تئوری موسیقی: بررسی 432 هرتز تنظیم مناظره

Most of the world now uses 440 Hz as the standard pitch tuning. However, this has been a relatively recent standard, and 432 Hz is making a comeback. Lynda Arnold explores why with sound examples.  

صنعت موسیقی و صوتی در حال حاضر با استفاده از A = 440 هرتز استاندارد جهانی تنظیم زمین در سراسر جهان. این نبود

این مقاله به طور خلاصه تاریخ تنظیم و برخی از نکات کلیدی است که حمایت از 432 هرتز به عنوان تنظیم علمی، با ارتباط آن را به روابط ریاضی، نسبت هارمونیک و فرکانس های موجود در طبیعت را توضیح می دهد. امیدوارم این چند بحث متفکر الهام بخش است. برخی از نمونه های صوتی برای مقایسه تنظیم گوش دادن انتقادی و توضیح مختصری در مورد چگونگی نوشتن در 432 هرتز تنظیم در منطق وجود دارد.

A Brief History of Tunings

نوشته شده توسط جان استوارت رید به نام

Pythagoras with his Monochord.

فیثاغورس با Monochord خود.

در اوایل قرن 20، نیاز به ایجاد یک استاندارد جهانی زمین توسط همه برای خاطر سازندگان ساز، آهنگسازان و ارکستر در همه جا استفاده می شود. حتی اگر 432 هرتز به طور کامل توسط آهنگسازان فرانسوی و ایتالیایی را از طریق بسیاری از دوره های موسیقی کلاسیک حمایت شده بود، 440 هرتز در نهایت استاندارد زمین جهانی شد. فیزیکدان آلمانی یوهان هاینریش Scheibler اختراع یک دستگاه به نام تونومتر و اولین تجربه با 440 تنظیم هرتز در اواسط 1800s بود. تونومتر از 54 چنگال تیونینگ با طیف وسیعی از 220 هرتز تا 440 هرتز فاصله در فاصله 4 هرتز تشکیل شده است. کار او تبدیل شد به طور گسترده ای به رسمیت شناخته شده و گفتگو در مورد یک تنظیم استاندارد آغاز شد.

Scheibler’s invention called the Tonometer.

Scheibler

پس از بحث های زیادی، آمریکا 440 هرتز به عنوان استاندارد در سال 1936. اروپا به تصویب رسید به زودی با سالها تصویب آن به دنبال پس از آن برای اولین بار در هر دو قاره ارائه شده است. حتی امروز، نوازندگان بر این باورند که موسیقی بازی در 432 هرتز تنظیم یک پاسخ مخاطب بهتر، دارای اثر آرام بخش و برای تلفن های موبایل کلی یکپارچه تر.

این است که هنوز واضح نیست که چرا 440 هرتز انتخاب شد. به نظر می رسد آزمایش های علمی توسط Scheibler بسیاری از نفوذ در این انتخاب به آنچه به عنوان تنظیم ممکن است بیشتر در خط با نسبت های هارمونیک و روابط موجود در طبیعت بوده است مخالفت کرده بود. من میتوانم

Mathematics, Nature and Frequency

جدول زیر نشان میدهد که چگونه 432 تنظیم هرتز بر اساس نسبت های هارمونی فیثاغورس مشتق شده است. تقسیم عددی بر مضرب 2 و 3 اشکال اساس نمودار، و در ستون سمت چپ نشان می دهد تمام مضربی از 2 به عنوان C. توجه داشته باشید در وسط، شما که A = 432 هرتز را ببینید. همچنین توجه داشته باشید که تعداد 108، در بسیاری از سنت های معنوی به عنوان یک عدد وحدت استفاده می شود. مالا دانه های تسبیح در رشته 108 می آیند و در سنت های یوگا، 108 سلام خورشید اغلب انجام می شود. تعداد 186،624 را در کادر آبی 432 مربع است و فرکانس سرعت نور در صدم اعشار است

Harmonic Ratio Chart   http://www.michaelleehill.net/wp-content/uploads/2015/02/UntitlMost-Harmonious.jpg  Nature’s Tuning – In line with 432 Hz

هارمونیک نمودار نسبت: طبیعت

زمین

Figure – Fundamental frequency of the sun and its harmonics  http://scalarheartconnection.blogspot.com/2014/11/the-sun-is-singing-to-our-hearts.html

فرکانس خورشید و هارمونیک آن

محققان موسیقی نیز مورد آزمایش قرار ابزار شفا سنتی، مانند کاسه تبتی از نپال، و متوجه آنها مطابق با A = 432 هرتز تنظیم ساخته شده است. ابزار ساخته شده برای درمان صدا لازم نیست که مطابق با استاندارد جهانی و زمین محبوب تر هستند در مراکز درمان صدا در سراسر جهان. ما می توانیم بسیاری از سنت های فرهنگی گیری ابزار، مربوط به تکنیک های که از نسلی به نسل یاد بگیرند.

