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हिंदीThe music and audio industry currently uses the A = 440 Hz universal standard pitch tuning around the world. It wasn’t always this way. In fact, 440 Hz has been the standard for less than a hundred years, a drop in the bucket in terms of music history. The tuning of A = 432 Hz, also used throughout music history, is making quite a comeback these days, especially in the field of sound healing and meditation. Researchers, scientists and musicians are leading a growing movement to prove this tuning is best for heart-centered, therapeutic sound work.
This article briefly explains the history of tuning and some key points that support 432 Hz as the scientific tuning, by relating it to mathematical relationships, harmonic ratios and frequencies found in nature. Hopefully this will inspire some thoughtful discussions. There are some audio examples to compare tuning for critical listening and a brief explanation on how to compose in 432 Hz tuning in Logic.
A Brief History of Tunings
An article by John Stuart Reid called the ‘Concert Pitch Conflict’ provides a comprehensive history of tunings and I reference many of his findings here. Greek philosopher and mathematician, Pythagoras (570–495 BC), is often credited with identifying musical harmonic ratios related to scientific pitch and the birth of 432 Hz tuning with his instrument called the monochord. It is believed, however, that instruments built accordingly to harmonic ratios were used in Egypt and Greece well before this time. The earliest instruments were flutes and lyres, often used for therapeutic purposes. Hundreds of years later during the classical periods of western music, it was documented that composers like Mozart and Verdi used the 432 Hz tuning. Verdi believed it was a much better tuning for Operatic voices. In the late 19th and early 20th centuries, 432 Hz tuning was challenged by other countries like Germany, the US and Britain who all seemed to be using and experimenting with different tunings.
Pythagoras with his Monochord.
In the early 20th century, there was a need to make a universal pitch standard used by all for sake of instrument makers, composers and orchestras everywhere. Even though 432 Hz was fully supported by the French and Italian composers through most of the classical music periods, 440 Hz eventually became the universal pitch standard. German Physicist Johann Heinrich Scheibler invented a device called the Tonometer and did the first experiments with 440 Hz tuning in the mid 1800s. The Tonometer consisted of 54 tuning forks with a range of 220 Hz to 440 Hz spaced at 4 Hz intervals. His work became widely recognized and a conversation began about a standardized tuning.
Scheibler’s invention called the Tonometer.
After much debate, the US adopted 440 Hz as the standard in 1936. Europe soon followed with its adoption many years after it was first proposed on both continents. Even today, musicians believe that music played in 432 Hz tuning has a better audience response, has a calming effect and sounds more integrated overall.
It is still not entirely clear why 440 Hz was chosen. It seems the scientific experiments by Scheibler had a lot of influence on this choice as opposed to what tuning may have been more in line with the harmonic ratios and relationships found in nature. I can’t help but notice how the music of India and the rest of Asia were left out of this discussion entirely. It is a testament to their unique musical and healing traditions that are affecting us more and more today.
Mathematics, Nature and Frequency
The chart below shows how 432 Hz tuning is derived based on Pythagorean harmonic ratios. Multiples of 2 and 3 forms the basis of the chart, and the left column shows all the multiples of 2 as the note C. In the middle, you will see that A=432 Hz. Also of note is the number 108, used in many spiritual traditions as a unifying number. Mala prayer beads come in strands of 108 and in yogic traditions, 108 sun salutations are often practiced. The number 186624 in the blue box is 432 squared and is the frequency of the speed of light within hundredths of a decimal—very close! Also, every column corresponds to a note with each being a 5th apart. You will recognize this as the Circle of Fifths—the basis for music theory, or at least Western music theory.
Harmonic Ratio Chart: Nature’s Tuning – In line with 432 Hz http://www.michaelleehill.net/wp-content/uploads/2015/02/UntitlMost-Harmonious.jpg
The Earth’s vibration, which is the frequency measured from the earth’s crust to the ionosphere fluctuates around 8 Hz. 8 Hz falls at the bottom end of where our calm, functioning brainwave state called Alpha is, and is almost in Theta (4-7 Hz), where we receive deep relaxation and healing during our sleep cycle or in deep meditation. Multiples of this frequency bring us to C = 64, 128 & 256 Hz (middle C), where the notes become audible to the human ear and then to our reference pitch A = 432 Hz. Recently, astronomers at Stanford found the fundamental frequency of the sun to be 144 Hz. The 2nd Overtone or 3rd Harmonic of this fundamental pitch is 432 Hz (see chart). These are auspicious findings indeed and point to a system that is connected in many ways.
Fundamental frequency of the sun and its harmonic— http://scalarheartconnection.blogspot.com/2014/11/the-sun-is-singing-to-our-hearts.html
Music researchers have also tested traditional healing instruments, like Tibetan Bowls from Nepal, and found they are made in accordance with A = 432 Hz tuning. Instruments made for sound therapy do not have to conform to a universal pitch standard and are becoming more popular in sound therapy centers around the world. We can learn a lot from cultural traditions of instrument making, linked to techniques being passed down through generations.
A Note on Equal Temperament VS Pythagorean Temperament
We have to keep in mind that our universal tuning system is based on 12-tone Equal Temperament. Meaning, all the intervals or adjacent notes are spaced evenly from each other in order for all the octaves to sound the same. In true Pythagorean temperament, this would not be the case. Equal temperament is required for instruments like piano where notes cannot be bent. Voices and string instruments however, are able to bend notes and change tuning easier to achieve the subtle differences between the notes. Roel Hollander describes this in detail on his blog post, ‘Concert Pitch vs Tuning System’ (http://www.roelhollander.eu/en/432-tuning/concert-pitch-vs-tuning-system/). Roel explains that in order to obtain a true representation of 432 Hz then, one would have to compose not only in A = 432 Hz but in combination with Pythagorean Temperament or a close implementation of it like Just Intonation or Twelve True Fifths Tuning. I did some investigating myself using the Cleartune App for iOS, a handy tool that allows you to change tunings. In Pythagorean tuning, A=432Hz, C =128 Hz, 256 Hz and 512 Hz and G below A = 384 Hz (as examples). When set to Equal Temperament, all the A’s calibrate the same and the others are C=128.4Hz, 256.9Hz, 513.7Hz and G=384.9Hz. There is a difference between .4 – 1.7Hz on those particular notes, but it’s a small difference compared to composing in any other tuning. Plus, when using equal temperament, it’s possible to play in an ensemble, for example, without reinventing instruments.
