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The “432 Hz vs. 440 Hz” conspiracy theory (jakubmarian.com)
447 points by mweibel on Oct 24, 2016 | hide | past | web | favorite | 315 comments

I have been following this for years, being both a sound engineer and a bit of a hippie who knows a lot of other hippies. The basic issue is that 432 is a numerologically interesting number compared to 440. So if it's more interesting it should be better for artistic purposes, goes the argument. However this falls flat as soon as you consider that the 432 is only interesting relative to the completely arbirtrary duration of a second. There is nothing special about the second from a human psychoacoustic point of view. We could have standardized on a longer or shorter time interval, but since we'd been using the Babylonian-originated divisions for centuries in the west the second is what we ended up with.

But unless the music also contains some 1Hz modulation (or a power-of-two multiple thereof) then the 432 base frequency isn't related to anything fundamental in musical terms. Speaking as a DJ, if you take a track and play it a little bit faster or slower it still sounds great or awful as at the default speed in most cases. 432Hz vs 440Hz is a ~2% difference, while DJ equipment commonly allows for +/-10% pitch variation so you can match the pace of different tracks smoothly while people are dancing. Only the very tiny number of people with perfect pitch find this disorienting to listen to. If there were really something special about the duration of the second and the base pitch relative to that, you'd have expected it to emerge from dancefloors years ago. In reality 432Hz is basically cargo cult numerology, something fun to think about when you are not having any success coming up with a kickass tune. And kickass tunes derive their quality from the relative rations of the note pitches, not from some absolute Magic Frequency.

Trust me on this. I really love numerology, sacred geometry and so on, and I try to integrate this into my artistic work regardless of medium. I would love for there to be some special key that would unlock the gate to cosmic/ biological/ quantum harmony and allow my artistic work to automatically echo the heartbeat of the universe. I'm a mystic by temperament and have been looking for such things my whole life. I would go so far as to say I have some religious faith in the significance of such things. But this ain't it.

"if you take a track and play it a little bit faster or slower it still sounds great or awful as at the default speed in most cases."

Yup. Another example: in most of the world (where the television system is PAL or SECAM) movies are played on TV or released on DVD at 25 frame per second. But to achieve this frame rate, they take the theatrical film release at 24 fps and speed the video and audio up by 25/24th (4.17%). Of course almost nobody knows this because nobody notices it. https://en.wikipedia.org/wiki/576i#PAL_speed-up

For NTSC, the film release is sped down by a much smaller amount (0.1%) during the 3:2 pulldown to adjust from 30 to the exact 29.97 fps that NTSC needs.

Another example is the kind of dastardly television trick of increasing the speed of a television program to shorten it and thus increase the amount of advertising space that can be run alongside the program.


This video claims that TBS is currently increasing the speed of Seinfeld episodes a whopping 9%, reducing a 25 minute episode to some 22.5 minutes.

"mpv -speed 1.1 file.webm" ... get 10% of your watching things time back, it does pitch correction, often its unnoticeable.

Technology can work in your favor too!

VLC can do this too:

Speed up: ] key Speed down: [ key Normal speed: = key

I use that to watch slow lectures at anywhere to 1.8x to 2.3x the speed. Turns a 40 minute lecture into a 20 minute lecture.

Some people one youtube speak really slowly, or are unprepared. The 1.25x speed button is great for that.

Also, some youtubers speak way too fast. Slowing them down helps comprehension a lot, I find.

I am used to speed up things, but last weekend I suddenly realised I can also slow down engrenages (a French show recommended in another HN thread, by the way) and suddenly I can understand so. much. French. It's like magic!

Not many people are aware that this is in fact the natural way spoken French sounds like in France, because of a difference in air composition and thus the speed of sound.

Uhm, no that's definitely not true.

Stanley Kubrick would have hated this. ;)


You absolutely see it in TBS broadcasts of Family Guy, where they can get away with speeding up the show without impacting its look and feel tremendously.