A Note on Equal Temperament VS Pythagorean Temperament

ما باید به خاطر داشته باشید که سیستم تنظیم جهانی ما در 12 تن خو برابر است. معنی، تمام فواصل و یا یادداشت های مجاور به طور مساوی از یکدیگر به منظور برای همه اکتاو را به صدا در همان فاصله. در خلق و خو فیثاغورس درست است، این امر می تواند این مورد نیست. خو برابر برای ابزار مثل پیانو که در آن یادداشت می تواند خم شود مورد نیاز است. صداها و سازهای زهی این حال، قادر به خم شدن یادداشت ها و تغییر تنظیم آسان تر برای رسیدن به تفاوت های ظریف بین یادداشت ها. روئل هولاندر این توصیف جزئیات در پست وبلاگ خود،

Audio Examples by Torkom Ji

Audio Examples recorded in Pro Tools from Torkom Ji’s Korg Electribe.

نمونه های صوتی ضبط شده در نرم افزار ابزار از Torkom جی

Torkom جی، بنیانگذار کوانتومی هارمونیکس صدا شفا، تا لطف Ask.Audio با 3 نمونه موسیقی در 432 هرتز، 440 هرتز و 444 هرتز ارائه شده است. Torkom تسهیل جلسات بهبود صدا در سراسر منطقه لس آنجلس با سفارشی خود ارگ تمام عیار Korg ELECTRIBE. او کارشناسی ارشد در ایجاد عمیق، سفرهای صوتی رزونانس با استفاده از فقط این ساز است. آی تی

MP3 چشم داخلی 432 هرتز:

[شناسه صوتی = "39526"]

MP3 چشم داخلی 440 هرتز:

[شناسه صوتی = "39524"]

MP3 چشم داخلی 444 هرتز:

[شناسه صوتی = "39525"]

* از هیروگلیف آلبوم:

همانطور که شما گوش دادن، خودتان این سوالات را بپرسید:

  1. آیا یک صدا یکپارچه تر از دیگر؟
  2. آیا یک به خارج کردن یک محدوده خاص از فرکانس؟
  3. آیا یک صدا نازک تر از دیگران؟
  4. آیا شما احساس آرامش بیشتری با یک، آشفته تر با یکی دیگر، و یا خنثی به همه؟

برخی از مردم در پاسخ دقیقی به این پرسش را باور دارند، اما واقعیت این است، تحقیقات بیشتری در این زمینه لازم است برای متقاعد کردن توده یک راه یا دیگری. از آنجا که وجود دارد پذیر

Try it Out In Logic 

Tuning Settings in Logic.

تنظیمات تنظیم در منطق.

منطق یک DAW بزرگ را امتحان کنید 432 هرتز یا تنظیم دیگری در است یک پنجره تنظیمات تنظیم جهانی واقع در منوی تنظیمات پروژه وجود دارد. تنظیم تنظیم در اینجا همه ابزار نرم افزار در منطق، به استثنای ابزار های شخص ثالث تاثیر می گذارد. تنظیم محدوده از 415.3 هرتز (-100 سنت) به 466.3 هرتز (100 سنت) با 440 هرتز به عنوان استاندارد زمین جاری است. هنگام تنظیم نوار لغزنده من متوجه من می تواند آن را به 432.2 هرتز یا 431.9 هرتز، اما در 432 هرتز درست نیست تنظیم شده است. دلیل بودن از نوار لغزنده کار کردن از افزایش درصد است. بنابراین، اگر شما زمین ضبط کنید و یا قطعات منحصر به فرد پایین، شما را از زمین های 31 یا 32 سنت کاهش به نزدیک به 432 هرتز. (یادداشت سردبیر:

The Great 432 Hz Debate

با خیلی از دنیای موسیقی (آکوستیک و الکترونیک) عامل در 440 هرتز تنظیم استاندارد امروز، آن را

اطلاعات بیشتر در مورد تئوری موسیقی در آکادمی Ask.Audio اینجا .