Audio Examples by Torkom Ji
Audio Examples recorded in Pro Tools from Torkom Ji’s Korg Electribe.
Torkom Ji, founder of Quantum Harmonix Sound Healing, has graciously provided Ask.Audio with 3 music examples in 432 Hz, 440 Hz and 444 Hz. Torkom facilitates sound healing sessions all over the Los Angeles area with his custom Korg Electribe. He is a master at creating deep, resonant soundscape journeys using just this instrument. It’s very different than what most sound healers are doing with acoustic instruments, but some would argue just as powerful. Listen to the examples below in headphones and through your monitors. Notice how the different tunings affect the entire range of frequencies you are hearing. The excerpt is from his track, Internal Eyes, originally composed in A = 432 Hz tuning.
MP3 Internal Eyes 432 Hz:
MP3 Internal Eyes 440 Hz:
MP3 Internal Eyes 444 Hz:
*From the Album Hieroglyph: https://torkom.bandcamp.com/album/hieroglyph-432hz
As you listen, ask yourself these questions:
- Does one sound more integrated than the other?
- Does one bring out a certain range of frequencies?
- Does one sound thinner than the others?
- Do you feel more relaxed with one, more agitated with another, or neutral to all?
Some people believe in specific answers to these questions, but the reality is, more research is needed in this area to convince the masses one way or another. Since there aren’t many online articles that actually provide solid listening examples for comparison, we at Ask.Audio hope to keep this conversation going by having our readers way in and share their experience.
Try it Out In Logic
Tuning Settings in Logic.
Logic is a great DAW to try 432 Hz or another tuning in. There is a global tuning settings window located in the Project Settings menu. Setting the tuning here affects all the software instruments in Logic, excluding third-party instruments. The tuning ranges from 415.3 Hz (-100 cents) to 466.3 Hz (+100 cents) with 440 Hz as the current pitch standard. When setting the slider I noticed I could set it to 432.2 Hz or 431.9 Hz, but not right on 432 Hz. The reason being the slider works off of cent increments. So, if you pitch your recordings or individual parts down, you would lower the pitch by 31 or 32 cents to get close to 432 Hz. (Editor's note: You can enter -31.7 manually to change the tuning to exactly 432 Hz.) This is helpful if you are working in another DAW that doesn’t have global tuning or if you are trying to match the tuning of a third-party instrument part in Logic for example. The good news is you can compose in 432 Hz tuning with acoustic musicians in conjunction with software instruments pretty easily in Logic.
The Great 432 Hz Debate
With so much of the musical world (acoustic and electronic) operating at 440 Hz standard tuning today, it’s hard to imagine the shift to 432 Hz happening on a large scale quickly. But there is a growing movement underway fueled by the sound healing community, select ensembles, researchers and scientists that will keep bringing this issue to light and allow music makers and listeners to consider the power of this tuning and how it affects the mind, body and spirit.
Learn more about Music Theory in Ask.Audio Academy here.
Addendum from the author (Lynda Arnold):
First of all, thank you readers for your thoughtful feedback and insight into this controversial topic. The following are some clarifications to the article to clarify a few points. I know there are many holes, but I’ve chosen a few to begin with here.
*In the opening paragraph, I mentioned explaining some ‘key points that support 432 Hz as the scientific tuning…’. In order to be fair to all our readers, I should have prefaced this article as an inquiry into some belief systems, philosophical approaches and creative practices surrounding the way and how of this tuning.
*Regarding the history of 432 Hz as it relates to Pythagoras, there is no concrete evidence that he used the reference pitch A=432 Hz with his work with harmonic ratios. The ‘Birth’ of A=432 Hz as concert pitch come about in the Classical era (’1800s) and you can read about this evolution in the article I reference called ‘The Curious Concert Pitch Conflict.’
*When I mentioned the Earth’s resonance, I was referring to the Schumann resonance which fluctuates as much as 5 Hz in either direction making it difficult to pinpoint it as directly and specifically correlated to 432 Hz. https://en.wikipedia.org/wiki/Schumann_resonances
*In regards to ancient instruments, like Tibetan Bowls, being tuned to the A=432 Hz, there is no concrete evidence that this was the case since in more ancient times, tuning was done by ear and passed down through generations. Jamie Buttruff has done some inquiry into the area and has video showing his particular Tibetan Bowls are tuned to A=432 Hz reference pitch. http://blisscodedsound.com . I would love to see more research on this topic, however, with other instruments too.
*I want to provide a listening link for the Sun’s frequency and correlating chart that I mention above. You can listen and use a tuner to check the frequency that they found. I found using Cleartune App that the tone fluctuated between 141–144 Hz— it’s a pretty dynamic tone. It’s important to note that researchers at Stanford calculated this by recording ‘acoustical pressure waves and sped them up approx. 42,000 times in order to produce a frequency that we can hear’. Here is the listen link and more information: http://solar-center.stanford.edu/singing/
*in my paragraph comparing Equal Temperament to other tunings, the term that fits best in the tittle and surrounding comparison is ‘Just Intonation’, not ‘Pythagorean Temperament’. ‘Just Intonation’ is the tuning that expresses the pure harmonic ratios.
https://en.wikipedia.org/wiki/Just_intonation
Despite the lack of concrete, scientific proof (and proliferation of false information) on this matter of using A=432 Hz tuning (just intonation, equal temperament or otherwise) for therapeutic work, I am encouraged to see so many people willing to try it on their own with an open mind and reach their own conclusions based on individual experience. Some readers weren’t even aware that tunings other than 440 Hz even exist at all!
