Blog » Overtones & Harmonics … 432Hz vs 440Hz

Approx. reading time: 5 minutes

HARMONICS / OVERTONES OF 432HZ VS 440HZ

RUMOR:  “432Hz TUNED MUSIC HAS MORE OVERTONES THEN 440Hz TUNED MUSIC.”

There are several articles available online about overtones and Concert Pitch 432Hz vs 440Hz. Some of these articles suggest / proclaim that 432Hz recorded (and/or pitched) music has more overtones then 440Hz recorded music.

Is this true and does that explain the difference in the change of sound?

OVERTONES

An overtone is any frequency higher than the fundamental frequency of a sound. The fundamental and the overtones together are called partials (a “partial wave” or “constituent frequency”).

HARMONICS

The term harmonic has a precise meaning – that of an integer (whole number) multiple of the fundamental frequency of a vibrating object. The term overtone is used to refer to any resonant frequency above the fundamental frequency – an overtone may or may not be a harmonic. Harmonic overtones are the fundamental frequency multiplied, for example of the fundamental 216Hz: 432Hz (216 x 2), 648Hz (216 x 3), 864Hz (216 x 4), et cetera.

PITCH, OVERTONES AND HUMAN HEARING

One of the reason for the proclaimed improvements of the sound of 432-pitched music is that lower pitches can potentially produce more overtones within the human hearing range. It is true that low tones can potentially produce more overtones within our hearing range then high tones can.

The human hearing range is commonly given as 20 to 20,000Hz. Under ideal laboratory conditions, humans can hear sound as low as 12 Hz. Some children are capable of hearing frequencies above 20,000Hz but with age this range will shrink usually beginning at around age of eight with the upper frequency limit being reduced.

It is important to understand that their is theoretically no limit to the number of potential overtones that can be generated. That we practically detect less overtones created by a piccolo Trumpet then by a Tuba is not because a piccolo produces less overtones, but many of it’s overtones might overshoot the high end boundary of our hearing.

So, to visualize the difference between two tones of different pitch I will calculate the number of the first overtone that overshoots 20,000Hz for A3 and A4 in the table below, starting with 432Hz and 440Hz as 1st Harmonic (Fundamental):  

1235102040478092
A3=216Hz4326481,0802,1604,3208,64010,15217,28020,088
A4=432Hz86412962,1604,3208,64017,28020,30434,56039,744

What we see in this table is that if we use 216Hz as fundamental, this tone could generate 92 overtones before we overshoot the 20,000Hz, but if we use 432Hz as fundamental, this tone could generate only 47 overtones before we overshoot the 20,000Hz.

So, YES, lower pitches can potentially produce more overtones within our ranges of hearing. 

BUT … does this also means that 432Hz music will have more overtones then 440Hz music, because of it’s lower pitch?


OVERTONES OF 432HZ VS 440HZ

Well, let’s just compare the difference between the tone fundamentals of 432Hz and 440Hz in a table: 

1235102040454647
4328641,2962,1604,3208,64017,28019,44019,87220,304
4408801,3202,2004,4008,80017,6001980020,24020,680

So, what the table above tells us, is that you could say that the tone 432Hz does generate 46 overtones before crossing the hearing limit, while 440Hz only generates 45 overtones before crossing the hearing limit.

So, the claim that 432Hz tuned music can contain more overtones (within the hearing range) is in true. BUT that difference is really small!

Even if we would take a tone in the lower register, let’s say for example A1=55Hz (if A4=440Hz) and A4=54Hz (if A4=432Hz), then a tone at 55Hz could in theory generate 363 overtones before overshooting 20,000Hz and a tone at 54Hz could in theory generate 370 overtones before overshooting 20,000Hz. 

I personally don’t think that that difference of 7 overtones (363 vs 370) is why 432-tuned music sounds different then 440-tuned music. 

So, if it’s not the change of the number overtones that make a noticeable difference, then what is?


FORMANTS, TIMBRE AND SYMPATHETIC RESONANCE

What really makes a difference is the formants, timbre and sympathetic resonance characteristic to the instrument / voice.

Continue reading the article: ‘Harmonics, Overtones, Formants, Timbre and Sympathetic Resonance‘.


ADDITIONAL FACTORS THAT PLAY A ROLE:

Of course not all sounds or instruments are equally rich when it comes to overtone production. Both for live performances and recordings various other things play a role, including:

  • The mic’s, amps, mixers, effect modules, cables, et cetera used.
  • The quality of the instruments used.
  • The “amplification” (Soundsystem – speakers, amps and/or other hardware) used.
  • The acoustics of the room you are in.

 … for recordings additional factors are:

  • The sample rate used during the recording.
  • The processing done during mixing and mastering.
  • The format of the “export”.
  • The (limitations of the) mediums the music is released on.

All of these aspects play a role and may determine if the lower pitch will actually be of any benefit to begin with. Of course we haven’t even mentioned the “condition” of your ears and bodily “sensitivity” (resonance) for the vibrations “floating” through the room …

A lot of “what if’s” ain’t it so?


POST PRODUCTION RE-PITCHING & OVERTONES

Changing the pitch of recorded material will NOT change / re-balance the harmonics of the instruments used for the recording. The number of overtones will NOT change when re-pitching recorded material! If you have a recording where the highest frequencies “die out” at for example 18kHz, then shifting the pitch down will not make a difference! No “additional” harmonics will appear “miraculously”.

The only thing that might change by re-pitching recorded material is the way the sound ‘interacts’ (acoustics) within the space were the music is played and thus how it is perceived by our senses and interpreted by our brains.

Post production re-pitching (like any other “manipulation” of the original recorded material) could cause loss of sound quality. This is most obvious with the higher frequencies (“high end”), in particular when only Pitch but not Tempo is changed (or visa versa). Only when both pitch and tempo are changed during post-production re-pitching, only then the loss of sound quality is “negligible”.

More information on how to change the concert pitch in post production if you do wish to do so …


CONCLUSION

Using a little lower pitch will make it theoretically possible to have more harmonics, but in reality the more harmonics claim is for most people under most conditions not of real impact. 

With other words:

IF the music was recorded at a top-level recording studio, by a skilled sound engineer … played with professional well build instruments … and the exports you listen to are use a very high sample rate and are uncompressed … and you are listening to this music with high-end (A Class) Hi-Fi system, in a balanced room (proper dimensions and acoustic treatment) … ONLY THEN you might be able to “benefit” from the difference in generated harmonics when a lower pitch is used.

BUTIF you are listening to MP3 exports on your telephone with 30 dollar in-ear headphones … then forget about the theoretically larger number of harmonics, they won’t be there.


REFERENCES:


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