Music Theory: 432 Hz Tuning - Separating Fact From Fiction

In exploring the 432 Hz debate at Ask.Audio, we soon realised this topic wasn't going to be resolved in one article. Here Assaf Dar Sagol explores the fact and fiction behind tuning to 432 Hz.  

This article represents the views and research of the author. If you're interested to read the 432 Hz article by Lynda Arnold which sparked a huge debate visit this page: Music Theory: Exploring The 432 Hz Tuning Debate.

432 Hz. The magic number everybody is talking about. It is said to be the natural frequency of the universe, to have cosmic healing powers and to attract masses of audience to our music. Just by tuning our music less than a semitone below our standard A=440Hz we are promised direct access to the universe's hidden treasures.

There are many articles presenting so-called “scientific evidence” in favor of 432 Hz. But how much of what are being presented with is fact, and how much of it is fiction? Let’s find out! 

Fact #1

Fiction: Ancient instruments such as Tibetan bowls, Pythagoras monochord, ancient flutes, have been found to use 432 Hz as their base pitch.

Fact: Hertz is a modern term coined in 1930. Before that it was referred as “Cycles Per Second”. The first time “Cycles Per Second” could be accurately measured was in 1834, when two instruments were invented: the (remodeled) Savart Wheel by Félix Savart, and the Tonometer by Johann Scheibler.

Further than that—the measurement of Seconds has only begun during the late 16th century.

Ancient Tibetans, Pythagoras and anyone before 1834 could not have intentionally tuned their instrument to measure 432 Hz as this frequency scale simply did not exist at the time. As for evidence, I could not find a single solid evidence for ancient flutes or bowls tuned to 432 Hz. If you find some - please let me know!

Pythagoras was born 1500 years before the idea of  a second was conceived.

Pythagoras was born 1500 years before the idea of  a second was conceived.

Resources:

http://hps4000.com/pages/special/sound_history.pdf

https://en.wikipedia.org/wiki/Second

Fact #2

Fiction: Pythagoras’ A was 432 Hz.

Fact: Pythagoras’ tuning system is ratio based. It is not based on an absolute pitch, but rather on the relations from an arbitrary reference pitch. We already know Pythagoras could not have known what a second is, so he could not know what Hz meant. Indeed 432 is a multiplication of the ratio between C and A, where C is 1 and A is 27/16 which is the same as 432/256—however this  applies to any base frequency and has nothing to do with a specific Hz. 

Pythagoras’s tuning system was based on cycling perfect fifths. However, cycling fifths will never get you to complete a circle—unless one of the fifths  is diminished. In other words, the Pythagorean scale has to be 'tuned-down' a little each octave in order to maintain its consistency. This makes the temperament uneven and sound “off” when playing music with complex harmonies, and this is exactly the reason it was abandoned. 

The monochord

The monochord

Listen for yourself:

Resources:

https://en.wikipedia.org/wiki/Pythagorean_tuning

Fact #3

Fiction: Mozart used 432 Hz for all of his music.

Fact: The only evidence for Mozart’s A comes from an ancient tuning fork from 1780 with the tone of A=421.6 Hz. This tuning fork belonged to the Viennese piano builder Johann Andreas Stein, the leading piano maker in Vienna at the time, who was responsible for Mozart's pianos as well as Haydn’s and Beethoven’s. It is likely that they have all used A=421.6Hz.

Handel’s personal pitch fork was found 30 years earlier in England and was tuned to A=422.5Hz - pretty close to Mozart! and pretty far from 432 Hz.

Resources:

https://books.google.com/books?id=hnkWAAAAYAAJ&pg=PA333#v=onepage&q&f=true 

Tuning fork

Antique Tuning Fork

Fact #4

Fiction: Verdi has used 432 Hz for all his music.

Fact: Verdi used several tunings across his life. As an opera composer he was aware of the pitch inflation (pitch standards rapidly rising to achieve a brighter orchestral sound) that was happening in his time, and was concerned it was putting a strain on singers voices as they struggle to hit the high notes on a score.

