Myth

Tuning to 432 Hz is better than 440 Hz. Or more accurately, tuning to A=432 Hz and using a "just intonation" tuning method (scientific tuning) is better than using A=440 Hz and "equal temperament" tuning (concert tuning).

Is 432 Hz Better than 440 Hz? Is Concert Tuning Better Than Scientific Tuning?

It’s theorized that using a starting pitch of A=432 Hz and a “just intonation” tuning method (scientific tuning) is more natural and mathematically symmetric than using A=440 Hz and “equal temperament” tuning (concert tuning). However, on this page we will argue that both methods have their pros and cons.

TIP: The full debate isn’t just around a starting pitch like A=440 Hz or A=432 Hz, it is the starting pitch and tuning method combined.

The Bottomline on the A=432 Hz and a “just intonation” tuning method (scientific tuning) vs. A=440 Hz and “equal temperament” tuning (concert tuning) Debate

In general:

  • Single notes produced by the combination of the starting pitch of A=432 Hz and scientific tuning have a “nice” harmonic quality (as can be seen using “cymatics experiments” that convert sound waves into visuals), but as a trade-off some chords and scales produce disharmony (“wolf harmonies“).
  • Meanwhile, the combination of A=440 Hz and concert tuning results in a more disharmonic quality for single notes, but as a trade-off all chords and scales sound rather harmonic (which is useful for concerts, composers, and consistency).

These two facts together help explain why A=440 concert tuning was generally adopted as the pitch standard.

Given the above, it is hard to conclude that concert tuning using an A=440 starting pitch is somehow inferior in all respects to scientific tuning using an A=432 starting pitch. Instead, as noted above, the reality is each method as its pros and cons, and each method is a sort of trade-off (as explained below).

Thus, while we will conclude that the idea that one tuning method is “better” (or conversely that another is inferior) is a myth (and that the conspiracy theories related to them are also myths), our conclusion shouldn’t be read as a dismissal of arguments for or against specific tuning methods and starting pitches.

FACT: Bach’s The Well-Tempered Clavier is written in all 24 major and minor keys. Such a piece is only possible to perform in a harmonically pleasing way on “well-tempered” instruments (instruments using “well temperament” tuning or other tuning methods more in-line with concert tuning than scientific tuning; here speaking more to tuning method than starting pitch). Before Bach’s time it was common to tune using a method in which instruments would have to be retuned when changing to some keys (which is a nightmare for composers who compose on pianos and other similar instruments like Bach did). Factors like this are likely what explains why modern tuning methods evolved the way they did. Still, with that noted, other tuning methods have their perks and merit discussion (and starting pitches merit their own debate as well).

The Main Points to Consider in the “Scientific Pitch vs. Concert Pitch” / “440 vs. 432” Debate

While our research seems to confirm aspects of the “Scientific Pitch vs. Concert Pitch” / “440 vs. 432” theory, there are a few major problems with claims that one method is better than another:

  1. Although a starting pitch of A=432 Hz and just intonation tuning pair nicely, as do A=440 and equal temperament, there is no inherent reason to connect a starting pitch and tuning method. These are two separate concepts. With that in mind, the reason they are connected is because they produce the desired results. A=432 Hz and just intonation produce those nice “cymatic” harmonies. A=440 and equal temperament produce a set of standard pitches that work well with western music’s scales and chords. If you start switching starting pitches and tuning methods, or picking different starting pitches and tuning methods, you get different results.
  2. Many pitches and tuning methods have been tried over the years, and each has been shown to have unique drawbacks. Literally, every combination of tuning method and starting pitches I researched seemed to have drawbacks.
  3. Modern studies are generally lacking regarding the effects of frequencies on our biology. We can speculate that single notes of A=432 “feel” better, and that is valid… but we don’t exactly have studies backing that up (nor do we have studies backing up the converse, that disharmony is “bad” in this sense). Doesn’t make it invalid, just isn’t backed by our current science.
  4. Just intonation (meaning intonation only, or “just ratios”) cannot produce a set of pitches that work well in every key. This means you can’t play in all keys on one instrument using this tuning method, some harmonics don’t work well, some chords don’t sound right, and it has general limitations as a pitch standard for concerts because of this (see a history of pythagorean and just intonation tuning, see basics of music theory, keys, harmonics, scales, chords, and intervals for why this matters). This is likely the main reason composers (who are almost all pianists) like Bach switched to a more “well tempered” tunings over the years. Concert tuning may have its problems, but at least all keys and chords sound “pretty good” played in it (especially important for concerts and for not having to re-tune your piano every-time you switch keys).[1]

This is to say:

  • Scientific tuning (just intonation and an A=432 Hz starting pitch) creates “pretty” harmonics that can be seen visually using cymatics experiments (see below). This has real merit for those playing single notes in a solo performance (like singers and violists)…
  • But for concerts, pianists, and composers, concert tuning (A=440 Hz and equal temperament) is much more consistent and practical (despite its sometimes slightly disharmonious nature).

Given this, it doesn’t make sense to tie this all to a conspiracy.[2][3]

We discuss the details of the above, cymatics experiments, and the history of the pitch debate below.

First, I suggest watching the following video, it does a good job of explaining some technicalities that should be considered in “the 432 vs. 440 debate”.

Why It’s Impossible to Tune a Piano. A string produces a mechanical wave when plucked, its frequency determines its pitch, this is sound. If you “fret” the string and shorten it by a ratio it produces a different sound, this is pitch. We can use pitches to create scales. When notes are played together we get chords. Only equal temperament tuning results in all chords and scales sounding good together (without changing the tuning). This video explains the mathematics behind just intonation and equal temperament, and it shows off a cymatics experiment as well.

What are 440 and 432 Hz? Scientific Pitch Versus Concert Pitch

There are lots of different ways to express the 440 Hz vs. 432 Hz debate, but specifically, the debate is over Scientific Pitch vs. Concert Pitch and is just as much about the tuning method as it is about the starting pitch.