Lynda Arnold is a singer/songwriter, multi-instrumentalist (voice, flute, piano, and guitar), and electronic musician/sound artist who has been producing, performing, and developing her own sound for over 12 years as ‘Divasonic;’ an ethereal, song driven electronic music project with multiple album and single releases on labels EMI, Cl... Read More

Discussion

Milton
Hi Lynda,
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.
Lynda Arnold
Hi Milton - are you the author of the 'Hertz So Good' article I reference above?
Milton
Hi Lynda!

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.
Lynda Arnold
Hi Milton -

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.
Lynda Arnold
Milton -

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.
Milton
Oh and indeed Babylon predates Pythagorus in the use of harmonic ratios ('God numbers') see e.g. fletcher, World Musics in Context.
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!
rovethegroove
I had my housemate play these in random order, so I wouldn't be biased. I could immediately tell the difference between the three. The 444 tuned version I had to stop the playback about 1/4 of the way through. Everything to me was too "screechy" and almost hurt my ears. I was surprised at how much I really loved the 432 tuning. It did indeed seemed to be more mellow and cohesive. Coming from the world of classical music, all I've ever performed or composed in is 440. Seeing as how Ambient music is currently my main genre of composition, I'm going to go experiment with composing with my tuning at 432. Thanks for the insight.
Lynda Arnold
Hi there! I am so glad you listened to the examples and are inspired to experiment composing at 432HZ yourself!
Greg
Regarding being unbiased: Did you hear the samples before reading the article? Despite random order, it would still be very easy to tell which of the three were higher, and which (432) was much lower, so you may not actually be blinded at all by the random order. Did you take a good break between each one, and not listen to any music during that time? If you have perfect pitch, of course, none of that will matter, a listener with perfect pitch can't really be a 'blind' subject in this situation once they've read about what they are expected to prefer.
johanneskeller
I don't have any experience with therapeutic sound work. My background is the performance of renaissance and baroque music. This discussion about reference pitch is based on two misunderstandings:

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).
Lynda Arnold
Thank you for these valuable insights Johannes. I've only come into the study of tunings and pitch through my work in sound healing and I find there is much to learn and study here. There's also been so much research into specific frequencies and their healing potential as well - Rudolph Steiner, etc. Much of sound healing work is based on 'intention' which is pretty much of the opposite of the proven hard facts that science presents and demands. Thank you for pointing out that you are convinced that music and sound influences our body and well-being. I think that is true and is also why I cover many different subjects and approaches related to this in my 'How Sound Affects You' series. This particular subject is one I am still learning about. I'm fine with any inaccuracies being corrected and welcome any links to articles or journals that prove them otherwise. Blessings.
Milton
Johannes' comment is spot on. This article makes the oft-repeated error of conflating pitch standard with temperament, and repeats many historical (and theoretical myths) without critical awareness. To claim that 432 Hz is in any way ancient (and predates the tuning fork) is completely unfounded (I'm trying to be nice). For a more accurate history of pitch standard see http://www.wam.hr/sadrzaj/us/Cavanagh_440Hz.pdf
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.
synthguy
There is nothing in this article except a little anecdotal evidence that demonstrates the superiority of 432 Hz over 440 Hz. Much of the article is actually a clumsy explanation of the difference between Pythagorean Temperament and Equal Temperament. The article's explanation for the development of Equal Temperament misses the point - that it was designed to permit a keyboard instrument to play music in any key without suffering the dissonance that Just Intonation produces when you play music outside the fundamental key of the instrument’s open strings.

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.
Ed Foote
Greetings,
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
Polarbreeze
+1
Rounik
Hello Milton. You said: "A shame this site repeats such inaccuracies." Would you care to expand on this by telling me which of our other articles "repeat inaccuracies"? That's a pretty big claim to make especially considering we publish between 3-6 articles on an average day and you're implying many of our articles on music theory are inaccurate??
Milton
No, that is not what I am implying.

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).

Rounik
Hi MIlton, thanks for clarifying! Appreciate you taking the time to list what you feel the inaccuracies are. We have a number of follow up articles on this debate lined up. After all, it wouldn't be a debate without more voices! I'm not sure 3), 5), 6) can be proved one way or another. RE: 7) I don't believe Lynda is suggesting Pythagorean tuning is the only alternative. At least I don't read it that way.

