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:
  • 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.
The resulting sequence of numbers is the 1–2–3–5–8–13 pure Fibonacci.

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
Source: https://www.goldennumber.net/music.htm