  • 432 Hz AKA Scientific pitch (“Verdi Tuning”, philosophical pitch, A=432 Hz, middle C=256). This uses a starting pitch of A=432 Hz and “Pythagorean” (ratios) and/or “just intonation” (ratios of small whole numbers) tuning methods. This results in whole numbers pitches and symmetric and visually pleasing patterns in cymatics experiments… but some awkward “wolf” harmonics.[1][8]
  • 440 Hz AKA Concert pitch (“the pitch standard”, “standard western tuning”, A=440 Hz, middle C=261.63). This uses a starting pitch of A=440 Hz and “equal temperament tuning” to separate notes by logarithmic equal distances (100 cents). This results results in non-whole number pitches and “messy” patterns in cymatics experiments… but all keys, chords, and pitches are usable.[1][8]

TIP: Want to try hearing the difference? Keep in mind you need to not only change the starting pitch of A (the A above middle C, AKA the A4  above C4) but also the tuning method. Some music programs (like Logic) will give you the option, or you can do it by hand on a stringed instrument (by tuning each string to its respective starting pitch).

Understanding Pitches, Tuning, and Cymatics for the 440 Hz Debate

Above we summarized the argument, below we give the details needed to understand each aspect of the “440 Hz debate”.

Summary of the Benefits of Just Intonation Vs. Equal Temperament

Starting pitch aside, we can sum up the benefits of each tuning type by saying:

  • Equal temperament results in all keys on a piano being playable in any interval, key or scale.
  • Just tonic results in beautiful cymatic patterns that resonate with the physical universe (but only when single notes and certain intervals are played).

Understanding the Mathematics of Just Intonation and Equal Temperament

All tuning types use mathematics to define their tuning.

  • Just tonic and pythagorean use ratios like 3:2 ratio for dominants, 11:8 for sub-dominants, 2:1 for octaves.
  • Equal temperament uses imaginary numbers, square roots, and complex mathematics like 2^{1/12}={\sqrt[{12}]{2}} for a minor second and 2^{2/12}={\sqrt[{6}]{2}} for a major second (each step increases by a power of 1/12).
  • To compare the two: a Tritone (an augmented fourth or diminished fifth) in equal temperament is 2^{6/12}={\sqrt {2}}  = 1.414214 and just intonation is{\begin{matrix}{\frac {7}{5}}\end{matrix}} = 1.4000000. This means, on a stringed instrument for an example, a tritone is defined in just intonation by cutting the string in by{\begin{matrix}{\frac {7}{5}}\end{matrix}}and by 2^{6/12}={\sqrt {2}} in equal temperament. Each gives a slightly different result, in this case equal temperament is off by +17.49 cents (it gives 582.51 cents, while just intonation gives 600 cents). See all mathematical comparisons of the tunings here. The ratios may seem more mathematical to you, but I reckon Ramanujan would have appreciated modern western tuning due to its use of complex mathematics (despite his heritage).

Piano Tuner Shows Classical Repertoire Performed in Historical Tunings. Here is a comparison and discussion of different tuning methods done by a classical pianist.

FACT: In most tuning systems used before 1700, one or more intervals on the twelve-note keyboard were so far from any pure interval that they were unusable in harmony and were called a “wolf” (likely because it sounds like a howling wolf). The only real conspiracy here is the conspiracy of composers trying to avoid “wolf” harmonies.

Understanding Starting Pitch Vs. Tuning Method

  • If you just consider starting pitch, and not tuning method (and thus use only equal temperament standard tuning), both will produce “messy” results (on all other notes except A4).
  • If you consider only tuning method, and not starting pitch (and thus use only 440 or 432), both tuning methods will produce “messy” results” (on all other notes except A4 in 432).

Only 432Hz with just intonation produces the “pretty” geometric patterns featured in the cymatics experiments below (and this is only true when some combinations of notes or single notes are played).

When people say “scientific tuning” they are referring to both starting pitch and tuning method.

TIP: This is to say, for 432 Hz to look great mathematically you have to crunch the numbers like this (Scientific Tuning), if you crunch the numbers like this (equal temperament) both 432 Hz and 440 Hz lack elegance. Ratios are prettier, equal tempered’s complex mathematics and cents are better for tuning pianos for general use and for concerts.[4]

The Pitches and Cymatics

Cymatics is when sound is represented visually. Since all waves are energy, it is easy to translate a sound wave to an accurate visual, and this sort of demonstration is the best proof that the 432Hz debate has merit.

As you can see in the video featuring a cymatic experiment below, 432Hz paired with just intonation creates a visually pleasing, symmetric, geometric representation of the sound, while 440Hz and equal temperament a less pleasing and less symmetric one.

This makes sense on paper, as dividing notes by “100 cents” each is less natural than using ratios (see “why the conversation came up in the first place”).

Think about a violin, if you fret a given string so you divide it in half, you get an octave. Just intonation says “divide the string and you get an octave”. However, equal temperament says “move 1,200 cents and you’ll get an octave”. Both cents and ratios work perfectly for an octave, however, cents gives a “slightly-off” result for any other interval (and thus, in some respects, is a little like using feet and inches rather than planck lengths).

Despite this, as we have noted above, cents and equal temperament generally work better when all factors are considered (as those pure ratio-based notes don’t play well together, on say, an 88 key piano). See table of just intonation compared to equal temperament.

Just Intonation (scientific pitch) vs Equal Temperament (concert pitch).

TIP: Consider using effects or a distortion pedal, or playing a disharmonious harmony on purpose. Western music may be “a little off”, but one can argue that gives music life, character, and energy.

FACT: Tuning forks of the 1700 and 1800’s can be found that set ‘A’ from everything to between about 400 Hz to 500 Hz. It’s likely the attempt to standardize tuning arises, simply, out of necessity as travel becomes more popular and possible throughout history.[10]

TIP: For more information on tuning systems check out Wikipedia’s breakdown tuning and temperament or see Scientific Pitch specifically.
A-440 Hz V. A-432

Verdi Tuning / Scientific Tuning Chart – C=256 and A=440

When C=256 and A=440 and a mix of Pythagorean and intonation tuning is used, the result is this whole number elegant pattern of frequencies (notice that the octaves of C below are an exact round number in the binary system).

