1 The Golden Ratio and Fibonacci Sequence in Music A project completed in partial fulfillment of the requirements for the Honor
![Fibonacci numbers. 1, 1, 2, 3, 5, 8, 13, 21, 34 a, a, (a+a), a+(a+a), (a+a) + (a+a+a) etc. Term = sum of 2 preceding terms = GOLDEN RATIO. - ppt download Fibonacci numbers. 1, 1, 2, 3, 5, 8, 13, 21, 34 a, a, (a+a), a+(a+a), (a+a) + (a+a+a) etc. Term = sum of 2 preceding terms = GOLDEN RATIO. - ppt download](https://images.slideplayer.com/25/8027692/slides/slide_3.jpg)
Fibonacci numbers. 1, 1, 2, 3, 5, 8, 13, 21, 34 a, a, (a+a), a+(a+a), (a+a) + (a+a+a) etc. Term = sum of 2 preceding terms = GOLDEN RATIO. - ppt download
![Golden ratio on piano scales. [The keys of a piano portray the Fibonacci numbers. Within the scale consisting of 13 keys 8 of … | Geometry, Music writing, Math art Golden ratio on piano scales. [The keys of a piano portray the Fibonacci numbers. Within the scale consisting of 13 keys 8 of … | Geometry, Music writing, Math art](https://i.pinimg.com/originals/40/89/cf/4089cfbe0ff96292a8bc3e56c58ce096.jpg)