음악 및 오디오 산업은 현재 전 세계 A = 440 Hz의 범용 표준 피치 조정을 사용합니다. 그것은 년후
이 문서에서는 간단히 튜닝의 역사와 수학의 관계, 자연에서 발견 고조파 비율 및 주파수에 관련하여, 과학적인 튜닝으로 432 Hz를 지원 핵심 사항에 대해 설명합니다. 희망이 좀 사려 깊은 토론을 자극 할 것이다. 중요한 듣기와 논리에서 432 Hz에서 조정에 구성하는 방법에 대한 간단한 설명을 위해 튜닝을 비교하는 일부 오디오 예제가 있습니다.
A Brief History of Tunings
존 스튜어트 리드로 기사라고
그의 Monochord와 피타고라스.
초기 20 세기에, 사방 장비 업체, 작곡가 및 오케스트라 위해 모두가 사용하는 보편적 인 피치 표준을 할 필요가 있었다. 432 Hz에서 완전히 클래식 음악 기간의 대부분을 통해 프랑스와 이탈리아 작곡가에 의해 지원되었다하더라도, 440 Hz에서 결국 보편적 인 피치 표준이되었다. 독일의 물리학 요한 하인리히 Scheibler는 안압계라는 장치를 발명하고 1800 년대 중반에서 440 Hz에서 튜닝 최초의 실험을했다. 안압계는 4 Hz에서의 간격으로 440 Hz에서 220 Hz의 범위 튜닝 포크 (54)로 구성되었다. 그의 작품은 널리 인정되었고 대화는 표준화 된 튜닝에 대해 시작했다.
많은 논쟁 후, 미국은 처음 두 대륙에 제안 된 후 곧 채택 몇 년에 이어 1936 년 유럽에서 표준으로 440 Hz에서 채택했다. 오늘날에도, 음악가는 432 Hz에서 조정에서 연주 음악이 더 나은 고객 응답이 진정 효과가 더 통합 된 전체 사운드 있다고 생각합니다.
440 Hz에서이 선택된 이유는 아직 완전히 명확하지 않다. Scheibler에 의해 과학 실험 튜닝이 더 자연에서 발견 고조파 비율과 관계 라인 내부에 무엇이 있었는지 반대로이 선택에 영향을 많이 한 것 같다. 저 할 수 있어요
Mathematics, Nature and Frequency
아래의 차트는 432 Hz에서 튜닝이 피타고라스의 고조파 비율에 기초하여 유도하는 방법을 보여줍니다. 2, 3 형태 차트의 기초 및 왼쪽 컬럼의 배수가 중간에 메모 C., 당신은 그 A = 432 Hz에서 볼로 (2)의 모든 배수를 보여줍니다. 또한 노트의 통합 수가 많은 영적 전통에 사용 된 번호 (108)이다. 말라기도 구슬 (108)의 가닥에 와서 요가 전통에서, 108 일의 인사는 종종 실시된다. 파란색 상자의 숫자 186624은 432 제곱이며, 소수의 백분 내에서 빛의 속도의 주파수
지구
태양과 조화의 기본 주파수
음악 연구자들은 또한 네팔에서 티베트어 그릇 같은 전통적인 치유 악기를 테스트, 그들은 A = 432 Hz의 조정에 따라 만들어진 발견했다. 소리 치료를 위해 만든 악기는 보편적 인 피치 표준을 준수하지 않아도 전 세계 소리 치료 센터에서 더 많은 인기를 끌고있다. 우리는 세대를 통해 아래로 전달되는 기술에 연결된 악기 만들기의 문화적 전통에서 많은 것을 배울 수 있습니다.
A Note on Equal Temperament VS Pythagorean Temperament
우리는 우리의 보편적 인 튜닝 시스템이 12 톤 동음 평균율에 근거 것을 명심해야한다. 의미, 모든 간격 또는 인접 노트는 모든 옥타브가 같은 소리를하기 위해서는 서로 균등하게된다. 사실 피타고라스의 기질,이 사건 없을 것이다. 평균율은 노트 구부릴 수 없습니다 피아노 등의 악기가 필요합니다. 목소리와 현악기 그러나, 메모를 구부리고 음 사이의 미묘한 차이를 달성하기 위해 쉽게 조정 변경 할 수 있습니다. 로엘 홀랜더는 자신의 블로그 게시물에 자세하게 설명
Audio Examples by Torkom Ji
Torkom 지, 양자 하모닉스 소리 치유의 설립자는 기꺼이 432 Hz에서 3 음악 예, 440 Hz에서 444 Hz에서 함께 Ask.Audio 제공하고 있습니다. Torkom 그의 모든 사용자 정의 코르그 ELECTRIBE와 로스 앤젤레스 지역에 걸쳐 사운드 치유 세션을 용이하게한다. 그는 단지이 악기를 사용하여 깊은, 공진 사운드 스케이프 여행을 만들기에 마스터입니다. 그것
MP3 내부 눈 432 Hz에서 :
[오디오 ID = "39526"]
MP3 내부 눈 440 Hz에서 :
[오디오 ID = "39524"]
MP3 내부 눈 444 Hz에서 :
[오디오 ID = "39525"]
* 앨범 상형 문자에서 :
당신이 듣고, 이러한 질문을 스스로에게 물어 :
- 하나가 다른 것보다 더 통합 된 소리를합니까?
- 하나는 주파수의 특정 범위를 가지고 있습니까?
- 하나는 다른 사람보다 얇은 소리를합니까?
- 당신은 모든 더 서로 흥분, 또는 중성 하나, 더 편안하십니까?
어떤 사람들은 이러한 질문에 대한 구체적인 답변에 생각하지만, 현실은 더 많은 연구가 대중에게 어떤 식 으로든 설득이 분야에서 필요하다. 이 때로 믿을 수 있기 때문에
Try it Out In Logic
로직은 432 Hz에서 또는 다른 조정을 시도 할 수있는 좋은 DAW이다. 프로젝트 설정 메뉴에있는 글로벌 조정 설정 창이 있습니다. 여기에 튜닝을 설정하면 타사 상품 제외 논리의 모든 소프트웨어 악기를 영향을줍니다. 튜닝은 현재 피치 기준으로 440 Hz에서와 466.3 Hz에서 (100 센트)에 415.3 Hz에서 (-100 센트)의 범위. 슬라이더를 설정하면 내가 432.2 Hz에서 또는 431.9 Hz로하지만, 432 Hz에서 오른쪽하지 않도록 설정할 수 있습니다 나타났습니다. 슬라이더되는 이유는 센트 단위의 떨어져 작동합니다. 당신이 아래로 녹음 또는 개별 부품을 투구한다면, 당신은 432 Hz에서 가까운 얻기 위해 31 또는 32 센트 피치를 낮출 것이다. (편집자 주 :
The Great 432 Hz Debate
440 Hz에서 표준 튜닝 오늘에서 작동하는 음악 세계의 너무 많은 (어쿠스틱 및 전자)와, 그것을
에 대해 자세히 알아보기 여기 Ask.Audio 아카데미에서 음악 이론을 .
기사, 블로그 및 추가 연구를위한 사이트; 과에 강한 인수 일부 :
콘서트 피치 충돌 :
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/
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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