Maybe these experiments will serve as a vehicle for more research or just provide another color for artists to use in their sonic canvases. The world of music and sound is complex, with many dialects. Meaning, some people approach music in a more technical, precise way while others choose to play based on feeling alone, letting the muse be their guide. However we get to the truth in this matter, it’s clear that people love music and have a special and unique relationship to sound that should continue be respected, inspired and cultivated.
Articles, blogs and sites for further research; some with strong arguments for and against:
Concert Pitch Conflict:
https://www.cymascope.com/shop/products/the-curious-concert-pitch-conflict-pdf-download/
http://scalarheartconnection.blogspot.com/2014/11/the-sun-is-singing-to-our-hearts.html
https://en.wikipedia.org/wiki/Scientific_pitch
https://attunedvibrations.com/432hz/
http://www.miltonline.com/2014/01/07/hertz-so-good/
http://www.roelhollander.eu/en/432-tuning/concert-pitch-vs-tuning-system/
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Discussion
Thanks for the article! Could you please provide your evidential source for the claim that Pythagorus tuned to 432Hz? I have found no good evidence for this. Also my extensive study of Tibetan bowls has shown no significant correlation with 432hz despite its frequent repetition.
Thanks.
Indeed I am (although you only just alerted me to the reference, thanks for including it)
I have to say that (and this is from an advocate of using the full range of tuning references and temperaments) that your sources have misled you and your article is full of many errors, myths and mistruths. It's not a matter of 'opinion', they are demonstrably incorrect.
Again I'm not saying that 440Hz is in ANY WAY better than 432Hz (It's absolutely not - and I use many different tuning references, but more significantly tuning temperaments). All I'm saying is that the arguments that you have presented for the superiority of 432Hz are entirely invalid (as well as much of the history and science of tuning for that matter). They would also be invalid if they were made in support of 440Hz or any other tuning reference. so this is nothing ideological about 432Hz vs 440Hz, it's about quality representation of music theory, sound science and history.
I could show you the contentions (and much of my article addresses them), should you be interested.
There is however a valid debate on the acoustic and timbral effect of detuning (or tuning high) instruments (or pieces) designed for other reference pitches. There is also an interesting debate around the psychological priming effect of listeners and performers believing that a pitch (instrument etc.) is in some way 'special'. However to argue that 432Hz is better than (rather than slightly different to) 440Hz (or any other reference you could name) is to misunderstand (and I think cheapen the beauty of) sound science, music theory and history.
What do you think?
Blessings.
I agree with what you are saying and it wasn't the point of my article to see unequivocally that 432Hz reference pitch is far superior for mass human consciousness or for healing work. Thank you for your corrections. Yet, in all my sound healing training, especially with tuning forks, it seems that frequencies related to 432Hz are used extensively at the moment. Look up the work of John Beaulieu. And tuning forks and gongs tuned to the frequencies of the planets are used extensively in sound baths as well.. This is a vast subject in its' infancy and most of what's happening could be a grand experiment with no scientific end. OR, one day these disciplines will intersect in a way that proves that are all connected, ushering in a new era of healing and consciousness. Since you wrote the article above which is lengthy and includes many references, you obviously know more detail about this subject than I do and people should read your article. You do much to disprove the 432Hz has any significance what so ever and that's why I included it as suggested reading.
also thank you for this comment: 'There is also an interesting debate around the psychological priming effect of listeners and performers believing that a pitch (instrument etc.) is in some way 'special'.
Yes, there could be a placebo effect happening here…the power of suggestion is no doubt influential. More research needs to be done with different tunings, but I doubt people would find Just Intonation or any other experimental tuning pleasing to listen to when they have listened to Equal Temperament their whole life.
Your history of reference turnings is also inaccurate (there's evidence in fact that 440 as well as other references predates 432, with no or only localised references being the prevailing case pre 19th century). See e.g. Cavanagh.
Would be good to know your sources here also. Thanks!
1) interval rations (2:1 for the octave, 3:2 for the fifth, etc.) must not be compared to absolute pitch. They are a complete different concept of describing sound with numbers: proportions describe intervals, the relative distance between two notes. Pitch (base frequency of a note, in Hz) describes just one single note. Hz is based on the unit of seconds, which is a highly artificial and manmade unit. The fact that the product of 27 and 16 is 432 does not make a note with the base frequency of 432 Hz anything special.
2) there is technically no possibility to know the reference pitch of a historical instrument before frequency measurements were discovered in the 19th and 20th century. In all the many sources about tuning and temperaments from the 9th to the 18th century there are no indications of an absolute pitch. It's all about relative pitch, about the qualities of intervals in different tuning systems etc. It's quite evident that before the 18th century nobody cared about a standard pitch: they just adapted the instruments to the performance context: climate, room size, singers' health, etc.
I'm convinced that music and sound influences our body and well-being. I'm also convinced that our conventional practice is not using the full potential that fact. But instead of experimenting with standard pitch, I recommend very much experimenting with tuning systems. Listening to pure (pythagorean / meantone systems) or to constantly impure (piano tuning) intervals makes a huge difference! (And the difference can't be described in cent derivations on Cleartune, you have to hear them on proper, good, and real (not electronic) instruments, to understand what's really happening).
And instead of transforming music that has been developed in a culture of the piano tuning, I recommend listening to music from a culture that used pure intervals. Try listening to groups that perform medieval music in pythagorean tuning (and don't even ask about the reference pitch: there is none).
For a better overview of temperament (and its history) see e.g. Duffin's Why Equal Temperament Ruined Harmony (And Why You Should Care).
A shame this site repeats such inaccuracies.
There is no proof that Ancient cultures used A432 as a tuning reference, and no way to verify it. Furthermore, prior to the ‘ruination’ of Western music by the establishment of A440, a common tuning reference was 435 Hz, not 432 Hz, as implied by the article. In fact, over the past few centuries, tuning standards have fluctuated hugely.
