The real problem with this question is that the expression "music tuned to 432 Hz" (or "to 440 Hz") hardly makes sense. First of all, it should give a note name. One probably must understand "music tuned to A3=432 Hz", but it would be better to say so. Then, suppose that A3 indeed is tuned to that frequency. What is the frequency of the other notes? This depends on several factors:

-- What instrument?

-- In what tuning or temperament is one tuning?

-- How long after the tuning does one measure the effect?

-- What kind of music is played?

It must be realized that an orchestra may have tuned to any pitch standard to start with -- say A3=432 Hz -- and neverteless may play at some other pitch standard -- say A3=440 Hz -- after half an hour, if only because of the increase in temperature in the room.

The French Government decided in the mid 19th century that the French standard pitch should be A3=435 Hz. Then the Austrians wrongly believed that this pitch had been measured at too low a temperature (around 15° centigrade) and estimated that pitch would raise by 5 Hz between 15° and 20°: this is the origin of A3=440 Hz.

Most instruments do not tune from A; D often is considered a better choice. But then the frequency of A will depend on the size of the fifth tuned in the particular temperament (or tuning system) considered.

Also, it is well known that choirs singing a capella (without instruments) tend to lower in pitch. The cause is often believed to be that the singers get tired, but it has been shown that the effect of tonality is much more important, because it entails harmonic progressions in one direction. Tonal music tends to lower in pitch, and the effect may be quite more important than the difference between 440 and 432 Hz (32 cents, only about 1.5 comma).

To sum up: this whole affair about playing at 432 Hz is nonsense. It is probable that a lot of music has been played "at 432 Hz" throughout history, and that nobody ever noticed. (Ellis, it the late 19th century, was able to document hundreds of historical pitch standards.)

Hello,

Unfortunately, I am not aware of ANY research that has been conducted examining differences between music tuned to 432 Hz and 440 Hz and I imagine (as perhaps you do) there would be numerous challenges associated with doing this research. If you do not already know of it I refer you to a product (both audiovisual recordings and a book about the underlying concepts) that was created using instruments tuned to 444 Hz. See Michael S. Tyrrell's Wholetones (www.wholetones.com) and his book The Sound of Healing: Unveiling the Phenomena of Wholetones (www.MichaelTyrrell.com).

As you have probably already discovered, there are scores, if not hundreds, of YouTube videos on solfeggio frequencies (a related phenomena) and sounds promoted as healing that result from 432 Hz tuning. To the best of my knowledge none of these products have been tested for their veracity. In addition, it is also true that numerous musical recordings resulting from the current Western music standard 440 Hz tuning have been used to support healing processes, which suggests that the tuning is not essential to a particular healing response. Of course, one must also determine what "healing" means, which begs the question of whether or not a given healing response is ever comparable to any other healing response. These are knotty issues and a survey of the literature in this field quickly demonstrates their complexity.

Having listened to Tyrrell's Wholetones recordings, having read his book and after experimenting with tuning various instruments (guitar, harp, electronic keyboard) to 432/444 Hz, I am not persuaded that promotion of 432 Hz tuning compositions is more substantive than the marketing process. While writing this response to your question I thought of one way to begin exploring possible differences. Perhaps someone has already done this; I haven't searched to see. Using Dr. Hans Jenny's cymatics research methodology (you'll find an abundance of information about his work and its current applications online), one could experiment with changing the fundamental tones to see how the resulting figures were affected. Of course, this would be a very basic tool for identifying what, if any, differences could be observed/determined and it does not address the specifics of making music with instruments tuned to a different fundamental.

If my response to your question prompts you to want to discuss this further, I'd be very happy to expand the dialogue. And, if you have questions about anything I wrote it would be my pleasure to respond again. I am curious to know what stimulated you to post this question!

