Fibonacci and the Golden Ratio
Download as PPTX, PDF3 likes1,065 views
The document discusses the Fibonacci sequence and the Golden Ratio. It provides a table that lists Fibonacci ratios, their calculated frequencies based on A=440 Hz, tempered frequencies, the associated note in the musical scale, and the musical relationship between notes. It shows that many musical intervals correspond to Fibonacci ratios and their approximations in the tempered scale.
Fibonacci and the Golden Ratio
- 1. FIBONACCI AND THE GOLDEN RATIO
- 54. Fibonacci Ratio Calculated Frequency Tempered Frequency Note in Scale Musical Relationship When A=432 * Octave below Octave above 1/1 440 440.00 A Root 432 216 864 2/1 880 880.00 A Octave 864 432 1728 2/3 293.33 293.66 D Fourth 288 144 576 2/5 176 174.62 F Aug Fifth 172.8 86.4 345.6 3/2 660 659.26 E Fifth 648 324 1296 3/5 264 261.63 C Minor Third 259.2 129.6 518.4 3/8 165 164.82 E Fifth 162 (Phi) 81 324 5/2 1,100.00 1,108.72 C# Third 1080 540 2160 5/3 733.33 740.00 F# Sixth 720 360 1440 5/8 275 277.18 C# Third 270 135 540 8/3 1,173.33 1,174.64 D Fourth 1152 576 2304 8/5 704 698.46 F Aug. Fifth 691.2 345.6 1382.4