Can't skip frames when there are none.

USA network used to do this.

Of course almost nobody knows this because nobody notices it.

Though, I can now instantly tell if I'm watching a PAL or NTSC version of Star Trek TNG based on the the first few bars of the opening song.

Which is weird, because I don't even have pitch perfect hearing and I'm not even that musically inclined.

I'm guessing you've watched a lot of Star Trek? I figure this is just the human mind's wonderful proclivity towards learning patterns.

I was actually thinking about a similar but less subtle example: I use a transit system that involves tagging on and off with an RFID card (Clipper on Caltrain). When you tag your card, it makes one of three different noises depending on what happen—and I couldn't possibly tell you which one corresponds to what. But if I'm actually using it and I make a mistake, I notice immediately because I'm so acclimated to the pattern it normally makes!

If I hadn't realized this, the UI for the system would have looked absolutely terrible. The different beeps are the auditory equivalent of "mystery meat navigation" but even worse because they don't carry any semantic meaning at all. But because I always use the system in the same way and the noises were consistent, it actually works really well even if I never consciously learned what noise corresponds to what.

(The fact that there are wrong ways to use the system is bad design, but it's a function of how the whole train system is set up, not the fault of Clipper's designers.)

I wouldn't be surprised if there was some psychology behind the choice of sounds when you tag the transit card. Just like visual "affordances" in UI design, there may be certain audio characteristics that people will associate with "good" vs. "error," for example. I recall one study showing that people almost universally feel certain shapes and word sounds are "friendlier" than others (albeit by very subtle margins). And I believe in many languages people interpret pitch inflections to tell when a sentence is continuing vs. finished - think about reading someone a serial number out loud, and how if you were to pronounce the last number the same as all the others it will sound like you left the sentence dangling, with more digits still to come.

I'd be really interested to read anything more concrete about audio affordances though, if anyone knows of links to further research, etc!

I can list at least three linked ones: with two beeps, if the second's pitch is higher, means "on" or "ok" or "up", whereas if the second's pitch is lower, the other way around.

A fantastic book on how these are all related is "metaphors we live by". I'd expand on this but I'm typing on mobile and on a hurry. But seriously: read the book. It takes a long afternoon. It's great, short, illuminating, and not excessively dense or padded.

Yeah, there's quite a lot of this but I can't think of any good references offhand. When doing audio logos I've always looked to catchphrases and famous movie quotes and tried to emulate the underlying intonation/cadences. I'm not aware of this knowledge being systematized anywhere though.

"Audio logos" - that's a fascinating concept I've never really thought about. Any recommended reading about that field?

There are several different Clipper beeps:

* One beep - successfully paid fare

* Two beeps (different) - successfully paid fare, and you're about to run out of money on your card

* Two beeps (equal) - tagged off (e.g. on Caltrain or San Francisco Bay Ferry)

* Three beeps - read error or insufficient value

There might be others. Indeed, they've introduced a quieter "here is a Clipper reader" beep to help visually impaired people locate them: https://vimeo.com/183916243

You can train your brain to remember pitches. Try humming your favorite song, then play it and see if you picked the right key. I did this as a game with a friend one afternoon with maybe 80% success rate across 50 songs.

Does that mean you can train yourself to have perfect pitch?

As I understand, no. There's some suggestion that small children, usually under the age of 10, can acquire perfect pitch, but no adult has ever been documented acquiring it.

Source: http://www.zainea.com/absolpitch.pdf

There seems to be some controversy about this though. I've seen other papers[1] claiming that adults can acquire it, albeit only to a limited extent.

[1] e.g. http://www.sciencedirect.com/science/article/pii/S0010027715...

That seems like a logical conclusion

I know what you mean, when I was living in Australia I could swear the voices sounded off on The Simpsons.

Might not be the change in pitch you are noticing but the speed of the music

This explains the years of confusion I've suffered noticing sharp pianos in films. I could never work out what was wrong with American film pianos! Thank you, seriously.