Regards,

Karolyn van Putten

The real problem with this question is that the expression "music tuned to 432 Hz" (or "to 440 Hz") hardly makes sense. First of all, it should give a note name. One probably must understand "music tuned to A3=432 Hz", but it would be better to say so. Then, suppose that A3 indeed is tuned to that frequency. What is the frequency of the other notes? This depends on several factors:

-- What instrument?

-- In what tuning or temperament is one tuning?

-- How long after the tuning does one measure the effect?

-- What kind of music is played?

It must be realized that an orchestra may have tuned to any pitch standard to start with -- say A3=432 Hz -- and neverteless may play at some other pitch standard -- say A3=440 Hz -- after half an hour, if only because of the increase in temperature in the room.

The French Government decided in the mid 19th century that the French standard pitch should be A3=435 Hz. Then the Austrians wrongly believed that this pitch had been measured at too low a temperature (around 15° centigrade) and estimated that pitch would raise by 5 Hz between 15° and 20°: this is the origin of A3=440 Hz.

Most instruments do not tune from A; D often is considered a better choice. But then the frequency of A will depend on the size of the fifth tuned in the particular temperament (or tuning system) considered.

Also, it is well known that choirs singing a capella (without instruments) tend to lower in pitch. The cause is often believed to be that the singers get tired, but it has been shown that the effect of tonality is much more important, because it entails harmonic progressions in one direction. Tonal music tends to lower in pitch, and the effect may be quite more important than the difference between 440 and 432 Hz (32 cents, only about 1.5 comma).

To sum up: this whole affair about playing at 432 Hz is nonsense. It is probable that a lot of music has been played "at 432 Hz" throughout history, and that nobody ever noticed. (Ellis, it the late 19th century, was able to document hundreds of historical pitch standards.)

As far as I'm aware, the idea that 432Hz, or indeed any particular Hz tuning has specific healing properties is largely pseudoscience and as Karolyn points out above, many different Hz tunings have been used throughout history. Relaxation is very much in the eye (or ear!) of the beholder, and also if you believe that something has healing properties, it very well may do, for you. But that is due to the placebo effect, not the music or tuning system itself. That's not insignificant either, in many ways the placebo effect is a truly miraculous and mysterious thing.

There are also two distinct issues here which are often incorrectly conflated. Firstly there is the specific frequency value that is used as the basis for the tuning system such as 440Hz, or 432 Hz, or 444 Hz, or 439.33 Hz if you like. Secondly though there is the question of intonation, and the intervals that are derived from that reference frequency. In equal temperament (ie standard tuning) certain intervals between two notes are deliberately slightly out of tune, as this makes it easier to play or move between different keys, which is very useful practically when building an instrument. However it is possible to use pure harmonic tuning systems (like Just Intonation) based on integer multiples of the reference frequency which absolutely do sound different, and although a little strange at first are more perfectly in tune than equal temperament. The problem of course is that such tuning systems make it very difficult to move between different keys, or to make an instrument that can play in more than one key without having to retune (which is why equal temperament was developed in the first place).

These are two distinct issues though, and you can easily use equal temperament based on 432Hz, or just intonation based on 440Hz. The specific starting frequency doesn't really matter, but the way other notes are derived from that starting frequency does make a difference.

Here's a nice video that demonstrates the difference between these two tuning systems, and some of the practical challenges.

https://www.youtube.com/watch?v=Yqa2Hbb_eIs

Here's a nice piece by Michael Harrison entirely in a pure intonation tuning system.

https://www.youtube.com/watch?v=D4oKzSRs3sA

And finally, here's an interesting piece which moves between these two tuning systems at different times during the piece.

https://vimeo.com/65139727

I must confess a confusion, in my answer above, between the French and the American standard designation of the octaves. The note to be considered for establishing a pitch standard is A4 (which the French name la3), not A3.

On the history of pitch standards, the Wikipedia article https://en.wikipedia.org/wiki/Concert_pitch is not bad. (There is none in French.)

I would just like to add a few comments to the already excellent responses regarding the history of pitch in the Occidental music tradition.