Any other method, including concert pitch tuning, results in “messy” fractions when a single note is played, the problem is in harmonics and thus scales and chords, not single notes.

You can see the popular equal-tempered fraction-based frequencies here. You can see a comparison chart at viewzone.com.

Note Frequency (Hz) Audible
C-4 1
C-3 2
C-2 4
C-1 8
C0 16
C1 32
C2 64
C3 128
C4 256
C5 512
C6 1,024
C7 2,048
C8 4,096
C9 8,192
C10 16,384
C11 32,768
C12 65,536

The 440 Hz vs 432 Hz Conspiracy: Why is There a Controversy Over Pitch Types?

There are two controversies over pitch, one is conspiracy oriented and the other is more level headed:

  • As noted above, the controversy says: The pattern 432 Hz (plus scientific tuning) creates is more mathematically pleasing. Composers made the wrong choice with 440 Hz (plus equal temperament tuning), but there was no underlying conspiracy.
  • The general conspiracy says: 440 Hz (plus equal temperament tuning) was specifically chosen for its negative effects as a tool of psychological warfare. There is essentially no truth to back this up, but has become part of the conversation none-the-less.

Anyway, here is the actual story behind 440 Hz (Scientific pitch).

The Story Behind Scientific pitch

The Scientific pitch was first proposed in 1713 by French physicist Joseph Sauveur (and thus is also sometimes called Sauveur pitch), promoted briefly by Italian composer Giuseppe Verdi in the 19th century (why its sometimes called Verdi pitch), and then advocated by the Schiller Institute beginning in the 1980s (as a conspiracy theory). 432 Hz (plus scientific) is thought of as more symmetric, as we noted below, but reasoning for promoting it differs with each advocate.[8]

The Schiller Institute Versus the Beatles

Since the 80’s scientific pitch been the subject of many conspiracy theories, in no small part due to the very controversial Schiller Institute, which has been its main promoter.

Lyndon LaRouche, the leader of the Institute, claims among other things, that concert pitch, rock music, and acts like the Beatles were “a product shaped according to British Psychological Warfare Division specifications”. Specifically, he claimed that the asymmetric waveform of 440 Hz was being used in a negative fashion to “depress” society.[9][10]

So Is 440Hz a Conspiracy?

While I agree that 432Hz (plus scientific) has merit, I found no evidence that 440Hz (plus just intonation) was chosen for any malicious reason. Rather, it seems much more like it was chosen and stuck to for two reasons 1. because it works for all of western music and is practical, and 2. the same reason that us Americans use Feet and Inches (cause’; we picked a standard and we are sticking with it).

TIP: Some charge that 440Hz (plus just intonation) has roots with NAZI or British psychological warfare. However, both these conspiracy theories ignore the history of the tuning debate and the fact that 432Hz (plus scientific) produces a ton of disharmony itself (even if only when specific chords and intervals are played). So its not like 432Hz (plus scientific) is completely harmonious in every situation. How often is music just comprised of single notes?

TIP: See “The Foundations of Scientific Musical Tuning” for the Schiller perspective.

FACT: Ultimately sound manifests as a classical wave, that means it must travel through something to be heard. In a broad sense, we are made out of the same stuff sound travels through (molecules made of star stuff). So an elegant pattern might be more central to our experience than western science gives it credit.

Cymatics Experiment tonoscope 432-440Hz.

TIP: Many would consider the topic as strictly pseudoscience (as explained by this Reddit post), but some make solid arguments for 432 Hz that are hard not to at least consider (as explained by viewzone.com). I would submit both have merit.

Facts About Frequency

Below are a few facts about frequency and harmonics to help you understand the debate.

Frequency is based on “seconds” (frequency = cycles-per-second, 1 cycle per second is 1 Hz). Seconds are a human-invented measure of time (see time is relative).

According to Scientific American, for stringed instruments (specifically a piano): “The precise formula for the frequency (f) of a note on a vibrating string based on length (L), tension (T), and density (μ) of the string is shown below”.[7]

Pitch is relative. Regardless of which pitch you tune a string to, the other pitches must be relative to that. The fretted guitar is a good example of this. If I tune up or down, it doesn’t matter. Each fret still represents a relative half-step interval.

Harmonics, Bach, and Well Tempered Clavs

Taking frequency into account alone, it makes sense to use a ratio tuning (you divide the string, you change the note, very natural). However, the problem is when we pair notes together and change keys it creates disharmony. Thus, way back when J.S. Bach and others were like “actually I want my stuff to sound good” and thus created types of “equal tempered tuning” (why Bach is for “a well tempered calv”; AKA a clav tuned using equal tempered tuning instead of just intonation).

Today we use some complex mathematics to determine pitch and then divide those values into units of 100 cents.

Return to Verdi Tuning (Classical Revolution #3).

Other Factors of Note

  • The difference between 440 Hz and 432 Hz isn’t something the average non-musician can hear.
  • If you drop Hz, generally by any amount, you get a more relaxed sound. If you increase Hz, you get a more tense sound.
  • Staying in perfect pitch as an orchestra depends on temperature, acoustics, and instruments. It’s not reasonable to think an orchestra could or would stay in perfect pitch relative to their starting pitch.
  • Different tunings have been used at different times in different places. Tuning varied wildly over time, and standard tuning of 440 in western music is a very recent thing, although Bach and others begin changing pitches in the 1700’s (because just intonation was historically problematic; the Greeks had noted this as did many others).
  • If a perfect tuning fork is used the chances are that people will tune to an exact frequency and will tune “by ear” to the instrument and the room.

The Importance of A=432hz Music.

