### HISTORY

### MATHEMATICS

### ARCHITECTURE

### PAINTING

### MUSIC

### CONCLUSIONS

The very matrix of music is rooted in the Fibonacci series, which comes as no surprise since how Pythagoras and his followers were credited by the Greeks with its discovery.

The fundamental Western scale can be seen as a product of the series:

Notes in the scale of Western music are based on natural harmonics that are created by ratios of frequencies. Ratios found in the first seven numbers of the Fibonacci series (0, 1, 1, 2, 3, 5, 8) are related to key frequencies of musical notes.

The Fibonacci ratio ⅜, representing the Perfect Fifth leads to the Golden Mean, in this case 162 (0.62).

The fundamental Western scale can be seen as a product of the series:

- There are 13 notes in the span of any note through its octave.
- A scale is composed of eight notes, of which the fifth and third notes create the basic foundation of all chords, and are based on whole tone which is two steps from the root—that is the first note of the scale.

Notes in the scale of Western music are based on natural harmonics that are created by ratios of frequencies. Ratios found in the first seven numbers of the Fibonacci series (0, 1, 1, 2, 3, 5, 8) are related to key frequencies of musical notes.

The Fibonacci ratio ⅜, representing the Perfect Fifth leads to the Golden Mean, in this case 162 (0.62).

Fibonacci Ratio |
Calculated Frequency |
Tempered Frequency |
Note in Scale |
Musical Relationship |
When A=432 |
Octave Below |
Octave Above |

1/1 | 440.00 | 440.00 | A | Root | 432.00 | 216.00 | 864.00 |

2/1 | 880.00 | 880.00 | A | Octave | 864.00 | 432.00 | 1728.00 |

2/3 | 293.33 | 293.66 | D | Fourth | 288.00 | 144.00 | 576.00 |

2/5 | 176.00 | 174.62 | E# | Aug Fifth | 172.80 | 86.40 | 345.60 |

3/2 | 660.00 | 659.26 | E | Fifth | 648.00 | 324.00 | 1296.00 |

3/5 | 264.00 | 261.63 | C | Minor Third | 259.20 | 129.60 | 518.40 |

3/8 | 165.00 | 164.82 | E | Fifth | 162.00 | 81.00 | 324.00 |

5/2 | 1100.00 | 1108.72 | C# | Major Third | 1080.00 | 540.00 | 2160.00 |

5/3 | 733.33 | 740.00 | F# | Major Sixth | 720.00 | 360.00 | 1440.00 |

5/8 | 275.00 | 277.18 | C# | Major Third | 270.00 | 135.00 | 540.00 |

8/3 | 1173.33 | 1174.64 | D | Fourth | 1152.00 | 576.00 | 2304.00 |

8/5 | 704.00 | 698.46 | E# | Aug Fifth | 691.20 | 345.60 | 1382.40 |