It does help and I'm sure your comments are of use for those interested in a counter-approach.

Best,
Rounik
synthguy
Obviously I'm biased towards the scientific, as my comment above demonstrates. So I'm intrigued when Lynda writes that "There's also been so much research into specific frequencies and their healing potential as well - Rudolph Steiner". I can't find anything specific from Steiner about the healing potential of specific frequencies. Lynda, can you point us in the direction of the research you're describing?
Skye
For some obscure reason the moderator apparently has censored my submitted (and decent but critical) comment where I also refer to what I have researched abut the Rudolf Steiner connection. You may find my article here: http://goo.gl/31m1gg
Lynda Arnold
Hi Synthguy - I think a great historical article that mentions Steiner as a proponent of 432Hz is the one I reference above - 'The Curious Concert Pitch Conflict' - he was a philosopher and spiritualist that lectured on this subject and believed 432Hz pitch was the 'correct pitch for human minds and spirits.' He also believed that C = 128Hz was a frequency of upmost importance (falls in 432Hz tuning as the C below middle C. Another great research on this subject as it relates to the use of tuning forks, sound healing, specific frequencies and the significance of Schumann resonance is 'Human Tuning' by John Beaulieu. There are other researchers who have gone way more in depth into the study of specific frequencies and how they affect the body - even mapped out the range of frequencies of our organs. Yes, there is a lot of gray area when it comes to sound healing based work and the work with specific frequencies - but I also think the study of how pitch and frequencies affects human consciousness is in its infancy. As time goes on I think there will be more and more correllation between scientists, spiritualists, musicians, researchers and healers on the matter. Again, i'm giving you a non-science approach but I encourage you to keep an open mind.
Lynda Arnold
also check out:

http://omega432.com
TL2Bass
These mixes are different performances. At least the 432 and 440/444 ones are. There is a missing synth element in the two 440 and 444 mixes that is present in the 432. It's a very important element that aids in the relaxed feel of the 432 piece and by not having it in the other two mixes, is very unfair. And yes, I am a professional Music Producer (ie... a trained ear - heard it right away) in LA that curiously stumbled upon this site/article with an open mind and zero agenda. If you can get the same exact mixes uploaded with the exact same elements in all three, that would be a fair comparison. For now, I see why most everyone might choose 432 as the "best" or most "relaxing" piece of music. This doesn't negate the comparison or the discussion of which may be "better" or more "healing", just that the sample MP3's are not identical in performance. Thanks for reading.
Lynda Arnold
Hi TL2 Bass - Thanks for your comment and for your critical listening of the tracks. Yes, the tracks are identical mixes. They were recorded from Torkom's Korg Electribe, the only difference being the reference pitch/tuning. This shows how the different tunings affect the frequencies and what you hear stand out or masked entirely in the mix. Perhaps, the 440Hz and 444Hz tracks would need to be mixed down differently - even EQ'd - to match the 432Hz track? Possible, but that defeats the purpose of the exercise. The tuning the track is originally composed in makes a huge difference as well, which is why I mentioned that in the article. Many people into 432Hz tuning do report hearing deeper mid and low range frequencies, feeling these tones in the body more and also more integration across the entire range of frequencies. Another experiment would be to compose a track in both 440Hz and 444Hz mixed to you liking and then pitch them to the other two to hear and feel the difference between them.
Vince
I get that Pythagoras was able to create a tuning system based on ratios and relative pitch.. But I have difficulty swallowing the fact that there was a stable pitch that was used as a reference. The very concept of a second wasn't invented until 1500 years later. Without a constant unit of time, there can be no Hz (frequency per second). Without Hz, there can be no tuning standard other than ratios.

I see this as a major claim for the purity and "goodness" of the 432Hz.. But it just doesn't hold water.

Thoughts?
Polarbreeze
+1
Rounik
Thanks for all the comments so far. This article has sparked a lot of debate. Some healthy... some not as much. We've taken on board everything that has been posted and as a result are working on some follow-up articles to further explore the 432 / 440 / 444 Hz area. At least one will involve a counter-argument. Please give us time as our authors are gong through thorough research.