THOUGHTS: Orchestras may not be able to tune correctly, but electronic music can. So it is most certainly worth looking into the effects of sound waves and frequencies on listeners. If you are going to use just intonation for electronic music, make sure you take into account all aspects of the tuning debate (like issues with key changes and harmonics). Remember, you can’t only change starting pitch, you need to change tuning method too.

For the Composers Sake – Why Concert Tuning Makes Sense, Despite the Perks of Scientific Tuning

All theories aside, it’s hard to argue that the main goal of standardized pitch (for any group) was anything other than keeping traveling orchestras in tune for the sake of composers and ensuring songs were played as composers intended.

Tuning up or down drastically changes the tone of the music, and using different calculations for divisions of notes affects the way certain tones and intervals harmonize.

I can’t even imagine writing something in 400 Hz with just intonation for piano and having it played in 500 Hz on a well-tempered Clav it would hardly sound like the same song.

Here are some metaphysical musings on different frequencies including 528. Everyone really wants this to be a conspiracy, but I mean, people think the earth is flat… so keep that in mind.

Keep it Simple, not Every Pattern Humans See is a Conspiracy

As noted by viewzone.com, sometimes the simplest answer is the best. This logic could have us finding that there is no conspiracy, but perhaps also conclude that a non-440 Hz tuning is more “in-tune” with nature.

When you look at orchestras, acoustics, climates musicians play in, personal preferences, and then think about instruments staying in tune, it’s a little unreasonable to debate a few Hertz here or there. Composers have long been adjusting tuning methods, knowing full well they were off by a few cents.

In reality, an orchestra is going to sound best when they tune based on the room, the instruments, and each other. A string player is always going to adjust to harmonics on the fly, playing this note a little flat, this one a few cents sharp. Likely, it’ll sound good in the 440 Hz range. Of course 432 Hz is mainly in the 440 Hz range, so just on chance musicians would often tune there.

Starting pitch aside, people will naturally use a tuning much closer to just intonation and not equal temperament. So, with all this said, there is real merit in just intonation… its just that there is also merit in other pitches and other temperaments as well.

All of this said, the pitch standard makes sense for concerts, but in electronic music where everyone records in 128 beats-per-minute in the key of C, the debate starts to really matter.

It’s a problem if decades of recorded music is all out of tune with the universe when it doesn’t need to be, so hopefully real science will ignore the conspiracies and get to work studying everyone’s favorite mechanical wave.



Conclusion

One can’t rule out the perks of scientific tuning with an A=432 Hz starting pitch, but given the history of musical pitches and tunings, and lack of studies, it’s hard to conclude that concert tuning and 440 Hz are “bad”.

From the evidence I think its clear that 432 and just intonation are worth more examination, but for now, 440Hz and equal temperament are “better” for practical purposes. Thus, the idea that 432 Hz is better (as a general statement), or that 440 Hz is used with malicious intent is a myth.


References

  1. Why is 432 Hz better than 440 Hz?” Viewzone.com
  2. A440 (pitch standard)” Wikipedia.org
  3. 432 hz vs. 440 hz” Reddit.com
  4. A Brief History of Musical Tuning” Schillerinstitute.org
  5. Musical tuning” Wikipedia.org
  6. Could You Tune Every Key on a Piano to a Middle C?” Scientificamerican.com
  7. Scientific pitch” Wikipedia.org
  8. Lyndon LaRouche” Wikipedia.org
  9. Concert pitch” Wikipedia.org
  10. The Foundations of Scientific Musical Tuning” Schillerinstitute.org

Citations

  1. Why Is Just Intonation Impractical?
  2. The “432 Hz vs. 440 Hz” conspiracy theory by Jakub Marian
  3. 440hz Conspiracy – Why Don’t You Try This


"432 Hz is Better than 440 Hz" is tagged with: Conspiracy Theories, Music Theory, Senses, Sound, Theories


Vote Fact or Myth: "432 Hz is Better than 440 Hz"

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Manuel romo on

Rockefeller order change 432 to 440… Why?

Thomas DeMichele
Thomas DeMichele on

So, if we read this: //www.viewzone.com/432hertz.html

We get the idea that the 440 debate is some new world order conspiracy.

However, from a purely musical and older standpoint, concert tuning is used so you don’t have to retune the harpsichord every-time you want to change keys. It simply avoids wolf chords, as discussed above.

Those who are trained in music theory know 440 is slightly off, it is a happy medium.

Meanwhile, the conspiracy theory, from what I can tell, a giant misunderstanding of the facts. Here are some points (on the theory from the above link):