The article mis-states the Earth's fundamental frequency, by which it seems to be referring to the Schumann Frequency, which the resonant frequency of the Earth's magnetic field between the ground and the outer atmosphere. It is not a vibration, it is electromagnetic, and it is not 8Hz, it is 7.8Hz. Multiples of this frequency, which the article claims will be nice round numbers like 64, 128, and 256, are closer to 62, 125, and 249, numbers which don’t fit quite as prettily with the 432 Hz theory. Furthermore, the article states that the Earth’s frequency is 'almost in Theta' (4-7Hz), but 'almost' is not the same as 'is', and 5Hz, 6Hz, and 7Hz don't appear in the colourful graph. Articles like this conveniently choose to ignore inaccuracies when it suits them.
The article claims that the Sun’s ‘fundamental frequency’ is 144 Hz, but it doesn’t tell us what exactly that means. If it’s talking about electromagnetic radiation, then the number is out by several orders of magnitude (visible light is in the range of 300 Terrahertz). If it’s talking about seismic vibration, it’s also way out, as the typical acoustic wave frequency of the sun is about 2-3 mHz (about 5 minutes per cycle).
The coincidence of the number 186624 being close to the speed of light (in miles per second) and its appearance in the chart proves nothing. The speed of light is also 299,792,458 meters per second, a number which does not appear on the chart, or 1080 million kph (oh, right, 1080 is pretty close to 1024, which does appear on the chart, so that must mean something right?). Incidentally, the article describes the speed of light as the ‘frequency’ of the speed of light, an incorrect use of the most popular ‘scientific’ word amongst the people who promote pseudo-science.
When articles like this play with numbers to make things look pretty, the result is just pretty nonsense. Proof of the superiority of 432Hz is nowhere to be seen, not yet anyways.
I would suggest that the temperament has more to do with the listener's response than the reference pitch. Temperament and pitch standard are NOT the same. Equal temperament has an unrelenting, stimulative, effect on the human psyche, as there is nothing consonant beyond the octave. Every third, (which is the most emotionally affecting interval) in ET is out of tune by 13.7 cents. This is dissonant, but its ubiquitous presence gradually erodes the listener's ability to detect differences of consonance. Hence, the texture of ET in piano music becomes one of unchanging effect. In contrast, the unequal temperaments of the 1700 and 1800's produce a palette of consonance/dissonance that follows the key signature, (the circle of fifths with the C-E third the most consonant. This creates a texture to classical piano music that consists of various levels of stimulation or sedation in the music. Beethoven is the master of this. More of this concept is available on my web site, and there is a free Temperament comparison of a Mozart piece in Equal temperament, Meantone tuning, and a Well-Temperament. Listen to the difference the temperament makes, and I think most will agree that it is a larger factor in how music is perceived than the pitch standard.
You can listen to this comparison at http://www.piano-tuners.org/edfoote/well_tempered_piano.html
What I am saying is: This site published this article that is repeating many inaccuracies (repeated from elsewhere on the internet), and that is a shame.
Here are just some of the inaccuracies:
1) conflation of reference pitch with temperament
2) claim that 432Hz is 'ancient'
3) Inaccurate (in fact fictional) historical content
4) Confused mathematics
5) Presentation of poorly controlled anecdotal response as some kind of evidence
6) False balance by listing pseudoscientific sites as some sort of authority on the 'debate'
7) Implication that the only alternative to 12-tone equal temperament is 3-limit pythagorean tuning (hindustani music uses 5-limit, Tuvan music way higher)
I could go on.
Hope that helps.
PS. I happen to love (an an advocate) using a range of tuning references, but more significantly, different temperaments. But articles like this are totally counter-productive (and wrong).
It does help and I'm sure your comments are of use for those interested in a counter-approach.
Best,
Rounik
http://omega432.com
I see this as a major claim for the purity and "goodness" of the 432Hz.. But it just doesn't hold water.
Thoughts?
Thanks!
Rounik
Exec. Editor, Ask.Audio
More detail below:
1. There is nothing special in nature about the number 432. It is a count of the number of events per second – and the crucial point is that there is nothing special in nature about the definition of a second. A second is an arbitrary period of time which for the convenience of humanity has been given a precise scientific definition: “the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atomâ€. Hardly a fundamental characteristic of sound in nature.
2. The frequency of the note “Aâ€, whether it’s 432 Hz or 440 Hz or some other reference, is the frequency of only one note in the scale. In anybody’s theory, all other notes in the scale (whether tempered, Pythagorean or other) are related mathematically to that reference frequency and so will end up at all kinds of strange non-magical numbers. So the numerology of the note “Aâ€, even if it meant something in itself, would break down for all other notes in the scale and so would have no meaning for the music as a whole.
http://hyperphysics.phy-astr.gsu.edu/hbase/acloc.html
Thank you for your post! I'm learning more all the time about this subject. I use sound as a vehicle for transformation and healing, which is a different conversation from the scientific, of which I have a more limited understanding. I have seen transformation and emotional release in people through the use of this work and with the 432Hz reference pitch (even equal tempered!). There's something to it, it may be this tuning or the work of subtle energies, a larger consciousness or just having the 'space' created for such healing….these are things that we are not even capable of explaining yet, especially to folks who need hard and concrete evidence of such effects.
I'm sure there's lots of good and effective and very interesting stuff in there but it will be related to the various kinds of tuning - such as the example you're using of Pythagorean vs ET, not to the actual frequency
. Attributing a special meaning to the value of 432 has no basis in actual experience - and the reason is that the value of 432 is a complete accident arising from the arbitrary definition of the length of a second. If scientists had chosen a different measure for time, then the number would have turned out to be completely different. Therefore all that is written about the numerology of that number 432 has no possible foundation. I don't dispute the subjective effects you're referring to - that's all good stuff - it's just that the number 432 does not have the magic you're attributing to it. If you have experimental evidence to the contrary I'd love to hear it.