Thanks!
Rounik
Exec. Editor, Ask.Audio
Polarbreeze
That numerology about 432 has no possible justification. They overlook the fact that Hz means cycles per "second" - and a "second" is an arbitrary construct of humans. Also, any numerology they can find relating to the note "A" will immediately fall apart for any other note in the scale and so cannot apply to the whole music. It's disappointing to see this kind of an article posted here - I'd have hoped for better.

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 atom”. Hardly a fundamental characteristic of sound in nature.

2. The frequency of the note “A”, 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 “A”, 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.
Lynda Arnold
Here's a site describing the 'Atomic' clock and argument against the 'second' being 'arbitrary.' Someone sent this to me - is this what you are referencing in #1?

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.
Polarbreeze
Hi Lynda,
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.
synthguy
"And tuning forks and gongs tuned to the frequencies of the planets"

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.
Graham
Another way of looking at the possible origin of our measuring units is to notice our bodily processes. Exactly an hour after a heavy meal, your mental capacities will be slightly dulled, while a cup of coffee will do the opposite, and at the same point will stimulate the bowels.
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.
Lynda Arnold
Thank you Graham - Very useful and interesting information. I will certainly check out your book!
Polarbreeze
Graham, there are two different things going on here. (a) the "12 true-fifths tuning" would no doubt make a huge difference to the perception of the music and to the feeling you get from it - and that would be different depending on what key you played in (b) however, there is no evidence that the absolute value of the tuning reference, whether 432 Hz or 440 Hz or any other value, has any subjective effect at all. Anecdotal reports tend to mix up these two totally different concepts and so do not give us any useful insights about the magical 432 itself. It seems to me that your piano example may have fallen into the same trap?
Graham
When people claim there is only "anecdotal" evidence of an effect, I often suspect that any merely subjective reaction would be unacceptable to them--not "scientific". But what if there is a mountain of such "subjective" and "anecdotal" evidence? That is the case for the preference for the A=432 pitch, even if there has not been a test under strict "scientific" conditions. It is similar with e.g "near-death experiences" of another world.
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.
Lynda Arnold
Graham - You make some excellent points here. Thank you for sharing. It's also fascinating that you actually participated in Maria Renold's blind listening study. It's great to hear that she tested this so vigorously.
Polarbreeze
Graham, I don't think I got my point across so I'll try again. Because MR always uses those special tuning intervals when she is using 432 Hz, we have no way of telling whether the (undisputed) different psychological effect is due to (a) the special intervals or (b) the absolute pitch of 432 vs 440. It's great to know that you've actually participated in one of her testings - what was the test she did that convinced you the differences you heard were indeed due to 432 vs 440, and not simply due to her special intervals?
Milton
The issue is that even the most intelligent and honest people underestimate the power of suggestion. We experience and sense through our filters of belief. Cognitive bias is very very powerful. When we control for these through scientific method that's when we separate the imagined from the real. And with that scientific method we have amassed so much knowledge so quickly, and have had to accept completely mind bending concepts due to the overwhelming evidence. For example, the number of people who claim to have (or have witnessed) psychic abilities is vast but these skills disappear magically as soon as proper controls are in place. So there is no surprise that people will spend £15k on audio cables or stilts that lift the cables of the carpet or 'directional' AC cables when it comes to the subjective field of music. I've yet to see a properly blinded tuning reference test so I'm designing one with some other academics. I extend a warm invitation to all (432 advocates or otherwise) to take part, to see if this hypothesised preference persists when biases have been minimised. Should be ready this year. Anyone interested?
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.
Ed Foote
Greetings,
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,
Lynda Arnold
I am very interested in participating in your blinded tuning reference test this year. Keep me posted! I am glad you are putting it together.
Polarbreeze
Well said, Ed - and you bring up another very good point. It is of course true that if an instrument is tuned to a different pitch from the one it was designed for its tonal quality will be different (looser vs slacker strings for example). So this is sure to affect listener perceptions - in fact it's easy to imagine that a period instrument will sound most authentic when tuned to the norm of the period (if we could ever know what that was).