The New World is what America is called. The European old world is the old world, the Americas are the new world. So if there is a “new world order” it is what has been happening for the past 200 years in “the new world”. Now you might think, well WWII hurt Europe badly, not the U.S. as much, maybe that was on purpose?… but not really.
Hitler was a German nationalist socialist who hated bankers and Jews: Really odd to mix him up with the international bankers who were for all purposes his mortal enemies. Also, the anti-Jewish propaganda originates in Russia, not via the American and international bankers. America and the bankers are always focused on trade and stability (historically, including in the post WWI treaty debates). I really don’t think depressing people and backing Hitler was in anyone’s interest. If anything Wilson had the 14 point plan, and it was the European powers that punished Germany after WWI.
Next, John Calhoun Deagan was a music nerd and Navy guy who got people to adopt 440 (but also has a ton of other credits to his name)… 440 is one of the few popular choices from history and the one preferred by most classical pianists and composers, to know its merits one has to be smart, perhaps he did communicate with the Navy, Edison, and Morgan about creating a standard… but that doesn’t spell bad intentions anymore than powerful forces coordinating a central bank does. Way too easy to read negative intent into something after the fact. //www.pas.org/About/the-society/halloffame/DeaganJC.aspx
Next, Edison and Morgan co-owned General electric, perhaps they wanted to have a stable tuning for the new records coming out? Makes sense, but like the underlying theory, it’s speculative.
Lastly, Freud and Bernays are also pretty cool figures who, if you read their writing, were about as liberal as they get. I’ve studied most of these figures and, while the Eugenics stuff is real and was a big deal at the turn of the 20th century, I don’t know how into that Rockefeller was or how it relates to 440 (even after reading the article), seems more like a Henry Ford thing to me, either way it is a dumb old theory like Prohibition or lobotomy that unfortunately both good and bad people bought into.
Another note, the Jews of the Italian ghettos, when banking was first coming to the west, used to have to wear yellow ribbons (and sometimes red hats) similar to how Hitler made them wear marks in his time (he stole the idea directly from history, like many of his ideas).
For all these reasons and far more, it is hard to see a music conspiracy by industrialists, the U.S. Government, Jewish bankers and their Christian counterparts… Hollywood maybe, the propaganda about buying eggs or supporting United Fruit… yeah I get that… but mass death camps and depressing music, not so much, neither of those fit the pattern of what has consistently been the intentions of the forces thus described.
I guess, the key here is separating all conspiracy theories surrounding bankers, NAZAIs, industrialists, and the U.S. from the pitch debate.
The other thing i’ve come across in my travels that has the same level of conspiracy attached to it is flat earth. Again, this is a topic where we attempt to explain the earth is round and end up having to explain the history of international politics and banking and ward off ideas that a race or other group of people is secretly trying to take over the world with a theory of music or geometry. It gets dark. Writing this I am reminded why I didn’t go into this diatribe above, kind of takes away from the very interesting music debate and gets uncomfortably dark. With that said, I think this is why those who know the truth don’t stand up and clear the slate.
Simply, I think this can all be attributed to a simple truism: When people see things they don’t understand, then they invent conspiracies around it. That is fine, but if your conspiracy has an enemy you are supposed to hate, and that enemy is 1/2 your countrymen and 1/2 a people who have historically been oppressed, you might be batting for the wrong team. Check out the videos above for way more info on the 440 debate.

Anders barfod on

Good clarification on the topic tunings vs pitch.
But my thought on pitch is that 440hz is not appropiate for the voice .. it seems to separata the notes in the 12-TET unevenly and have a resonance that higher notes in the singers middle register sits very high in the throat.
The more natural relaxed range for the voice is between 430hz and 435hz. The latter being the highest pitch where E4 can be included in s baritons middle register, An F4 for a Bright baritone and F#4 for a True tenor. At 440-443hz you need to sing that note in a headvoice fashion.

Thomas DeMichele
Thomas DeMichele on

I agree. For solo voice the other pitches start making a lot of sense. Concert tuning makes sense for concerts and pianists (and their corresponding composers), but for solo vocal, or vocal + non-fretted instrument, there is a whole other conversation to have. For those who want more information on voice types see: //factmyth.com/factoids/whistle-voice-is-different-than-falsetto/

Dr Petrus Krige on

There is no relationship between tuning pitch A432 or A440 and just intonation according to the harmonics or well tempered tuning.
A432 or A440 is merely a starting point to start tuning. So there are no sientific grounds to pair A432 with pure tuning and to link A440 with well-tempered tuning.
The writer must please take note of the meaning of a tritone (tritonus). It is not a third. It is either an augmemted 4th or a diminished 5th.

Thomas DeMichele
Thomas DeMichele on

Thank you for the feedback! I agree that there is no inherent relation between the starting pitches and tuning types. The pairing of the two is a reference to the “pitch debate”. As for the other point, I will research and edit to ensure the accuracy of the article and generally seek to clarify the statements made. UPDATE: Indeed, I was confusing tritone and third in the comparison of equal temperament and just intonation. Good catch. It is fixed.

Anders Barfod on

I tested the A3 note one octave below A4 on pitches from 442Hz to 430Hz. The most relaxed pitch in that interval was 216Hz/432Hz. Going down to 215Hz/430Hz and the note started to sit a little low. The A3 note 219Hz/438Hz was the highest I could pull the A3 up to before it began to sit weird and high, transitioning to far into middle register for my voice. I had this confirmed by an opera singer,, For heavy voices like dramatic baritone the highest possible pitch is 438Hz.. So my test confirmed his sayings.
So for A3 my experience is that when the pitch is from 432Hz (-32 cents) to 435Hz (-20 cents) it feels good and natural with 435Hz requiring a little shift but is doable as long as you have done a proper voice warmup. Above 435Hz to 438Hz more and more weight has to be lifted of but when you get to 220Hz/440Hz it feel far to tense and hard to lay steady on the pitch. The voice always wants to drop down 8 cents to 219Hz.
THe other discussion is that even 216Hz/432Hz is optimal for A what about the other notes in the scale. 432Hz is in pythagoran tuning with C4=256Hz or scientific C. With C4=256H A4 is 430.54Hz with 12-TET. But since I feel A3=215Hz is to sunk down maybe try 431Hz instead. At least then the C note does not drop below 256Hz and the A being just 4 cents flat.. instead of 8 cents if you tune to 430Hz.

Thomas DeMichele
Thomas DeMichele on

Interesting. Thanks for sharing. To those who think there is a conspiracy, I would point to comments like this. From a musical standpoint, things are hardly clear cut. To conspire, someone would have to figure out the right and wrong answers first 😀

Nick on

Wouldn’t following scientific pitch result in A ~ 430.52 not 432?

Thomas DeMichele
Thomas DeMichele on

If you start your tuning on A = 432 and then use scientific pitch and just intonation then you necessarily have that whole number for A = 432.

That is my amateur musician plus researching this article answer.

Maybe I’m missing something though? Would be looking to others who know more to shed light on the aspects I haven’t been able to shed light on 😀

Michael on

I tune to classical pitch (430 Hz), equal temperament (I have no other choice; I play a fretted bass guitar), and it works just fine. And contrary to the claim that lower pitch tuning sounds more “relaxed”, it actually makes the music sound more intense, not less. Pantera tuned to 430 Hz; so did a number of other bands from that era that had an intense, gut-churning sound.

If you listen to any Beethoven symphony played tuned to 430 Hz by an orchestra that does period reproduction, you can hear the difference from 440 renderings. You can feel the music in your body more with 430 tuning; it’s a visceral experience. The 432 experience is just a taste of what 430 tuning can do.