Verdi has requested his Requiem to be tuned to 435 Hz (according to the 1859 French “diapason normal” standard) and in a later letter he has expressed a slight preference for 432 Hz. Verdi is the only known composer to even hint towards 432 Hz, and it was obviously for completely different reasons than cosmic spirituality.

Resources:

https://books.google.com/books?id=t_iB90JnPrwC&lpg=PA17&dq=Verdi%20tuning&pg=PA17#v=onepage&q=Verdi%20tuning&f=false

Fact #5

Fiction: 432 Hz is the way everybody used to tune in the past, but we have now forgotten the ancient wisdom of our ancestors.

Fact: Musicologist Alexander John Ellis has searched, measured and documented ancient pipe organs and tuning forks. Here is a graph representing his most important findings—as you can see the only mention of 432 Hz was proposed in Italy in 1880 (by Verdi), and we already know that this was done for practical reasons rather than spiritual ones. The fact is that before standardization, the pitch of A fluctuated heavily between 400 Hz and 460 Hz. 

Historic tunings graph.

Historic tunings graph.

Resources:

https://books.google.com/books?id=hnkWAAAAYAAJ&pg=PA333#v=onepage&q&f=true

Fact #6

Fiction: 432 Hz is the frequency of the heart / brain / earth / sun / water

Fact: The frequency of the heart fluctuates between approximately 1 Hz to 2.5Hz. It does not have a steady frequency that can be multiplied to achieve 432 Hz. 

Brainwaves or Neural Oscillations range between approximately 1 Hz and 70 Hz and are not tuned to 8 Hz or other divisions of 432 Hz in any way.

The Schumann resonance is a set of electromagnetic oscillations that originate from earth. One of them currently resonates at an average of 7.83Hz and not 8 Hz. which if multiplied by 55 gives us an A=430.65 Hz. Close, but no cigar.

Astronomers at Stanford have recorded super sonic oscillations from the sun at around 5.964 GHz. They had to slow them down (change their pitch) by 42,000 times to accidentally hit the frequency of 142 Hz - and not 144 as claimed by some which would again bring us a frequency of A=426Hz. 

Water molecules can vibrate in a wide band of extremely high frequencies close to the infrared spectrum (90–110 Tera Hz). The band is wide enough to not favor any specific frequency, let alone 432 Hz. 

Natural frequencies.

Natural frequencies.

Resources:

https://en.wikipedia.org/wiki/Heart_rate

https://en.wikipedia.org/wiki/Brain_wave

https://en.wikipedia.org/wiki/Schumann_resonances

http://solar-center.stanford.edu/singing/

http://www1.lsbu.ac.uk/water/magnetic_electric_effects.html

Fact #7

Fiction: Goebbels and the Nazis tried to take over the world with A440Hz. 

Fact: In fact, it was the British Standards Institute who arranged an international conference in London 1939 where it was internationally agreed for A=440Hz to be the standard.

Resources:

http://www.wam.hr/sadrzaj/us/Cavanagh_440Hz.pdf

Fact #8

Fiction: Cymatics—the unexplored scientific realm, provides images as proof for 432 Hz being the frequency of water/universe.

Fact: There have been several videos and images out there presenting beautiful cymatic imagery as proof for the 432 Hz theory. However these images are produced by resonant bodies (water or metal plates) which can be tuned to resonate at different frequencies.

Chladni Plate

Chladni Plate 

This means that metal plates or bodies of water that are tuned to resonate at 440 Hz (just like a string on a guitar) will produce lovely cymatic shapes at… you guessed it, 440 Hz! 

The geometric shapes are created due to a well known phenomena called standing waves.