The European (PAL) ones are sharp. The American (NTSC) ones are accurate (or very very slightly flat).

Late night error, thank you for pointing that out. European etc PAL formats go sharp when transcribed to. So American and all films transcribed into PAL go sharp, which happens a lot. So it's not the origin of the film, but the (usually) PAL format I historically watched them in that caused this.

And in cinema they were better (I seem to remember Geoffrey Rush 'playing' Rachmaninov 3rd Piano Concerto in that film, at excellent pitch in the cinema), so I knew they were sometimes right. But i think the tape, TV and DVD formats I'll have rewound most often in perplexity.

Another confounding: living in California a lot and not having incorrect pitch on local copies. And nowadays, when sources are digital, bit may have originated from analogue recordings, it's now very unclear what to expect.

> For NTSC, the film release is sped down by a much smaller amount (0.1%) during the 3:2 pulldown to adjust from 30 to the exact 29.97 fps that NTSC needs.

No. For NTSC they just drop (throw away) 1 frame from every 1000 frames, so there's no speed-up or speed-down in audio track.

This is incorrect. I worked for a decade as a film sound engineer. If you don't implement the 0.1% pull-up/pull-down, then sync will begin to drift noticeably.


There must be a speed-up since the audio track is not divided into frames. Dropping a 33ms chunk of audio would be very noticeable.

No, you don't have to alter audio in any way, you just leave it untouched.

Let's say you have 100 seconds of film material with corresponding audio duration. That would be exactly 2400 frames, because film is 24 fps. When you do 2:3 pulldown (that's one of the methods used to do telecine, i.e. film conversion to television format) you'll get back exactly 3000 video frames. But in NTSC format, (if you'll leave audio untouched, i.e. it's duration didn't change, it's still is 100 seconds) for 100 seconds of video duration you must display 2997 video frames, not 3000. So you just throw away 1 frame from every 1000 frames to get the exact 29.97 fps.

Doing this, at worst case you'll get audio/video desynchronization of 33 ms, which I don't think is noticeable (I tend to visually notice desynchronization when it's at about 100 ms or more). But if you'll drop that 1 excessive frame in the middle (not at the end) of the sequence of 1000 frames, you'll get audio/video desynchronization which only varies from -16 ms to +16 ms. Which is not worth the trouble of fixing this by going the other way around it: leaving video untouched and slowing down the audio by 0.1%.

The first time I remember hearing about this was in regard to the semi-famous "Wizard Of Oz / Dark Side Of The Moon" combination, which supposedly only works at the theatrical frame rate.

If anyone wonders where the odd NTSC frame-rate ratio originated from, Matt Parker (standupmaths) did a comprehensive video, with some original write-up on this recently: https://www.youtube.com/watch?v=3GJUM6pCpew

Whilst conversions that speed up video do happen, It's not really intentional or desirable.

A friend of mine bought the DVD of 'Rent' when it first came out in our region. A month or two after it came out, the DVD got re-issued because it's a musical, and people had been complaining that the conversion had been messed up. I think she got the re-release for free.

Rate changes are a bigger issue for musical features like Rent, as it makes them difficult to play along with. For a more typical dramatic feature, it's less noticeable.

There's a really interesting video by Matt Parker about why 29.97 is the magic number.[1]

[1]: https://youtu.be/3GJUM6pCpew

The second is defined as the time it takes for two hyperfine levels of the ground state of the 133 Ce atom to make 9,192,631,770 transitions. How is that not special?

Because that definition was grandfathered in such that it matched the previous definition of a second up to the previously specified precision. You've just moved the arbitrary part to the number 9,192,631,770. The same thing was done for the meter (defined such that the speed of light is precisely 299,792,458 m/s), ampere (current which produces 2 × 10−7 N/m of force between two parallel conductors). There's plans to do the same thing for the kilogram using Plank's constant, but for now we're stuck with the prototype kilogram whose mass unfortunately changes more than we'd like.