The Schiller institute nonsense about whole numbers and their faulty numerological correspondences doesn’t really have anything to do with scientific pitch, which itself has nothing to do with any specific temperament, but with making either 256 Hz or 430 Hz a pitch standard, because of discoveries about the resonance-inducing properties of both those frequencies during the classical era. The Schiller institute and many other people falsely conflate scientific pitch with Pythagorean ratios, which is where they get the association of 256 and 432. Those numbers only line up that way in Pythagorean ratios. It’s an odd obsession, considering that at some point, octaves of the whole numbers end up with decimals. There can be no temperament consisting purely of whole numbers that works in practice, so it’s an absurd notion that it has any relevance besides the practicality and convenience of using a whole number as a standard.

As for Verdi himself, he only made one reference to 432 Hz as a compromise between French pitch (435 Hz) and classical pitch; he himself preferred classical pitch when performing in Italy, as demonstrated by the fact that he had a horn specially made for 430 Hz tuning for use in his orchestra. He himself never tuned his orchestras to 432 Hz. So true Verdi tuning is 430 Hz, not 432 Hz. Many conductors of his time preferred 430 Hz over 435 or 440, simply because so many musicians were still playing instruments made during the classical era designed to be tuned to that frequency. The only orchestras playing romantic pitch (435 and above) were the ones that could afford newer instruments designed for the higher tension. Even an increase of just 5 Hz above an instrument’s design specifications can damage it, or break strings designed for lower tuning. It equates to additional pounds of pressure.

Any composition incorporating bel canto was played tuned low pitch, simply because it is impossible to get the intended fullness of sound with high pitch singing due to the difficulty of register shifts when singing to 440 tuning or above. So despite the German trend of rendering opera in 440, the Italians mostly stuck to classical pitch to facilitate bel canto. That–not any presumption of mysticism, Pythagorean whole number purity or scientific tuning–was the reason for the Italian protest against higher pitch standards.

High pitch is sharp and tense, but not full and intense. You also lose some of the midrange and upper bass frequencies necessary for loudness projection with high pitch tuning. An orchestra playing tuned to 430 will actually sound louder than one tuned to 440 because of the accentuation of those frequencies. Sharpness does not always translate to loudness, contrary to the underlying presumption of the pitch wars. More stimulating, yes, but louder, no.

Verdi also used equal temperament; instruments manufactured during the late classical era (those designed for his preferred 430 Hz tuning) were designed for ET, because by that time, ET was considered to be the most scientific temperament. Instruments made in the romantic era were likewise designed for ET, unless you wanted to pay extra money for a custom instrument. Although middle C for 430 Hz tuning in ET is about half a Hz flat of 256, in an orchestra, both can be used as references and the entire orchestra will still sound in tune, because the A4 of C-tuned instruments ends up only slightly sharp of 430 and the C4 of A-tuned instruments ends up only slightly flat of 256. Humans can’t hear a deviation of less than 1 Hz; any beating is practically imperceptible at such a level.

What it comes down to is a difference in where the resonance is experienced. 440 tuning causes superficial resonance in the skin and sternum; 430 tuning causes resonance in water, which translates to increased pressure in/on neurons, which is why 432 advocates (and classical purists who prefer 430) describe feeling the music in their solar plexus or in their nerve plexuses in general. Here’s a video demonstrating this effect on water:

//www.youtube.com/watch?v=mzVlCLnwLfs

Induced mass in the water pushes the bubble down, with the maximum effect occurring when the pitch drops down to 430 Hz, and less potent effect occurring as the tone rises above 430.

Here’s another video, showing the effects of a cello performance on water, rendered by Yo-Yo Ma, tuned to 430 Hz (it doesn’t mention the tuning; I only know because I tested it):

//www.youtube.com/watch?v=KJDEsAy9RyM&t=0s

As noted in the video, those effects were not produced with modern, 440-tuned rock music.

So the classical era adherents of scientific pitch (C256 or A430, in ET) had the right idea. It’s what made Beethoven the rock star of his time. It internalizes and therefore enriches the experience of the music in a way that is not possible with higher pitch standards. You can literally feel the music more than you can hear it. That, rather than 432 in just intonation or Pythagorean temperament, is the true scientific tuning. You simply can’t produce that fullness of effect tuning to 432 Hz, whether in ET or some other temperament.

As you can see in the first video, any frequency above 430 does not maximize mass induction in fluid; as the tone rises, the bubble rises. Since resonance is produced throughout a temperament based on a particularly resonant tone (as demonstrated in the second video), any deviation above or below the point of optimum mass induction will not produce the same end effect. So the experience associated with 432 tuning will be milder that the experience associated with 430. It misses the mark, so to speak; it only provides a taste of the full experience. It’s a nice introduction to truly scientific tuning, but it can’t be anything more than that.

Thomas DeMichele
Thomas DeMichele on

Really excellent insight. Thank you!

I’ll give it some time to consider and offer feedback if needed.

Anders Barfod on

Good post Michael.

This is what I keep discussing with people. The register shift (passaggio) is not arbitary. When you place the A4 at 430.54Hz (C4=256Hz) all the notes in the 12-TET scale is going to be divided in such a way that a certain note that is in headvoice at A4=440 in now in middle register for that singer. Move the pitch ~ 100 cents up or down from ~431Hz and you get into other vocal fachs. For my voice the E4 using 440Hz is the most difficult note to find the balance for. It sits in between register. If I move the pitch down to A4=431Hz (-35.8 cents) that E4 now sits nice and intuitively easy to find the balance for.

Now you can argue with this knowledge whether the modern standard A4 should hover around 430.54Hz. Does it sound “right” for contemporary pop/rock music. Have we been wired to 440Hz since 99% of all music on the radio is in this pitch so a pitch like 430Hz (-39.8 cents) sound way too flat ad off to our mind and ears.
I think it depends on the style. 430Hz is fat, sonorous, and at the same time calming. But take a track like Cindy Lauper’s “girls just wanna have fun” played in 430Hz tuning. A completely different expression. For certain songs and styles a little vocal lift (early transitioning) gives an added color.