Resources:
https://en.wikipedia.org/wiki/Cymatics

https://en.wikipedia.org/wiki/Ernst_Chladni

https://en.wikipedia.org/wiki/Standing_wave

Fact #9

Fiction: Your music will sound better at A=432Hz

Fact: Musical aesthetics is a flexible thing. Musicians are not obligated to use 440 Hz as their base frequencies, and many orchestras around the world use different pitches according to the music they are about to play. It is generally agreed that baroque music is to be played at around A 415Hz, classical and early romantic eras at around 425 Hz and later repertoire at 440 Hz and up. 

Tuning to different pitches has subtle effects on the timbre of acoustic instruments, but makes no difference to electronically generated sounds. 

Resources:

http://www.the-compound.org/writing/classicaltuning.pdf

In Conclusion

432 Hz seems to be just another number without any special significance over others. Tuning your music to a specific frequency will not unlock cosmic powers, or make your music sound better or worse. Having said that, there is no rule or law that requires musicians to stick to the standard tuning of A=440Hz. Serious musicians should all use alternate tunings for viable reasons such as the instruments timbre and build, the musical demands and the historic background of the composition. 

On a personal note, while working in Polyverse Music,  I have been receiving requests to enable 432 Hz in our new plug-in “I Wish”. Even though I do not believe in 432 Hz, I do believe that musicians should be able to tune to any base frequency they like, which is why we have decided our next update will include a master tuning setting. After all, i see no reason not to tune to 432 Hz.

Have fun, create and experiment, and don’t let standards hold you back!

Interested in music theory? Check out the Music Theory video courses in the Ask.Audio Academy (featuring musicians like Jordan Rudess!)

 

Assaf Dar Sagol is the co-founder and CEO of Polyverse Music. A company that creates unique plug-ins in collaboration with world renowned artists. Their first release is I Wish By Infected Mushroom. Assaf has produced and arranged albums for all major record companies in Israel, working with top notch artists and professionals of the ... Read More

Discussion

Tyler
Thank you for injecting reason into this "argument."
Milton
These facts are well known and just plain ignored by many 432hz advocates so still not sure why this is considered a 'debate' any more than a 'Flat Earth' debate. When 433hz sites start correcting errors that will be something. Nonetheless kudos for these succinct and accurate corrections!
Milton
432 not 433. Although 433hz is of course the actual magical frequency.
airforceguitar
Thank you so much for injecting a researched and informed perspective on this. Music is a "magical" endeavor, but please, let's get rid of the ridiculous non-scientific claims in music!
Earful
Tibetan singing bowls are specifically designed to the standards of Tibetan medicine, which recognizes winds, orbs, and channels in the body. I think that making a statement that "the Tibetans could never have done this intentionally" misses the basis of Tibetan physiology. It is based upon a conception of energy. I myself have an old Tibetan bowl which is exactly design to stimulate the Heart Chakra. If stimulating that Chakra happens to exactly match the 432hz frequency, then that would be evidence for the case that those who emotionally respond to 432hz. A composer friend of mine thinks it is all rubbish. I find that 432 is warmer and less stressful, i use 440 for the electric and 432 for the folk guitar. It is easier to hit the higher notes. Much better to drop a whole step to about 426.
Todd
On board with you here about these theories supporting 432. However, I think there is a better and more interesting avenue to explore. There is supporting evidence of 432 and its related numbers concerning the ratios of the earth and ancient cultures that build structures to reflect this. Not surprisingly...the pyramids of Egypt. If there is any validity to this frequency being "special" it probably comes from this conversation. Graham Hancock is one person among many who has compiled some of this information and explored it. Interestingly, I don't believe he has spoken about the frequency. Only the ancient geometry associated with the number 432.
Mihai Sorohan
"We can fix history at will and pick measures by matching theories. We know that the Egyptians used as a basis for measuring the "Small Cubit", equal to about 45 cm (24 fingers); inherited from the "Nippur Cubit", which found use in Sumer about 6,000 years ago. The conventional value of this 24 fingers cubit is approximately 45 centimeters. The Egyptians of the Old Kingdom used the 28 fingers from the Sumerian division to determine their Royal Master Cubit (or Sacred Cubit) of 52.5 cm. Later, during the 26th dynasty, it was extended to 52.9 cm. The base of the pyramid is 440 Royal Master Cubits, approximately 230.5 meters. There is no 432 anymore, but 440 Cubits! But 440 or 432 should be no concern because Cubits are not Hertz, as discussed in the previous paragraph"

http://www.medson.net/A432hz-myth.html
CalebGrayson
I had so much respect for this informative article until this like:
" Tuning your music to a specific frequency will not unlock cosmic powers, or make your music sound better or worse."