I could see making a case that Planck time is special enough for 440 vs 432 to matter, but it is so far off the scale of human hearing that its even integer points would form an effectively continuous scale when it comes to audio.

I suspect the poster's tongue was firmly in his or her cheek.

Indeed. But damn, this is a tough crowd :)


> current which produces 2 × 10−7 N/m of force between two parallel conductors

Hate to be a stickler, but: "...conductors of negligible cross-section and of infinite length." It's still one of my least favorite SI definitions.

If anybody wants to read lots of commentary on units and their definitions, take a look at the data sheets for the Frink language. The ampere and the candela are two of the more irksome ones, as described by the author.


Fascinating. Thanks! At one point I wrote a unit conversion program before such things were ubiquitous and I included a field that had information about the units involved. In service of this, I copied a number of older books on measurement units though I never got around to folding most of this into my program.

Couldn't the Kilogram be derived from the Liter, which in turn can be derived from the Meter? From what I recall:

- 1 Liter of pure water at 4 Celsius is 1 Kg.

- 1 Liter is a cube with 10 cm on each side.

Generating a perfectly homogenous 4C over an environment large enough to contain a kilogram of any useful substance is going to be incredibly difficult and mearusing it even moreso. There's a reason every unit of measurement aside from mass is derived from an electrical property; we can measure electrical properties down to ridiculous precision, measurements small enough that all measurement uncertainty is removed.

Werent they trying to count the atoms in a perfect sphere of silicon?

That is good to know.

You could do that, but if you're trying to set standards, you have to take into account your ability to measure these things reliably and accurately. (It doesn't do any good to set standards that nobody can conform to because their equipment is never sensitive enough to use them.) Can you measure a liter more accurately than you can measure a kilogram of some reference material?

I always thought it was amusing that the basic definition of the liter was taken at 4C, but that lab equipment was calibrated at 20C...

I think that's because 4C is the point where water is the densest, whereas 20C is a comfortable room temperature.

Interestingly enough it started out as being defined as 1 dm³ in the 18th century, then in the early 20th century was defined through water at highest density, then in the 60s back to 1 dm³.

Imagine if it had been defined as the time it takes to make 9,192,631,771 transitions.

All our music would sound wrong.

It's less special and more pretty much arbitrary. It's a slightly fudged mean[0] of the number of transitions matching the ephemeral second according to Markowitz, Hall, Essen and Parry ("Frequency of Cesium in terms of ephemeris time", 1957), with the original paper adopting "a probable error of ±20".

[0] of 4 measurements (761, 767, 771, 780) — the exact mean being 769.75

It's not a power of 2 or 10 :-)

9,192,631,770 is divisible by 441, why are we not using 441Hz?!

I thought the definition of one second had been updated to the time it takes light to travel c meters? Although when I think about it, it does seem very circular.


Anywhere in the USA where there's electricity, the frequency we're hearing the most is probably 60Hz and a couple harmonics thereof. It's between B and B-flat. I've been curious for some time now what it would sound like to perform in a scale tempered around that, such as B = 480 (and 60), which translates to A = about 427.6 by my rough calculation.

60 Hz is everywhere, often at a subliminal level, sometimes at an obvious/conscious level like when you walk underneath powerlines or use a garage-door opener. In any case I suspect it's a lot more obvious and perceptible to most people than any cosmic vibrations. I bet fixing your music to resonate with THAT, would (perhaps sadly) feel a lot more "cosmically in-tune" than what they're proposing with 432 Hz.

Perhaps it is fortuitous that music isn't 'in tune' with everyday background noise. The fact that the frequencies (now consistent) are entirely separate from the buzz of a transformer or garage door opener puts music in its own plane just a bit more magical and pleasing than the quotidian drone we tend to ignore.

Then again, maybe it's just a number and our brains couldn't care less either way.