Lynda, this is an example of where I start to have a problem with the confusion of good science with good intent. It's comforting to think of being 'tuned' in to the cosmos, but as soon as the discussion begins to use specific values and specific units of measurement without clarifying what they are, or by simply letting the 'feeling' that the words evoke be enough, then I don't think it's valid to use those specifics. Yes, 432Hz might have a certain psychic effect, but if the argument insists on using scientific measurements to support itself, then it is obligated to use those measurements correctly, instead of just tossing them around because they sound meaningful.
M.M.60 is very close to the average heartbeat, and perhaps in an earlier, less stressful time, established the second as a time-unit. The division into 60 comes from ancient Chaldea.
Rudolf Steiner told two different musicians that the organ of Corti, the middle ear, is based on the C=256, which is the C resulting from a tuning from A=432. It is remarkable that ear-doctors, both in Europe and America, to test hearing, use a tuning-fork tuned to 512 Hz, the octave of 256, without knowing why.
Over 25 years ago, I had my piano tuned to A=432, and after half an hour of playing it for the first time, I was surprised to find myself feeling healthier. Also the piano was tuned to the "12 true-fifths tuning" of Maria Renold. She has tested hundreds of people in audiences as to which pitch they preferred for the A, without telling them which they were hearing. The vast majority preferred the 432, finding the 440 "stressful, over-stimulating", and the 432 more comfortable and "normal". There was a still lower pitch that felt comfortable, but eventually too "heavy". There are many more such anecdotes.
You can listen to the effect of the 432 on my CD's--one of Chopin and two of relaxing improvisations--to be found on my website, www.grahamsmusic.com. Also my book is obtainable there--"The Spiritual Basis of Musical Harmony", which goes into these questions in more detail, along with much else.
It was Rudolf Steiner's great achievement to build a "spiritual science" he called anthroposophy which integrated such experiences with the outer evidence of materialistic science. It has proven its worth through its practical applications, of which Waldorf Education and bio-dynamic farming are only the best-known.
It is true, Polarbreeze, that Maria Renold's tuning is a different factor than the absolute pitch, although her scale system apparently does affect us deeper, probably because it uses mostly natural 5ths. She even recommends not to use it at the 440 pitch because her experience shows that it makes people irritable. I have even participated in one of her testings with an audience, and surprised myself with how acutely I could detect the differences when I really listened. She had various ways of making sure we did not know which was which.
Ps. I've been accused of being 'close-minded' to 432. Quite the opposite, I've studied its claims deeply and give it the same respect I would give any other hypothesis. For me, it's so far fallen very very short of evidence on both theoretical a and empirical grounds. I still get (very weird) hate mail for not accepting the claims, but I would openly admit if the evidence appeared.
I would be interested. The question of interval values intruding on a discussion of effects due to a pitch "standard" is a common detour. We know (scientifically), that various sizes of octaves, thirds, and fifths create relative changes inre stimulative/sedative responses. That is a question of temperament.
If we wanted to isolate the pitch as the variable, I would suggest that we compare a strict equal temperament at 432 and 440. This is as close to standardizing the interval values of an acoustic instrument as we can get. Whatever psycho-emotive effects of tempering arise should be a wash between them.
I have done this on pianos as I string them, pausing at various historical stages of pitch as I bring them up to wherever they are going, (things vary, these days). I maintain instruments at a university, so I have some latitude and a lot of musicians around. One of the early events was at Steinway B at 415, so a baroque group could try a piano instead of the harpsichord. They were naive and requested ET. Though it sent them fleeing for the quills, I think a Valotti temperament would have been received entirely different reception. The piano sounds quite soft at that tension, and there is certainly a lessening of its aggressive tonal nature. Normal players felt it was flat and loose.
I took a later restringing to 432, and the response was less dramatic, but the loss of brilliance due to looser strings was still a factor. Feedback was mixed as to what different feeling there was, but most of the heavy ears certainly wondered about the flatness. Other instruments more easily inhabit the 432 realm with little compromise of tone. ( I have a hurdy-gurdy that can do that).
I have, on request, taken a piano to 445. Most musical sensitives got tense around it, (as did I). The effect is definitely stimulative. That is 20 cents higher than the norm of 440. ( 20 cents is very close to the syntonic comma found in the remote thirds of older tunings, and may actually indicate some limit to comfort in sharpening. I hope so, as the move upwards seems to continue unabated, these days). .
The investigation into pitch's effect on mood and health is a good one. I want to get all the right answers, too, and I recognize my bias towards wanting everything to be connected. Even so, I have come to believe more in a continuum definition of pitch effect rather than specific locations representing greater or lesser impact because of numerical co-incidence. Perhaps it is just the wood and strings, with the magic of computer power, synths might be on to something different at 432.
Regards,
Unfortunately some people don't understand the difference between those real effects versus the idea that the value of 432 is somehow magical just because of its numerology.
http://quake.stanford.edu/~sasha/PAPERS/diam_3.pdf
Also, do you have any the claims of the tibetian stuff tuned at 432Hz?
Furthermore, and this is the key problem of all the arguments for the 432Hz base: All frequencies are based on the time unit the "second". Herz is defined as: "The number of vibrations per second". And this is where the problem lies: The length of the second is just an invention of mankind and could be longer or shorter which would make the frequency different. If we had chosen a different length for the second 432Hz would mean a faster or slower vibration. So any "number-games" with that 432Hz thing are not making sense to me at all. Because it's all relative to the second and the second is a relatively "new" invention. The definition of the length of the second has changed once in the 20iest century and therefore the number of vibrations within a given time intervall has changed too. In other words: 432Hz in 1900 was SLOWER than it is in 2000. So why should 432Hz be special, if it has changed?