First of all, the note used in order to fix the pitch level, usually referred to as the reference pitch. My own examination of the large number of historical works regarding the tuning, tempering, design and construction keyboard instruments as well as theoretical works on temperament and acoustics has demonstrated that the use of the note A for a reference pitch is a 19th-century development. Before then, the reference note whas almost always C, with the occasional use of F, the latter being somewhat more common in the late Renaissance and early Baroque. Until then, the note A had been one of the 11 floating pitches, the precise height of which depended upon the temperament chosen. It is important to realize that while it maybe possible to make broad generalizations about temperament use in regards to keyboard instruments - the use of meantone during the 17th century, for example - in a larger musical context, such generalizations do not apply. Equal temperament has been used since the Renaissance as a common means of setting the frets on lutes, guitars, and violas da gamba. Historical literature is replete with comments about the problems of combining fretted instruments with keyboard instruments due to their different modes of tempering, and in fact, resolving this issue was one of the advantages cited by proponents of the adoption of equal temperament. See, for example, the comments of Jean Deny in his 1636 treatise on tuning the harpsichord, in which he describes attending a concert in Paris for which the harpsichord had been tuned in equal temperament. This issue of historical reference pitch is the only aspect on which one may fault the otherwise excellent survey of historical pitch practice written by Bruce Haynes. It's a pity that while correcting many traditional misconceptions about pitch practice he did not take advantage of the opportunity to also set the record straight about the historical practice regarding reference pitch.

Secondly, while I agree that the Wikipedia article on pitch is reasonably reliable, it fails miserably in one aspect; it continues to present the misconception that pitch has risen over the centuries. The work of Haynes and others has demonstrated that for as long as one could speak of even a general sense of pitch standards, there have been four relatively stable pitch levels separated by a half step, from A≈ 392, French opera pitch, up to A≈ 465, standard German mid and late Baroque chor/cornet/trumpetthon, the pitch at which most German organs were tuned. This historical gamut already included 440, which some Baroque writers referred to as "the exotic Venetian pitch". A number of organs in northern Germany were tuned yet another semitone higher, around A≈494. Thus the modern adoption of A≈440 is more a process of the consolidation towards the center of the historical range rather than the imposition of a limit upon a historical tendency to rise constantly. In any case, as Nicolas Meeus has already described, 440 was already recognized as a commonly used pitch level in Germany during the first half of 19th century. It is found not only in the writings of Scheibler, but it also in works on the theory of design of pianos, such as those by Carl Kützing and J. G. Töpfer.

Regarding the various videos which one may find on the Internet which ostensibly demonstrate the resonance of water etc. Any physical object will demonstrate a number of modes of vibration at different frequencies, depending upon its physical dimensions and the physical characteristics of its material. Liquids in a container will also demonstrate the formation of stable surface wave patterns depending upon the physical characteristics of the liquid, the amount in the container, and the shape of the container. Vibrational modes of the container itself can also affect the formation of such wave patterns. The possibilities are endless, and one can easily manipulate the frequencies simply by varying the dimensions of the object. This has been known at least since the late 18th century, when Ernst Chladni became famous for his demonstrations of modal vibration of plates. Thus all such videos are nothing more then mere trickery designed to beguile the ignorant.

Regarding the use of pure intervals or Just Intonation as it is often called, there is a widespread modern misconception about historical practice. Just about any modern text on acoustics or the physics of musical instruments will inevitably contain an example of a series of chord progressions in which the application of Just Intonation will require a global pitch change of the entire piece in order to agree with a sustained tone which changes its harmonic function, examples which are ubiquitously offered as proof that the use of Just Intonation is impossible. Many historical authors however describe a standard practice of using flexible Just intonation, in which the upper parts are constantly varying their intonation in order to form pure intervals with the bass part, regardless of the temperament employed by the harmonic continuo instrument, be it keyboard, fretted string, or harp. An excellent survey of such comments can be found in the article by Bruce Haynes "Beyond Temperament: Non-keyboard Intonation in the 17th and 18th Centuries" (Early Music, 1991, vol 19 #3). One of the most succinct descriptions of this practice was given by Robert Smith in 1749, which I will reproduce here below. Thus in the context of flexible JI, the idea that music is "tuned" to any precise frequency is only valid in regards to the reference pitch, which was, as I have already stated, most often C and occasionally F.