My middle school band director told us that the hum of the lights was B-flat, but that would make A=453, which is rather high. My Yamaha flute is A=442, which is pretty common. You can always pull a headjoint out (lowers pitch), but there's a limit to how far in you can push it in.

There's something special about 432 Hz that has nothing to do with how the music is perceived -- if you're tuning the traditional way, by forming fifths above and below A as ratios of 3/2 and 2/3, then a lot of the numbers you hit are nice integer numbers of hertz as well, because 432 is 2^4 * 3^3.

Meaningless in practice, but it makes it convenient to describe the tuning of, for example, a stringed instrument.

Main> majscale


Main> map (\(x,y) -> (432.0 * (fromIntegral x)) / (fromIntegral y)) majscale


That's pretty cool. The whole major scale comes out as whole numbers in just intonation. (In 12-tone equal temperament it doesn't, because 12TET uses the 12th root of 2 as a uniform division of the octave.) This looks like your explanation isn't just a neat trick, it's likely to be the reason why 432hz was proposed as a standard in the first place.

Main> let scale = [(1,1),(16,15),(10,9),(9,8),(6,5),(5,4),(4,3),(45,32),(3,2),(8,5),(5,3),(15,8),(9,5),(15,8),(2,1)]

Main> map (\(x,y) -> (432.0 * (fromIntegral x)) / (fromIntegral y)) scale


..and if we construct a more chromatic scale, not all of them come out quite as whole numbers, but we don't have any repeating decimals or anything like that (though we would if we included weirder intervals like 8/7). Nice.

edit: This works for a just major scale constructed starting from A. If you construct a scale from a different root note, it might not work out quite as cleanly.

I was thinking it's kind of sad that A minor is the scale that's more fundamental in musical notation -- going up to C with a just minor third gets you the not-so-pretty 518.4 because there's no factor of 5 to divide by.

But really, the moment you decide thirds and fifths both matter, and you want to build them on more than one note, you have to either continuously re-tune or give up on JI and worry about temperament instead. The numbers work great in a Pythagorean tuning, where only fifths matter: that tuning gets you both A=432 and C=512 (middle C = 256).

If it's a high composite number is all you need, then why not define 440 Hz as any highly composite number of your liking, ignore the SI-related-fractions and don't worry about odd ratios anymore. Or is this more about an issue with cumbersome input on digital (tuning) devices?

Just to pick two:

45360/100 is not that far away either

55440 (a superior highly composite number, 2ˆ4 ⋅ 3ˆ2 ⋅ 5 ⋅ 7 ⋅ 11 ) would have a built in Base-10 mnemonic



Well, we've never really used prime factors of 7 and 11 in Western music.

Even introducing the factors of 5 creates centuries of complications (temperament) that caused us to finally give up and throw out all the integer factors, replacing them with the twelfth root of 2.

(Anyone who wants to reply saying that factors of 7 explain "blue notes", please be specific about how this works. I think this is a fictitious idea in music theory that propagates itself because it would be really cool if it were true, but the usual explanations produce false predictions.)

This isn't entirely true…… You're basically saying that because our measurement system is arbitrary, the numbers that are yielded as a result of our measurements are irrelevant. Sure, the exact numbers assigned to said measurements might be arbitrary, however the relationship between values still exists. As proportions, percentages, whatever. However you choose to measure, things still relate to each other in some way. My understanding of the 432Hz conspiracy doesn't rely so heavily on the number "432" vs "440", so much as it relies on the correspondence between our vibration, the earth's vibration, and the vibrations coinciding with 432Hz. Again, rearrange these numbers any way you like, but there is still a relationship between the earth, us, sound, etc.

I wouldn't be so sure there is nothing special about the duration of a second. It comes from dividing a day into two sets of 12, then those 12 into five sets of 12 (12x5=60), then those 60s into 60 each.

