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
- 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:
- 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.
- 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.
- 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.
- 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).
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).
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.
- 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.
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 for a minor second and 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 = 1.414214 and just intonation is = 1.4000000. This means, on a stringed instrument for an example, a tritone is defined in just intonation by cutting the string in byand by 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.
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.
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.
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.
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.
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”.
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.