this claim is as much unfounded opinion as the pro-432 claims you spend this whole article refuting!
Mihai Sorohan
Music is a language (pretty much) and the ideas and emotions are carried by construction of the melody, phrasing, arranging, performance...etc, not by the reference pitch.
If I would read a poem with a low voice or high voice, would it make magically change the meaning of the poem?
CalebGrayson
yes. of course it would, because music is not just a language of numbers.
the mathematical abstraction of music — into notes and frequencies and rhythms, these language bits — is a simplification. it can not capture all of music and is not meant to as a map to same scale is not useful. this is why sampling/looping has become its own 'genre' as it contains a complexity that can't be notated or given a single pitch.

the minute you think that a note IS its frequency or that a frequency of sound is only its mathematical value then you make the fallacy that Philosopher Alfred North Whitehead calls misplaced concreteness — you've taken the idea that represents a thing and beloved that idea is the real concrete thing itself.
there has been a shift in education that have moved towards specialization — a lack of broad understanding of the world and a focus on particular areas of study with a bent on technique instead of theory of a particular theory taught without the theory of theory taught. this has led to a rational-materialism that isolates certian fields of learning.
numbers have cardinal value such as 432 being a measure of frequency, but the alps have ordinal value as a single point in a series or a unique place and identity in relation to all other numbers, the 432nd frequency. it's the ordinality where the 'magic' lies. and let me say, if you think the words 'magic' and 'myth' are synonyms for 'irrational' or 'false' then that's clear evidence of my claim that education is lacking in the foundational humanities and moved towards a vocational methodology with a rational-materialistic bias.

I applaud the historical research on 432, but it may be that 432 is emerging in the collective unconsciousness for a reason and people's limited understanding as to why along with intellectual laziness has fabricated these false histories in attempt to bring more legitimacy to the 432 mythos. that doesn't me 432 is not magical or need now or an evolutionary step in man's æsthetic and healing expressions. so please don't shut that notion down simply because you think music Is just numbers. :)
CalebGrayson
sorry for typos. no edits allowed here.
mwchoi
if you think that some magical number will change your music you should quit producing. this so-called "argument" is the exact reason why producers should work on acoustics study, but not on boodooism.
Polarbreeze
Well done Assaf, you describe the situation perfectly.
Larissa Cantoni
Strange how Antonio Stradivari, who lived between 1600 and 1700, was able to build violins in resonant proportions of the harmonic scale that sees A=432Hz (ask a luthier how the proportions of an instrument have to do with the tension of the strings and their vibrational frequency), for example...

Strange how Pythagoras with his monochord was using frequencies concerning the mathematics of 8, using as a reference the8 Hz (third octave above the starting point of 1Hz, from where climbing some octaves up the ladder we get a frequency of 256Hz, which corresponds to a C in the scale where A has a frequency of 432Hz) for therapeutic purposes... In ancient Greece, as already earlier in ancient China, sound was used as medicine, and not for entertainment purposes as today (while we are (re)discovering more and more the therapeutic sound power)...

Strange how in ancient Egypt they were able to build the great Pyramid of in the proportions of the harmonics of 432, and used stones that resonate at 432Hz, like those of many other prehistoric constructions such as Stonegenge or african sound stones...