Funny enough I came here because I wrote about the matter too and someone pointed me in the comments to your article. I believe I have covered a couple of things that you didn't.
https://www.facebook.com/subconsciousmindmusic/posts/10153567726613740
OK, I get it that you do not accept subjective or "spiritual" evidence. Many people don't. But in rejecting the 432=A, are you doing it to defend the 440? Why defend it, except to preserve the status quo? I don't know of any group tests where people have preferred the 440, whereas there are many preferring the 432, for which you claim there is not a shred of objective evidence. Is there any at all for the 440?...
But that is subjective evidence, you may say. What else can you use? I, too, respect real science, but I also see its limitations. Science is useless in creating or judging art, including music. We have to use feelings of one sort or another, i.e. soul experiences. Rudolf Steiner showed however, how they can be pointers toward spiritual laws that underlie them. Hence he made artistic activities an essential part of Waldorf education, which turn out well-balanced and capable graduates that are welcomed by universities. Similarly, science is useless for much of daily life, which rests on experiences of soul and spirit.
(The German word "Geist" can be translated as "spirit" or "mind", depending on the context, and they are two aspects of the same thing. Care must be taken, however, not to think therefore that "intellect" or "logic" are therefore "spiritual". They represent a limited aspect of a much wider faculty.)
Yes, I am familiar with the monochord. There are several reasons why this instrument is not suitable for a study such as this. The main one is that because it is played with a bow its timbre (ie harmonic content) is poorly controlled and will vary from one bowing to the next with a significant effect of the subjective experience of the listener. It would be easy to devise an experiment that eliminated this uncontrolled variable (or example, an electronic sound source) – one wonders why the 432 proponents have not done that.
You are wrong to assume that I do not accept subjective evidence – I don’t think I’ve said anything that would give that impression. On the contrary, subjective evidence (“do you prefer this one or that one?â€) is exactly what we’re all talking about here. However, to be able to draw conclusions from such a study, the things being compared must be rigorously defined in the first place. It would be very easy for the proponents of 432 to work with rigorously defined sources – one wonder why they have not done that.
You are wrong to assume that in questioning the magic of 432 I do it to defend another standard such as 440. Absolutely not: my point is that no specific frequency is, in itself, more special than any other. And there is no study (that I have found) that supports the notion because they are contaminated by issues such as those cited above and many others. If you know of such a study, please point me to it.
Your points about musical appreciation not being a “scientific†thing (if I paraphrase you correctly) are not in dispute – we have no disagreement about that. However, the proponents of 432 have chosen to enter the “scientific†space by their numerology and their comparisons with frequencies occurring in nature etc. If they use science-based arguments, then they must be prepared to defend those arguments on a scientific basis. They can’t have it both ways.
I am puzzled that again you say we have not done experiments which separate the pitch from the scales. Did I not point out that that was exactly what Maria Renold did when when she just played single tones and asked audiences for their reactions?
Maybe the example of how she got interested in the whole subject through a childhood experience, and how this led to further research into scales, also based on a hearing experience, confused the issue. But it should have been otherwise clear.
To produce a less ambiguous tone by using an electronic instrument is a dubious solution, according to Renold and also one of our correspondents here. She said experience with audiences has shown that electronic tone-production for some reason does not trigger the same deep subjective reaction that an acoustic instrument does.
The mathematical justifications for the pitches came AFTER the discoveries by listening. They only make sense if one accepts that there is a spiritual unity, a reconciliation of all the various viewpoints--scientific, mystical , etc.--which is what Rudolf Steiner brought.. I still maintain that, after studying Steiner (in my case,for 60 years), as did musicians Bruno Walter, Albert Schweitzer, and others, including the late Sergei O. Prokofiev, (whom I also met), grandson of the composer, though not especially a musician.
This is where we fundamentally disagree, as you say, when you maintain for instance there is no special quality to any particular frequency. Maybe you just mean the mathematical aspect, but I suspect we diverge much deeper than that.. No hard feelings, however.
Greetings,
Giving an audience various pitches on the same string will also be giving them various degrees of inharmonicity. If string length is changed to produce alternative pitches, the ratio of tension/length/wire size (what piano designers call "scaling") will have a definite effect on the "voice" of the string, and will insure that various pitches produce various tonal characters. If the length is kept the same, the slacker string will have a different composition of overtones than when it it is tighter, so that is another underlying problem with using an arm's stroke on a monochord to define audience response to a specific value of frequency.
Speaking from the instrument world, would we not all agree that an acoustic musical instrument is capable of transmitting human emotional information? And that information is dependent primarily on the human playing it? I would submit that it is virtually impossible to *remove* all emotional information from a musical signal produced by a human on an acoustic instrument, particualary if a vibrating string capable of the full spectrum is involved. If Maria Renold is capable of not only performing, free-hand, exactly identical notes, but also keep the playing devoid of her own conscious knowledge, that would be amazing. I suggest a mechanical arm on that bow, and pitches produced by similarly scaled strings.
Regards,
Yes, that's well put and certainly your suggestions would greatly improve the experiment. There would still be random variations in harmonicity because it would be hard to make the mechanical arm bow exactly the same way every time. However, random variations can be controlled for and eliminated in the results so that would be OK.
Of course, in any case the experiment needs to be carried out double-blind to eliminate the experimenter's bias (conscious or unconscious). There is a built in difficulty here because if we're comparing two tones (440 and 432) it cannot be hidden from the subject which is which: they will always know which one is which because anyone can tell which of two notes is higher or lower.
Therefore a variant of the experiment should be carried out with a different pair of tones, for example 432 and 424. The subject would not of course be told which pair they were listening to and therefore could not be biased as to which tone they were expected to prefer. This still has to be carefully presented because if we now have 3 tones involved, the subject must not be able to determine that the "middle" one is the one they are expected to prefer. Removal of this bias is very important because we're dealing with a subtle subjective effect here. There are probably other improvements along those lines needed to fully eliminate the fatal biases of the original experiment.