But 440Hz (~37 cents) has too much lift and goes to far into the next note in my opinion. A thin agile voice can better cope with this but the heavy dark voice can’t stand this amount of transitioning and why I think the French commission landed on 435Hz. It seemed that this pitch (though high in relation to the 430Hz pitch maintained a good vocal health and allowed the proper vocal fachs to perform the classical pieces as intended).
I have done a lot of test with my bass-baritone voice and keeping the pitch at 435Hz (-19.8 cents) or slightly below prevents the A3/E4/G#4 to flip too much into the next register. Though I need the pitch lowered to 431Hz (-35.8 cents) before the breaks become 100% clean (no lift required).

I really think that modern pitch for contemporary music should be lowered to at least 437Hz. The lift from 437Hz to 440-443Hz is basically removing a lot of heavier voices to find there place in the contemporary world of pop and rock (and opera). They always will need to transpose songs -100 cents and often then their voice sits too much in chest and lacks articulation for this kind of music, And it does nothing to fix the bad placement of the passaggios. The high pitches like A4=442-444Hz in the world of Opera means that the proper singers (often the heavier dramatic kind) can’t be find for numerous roles which was written for the then present pitch (435Hz) in Europe.
I will use a strong word here.. but I have started to really dispise and hate the 440Hz pitch. It is excluding a lot of voices to be heard and it is a rather “stressfull” pitch. WHenever I do test on my voice and see what the small 10 cents lift from 437.5Hz to 440Hz and can detect this effect on other voice when performing live I am shocked that nothing is done to lower the modern standard which is too far removed from the natural range for A4 (430Hz/431Hz) with our 12-TET tuning.

Yhoda on

Hahaha your the same as the rest! You dont understand the science! 440 is disharmonic cos it ouy of phase of the earth. Yes 432 hz requires different scales. The earths base frequency x5 octaves up to the next A is 432 hz. 440 is bad for us cos not cosof the conspiracies of mental control but because it distaches us from our heart. Our heart is unity and guess what we have 432 DNA . What does that mean? We have junk DNA that only response to 432 hz not 440. You need to first learn what phase cancelation is that will help you know why 432 is more harmonic. And almost all classical is in 432 so your lets make it sound good is aloud of dog shit. You notice it alot more whith chords you just have to change your scales cos 432 flat to 440 so for it to sound as good play sharpe scales in stead. Its all about being spiritual and 440 dont do you any favours. I had a spritual awaking last week which is awsome and 432 and 528 hz help that happen. Did i mention i produce psytrance and ive ditched 440 completly its shite and i get ZERO vibes of it. I can literay feel the 432 and 528 resonate throu my body 440 nothing plus it has horrible resonance as a result of harmonic cancelation and 432 has none

Yhoda on
Matthew Toomer on

For the mechanics of sound to work you need a source and carrier (radio waves). 432 hz is our radio frequency what will happen if you change 432fm to 434fm? Well you start to loose infomation in the hiss and crackle. The same happens with any other tunings. If you play a5 in 432 hz thats perfect to the earth as soon as you change to 440 you lose harmonics why cos the earth cannot push sine waves faster then 432 so you have to loose harmonics. And you loose the ones that connect your DNA and heart charkra. Love is the biggest healer and the most powerful energy there is. I know cos i feel this of my family when we are all happy and its a wonderful feeling. I feel energy everywhere all because im connected to my heart and DNA and 432 and only 432 can do this. 528 hz is even more pokey and can make you astral project!

Thomas DeMichele
Thomas DeMichele on

So, even if certain vibrations are more geometrically in line with nature, it doesn’t answer all question related.

In fact, we generally accept that some vibrations are more pleasing in the article.

It is only in respect to the specific starting pitch and tuning method that 440 with just intonation and other methods become sensible.

An orchestra might play ever scale in every key, not every tuning method allows for that, and there does need to be a standard.

So, we have to make sure we differentiate between conversations about the logic of tuning, the aesthetics of tuning, the physics of tuning, and the metaphysics of tuning… and I guess, if we want to get conspiratorial, the ethics of tuning.

For those interested in the metaphysics side of things, check out this article: //factmyth.com/the-spheres-of-human-understanding/

Yhoda on

//youtu.be/As4f1asei08

So what does this prove about 432 hz well nothing it just proves you cant just sweep 432 under the rug as a theory! Modern man dont understand suttle energy so how the fuck are you are suposed to trust modern man. There is only one generation i will listen to and thats the anceints. They knew things we dont understand or knew were there. Modern man is thick as fuck compared to the ancients, just cos we have technology bare in mind that we made it worse for ourselfs cos we didnt know why 432 was so important to us. There is ONLY one man in the last centurie who knew this and his name is Tesla.

andy on
Supports this as a Fact.

Is about feeling and not trying to explain that is just a myth because this and that reasons you find …

In 440 the notes and rythms are a little cold …I mean something is wrong in a subtle way .. Hard to explain

In 432 you feel connected with the music . Everything is easy to hear . You are able to “see” or to “look” at the song easy .

In 440 there is no pleasure to “see” or to “look” at the song notes . Is like something is missing .Is like there is a dark nasty ugly thing in the 440 but in a very subtle way ..

And this is because Cymatics looks ugly at 440 and very nice at 432 .

Of course someone can find arguments to say I;m wrong but I know I;m wright because

I feel I hear I know

Thomas DeMichele
Thomas DeMichele on

For sure, I think many people would agree.

The full debate isn’t just around a starting pitch like A=440 Hz or A=432 Hz, it is the starting pitch and tuning method combined.

So its A=432 Hz and a “just intonation” tuning method (scientific tuning) vs. A=440 Hz and “equal temperament” tuning (concert tuning).