These are just three examples (everyone is free to make their own research), but it is clear that even before the invention of the tonometer and the modern possibility to measure cycles per second,, thanks to astronomical observations, mathematics, or other, some cultures found a way to measure sound, or to define it, and check its effect on living beings and matter…

The implications and parallels between the microcosm at the molecular and atomic level, and the macrocosm in relation to the measures and distances of the planets and, through the discovery of Cymatics, with sacred geometry and the platonic solids, have only been rediscovered in modern times, but several great cultures of the past already had this knowledge!

Tuning systems such as the Equal Temperament and others, are applicable starting from a pitch of note, as is the A, at any frequency arbitrarily established, while the 432Hz Concert Pitch is called "Scientific Tuning" because of its correlations with mathematics, nature and the universe.

Consider that in the past, every family that was building musical instruments, before the mass production started, had its own pitch of intonation, as I was told by a musicologist, which varied from one family to another, according to what each luthier felt to be more correct... For example, some tuned their instruments to the singing of the birds. Every time a new instrument was built, it was tune to the previous one so that they could play together!

Giuseppe Verdi at one point decided to tune the note A to 432Hz because he had understood its mathematical and scientific implications (and not for cosmic and / or spiritual reasons)...

At a certain point of history, with the beginning of globalization on a musical level, and the development of industrial mass production of musical instruments, an international standardization was necessary, so that musicians of different nations could play together.
PS: See the intonation of Spanish Baroque music that was even at 415Hz... ;)

It is true that the brainwaves show a wide range of frequencies, but it is at 8Hz that the left and right hemispheres are working in perfect sync ...

Cymatics do not provide proof images that 432Hz is the frequency of the water or the universe (as written in the article).
It simply makes the effect of sound on matter visible, and the fact that certain harmonic frequencies form more precise patterns than other frequencies.., be they water waves or sand / salt designs on a metal plate.

It is curious that the global trend among orchestra musicians is to further raise the intonation frequency: In the US they are using frequencies between 444 and 450Hz, which implies, for example, that Pianos need to be reinforced of the with steel plates (to resist to the string's higher tension), and the life-span of concert Harps is reduced to a few years (as the extreme tension of the strings shortens the column)… In fact, we notice how the wood used to build these instruments, shows us the frequency of the natural concert pitch that should be used!

In the same way, a higher concert pitch frequency affects the vocal cords of the lyric singers, that see their vocal chords irreparably damaged after only a few years (and singers that can produce such high-pitched sounds are rare).

However music is also a personal experience and a matter of taste, hearing and individual sensitivity.