The problem is that Renolds' experiments were designed to reinforce the hypothesis, not to neutrally test the hypothesis - so they are fundamentally flawed. The technical term for that is "confirmation bias". Renolds reported that the effect is absent "for some reason" with electronic tone production. The "reason" is that electronic tone production does remove the human bias from the experiment and so it does provide a true neutral evaluation.
Ed, I am not sure what you mean by the word "inharmonicity". It seems to me the difference in tone-quality caused by the different slackness of the string, when we are talking of such tiny differences in pitch, would be so infinitesimal as to be inconsequential.
I think the discussion is losing its footing in reality. There are many testimonies in favour of 432, such as the group of world-famous singers who are campaigning for it. Is there ANY evidence of people who actually PREFER the 440? I have not heard of any.
Re "...when the harmonic variability is removed, the effect goes away..." I was referring to your own statement that when a properly controlled electronic sound source is used "to produce a less ambiguous tone" the 432 effect disappears.
Re "...that the bowing could be different could just as easily work against..." is very true if the variations are random - as I mentioned in the post above supporting Ed's idea for a mechanical bow. However, if a human is wielding the bow, and especially if that human has an interest in the outcome of the experiment, the variations are no longer random and so they cannot be corrected for.
Your state that "...each pitch would have the same pattern of overtones...". This is not true of the monochord because a change of pitch would change the relationship of the overtones to the resonances of the instrument. Incidentally, this may well result in a subjectively "preferred" frequency but that would be a function of the physical construction of that particular instrument and would have no absolute frequency relationship to nature.
If there is a campaign of world-famous singers urging the adoption of 432 Hz I'd appreciate your pointing me to references so I can learn about it - I can find nothing with a search. We are in agreement about one thing: like you I have found no evidence of a campaign for 440 Hz - nor for 427 Hz, nor for any other frequency for that matter.
One of the most organizers of the conferences has continued his researches, going into microtonal scales, etc. He is Bevis Stevens, a eurythmist formerly of Dornach, now in New Zealand. He can be found on the web. I have also now dipped into Milton's website and see a lot of this subject discussed thoroughly there. I am sure there are others I have not read, but I am not inclined to take the time to go through it all at this stage. I have made my main statements, and may bow out of this conversation. I still maintain there is a wealth of evidence in favour of 432. It may not be "scientific" in the sense some would want, but testimony of many, many people as to their subjective reactions I consider also an acceptable form of evidence in this matter.
Interesting stuff, clearly touched a nerve. You may want to check out a study done, if I recall properly, in 1962 at the University of Albany by a couple of acoustical physicists named, if you can believe it, Bloomslitter and Creel. These guys were top shelf geeks. And the study was called "Extended Reference in Auditory Perception". I came across this thing 20 years ago while hanging out with my crazy microtonal uncle. Long story short, they took some good musicians and got them to play melodies on free pitch instruments, then tried to figure out what the actual pythagorean ratios were between the notes they played. Basically they were trying to see what humans enjoy, scale wise. Somewhat similar to your line of inquiry, and certainly related. Their results were bizarre, unexpected, and completely counterintuitive : Simple ratios to the second note of the scale. Very strange, but apparently true. l When I came across their work it seemed to me to demonstrate that the proper approach is to work backwards from the data, not forwards. I met a lot of guys who had really elegant mathematical microtonal theories, but nobody seemed to be working backwards from raw data. So if you find people like stuff in 432, that's awesome, that's interesting, but the real reason why may be really, really strange, if and when we ever figure it out. Stranger than the reasons you propose, I would bet. But I believe you about the 432. It would be great if somebody would do a study like the one I mention, but with an ear to figuring out our preffered frequency palate. Thanks for the article, really enjoyed it.
Digging the debate immensely!
https://www.youtube.com/watch?v=FY74AFQl2qQ&app=desktop
Also you told us the key of everything you notice about this different tuning/temperament and this "mystic" properties "Yes, there could be a placebo effect happening here…the power of suggestion is no doubt influential."
If it sounds good, makes me feel good, I'll choose the alternate tuning every time.
You folks forget that the end result to making music is to have it heard. Perhaps in time the "market" will move some of you since it seems that only money seems to make people wake up and take notice.
Shame, really, in the arts.
If 432 Hz sounds better to them, if they love the experience and don't experience nervousness, jitters, anger, etc., when listening and they like THAT then they should listen to it that way.
Tsk, music is to be ENJOYED, not tolerated. Most alleged music being produced today - to me - is discordant, jagged and nasty. It's nice to listen to House of the Rising Sun and not feel impatient with the recording aka wanting it to be over.
So it's about energy harmonics after all even if the above isnt a propper relativity equation (E=mc2).
c for 440 becomes phi of 360: 137.5 times square-root of two. c for 432 becomes 135 times square-root of two.
And 135 might be sought after as good because it was the smallest number with exactly 7 representations as a sum of 4 positive squares: 135 == 1^2+2^2+3^2+11^2 == 1^2+2^2+7^2+9^2 == 1^2+3^2+5^2+10^2 == 1^2+6^2+7^2+7^2 == 2^2+5^2+5^2+9^2==3^2+3^2+6^2+9^2==5^2+5^2+6^2+7^2
Ask yourself - what if you compare the 440 variant with another 440 variant, but with the instruments transposed a semi-tone down? Most likely the lower-register version will sound "more soothing".
Similarly, why stop the detuning at 432? Let's do another variant at 424. Maybe that one will be even more soothing.
If you can show a preference for 432 among 424, 432, and 440, that would point more clearly to some intrinsic "magic" or beneficial interaction with the human body. Otherwise, the takeaway is simply "lower frequency = more soothing".
Maybe this is simply a musical contribution to the "post truth" era - "relating to or denoting circumstances in which objective facts are less influential in shaping opinion than appeals to emotion and personal belief' - Oxford Dictionary word of the year. People aren't doing these tests double-blind!
Maria Renold Handbook for tuners:
react-text: 948 http://www.eurythmy.co.nz/Files/Handbook/handbook-2.pdf
Maria said: For the fisrt time all the Major and Minor chords sound harmonic.