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.
Don
Happy to participate! :-)
Graham
Polarbreeze, it was a long time ago that I participated in one of Maria Renold's tests with an audience--maybe 50 years ago. As far I remember, she just played single notes--on a violin, I think-- perhaps half a dozen slightly different pitches of A, and recorded reactions with a show of hands. The audience reactions were strikingly consistent--432 was the favourite, most "normal, comfortable" one. Thus the scale tunings were not involved.
Polarbreeze
On a violin. So how did she ensure that the vibrato and the bowing and all the other performance variables were the same for the 432 note versus the 440 note?
synthguy
And how did she ensure that the pitch was exactly 432 Hz? On a violin, with no frets, it's really easy to be out of tune by a Hz or two every time you play the same note. A test like this should be done on an instrument that holds pitch precisely, like a piano.
Graham
Polarbreeze--It would have been in the 1960's that I participated in the test. Even as I wrote that, I was wondering if I was accurate. It turns out I was not. I based it partly on knowing that Maria Renold played viola with the Busch Quartet for years. So I phoned her daughter, Barbara Renold, in Spring Valley, N.Y. She said her mother used a monochord for such tests, played with a bow, and would have played at least three pitches--she wasn't sure how many. Her researches always started from the hearing, and only used the mathematics later as confirmation. She said her mother as a little child visited the first Goetheanum that Rudolf Steiner built in Dornach, Switzerland (and which burned down shortly afterward). She said that while there she heard inwardly a tone that greatly impressed her. It turned out to be Hz 256, which is the C associated with A=432. The scales she developed, she said she also first heard inwardly and only later discovered the theoretical justification for them.
Raphael - SubConsciousMind
The researchers at stanford did NOT put the fundamental frequency of the sun at 144Hz! The measured over a period of 144 days and the found a frequency in the microHz range.
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
Polarbreeze
OK, Graham, I'm out of patience now. There's a very interesting line of discussion here, which is all about the various ways in which a series of intervals can be put together to solve one of nature's conundrums: that the harmonic series does not exactly match the circle of fifths. The different intervals and scales certainly have different subjective qualities about them. That's all great, and it's fascinating, and worthy of principled discussion. However, in stark contrast to that, this whole 432 Hz thing is poppycock and has not a single shred of objective evidence.
Graham
Polarbreeze --I still see a confusion of absolute pitch and scales. They are two separate subjects. In Maria Renold's tests with an audience, she used tuning-forks to establish the pitch on the monochord. Have you ever used a monochord? It is easy to tune one exactly with a moveable bridge, especially if it is a long one. The one I built has strings nearly five feet long.
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.)
Polarbreeze
Yes, Graham, this is my point exactly. Absolute frequency is an entirely different subject from scales/intervals/harmonics. The problem here is that the “evidence” presented does not separate those two different concepts - and therefore it attributes to absolute frequency an effect that is actually due to scales/intervals/harmonics. It would be easy to devise an experiment that separates the two – one wonders why the 432 proponents have not done that.

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?”) 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.
Graham
(Please ignore a shorter version of this comment which got submitted by mistake, by a careless key-stroke, just a little while ago.)
Graham
Polarbreeze --

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.
Ed Foote
"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."

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,
Polarbreeze
Hi Ed,

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.
Polarbreeze
You pointed out that the notes were generated with a bow on a Monochord. Therefore the timbre (i.e. harmonics) could change each time the instrument was bowed. To use your word, the result is then ambiguous - furthermore, as you point out, when the harmonic variability is removed, the effect goes away. The most likely explanation for this is that the change in timbre/harmonics is what causes the observed "deep subjective reaction". It would be very easy to devise a study in which the variations in harmonics (i.e. timbre, scale, temperament, intervals) are controlled for. However, those who believe it's a matter of the absolute 432 Hz frequency have not reported any supporting results from such a study. Or, if they have, perhaps you could point me to them because I'd be very interested to learn from them.
Graham
The confusion continues. Have I really not made myself clear? First, the only "ambiguity" i was referring to was the fact that Maria Renold's personal biography included references to both single tones and scales. Beyond that, the latest objections seem to me to be a "red herring" that is purely speculative. Polarbreeze, where on earth did you get the statement that "when the harmonic variability is removed, the effect goes away". I see no such evidence in what has been presented. That the bowing could be different could just as easily work AGAINST e.g. the 432, as FOR it. Also, as I mentioned, in her public tests, Renold did not always put the desired frequency in the middle of three. I forget the details, but I know she guarded against that kind of thing. Variations in timbre purely because of a different pitch would simply be part of the different quality of the different pitch. Each pitch would have the same pattern of overtones. And, as should be obvious, "scale, temperament, intervals" are different questions.
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.
Polarbreeze
Hi Graham. No confusion here. I have no issue at all with you or anyone else having a personal preference for A=432. What I take issue with is the notion that A=432 has some special quality endowed to it by nature that makes it somehow superior to other reference frequencies for A. There is no evidence whatsoever for that and although I've invited you to do so several times you have still not produced any such evidence.