I personally prefer music tuned to A = 423Hz :) and I also have been able to notice a big difference for its calming and centering effect on hyperactive and autistic children…
Pierre_Engel
Good morning to all. I wish to add my 2-bit piece about this "magical number" of 432, taking as a reference Joseph Campbell's conference on gods and goddesses of the Neolithic period (a Peter Donat video of the late 80's). Campbell mentions the Indian Puranas composed between 400 and 1000 CE, where a cycle of time lasts 432,000 earthly years and is called a "Yuga", each Yuga being registered is a "Maha Yuga" (great cycle) of 4,320,000 earthly years. Each Maha Yuga is registered in a "Kalpa" of 4,320,000,000 earthly years... In the Rig Veda (written in 1500-900 BC), on reads: "the 12-ray wheel where 720 sons of Agni are established", where 720*12 = 8,640 or a half-cycle of 4320.
The height of the Great Pyramid of Kheops is originally 146,7m high, which corresponds to the length of the Earth radius at the scale 1:43,200. Coincidence? In the Islandic Grimnismal, drawn from the poetic Edda composed between the 8th and the 12th centuries, the Walholl or Walhalla, palace of the paradise of Wotan, or Odin, is structured by 540 gates. During the "Day of the Wolf", 800 warriers will go through each of these gates to fight the ennemies of the gods in a great total annihilation. This will be the end of times, before a new cycle. 540*800=432,000: it is the same number.
In the 3rd century BC, the second book of Berosus, a chaldean priest who was translting the Babylonian myths into Greek, tells the story of the Creation with the 10 legendary kings before the deluge of Utnapishtim (the Babylonian Noah) of the Kingdom of Kish. Between the Creation and the Utnapishtim Deluge, 432,000 years have passed. The Sumerians, who did invent the sexagesimal base, but were also using the decimal base, are considering that a "sar" (a universe) lasts 60*60=3,600 years, and that 120 sars make up 432,000 years, and that 60 * 432 make a "great cycle" of 25,920 years. That figure corresponds to the cycle of the precession of the Equinoxes.
10 legendary kings for 432,000 years, this makes long-lived kings...!!
In the Bible, Genesis, there are also 10 patriarchs between Adam and Noah (the biblical Deluge), and it is said that at the time of the Deluge, Noah is exactly 600 years, 2 months and 17 days old... The 10 patriarchs are listed and are: Adam, Seth, Enosh, Kenan, Mahalaleel, Jered, Henokh, Metuselah (Matusalem), Lemek and Noah. The text allows the computation of the date of birth of each of these patriarchs, which is: Time of the Creation T for Adam, and then/ +130, +235, +325, +395, +460, +622, +687, +874 and so T+1056 for Noah. Noah being 600 years old at the time of the Deluge, the date of the Deluge is T+1656 years (after the Creation). This number of 1656 years, if transcribed in "creation periods of 7 'days' each" corresponds to 86,400 "periods", or 2 cycles of 43,200 periods each. We find here again the 432 number and its double 864 as in the Rig Vedas.
The question of linking 432 to 864 is to be considered with respect to the ancient culture of the "wise men" and priests/magicians of the Sumer / Babylonian / Ancient Greece periods, where the "Cosmic Order" was at the center of the question of Man's position in the Universe. At this time, it was thought that there was a correspondance between the cosmic laws and the Human existence on Earth, and that Humanity was a reversed image of the Cosmic Order: What is above is as what is below (but as a "reversed" or "inverted" image). So there is a 432 "time" unit for what is below, and another 432 "time" for what is above, the whole Cosmic Order being ruled by a great cycle of 432 * 60 = 25,920 years or 1 revolution of the "world axis" (known today as the precession of the equinoxes).
And Campbell concludes that for a Man at rest, the heart beats on average at 60 beats per minute or 3600 beats per hour - and the "hour" was known at the time of the Ancient Sumerians, Babylonians and Egyptians, as the day was split already in twice 12 hours. For the Egyptians, the day was 12-hour long and the night was also 12-hour long, so these hours were not lasting the same "time" in winter as opposed to summer - but nevertheless, one full day was always 24 hours with 12 hours for the (masculine, sun-driven) day and 12 hours for the (feminine, lunar-driven) night. The Greek Odyssey has 24 "songs", each representing such a "time" in the wandering of Ulysse. In other words, the human heart beats 43,200 times during the (masculine) day, and 43,200 times during the (feminine) night.
So this figure of 432 represents the rythm of the universe that connects Man to God (or gods), by being the link between the cosmic precession of the equinoxes and the fundamental rythm of Mankind. It is then no surprise that Pythagore ended-up advocating that the "music of the spheres" was related to this figure.
Some bibliography of interest: The Shape of the Ancient Thought, Conparative Studies in Greek and Indian Philosophies, Thomas McEvilley, 2002.
CalebGrayson
excellent! thank you so much Pierre.

I had just graduated with my BA in analytic philosophy, mathematics, and Greek which was taught in an unusually analytic way.

it wasn't until I owned a coffeehouse/art space in Detroit that I was confronted with the magical nature of numbers in astrology — who's mechanism really is best described as the music of the the spheres and only deeply understood by a musician with a theoretical foundation.

my brain was totally wired for analytic thought and it took me years to 'get' archetypal image, the symbolic depth of meaning that transcends pure rationality.

