432HZ & TUNING … WHAT IS RELATED AND WHAT IS NOT?
On many web sites and blogs about 432-Tuning various presumed relationships between musical tuning and the presence of number 432 in other fields are shared to validate 432-Tuning. The number 432 can be found in a large number of “things”, in music, sacred geometry, astronomy, philosophy, religion, et cetera. But, numbers without units are nothing more then symbols, and symbols don’t sound! In order for something to “relate”, there have to be units and characteristics that match.
In this blog article I will take a look at some of the “evidence” presented by other web sites and blogs … Why? Well, misinformation is counterproductive for the development and implementation of 432-Tuning. It is important that we demystify the myths and get rid of the clutter. Hopefully this article contributes to that.
Now, important to note, is that I do not deny the similarities between patterns or formulas and ratios in music and those in for example (sacred) Geometry and Nature. Music – like anything in existence – has patterns and can be formulated and placed in perspective by the use of formulas and ratios.
BUT … not every pattern can be used to create music. Sound yes, but not all sound is music. The same can be said about Math, relationships between tones can be explained with mathematical formulas and ratios, and formulas can be used to generate sound, but not all sound is music! (and that of course depends on what you call “music”).
“432” AND SOUND (Hz) …
So, what about the unit used for sound? Well, there are various units used to measure sound, but when we speak about tuning we talk about “Pitch” and therefor the unit Hertz (Hz). If you do not understand what Hertz is, then I suggest you first read about it at Wikipedia.
In short: “Hertz is a particular number of occurrences of a repeating event per unit time.”
IMPORTANT: Not everything measured in Hz (like Electromagnetic Radiation, CPU clock rate, and Sampling Frequency / Sampling Rate) will relate to tuning, pitch and temperament.
So, if we would like to verify the relationship of the number 432 of “something” to 432Hz (sound) or it’s octaves (A3=216Hz, A5=864Hz, et cetera) then for that “something” should count:
A “particular number of occurrences” + repeating event + “time unit”.
WHAT HAS SIMILARITIES WITH PITCH (SOUND) RELATED HZ?
(radio waves, microwaves, Infrared, visible light, Ultraviolet, X-rays and Gamma rays)
Electromagnetic radiation has a “wave-like” nature and like sound uses the unit Hz. Even though sound and light uses the same unit Hertz, they still differ more then they have in common.
WHAT DO SOUND AND LIGHT HAVE IN COMMON?
- Sound and light both exhibit oscillatory wavelike characteristics with various frequencies, wavelengths, and amplitudes.
- Both propagate at a finite speed.
- Both exhibit Doppler shifts toward higher frequencies when the source of the wave is approaching us.
- The sensed intensity is dependent on the amplitude of the wave.
WHAT IS THE DIFFERENCE BETWEEN SOUND AND LIGHT?
- The frequencies of visible light and audible sound differ from each other by more than ten orders of magnitude. Audible acoustic range: roughly 20 Hz to 20,000 Hz vs. visible optical range: roughly 380 trillion Hz to 760 trillion Hz.
- Light waves are composed of transverse waves in an electromagnetic field, while sound waves are mechanical longitudinal waves (alternate compression and expansion of matter).
- Sound requires a “medium” to propagate, light does not. Therefor while light does propagate through a vacuum (absence of a medium), sound does not.
- The denser the medium, the greater the speed of sound. The opposite is true of light.
- The speed of light in a medium is constant. The velocity of sound in a medium can change.
- Electromagnetic waves, including light is a “stream of particles” (photons). Sound does not consist out of particles.
- Light waves can be polarized, but sound waves cannot.
It’s also worth noting that while the frequency range of audible sound covers a factor of 1000, (about 10 octaves), the range of visible light covers only a factor of 2 (just one octave).
Read more about the relationship between sound and light in the article “Sound & Light (color).
WHAT DOES NOT RELATE TO 432 IN SOUND (HZ) & MUSIC?
When the number 432 (or half: 216, or double: 864) appears, but with a different unit (other then Hz) and characteristics, then we can conclude there is no direct relationship with or to 432Hz (sound) other then the number itself and might be nothing more then symbolism..
