# Blog » Fibonacci 432Hz Temperament

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#### FIBONACCI 432Hz TEMPERAMENT

##### 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 withFibonacci Numbers Note inScale MusicalInterval WhenA4=432Hz 1/1 A3 Tonic (1/1) 216Hz 28/35 A#/Bb Pythagorean Minor Second (256/243) 230.4Hz 5·23232/8 B Pythagorean Major Second (10/9)Just Major Second (9/8) 240Hz243Hz 3/5 (8va) C Just Minor Third (6/5) 259,2Hz 5/8 (8va) C#/Db Just Major Third (5/4) 270Hz 2/3  (8va) D Just Fourth (4/3) 288Hz 32·5/25√2/1 D#/Eb Just Tritone (45/32)Equal-Tempered Tritone (26/12) 303,75Hz305,470…Hz 3/2 E Just / Pythgorean Fifth (3/2) 324Hz 8/5 F Just Minor Sixt (8/5) 345,6Hz 5/3 F#/Gb Just Major Sixt (5/3) 360Hz 24/3232/5 G Pythagorean Minor Seventh (16/9)Just Minor Seventh (9/5) 384Hz388,8Hz ·5/8 G#/Ab Just Major Seventh (15:8) 405Hz 2/1 A4 Octave (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 withFibonacci Numbers Note inScale MusicalInterval WhenA4=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 8/21 E↑ ? 329,142…Hz 5/13 (15ma) F↓ ? 332,307…Hz 21/13 F↑ ? 348,923Hz 13/8 F#↓ ? 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.