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Recalculation of Fundamental Vibration Frequency and music harmonic octave ranges

After spending quite some time investigating common musical scales and discovering the underlying symmetry of the 12 even tone scale, as most commonly seen on piano keyboards, i can present the following 'pure'  musical note frequencies that should harmonise perfectly with the Fundamental Vibration Frequency of 1 cycle per second (1 hertz)

These are for the 9th and 10th harmonic octaves from the FVF setting D as the middle note to which all 6 other notes and 5(6) half tones make perfect symmetry.

9th Harmonic 10th Harmonic


Ab    181.019    362.039
A    191.783       383.567 A1
Bb    203.187    406.375
B     215.269      430.539 B1
C    228.070      456.140 C1
Cb  241.632     483.264
D     256.000     512.000 D1
D#  271.223     542.445
E     287.350      574.701 E1
F     304.437      608.874 F1
F#  322.540      645.080
G     341.719     683.438 G1
G#  362.039     724.077

In relation to D: Ab = D x (Root 2)/2; G# = D x Root 2 = Ab in next octave.


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Comment by neophyte on August 12, 2018 at 4:38am

Fair question Chris.:-)

Around a hundred years or more ago someone decided to set a 'standard' for musical tuning and that was adopted by American musicians and was common through most of the European countries also. This standard (for tuning of musical instrumentation purposes) was for an 'A' of 440 hz. Pretty much all guitars and orchestras today are tuned with this frequency as the base note. Previously 435 was one common standard. There was also a baroque tuning of 415 and a concert tuning of 430 ( and another at 466). Beethoven had a tuning fork that was set to 455.4Hz?

As you can see i have used D as my base and set it as 1 Hz then found the relevant octaves (harmonics of the Fundamental Octave with D in the middle note of the Fundamental Octave) This gives me an A of 383.5 Hz compared to their 440Hz or if you scale up my 'B' is the closest note to their base A with a frequency of some 10 Hz lower - 430.5 Hz. My 'C' is 456Hz.

You could tune any instrument to any starting note frequency of course to play music with but 440 Hz A is the most common today This is much higher, by a factor of almost 14% (+56Hz/383.5) than where I would suggest music in harmony with the fundamental vibration should be - we've 'speeded' up our music?

It would be interesting to hear the harmony or dissonance between my A and the 'standard'?

In early renaissance times musicians would 'compete' against each other by increasing their standard tuning frequency as this seemed to give violins a 'brighter' sound - apparently the tighter string tunings gave a greater amplitude of sound wave when played.

It seems that our original music was set to lower frequencies than we most commonly use today but the fundamental note of 1 Hz does not vary and i believe our music should be set to notes that are in better harmony with it. Frequencies like 256 Hz, 384, Hz 512 Hz and 767Hz (D3, A4, D4, A5).

Hope that helps? :-)

Comment by Chris Kelley on August 10, 2018 at 11:22pm

How do these frequencies compare to say the frequencies used in radio/"pop" music?

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