The problem is, if you start on 432 and use the concert tuning, you don’t end up with nice cymatic patterns for all notes. If you start on 440 and use just intonation, you are still off. If you use 432 and scientific tuning, then there are harmonic problems with specific scales and chords (you get “wolf harmonies”).

In other words if we consider a full orchestra playing the full range of notes then every single tuning method has pros and cons.

If however you are creating electronic music, or if you are playing a solo stringed instrument, or if you are singing you can make a strong case for using 432 as a matter of taste and feeling.

I don’t think your intuition is wrong, but there are a few things to consider here to ensure you are picking a tuning method that works for you.

andy on
Supports this as a Fact.

I think there are secrets involved regarding what tuning will work best for what different styles .

Maybe 430.65 can work best for some instrumets and styles while 448 can work for something else .

But I’m 100% sure that 440 has something ugly or evil no matter what style or instruments is used

I converted some normal commercial songs from 440 to 432 and the sensation was like the song was cleaned BY SOMETHING and while listening there was no fatique after 2 hours ..

In fact after 2 hours I was fresh and not tired for the first time in 20 years…

If some illuminati ordered the change to 440 HZ I think that bastards are listening in 432 ))) and they are happy because almost everyone is testing some 440 poison daily .

.

Nick BURNS on
Supports this as a Fact.

This guy is ignorant classical music wasn’t composed in 440hz. I have studied this extensively. 432hz has all the overtone of all 12 notes 440hz doesn’t it has 8 overtones instead of 12 because the tuning shifted higher missing 4 overtones.Birds sing in 432hz case closed.The music industry is as evil as it gets next to Hollywood. No i am not saying 440hz is evil but they don’t want us connecting to music through the heart as 432 connect to listeners emotions at the heat & soul level unlike 440hz at a mind level.432hz is a different experience as it sounds many times better warmer fatter and cleaner and way more harmonious.It might suit rock music b/c it edging and distorted and dissonance like 440hz as it has the same characteristics,although 432 sound good too with that material.

Anders barfod on
Supports this as a Fact.

When is an A an A and not a Ab or a A#.. If we look at the interval of A4 in our modern world it is from 430Hz (classical pitch) to modern high orchesteral A4 at 442-443Hz (Berlin philharmonic came down from 445Hz to 443Hz). A span of 51.6 cents.. Baroque pitch is simply down a half note from 440Hz to 415Hz with 12-TET so I do not consider this an A.
The inherent disharmonic chaotic nature of 12-TET is accentuated the higher you tune your A (base point). So the sharper you tune your A like 443Hz the more evident those clashing harmonics become obvious. But the main point is that tuning to far north of 430/432Hz simply removes you from the place that the voice will naturally sit.
My main problem with A4=430Hz with 12-TET is that I feel contemporary pop and rock music gets slightly too dark at this pitch.. Songs in C-major at A4=430Hz like “love is in the air” gets a little too heavy.
A4=438Hz is the true upper limit for dramatic voices.
My take on pitch with 12-TET
Low A4=430Hz
Middle A4=434Hz
High pitch A4=438Hz
If you write songs where a male voice crosses the second passaggio never tune above 434Hz with 12-TET.
That modern orchestres tune higher than 437Hz is beyond me. This make it impossible to find the correct voices for Verdi, Puccini etc. Allthough true “bel canto” pitch sits down at 430-432Hz.

Philip Wendling on

So the “experiment” to decide which freq is better starts out with the term “Myth”

-for the allegation (other will call it truth) that 440 Hz is a Frequency of Abomination.

Thomas DeMichele
Thomas DeMichele on

“Better” is semantic… but the idea here is that to say one pitch standard is “better” than the other is a myth. more like they all have things going for them and the current pitch standard is likely picked for its flexibility rather than psychological warfare 😉

gustavo del Valle on
Supports this as a Fact.

Try this: Use this web site: //www.szynalski.com/tone-generator/

open three different tabs of szynalski. In each one of them put: 432hz (A) in the first one, 486hz (B) in the second one, and 324hz (E) in the third one. (just as an additional data, all of this frequencies are multiples of nine )

it’s just a glory hearing that perfect combination! NOW TRY THIS:

Do the same thing with the pre established notes from the conventional equal temperament and tell me which one do you like most.

(that is: 329.6275569128699 for the note E (330 approximately)
440 for the note A
493.8833012561241 for the note B) (494 approximately)

look at that! hear that! even numerically is ugly! so, there’s no doubt about this, at least for me.

Now think about this: What do you want in your life, (it’s very well documented how sound affects water, a great percentage of our body is water), things that reflect perfection and harmony, or the exact opposite?

Blessings!
Stradivari/Verdi Tuning (A = 432 hz, C = 256 hz), calculated using the Pythagorean method of 3:2 ratio for dominants, 11:8 for sub-dominants, 2:1 for octaves.
Note Frequency (hz)
– Mid Low (1 octave below middle C)
C 128
D 144
E 162
F 176
G 192
A 216
B 243
— Mid (middle C)
C 256
D 288
E 324
F 352
G 384
A 432
B 486
— Mid High (1 octave above middle C)
C 512
D 576
E 648
F 704
G 768
A 864
B 972

Thomas DeMichele
Thomas DeMichele on

Very nice… but now do this. Re-read my arguments above and if you don’t trust what I’m saying try to put on a concert in non-standard tuning or to keep a single instrument in that tuning and then play complex chords with complex melodies and chord changes. TIP: Just play many traditionally complimentary tones at once using the above links if you wish, it’ll have somewhat of the same effect (try a C7♯11 which is: E G B♭ D F♯ A).

Now consider the frequencies created when all that is going on. At the end of the day, which result is the most pleasing to the ear? I will argue your answer will be our pitch standard and concert tuning.

Unless you are composing Koto for one (//www.youtube.com/watch?v=Tc7e4AhPt3E) or something, you have to consider the cumulative effect, not just single tones. Music is not single tones in isolation 😉

Concert tuning is a compromise tuning meant for the benefit of composers and orchestras. It is not an attempt to tune single notes in with our chi.