Robert Smith, 1749: Harmonics, or the Philosophy of Musical Sounds, page 240

PROPOSITION XXII.

The several parts of a concert well performed upon perfect instruments [i.e. those with flexible intonation] do not move exactly by the given intervals of any one system whatever, but only pretty nearly, and so as to make perfect harmony as near as possible. For instance, if the base be supposed to move by the best scale of perfect intervals (a), the other part or parts cannot constantly move by it too, without making some of the concords imperfect by a comma (b), which would grievously offend the performers (c). Consequently if they are pleased, those intervals are occasionally tempered by the upper part or parts, which therefore do not move by the same scale which the base is supposed to move by. Likewise if the base be suppossed to move by the scale of mean tones and limmas (d), the other part or parts cannot constantly do so too, without making about two thirds of all the concords

imperfect by a quarter of a comma (e). But whenever concords are held out by good performers, they seem to me to be always perfect. And if so, the upper part or parts cannot

move by the scale of mean tones, which the base is supposed to move by. And the argument is the same if the base be supposed to move by any other scale of tempered intervals: and that it cannot constantly move by perfect ones, I shaIl shew in the next scholium.

What has been said of perfect and imperfect concords, is applicable to discords too, a good ear being critical in both. Now the reason why the best performers acquire a habit of making perfect harmony [i.e. Just Intonation], as near as possible, is plainly this. When the harmony is made perfect they are pleased and satisfied, though the several parts do not move by perfect intervals. For the passing from one sound to the next, whether by a perfect or an imperfect interval, being nearly instantaneous, is almost, if not altogether imperceptible, and therefore is indifferent to the performer. But the succeeding consonance is long enough held out to give him pleasure or pain, according as he makes it perfect or imperfect. Q.E.D.

Coroll. I. Caeteris paribus the harmony will be the same whatever be the scale which the base moves by; but the sum of the occasional temperaments will be the least possible, if it moves by the scale of mean tones and limmas (g), and but very little bigger, if it moves by the scale of equal harmony (h).

Coroll. 2. The proposition holds true though some of the instruments be imperfect; as when the thorough-base is played upon an organ or harpsichord because the performers of the upper parts are more attentive to make perfect harmony with the·base notes, than with the chords to them. Consequently those parts do not move by the tempered scale of the thorough-base.

Coroll. 3. Caeteris paribus the same piece of music well performed upon perfect instruments, is more agreeable than it would be if it were as well performed upon imperfect ones, as an organ, &c. For nothing gives greater offence to the hearer, though ignorant of the cause of it, than those rapid, piercing beats of high and loud sounds, which make imperfect consonances with one another. And yet a few slow beats, like the slow

undulations of a close shake now and then introduced, are far from being disagreeable.

Coroll.4. Therefore the harmony of a concert will be smoother and distincter, and generally more pleasing, for taking the chords of the thorough-base as near as can to base notes,

no more of them than are necessary, these few upon the softer and simpler stops of an organ. Because the beats will then be fewer, slower and softer, and so the voices and

other inftruments will appear to greater advantage.

Coroll. 5. It appears also from the reasons above, that no voice-part ought to be played on the organ, unIess to assist an imperfect singer, and keep him from making worse concords with the base and other parts than the organ itself does.

As far as I see, this 432Hz thing is mostly pseudoscience. People who endorse this theory believe that 432 is better than 440 because 432 is a multiple of 8, which should resonate somehow with brain waves. Not trivial, there's an obscure and secret program run by certain clandestine groups and organisations to negatively impact humanity...which can be basically referred as conspiratorial belief.