Astrology is the mother of all esoteric sciences because it entirely integrates the rational with the non-rational. if one discounts magical systems as being non-rational (or unreal) with prejudice then that is itself an irrational belief.

one who does this has just as limited a grasp on reality as one who accepts all magical ideas without a critical eye.

there is a middle place — riding the line of in and outside the rational divide — a jazz of understanding that can't be explained only experienced. can't be notated. can't be recorded. can't be broken down into parts.

— though all these techniques can lead one there.
Larissa Cantoni
Thank you so much for all this precious information, Pierre Engel!
barfoden
Interesting article..

I have given this a lot of thought lately,, Been playing in different rock/pop coverbands for more than 20 years.. And is a deep baritone myself so I always played guitar as my voice does not seem to fit well with pop/rock music that sings rather high..

My present leadsinger struggles a bit with our material,, He is a baritenor or high pitched baritone and sings a lot of cover stuff in their original key, WE talked about detuning the guitar and bass to E-flat transposing all our material down a half note.. But to my ears a lot of songs sound less dramatic or energetic now when he sings then a half note deeper... Truth be told a lot of songs sound closer to my sweet spot now... I have at one single occasion a long time ago sang all his songs live detuned a half note by tuning the guitars and basses to e-flat, which we are in the mist of doing at the moment... I got through but just borderline... :-)

THis made me think that there is some truth to 432Hz and voice registrations.. A less dramatic downtune to 432Hz would make my leadsinger get through with less voice fatigue but still be more around his sweet spot than down at 415Hz downtune.. I think the voice and the entry to the passaggio is key.. For me it is a lot of singing on the E4 note (A4=440Hz) that wears me down,, For my leadsinger it is the F4 note that in the long run gives him trouble,,, Downtuning to 432Hz makes those passaggio note sit a little deeper more connected to the note below. In 440Hz my E4 note or his F4 note needs more weight lifted of the note which in a live situation can be difficult to do..
Rich G
Great article, Assaf, though it looks like you read my own article on the subject first and based the form and outline of yours on mine! Some of the information in our articles is the same, some different, so it's worth reading both for a greater perspective.
http://soundhealingforum.discussion.community/post/a432hz-truth-lies-and-creative-story-telling-7786262

Unfortunately, both Pierre Engel's and Larissa Cantoni's comments above perpetuate some of the false 'evidence'. Many of the points that both of you mention are simply not true. Instead of copying and pasting here, please read my article for clarification of some of those points.

There's nothing wrong with being 'wrong'. The problem comes when when refusing to update or change ones perspective when confronted with more accurate information - a common human trait, we've all done it. As Jon Anderson wrote in the Yes classic 'Perpetual Change': "As truth is gathered I rearrange...."
nanda
It's not about 440 or 432.. It's about The Audible scales which have been created. The twelve-tone equal temperament system A.K.A A=440hz has great limitations for musical expression. Any one can say what they want but ultimately the equal temperament system was made for modern ease with no regard to the natural world which is non constricting. While one has in just Intonation (AKA non constricting micro tonality) a large number of natural audible intervals available, one has in the twelve-tone equal temperament system (A.K.A- A=440) only 12 fixed intervals are to use. So to conclude Western musicology has made a prison for its music. It has locked it out from a vast universe of sounds and potential musical expressions. In addition, it has marred the harmony and beauty of the natural sound intervals by distorting their natural relationship. It has even conditioned musicians to hear music that are in accordance with natural harmonics as out of tune! By incorporating western musical instruments and equal temperament tuning into the ancient just intonation Gandharva Vedic tuning (Which most modern musicians have no idea about) is like night and day. And yes if we look to reference the modern measurable WAV of the seat of A in the Gandharva scale we will see it is closer to 432. In comparison equal temperament looses the original strength and purity of the music and musical mystics would say it sounds distorted and polluted. It is like bringing the music away from natural law, while it should do the opposite, bring us more in tune with natural law and Beauty, but hey this is the world we live in today.
Eber Nakamura Gomes
Fiction: This discussion will end someday.

Fact: Stubborn humans.
Sana-sol
There is no smoke without fire they say.