In the examples below (I will only give a few examples, I am sure you can find many others as well) you can see there are no similarities in “characteristics” (NO “particular number of occurrences” + repeating event + “time unit”), clear examples of “swapping” units: Apples and Oranges!
These examples do not proof or validates 432Hz as concert pitch or music frequency is of real importance or has any real meaning!
THE NUMBER 432 AND ASTRONOMY & MATH:
The diameter of the moon is 2160 miles (432 / 2), the diameter of the sun is 864,000 miles (2 · 432).
A mile is a unit of length. No occurrences, no repetition, and not a time unit.
The distance from the center of the earth to the average height of the atmosphere. This value is given as 4320 arc-minutes.
An Arc-minute is a unit of angular measurement equal to one sixtieth (1⁄60) of one degree. In turn, a second of arc or arc-second is one sixtieth (1⁄60) of one arc-minute. Because one degree is defined as one three hundred and sixtieth (1⁄360) of a rotation, one minute of arc is 1⁄21,600 of 360 degrees.
“Arc-minute” is NOT related to time, but Geometry and Trigonometry, (angle, degree).
THE NUMBER 432 AND HISTORICAL PLACES
It is true that in various historical places such as with the Latitude of Stonehenge, Height of the Great Pyramid, Buddah Statues in the Square of of the Borobudur Temple, a.o. the numner 432 pops up. The number 432 in these places relates to length, angle, degrees, et cetera. Units that do not correspond one-on-one to or are commonly “converted” to Hertz. The “connection” between these places and 432Hz-tuning is thus but a “symbolic” one.
MATH = SOUND ≠ MUSIC
Not every mathematical formula can be used for making music. Yes, any formula can render a series of numbers that can be used to generate sound. But sound and music are not synonyms, sound does not equal (≠) music.
This is in general the problem with tuning concepts made by mathematical minds with no (or insufficient) musical education and/or practical musical experiences. No matter how nice a formula looks on paper, the generated scale and/or Temperament could sound horrible nonetheless.
One of the most known tuning concepts exemplary of the mismatch between the formula on paper and the actual implementation, how it really sounds, is the “Ancient Solfeggio Frequencies” concept by Dr. Joseph Puleo and Leonard G. Horowitz. You can read more about this pseudo-scientific concept in my blog article “Myth: The Ancient Solfeggio Frequencies“.
MUSIC = MATH … and MATH = SOUND … but SOUND ≠ MUSIC.
MUSIC = MATH
All proper tuning systems used (now and in the past) can be explained with mathematical formulas. How? Well, we use ratios to determine the size of the intervals between tones.
EXAMPLE: 12-TONE EQUAL TEMPERAMENT (the present standard)
In twelve-tone equal temperament, which divides the octave into 12 equal parts, the width of a semitone, i.e. the frequency ratio of the interval between two adjacent notes, is the twelfth root of two:
There are many other Musical Temperaments (most more complicated then 12-TET), using various mathematical formulas to create other ratios then 1.059463. The most know Temperaments are the: Pythagorean Tuning, Meantone Temperament, Well Temperament, Just Intonation and Five-Limit Tuning.
For 432-Tuning the Pythagorean Tuning or modifications of if like Maria Renold’s “Scale of Fifths” is used.
CONCEIVABLE THEORIES & CONCEPTS:
CYMATICS – “THE SHAPE OF SOUND”
Cymatics is the study of visible sound and vibration. Typically the surface of a plate, diaphragm, or membrane is vibrated, and regions of maximum and minimum displacement are made visible in a thin coating of particles, paste, or liquid.