As far as I'm concerned, the idea that tuning an instrument at 432 Hz because it is a multiple of 8, doesn't really make much sense to me. Why 8 hz? Our ears filter all the frequencies above 20 Hz, what is below is artificially reconstructed by the cognitive system (see e.g., https://en.wikipedia.org/wiki/Missing_fundamental), so I personally don't see point in here.

As it has been said above, music appreciation does not really depend on absolute pitch, but rather on the relative ratios between sounds (in this case see e.g., natural (Zarlino/Pitagora) vs equal temperament). Assuming that a C is tuned at 8 Hz and given that octave has a ratio of 2/1, other Cs will be at 16, 32, 64, 128, and 256 Hz.

If we want to find the As of different tuning then we multiply 256 by the ratio associated with the major sixth at that tuning (C at 256Hz). So,

• natural (Pythagorean) == 256 * (27/16) == 432 Hz
• natural (Zarlinian) == 256 * (5/3) == 426,667 Hz
• equal == 256 * (2 ^(9/12)) == 430,539 Hz

So, which temperament should results in the "best" A? (obviously, by seen these numbers some would say Pythagoras!!1!)

• Not trivial (pt I). The equal temperament was a solution to play on the same instrument several tonalities (see e.g., the well tempered clavier). The point is that with the equal temperament, the "natural" ratios have been lost in favour of multiple tonalities.
• Not trivial (pt II) is the Western-centric approach of this 432 Hz. What do we know about nonWestern music at 432?

So, the most important thing:

There's an experiment on 432 vs 440 preference, unfortunately not published, run by Trevor Cox, Professor of Acoustic Engineering at the University of Salford. Results show there is no preference over the two conditions.

https://acousticengineering.wordpress.com/2013/12/13/pitch-shifting-to-432-hz-doesnt-improve-music/

It must be said that I also was interested in this topic, mostly to debunk the 432Hz. I wrote Trevor then asking whether he published the results, and he replied to me that most science journals would look at the premise and think 'why waste space proving something that is self-evident'.

'why waste space proving something that is self-evident'. Love it!!!

Two points that don't really concern the question but that have been raised above:

1. Paul Poletti, about "flexible just intonation". This question, whether flexible just intonation can be played (or sung), is not a modern one: it was first raised in the 16th century, in a famous correspondence between Benedetti and De Rore. The problem does not reduce to playing perfect intervals above the bass (as Robert Smith appears to believe), but it also involves adjusting common notes by a comma between one chord and the following one. This is recognized by professional performers as being highly tricky, much more difficult than playing or singing two successive notes a tempered fifth apart. As to Robert Smith's statement that playing in meantone would make "two thirds of the concords imperfect by a quarter of a comma", it merely evidences a poor understanding of the matter (which is possible even by an 18th-century author). In meantone tuning, all concords are imperfect by 1/4 comma as soon as they contain a 5th or its inversion. The whole point of meantone is that an imperfection by 1/4 comma is better than one by a full comma. To make my argument short, I'd say that just intonation can be called just only if it is just all the time. A "flexible" just intonation, one that allows some flexibility in the justness, is not a "just intonation" stricto sensu.

2. Alessandro Miani, about 432 Hz being a multiple of 8 (therefore also a multiple of 2, by the way). There is even more than that, namely that C4 at 256 Hz is a power of 2. This is the reason why it is called the "scientific pitch", that used by scientists (Sauveur, among others), because it facilitates calculations, especially before the advent of a common usage of logarithms. And it came back to the fore with binary calculations and with the age of computers. Many of our computers are "64 bits" machines, i.e. have numeric brains able to compute up to C2 ... ;--)) (It is not evident that they have a musical ear, though.)

Hi. I think that specialists in music performance had indifference between the use of 432 or 440. THe only solid argument that I heard was a friend of mine that is chorus master, because the use of 432 allows to non professional singers to reach high -pitched sounds easily compares with 440 tunning. Good luck!