That 432 is the Note of the Universe / God / or Water I am not sure of but it's certain that 1/432*6*6*6=3 where three there might have been though of as the various trinities in religions.

Besides 440 is calculated from the goldean mean phi of 360 with square-root of two, into the equation (4*(sqrt(2))/((1/c)*5/2)) i.e. 137.5*sqrt(2), though of course this might be a coincidence.

But 440 we must remember is 288 in octa-decimal (other way around actually), so it's further to think that 288 is sort-of inverse (1/x) Schuman Resonance, doubled, times synergetics constant 6 (1.125). Though only if Shuman Resonance is really actually 1/128..though this might be a co-incidence too and it's not really logical to think in decimal about octa-decimal system.

432 is 660 in Octal. But using this logic we arrive at 666 octal is 438 (in decimal) , and so that might be the next tuning.

And that last thing above isn't as far out as it sounds. Randal Roffe says the best tuning is to lower c a bit down towards Bb, Though we prefer 437.4 HZ which is from 1/(2**11)*6**7 so 136.6875*sqrt(2) in the relativity equation,

The Universe? If we really wanted a frequency tuned to that maybe we could use ((288/625)*2**3*6**2) since 625 was about the Higgs Boson (a.ka. The God particle) and again 288 claimed by some to represent anti-matter at least.
Eenor
Add up the inner angles of all platonic shapes and solids and you get a perfect F# Major chord in 432 tuning. Also in law of doubling (1+1=2 2+2=4 etc) you get perfect C's (256 512 1080 on up) in 432 tuning, which relates to factor 9 concepts and cell division. Much more elegant than 440 when you consider shapes create matter, does it matter? It does to me when I consider sympathetic resonance with the all and everything. Having said that, as a musician, I find all frequency relevant, and enjoy a bit of varietal drift from time to time, tuning to the moment.
Maxim
it is better to test the 432Hz sounding self. I would recommend a free iOS audio player www.alphasxplayer.com This let playback music in 432Hz instrument tuning and experiment with it
Micah
It's hard to believe (okay, maybe not so hard) that people are so enamored with numerology that they ignore the fact that, as the article points out repeatedly, the numerical value of a frequency is dependent on the length of one second in time, which is arbitrary. You could take any pleasing number you like and decide it's the key to the universe, but if we happened to measure time in seconds that were any shorter or longer than the standard second, a given frequency would be measured to be a different cycles per second (Hertz).

THAT SAID, *because* frequencies themselves are absolute, the article actually commits a fallacy when it says that ancient people could not have tuned their instruments to a certain frequency we now measure in Hertz: of course they could have happened on a certain frequency which we now measure to be 432 Hertz; they just wouldn't have identified as such.

THAT said, I'm not seeing any evidence that anyone did center on that specific frequency, and besides, for that to mean anything, they would have had to use the exact same major scale system as in Western music. For those that did use Western scales, before the Middle Ages there's no particular reason they would have used A4 as the centrally tuned pitch, which means you'd need to know the pitches of every note in a scale to know whether the equivalent of A4 was set a certain frequency.

HOWEVER, I do prefer 432 Hz myself.
Fact or fiction
FICTION: You think that all human beings on Earth are inferior to you (in some way) and that you can write utter rubbish and get away with it.

FACT: You're an idiot.
Gandalfthe5000ator
You said you've added pitch control to the software. What about functionality that let's me sweep between base pitches through the course of the song being played. A "modulation". A song starts in 432Hz A and ends in 440Hz A.
John Rando
OK. What about the frequency tables? If you tune A to 432 then all other note are integer numbers (C=256 Hz, D=288 Hz, E=324 Hz, F=352 Hz, G=384 Hz, H=486 Hz). If you tune A to 440 then every other note is a fractional number (C=261.626 Hz, D=293.665 Hz, E=329.628 Hz... and so on.
The full frequency table for A=440 is here: http://img.sadistic.pl/pics/ed7a0bc8fd36.jpg )

Doesn't it mean something?

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