We know our bodies do follow circadian rhythms, so you have the initial link to length of day. Then everything else is split into sets of 12, a number with exceptional properties that natural selection may optimize towards:

"The number twelve, a superior highly composite number, is the smallest number with four non-trivial factors (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4) within the subitizing range. As a result of this increased factorability of the radix and its divisibility by a wide range of the most elemental numbers (whereas ten has only two non-trivial factors: 2 and 5, and not 3, 4, or 6), duodecimal representations fit more easily than decimal ones into many common patterns, as evidenced by the higher regularity observable in the duodecimal multiplication table. As a result, duodecimal has been described as the optimal number system.[4]"

https://en.wikipedia.org/wiki/Duodecimal http://dozenal.org/


Another thing is that our current system of setting the duration of a second as a constant may be non-optimal for some purposes. Other systems let the length of time units vary with the seasons. It is interesting to think that under these systems, by maintaining the same base frequency, the tone of the note would change over the course of the year and with latitude. https://en.wikipedia.org/wiki/Roman_timekeeping

> I wouldn't be so sure there is nothing special about the duration of a second. It comes from dividing a day into two sets of 12, then those 12 into five sets of 12 (12x5=60), then those 60s into 60 each.

That's exactly why, actually. This is what the second was once defined as, but the problem is that the length of a day varies slightly - up to ~8s depending on the time of year and other seconds. As the article mentions, the amount of time that is defined as one second is now taken as an arbitrary fraction of the decay time for Cs-137 that is close the mean value of the length of the second defined relative to the time it takes the planet to rotate.

In terms of keeping time in our common lives it's not really a problem for there to be a little bit of ambiguity in how long a day/minute/second is, but this is important for things that rely on precision timing - like tuning in music. It'd also be crazy hard to keep track of how long a second is at any given moment, since some of the variation is random from tidal forces.

>"It'd also be crazy hard to keep track of how long a second is at any given moment, since some of the variation is random from tidal forces."

I think you could use something like this, which may be accurate enough:


It may be more accurate to use something like the JPL ephemerides to convert between the two though:


Finally, the current definition of a second is meant to approximate the previous definition of a second. I am saying the previous one may have some correlation with biological activity.

If I understand you correctly, you are advocating for defining the second such that its length varies, but its connection to a day does not? And you would also introduce locality to the definition?

edit: Or perhaps you meant to tune variably, and not redefine the second. That sounds more sensible, but not as practical.

Here is the scheme which I am thinking may better link timekeeping to biological clocks:

  A day is defined as sunrise to sundown.
  A night is defined as sundown to sunrise.

  Every day consists of 12 hours.
  Every night consists of 12 hours.
  Each hour consists of 60 minutes.
  Each minute consists of 60 seconds.

  There are always 60*60*12 = 43,200 seconds each day and night.
  Within a given day or night every second is of equal length.*

  On the equinox (length of day = length of night) we will have a "base unit" s0.
  At times/places when there is more daylight than that, the duration of a second 
  during the day s_d > s0 and during the night s_n < s0.

  *It may be better to continuously vary the duration of a second so there 
  is not a sudden change at sundown/sunup. It can perhaps be linked to   
  https://en.wikipedia.org/wiki/Solar_zenith_angle. I think the Egyptians used 
  to use Sirius at night for this, but don't remember where I heard that. 
  Anyway now we can always be monitoring the position of the sun even when we 
  cannot see it at the moment.
The second part of what I am suggesting is there may be aesthetic or health benefits to varying periodic phenomenon along with the relative duration of a second. So if frequency is f = cycles/sec and we want to maintain the same numerical value, the f/f0 should scale with s_d/s0 and s_n/s0 (or just s/s0 if we are continuously varying it). Consider if f0 = 432 is ideal at the equinox, and we are wondering about f = 440. I would say that we look for when/where s = 440/432 x s0 x k. Setting the scaling constant k =1 and using an R package that in turn uses noaa sunrise/sunset data[1], I got 3/26/2016 at + 18 degrees latitude. You could do the same calculation in reverse from a given time/latitude to choose a preferred frequency.

