **1:2** Pleasing harmony occurred when two hammers struck together, one hammer being two-thirds smaller, a ratio of **2:3** These ratios are the building blocks of **musical scales** Applying these same ratios to the weights on our pendulums, we can inspire our harmonograph to depict stencils of the vibration! ___ Here are some samples from the book: ![IMG_3764.JPG](https://steemitimages.com/DQmdSNWbEVfVQZY3sfVfH2mTZcCy96iUzC8tWFSPKEz1BH3/IMG_3764.JPG) ![IMG_3765.JPG](https://steemitimages.com/DQmVD6NqbgDspuPZSza2s2qC4vh8N4EZGE8gFnziK1Mqvnp/IMG_3765.JPG) ![IMG_3766.JPG](https://steemitimages.com/DQmXqWEj5ceR4cjLoSqvBzpgYdX5MphPXvZQ8xZQjfodSL7/IMG_3766.JPG) ![IMG_3763.JPG](https://steemitimages.com/DQmPfYZB9j62Kz1WwQ5WrHCV9CuEaoeVQiquvmdBqZ5h8fd/IMG_3763.JPG) ___ ___

Stars and Hearts

___ ___ ![IMG_3761.JPG](https://steemitimages.com/DQmSoEF6nW7jy12eMJthCJhYxxF2DxUgAfzySWPgNwVBMzJ/IMG_3761.JPG) I am flabbergasted by the truth revealed in these simple ratios. How can it be that **stars** and **hearts**, two of the most popular **symbols** in our culture, **naturally** appear in the **laws governing mathematical vibrations**? Perhaps this is why we have such an obsession with star and heart shapes. We intuitively recognize the **natural beauty** inherent inside them. They resonate in us. ___ If you enjoyed this post, I encourage you to purchase a copy of this wonderful book. It makes a fantastic gift for yourself or the fortunate recipient of your generosity. You may also find further delight exploring [Sir Thomas Bazley's *Index To The Geometric Chuck*](https://archive.org/details/indextogeometri00bazlgoog) ___ This is an original post for Steemit by @CosmicVibration on 6 November, 2017.