Maria Temperament tuning uses mostly natural 5ths
I suggest to compare Equal Temperement (by Bach), Kimberger 2 (student of Bach) and Maria Renold.
files here: http://cenaceara.net/MariaRenold.zip
Changing the temperament of course does change the subjective effect of the harmonies - because the temperament changes the relationships of the pitches of notes that are sounding at the same time.
On the other hand, the concert pitch is arbitrary and changing it makes no difference the subjective effect (colour) of the music. Any claims that it does are magical thinking and are not supported by any evidence.
It is possible for artefacts of the experiment to make it seem like a pitch change per se creates a colour change even though it does not. Examples are: resonance in the instrument being used to make the tones; sampling rate of a digital recording; resonances in the ear or in the room where the experiment is conducted; suggestion by the experimenter, deliberate or not; variations in loudness or the examples being compared; etc.
Finally, there is nothing special about "432" cycles per second - it is an arbitrary number because the duration of a second is itself an arbitrary value.
==>> Http://cenaceara.net/MariaRenold.zip
Both her Tuning in 432 and her Microtuning are in line with the Spiral of Fifhts, erroneously called the Circle of Fifths.
In her Tuning and Microtunig, Maria Renold stretched the octaves, where next is a little above the previous one.
Different from the astronomer Kepler. In this way solving the problem that Pythagoras called Comma.
When extending slightly the Fifths.
In the first Handbook for Tuners she says she had this idea but it did not work in 440.
Only after she had known how to make 432 and everything worked perfectly.
No other tuning and microtuning sounds so harmonious on all major and minor chords. But only in 432. Maria's words.
Test for yourself and comment.
(I have tested these microtuning files in Logic and Omnisphere, in both you need to use them together with the tuning in 432).
About Seconds_____________________________
"Seconds" is a scientific attempt to divide time equally. But no clock or calendar works without periodic adjustments.
432 deals with cycles. How many cycles every other cycle? That's what it's all about.
Independent of the duration in relation to a particular atom.
The base 60 count is a comparison between these astrological cycles, as well as their masses. We just try to quantify the time that is actually variable by nature. In a way an invention of the second atom for an invention of modern science. A paradox: by evolving scientifically we move away from the natural variable cycles. Calendars are seen by other cultures as a menu of qualities. And not as a cold count.
Curiously, the Sumerian people wrote that they received all this technology, which we still use today, from space gods. That's a fact, they left it written down. This same people who invented the foundations of modern science. This is at least curious.
432 is actually a number of cycles common to all areas of time and space. A kind of central node. Also 432 squared is light.
Independent of the "second atomic." I'm talking about relationship between physical cycles.
Even if you change the unit of measure, the ratio between the center note of the human audition (A4) and the speed of light will be the same. One squared from the other.
Favorite mind-boggling line: "432 deals with cycles. How many cycles every other cycle? That's what it's all about."
Huh?
May we show you scientific proof that 432 Hz is positioned in a Pythagorean like scale. We analysed 1600 papers about quantum entangled inanimate and animate (living) systems and found that we could normalise all these data into intervals of temperaments and a pitch. An algorithm could be derived: a Pythagorean like distribution, that is near to the Intervals of temperaments of Kirnberger, Zapf, and Lehman and shows a pitch at a= 432 Hz. It is possible to analytically calculate this scale making use of normalized Chern numbers, and is the following scale between 1.000 and 2.000 (Geesink publications 2016-2022):
1.0000, 1.0535, 1.1250, 1.1852, 1.2656, 1.3333, 1.4142, 1.5000, 1.5803, 1.6875, 1.7778, 1.8984.
Or in acoustics:
256.00, 269.70, 288.00, 303.41, 324.00, 341.33, 362.04, 384.00, 404.54, 432.00, 455.12, 486.00 Hz.
It is not yet known if Bach used a pitch near 432 Hz.
Kind regards, Hans Geesink
May we show you scientific proof that 432 Hz is positioned in a Pythagorean like scale. We analysed 1600 papers about quantum entangled inanimate and animate (living) systems and found that we could normalise all these data into intervals of temperaments and a pitch. An algorithm could be derived: a Pythagorean like distribution, that is near to the Intervals of temperaments of Kirnberger, Zapf, and Lehman and shows a pitch at a= 432 Hz. It is possible to analytically calculate this scale making use of normalized Chern numbers, and is the following scale between 1.000 and 2.000 (Geesink publications 2016-2022):
1.0000, 1.0535, 1.1250, 1.1852, 1.2656, 1.3333, 1.4142, 1.5000, 1.5803, 1.6875, 1.7778, 1.8984.
Or in acoustics:
256.00, 269.70, 288.00, 303.41, 324.00, 341.33, 362.04, 384.00, 404.54, 432.00, 455.12, 486.00 Hz.
It is not yet known if Bach used a pitch near 432 Hz.
Kind regards, Hans Geesink
May we show scientific proof that 432 Hz can be positioned in a Pythagorean like scale. We analysed 1600 papers about quantum entangled inanimate and animate (living) systems and found that we could normalise all these data into intervals of temperaments and a pitch. An algorithm could be derived: a Pythagorean like distribution, that is near to the Intervals of temperaments of Kirnberger, Zapf, and Lehman and shows a pitch at a= 432 Hz. It is possible to analytically calculated this scale by making use of normalized Chern numbers, and is the following scale between 1.000 and 2.000 (Geesink publications 2016-2022):
1.0000, 1.0535, 1.1250, 1.1852, 1.2656, 1.3333, 1.4142, 1.5000, 1.5803, 1.6875, 1.7778, 1.8984.
Or in acoustics:
256.00, 269.70, 288.00, 303.41, 324.00, 341.33, 362.04, 384.00, 404.54, 432.00, 455.12, 486.00 Hz.
It is not yet known if Bach used a pitch near 432 Hz.
Kind regards, Hans Geesink
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