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Blog » Fibonacci 432Hz Temperament

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October 27, 2013

FIBONACCI 432Hz TEMPERAMENT

This is the 432Hz related abstract of the blog article “Fibonacci & Tuning“. For more information and alternative temperaments do read the full article!

8-FIBONACCI (TEMPERAMENT)

Ratios made with the first 5 (unique) numbers of the Fibonacci series (1, 2, 3, 5, 8) are related to key intervals of musical temperaments:

  • 1/1 = Tonic
  • 2/1 = Octave
  • 2/3 = Just Fourth
  • 3/2 = Just Fifth
  • 3/5 = Just minor Third
  • 5/3 = Just Major Sixth
  • 5/8 = Just Major Third
  • 8/5 = Just minor Sixth

Some of the 13 tone interval ratios of 12-Tone scale contain numbers not found in the Fibonacci series, like the Perfect Fourth with ratio: 4/3. But you can use alternative mathematical formulas to replace those with using only Fibonacci numbers, in the case of the Perfect Fourth you could use 2/3·2 or 2/3 (8va). 8va = ‘ottava’ = transpose an octave up.

For my 12-Tone “8-Fibonacci” I will use the numbers 1, 2, 3, 5 and 8 for the ratio formulas.

WHEN USING A4=432HZ AS BASE:

Ratios with
Fibonacci Numbers
Note in
Scale		Musical
Interval		When
A4=432Hz
1/1A3Tonic (1/1)216Hz
28/35A#/BbPythagorean Minor Second (256/243)230.4Hz

5·232

32/8

B

Pythagorean Major Second (10/9)

Just Major Second (9/8)

240Hz

243Hz

3/5 (8va)CJust Minor Third (6/5)259,2Hz
5/8 (8va)C#/DbJust Major Third (5/4)270Hz
2/3  (8va)DJust Fourth (4/3)288Hz

32·5/25

√2/1

D#/Eb

Just Tritone (45/32)

Equal-Tempered Tritone (26/12)

303,75Hz

305,470…Hz

3/2EJust / Pythgorean Fifth (3/2)324Hz
8/5FJust Minor Sixt (8/5)345,6Hz
5/3F#/GbJust Major Sixt (5/3)360Hz

24/32

32/5

G

Pythagorean Minor Seventh (16/9)

Just Minor Seventh (9/5)

384Hz

388,8Hz

·5/8G#/AbJust Major Seventh (15:8)405Hz
2/1A4Octave (2/1)432Hz

WHAT ABOUT THE OTHER FIBONACCI NUMBERS?

Well if we use the next 2 numbers of the sequence for ratios we can add several more tones. The ORANGE bars are the tones related to number 13, the PURPLE bars to number 21. Here are a few …

Ratios with
Fibonacci Numbers		Note in
Scale		Musical
Interval		When
A4=432Hz
21/5 (-15ma)A#↓/Bb↑?226,8Hz

13/3 (-15ma)

B↓?

235Hz

3/21 (22ma)B↑?246,857…hz
8/13 (8va)C↑?265,846…Hz
13/21 (8va)C#↓?267,428…Hz
13/5 (8va)Db↑?280,8Hz
21/8 (-8va)D↓
?283,5Hz
8/21E↑?329,142…Hz
5/13 (15ma)F↓?332,307…Hz
21/13F↑?348,923Hz
13/8F#↓?351Hz

21/3 (22ma)

G↓?

378

3/13 (22ma)Gb↑/G#↓?398,769…
5/21 (22ma)G#↑?411,428…Hz

The arrows behind the tones (in column 2) tell you if the tones are a bit sharper (↑) or flatter (↓) in relationship to “8-Fibonacci”.

Naturally if you continue using more numbers of the Fibonacci Sequence (34, 55, …) you will be able to add many more tones in between those listed above … FIBONACCI TEMPERAMENTS:

  • 8-Fibonacci (1, 2, 3, 5, 8)
  • 13-Fibonacci (1, 2, 3, 5, 8, 13)
  • 21-Fibonacci (1, 2, 3, 5, 8, 13, 21)
  • et cetera.

This was the 432Hz related abstract of the blog article “Fibonacci & Tuning“. For more information and alternative temperaments do read the full article!

REFERENCES & CREDITS:

Banner images “Fibonacci Spiral” by Rahzizzle

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