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.
Polarbreeze
Hi Lynda, thanks for your new posts correcting some of the misinformation. It's appreciated.
Graham
Most of my work on this subject was done many years ago. Today I dipped into my notes on two tuning conferences I went to in 2007 and 2008 in Spring Valley, N.Y. Based on Rudolf Steiner, they were mostly people in favour of the 432. We discussed many aspects in detail, even the difference in tension in a monochord at two different pitches. There was a wealth of testimony that the A=432 was personally preferred after years of experience. It was said too that a number of singing teachers found that using it with their students improved their tone-production and endurance. The group of singers I mentioned, I read of some years ago at least twice in magazines or newspapers.
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.
rob wittman
Hi lynda

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.
Old Sideman
Keep it coming all !
Digging the debate immensely!
Lynda Arnold
Sonic Geometry: The Language of Frequency and Form (VIDEO)

https://www.youtube.com/watch?v=FY74AFQl2qQ&app=desktop
Aimar
Is not easy for believers to do this, so thanks for those corrections. Anyway if you don't want to fall again in the same errors you should be very careful about this youtube "documentaries", and if you want to understand the basics of physic and acoustic, there are some ways to do it without any ideology,propaganda or misinformation between lines.

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."
Polarbreeze
Cute video. It's fascinating to play with ratios and to observe the similarity to the harmonic series - and the way that geometrical shapes relate to natural formations and human artefacts. It may appear kind of mystical in some ways to some people. Back to the topic of this thread: there is nothing in this video to support the idea that the frequency of 432 Hz has any special significance in nature. On the other hand, I did note that at exactly 4:32 of the video it's shown that the natural circle of fifths is not a circle at all, but rather a spiral. A message no doubt planted in the video by the visitors from outer space that the narrator refers to.
Namma
All the math, all the taking it apart, all the reason...it all falls flat when I listen to it.

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.
Namma
I think that perhaps it should be left up to the listener what "tuning" they prefer.

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.
Sana-sol
It's small about different calculations at least and with the same formula A==E=(4*(sqrt(2))/((1/c)*5/2)).

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
Maxim
It is simple to start to heard music in A432Hz tuning. I would recommend a free iOS audio player what lets toggle between playing music in standard vs A432Hz tune. www.alphasxplayer.com/ Because compositors in past imagined their music exactly in 432Hz then it is better to heard it as it should sound originally
Kc
Hi, I listened to the three audio examples at 432, 440, and 444. Yes, I agree, the 432 sounds the most mellow and soothing. However, experimentally, I don't think this is a valid approach, because a lower frequency is bound to sound more relaxing, regardless of any associations with the earth's oscillation or the sun's "fundamental frequency."

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".
Polarbreeze
That certainly could be part of it. Another possibility is that the slight change in frequency creates a different relationship with the sampling frequency and so could change the harmonic content - everyone's listening to these samples through digital media. One thing's for sure it has nothing to do with the numerology about relationships to natural frequencies of the universe.

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!
synthguy
Polarbreeze - as with most New Age claptrap, the arguments in favour of 432Hz are entirely devoid of good science, and entirely built from 'emotion and personal belief'. There is no use in trying to find a reasonable, logical explanation for a phenomenon that doesn't exist, especially since the believers have a whole arsenal of fact-defying strategies to counter with.
Polarbreeze
Well put, synthguy
Toni Mazzotti
(please remove the my others comments, i put best on this)

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
Polarbreeze
Yes, the trouble is that she continually convolves two completely different concepts: (a) concert pitch; and (b) temperament.

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.
Toni Mazzotti
Read the Maria Renold books that are in this zip. All her work is based on 432.

==>> 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.
Polarbreeze
Tony, there are so many errors and inconsistencies in all of that - I don't even know where to start. I suggest you get yourself a good book on the science of all this. As for your comment about the ratio between A4 and the speed of light, and your assertion that one is the square of the other - this is gobbledegook. Sorry to be blunt.
synthguy
Tony, you should go in to politics. The convoluted, baffling way you communicate makes anyone with a brain doubt their own sanity.

Favorite mind-boggling line: "432 deals with cycles. How many cycles every other cycle? That's what it's all about."

Huh?

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