[ Read More ] ►
432 AND THE “SCHUMANN RESONANCE”
Using the Schumann Resonance as “solid evidence” to “prove” the A4=432Hz concert pitch is very “circumstantial”. HOWEVER, it is reasonable to say the Schumann fundamental “could be”, “could become”, and/or “might have been” at 8Hz at various moments in time … [ Read more ]►
MISINTERPRETATIONS, DISINFORMATION, AND FICTION (MYTHS):
SAMPLING FREQUENCY (RATE), OFTEN MISINTERPRETED
The sampling rate, sample rate, or sampling frequency defines the number of samples per second (or per other unit) taken from a continuous signal to make a discrete signal. For time-domain signals, the unit for sampling rate is hertz (inverse seconds, 1/s, s−1). The inverse of the sampling frequency is the sampling period or sampling interval, which is the time between samples.
So, what does this mean?
Well, when an continuous (analogue) signal is converted to digital data, the analogue signal is “sliced” into a large number of parts (samples) with a ADC (analog-to-digital converter). These “slices” refer to particular points in time of the original continuous signal. A DAC (digital-to-Analog converter) uses this data to “re-create” the original analogue signal, as good as possible. The larger the number of samples, the smoother the curve of the reconstructed analogue signal will become, and thus the better the overall sound quality.
This process though does not effect the Tuning properties. “Hertz” in this case has nothing to do with “Pitch”, but refers to the number of samples (particular number of occurrences) taken from a continuous signal (repeating event) per second (time unit).
More information available at Wikipedia.
432HZ WAS THE STANDARD BEFORE 440HZ
A4=432Hz (or for this matter C4=256Hz as well) has never been a standard. Those sources that suggest 440Hz replaced 432Hz as concert pitch are incorrect! [ Read more ]►
Often mentioned in alongside the “432Hz was the standard before 440Hz” myth, is yet another myth about a Nazi conspiracy (with Goebbels in a leading role). In this myth Goebbels is being held responsible for the introduction and standardization of the 440Hz C.P. [ Read more ]►
“432Hz IS THE SQUARE ROOT OF THE SPEED OF LIGHT”
This is one of the most flawed pieces of “evidence” offered by various sources online in support of 432-Tuning. Not only have they – who provide that info as “evidence” – failed to understand that sound waves and electromagnetic waves can not be related 1 on 1, they have also failed to realize that the Speed of Light is based upon electromagnetic waves traveling through a vacuum (no medium), while sound waves require a “medium” to travel (in a vacuum sound waves do not “travel”) … [ Read more ]►
“ALL CLASSICAL MUSIC BY BACH, BEETHOVEN, MOZART AND VERDI WAS ORIGINALLY COMPOSED AND PERFFORMED USING THE STANDARD OF A4=432HZ.”
This is one of those stories that keeps popping up online from time to time. What can we say about this?
- 432Hz has never been a standard. [ Read more ]►
- The Concert Pitch that Verdi and Bach (I have not found any references concerning Brahms) have been said to be in favor of, is C4=245Hz. BUT, since composers like Bach did not use Pythagorean Temperament anymore, their A4 would have been 428-430.5Hz, NOT 432Hz.
- There are hardly any historical reference at all that their work could have been “originally performed” in 432 in their days. Most instruments are designed for a particular Concert Pitch and Temperament. Only a small number of instruments can tune to any Concert Pitch and play in any Temperament. The C.P. and Temperament varied from region to region and from country to country. [ Read more about the standardization of the Concert Pitch ]►
Dear reader … after reading this article I do hope you have at least become aware of the possibility that some of the information you might have been reading, sharing and might have believed to be true is at least worth (re-)investigating.
I would like to urge you to dig deeper and to no longer simply copy ‘n paste “info” (that might sounds appealing) from blogs and websites without checking it’s sources (if they have) and looking into the matter. If you like to “inform” (or perhaps even “educate”) others, then make sure you have studied the material well enough, or make absolutely clear to your readers you are sharing something that you have not checked thoroughly and might not be true!
This way people can truly trust you and you won’t be making an “ass” out of yourself.
If you share “information” that turns out to be misinformation simply because you have not researched it yourself (laziness? ignorance?), then you are just as “guilty” for misinforming others as the writers of those articles are!
If you notice something written in my articles that you think is not correct, then please do contact me with info / data / evidence to correct possible mistakes. Thank you.