[1] http://www.esrl.noaa.gov/gmd/grad/solcalc/

I see. I can't really get on board with a system where half an an hour at lunch is twice as long as half an hour at dinner, and I have a suspicion that it would actually further mire arguments about music pitch, but it's certainly a funny thought.

>"I can't really get on board with a system where half an an hour at lunch is twice as long as half an hour at dinner"

Move to the equator? J/k, I would not think this system would be law, or used for all purposes. Despite the huge pain that dealing with timestamps from various locations can sometimes be today, I suspect my scheme would make it more difficult to synchronize long distance activities.

It would more be a chill, get back to nature, type of timekeeping. Used at resorts and rehab centers.

Here is what I mean, nothing needs to be vague. My model predicts that the preferred pitch should track something like this with date and latitude: https://s11.postimg.org/mkw753lpf/image.jpg

The only free parameters are:

  F0 = the pitch of A4 on the when there are 12 hours of day/night
  k  = a scaling factor that determines how much to change the pitch based on duration of the variable second
Here I used F0 = 432 and k = 1, but those values will probably need to be determined by experiment.

Except that our day length is also changing -- very slowly, but changing it is. Further, given that the human clock, disconnected from day/night feedback, apparently treats 24.2 hours as a day.... https://en.wikipedia.org/wiki/Circadian_clock

>"the human clock, disconnected from day/night feedback"

I am saying the second was originally linked to length of day, so the calibrated clock should be used. Also, at some point the differences due to latitude changes, etc will be biologically indistinguishable from stuff like the effect of clouds.

So, we could say that a "circadian second" is about 1.008 seconds? (On average)

How precisely is that 24.2 known I wonder..

From the referenced Wikipedia link:

By recording the daily rhythms of hormones and body temperatures in 24 healthy young and old men and women over a one-month period, the researchers conclude that our internal clocks run on a daily cycle of 24 hours, 11 minutes.


Researchers previously reported a range of 13 to 65 hours, with a median of 25 hours, 12 minutes. The variation between our subjects, with a 95 percent level of confidence, was no more than plus or minus 16 minutes, a remarkably small range.


I did refer to this with the Babylonian thing but I didn't want to get sidetracked into a review of ancient number bases. I love your reference about non-constant time though, most interesting.

According to NIST It's slightly more arbitrary than that:

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

Not sure of the numerological significance of 9192631770.

> Not sure of the numerological significance of 9192631770.

It has none. It just happens to make the new cesium-based definition of a second roughly equal to the historical definition of a second as 1/86400 of a mean solar day.

12 is a funky number, but arbitrarily grouping them into 2's and 5's takes the shine off.

This is all true, of course. Only thing that might make some impact is the prevalence of electronic music devices that default to 120BPM, which of course gives you a downbeat every second. but 432 is not an interesting number for a computer, so that doesn't help. If music was made by robots, we'd have standardized on a middle C at 256Hz and 120BPM for everything.

The article gives the same reason of arbitrariness of the second to debunk the numerology, but then goes on to say that the BBC chose 440hz because 439 is a prime number and is harder to generate electronically ... Which is nonsense as well ... Though it may have been true relative to price of components at the time.

Consider that as late as in the 80's on home computers, frequencies for all kinds of stuff were often chosen to be convenient factors of a suitable starting point so that they could be generated by stepping down frequencies from a single crystal.

Frequency choices even then were driven by cost/complexity to the extent that e.g. rather than trying to synchronise things in other ways or decoupling various clock rates, the CPU clock rate of many computer models were chosen based on how other things were clocked.

The Commodore 64's and Amiga's at least were both clocked slightly differently in the US and Europe because the CPU clock affected bus timings, and bus timings affected the custom chips for graphics and sound, and it was most convenient to time it all to match the video refresh rate of NTSC and PAL respectively.

Given that, I'm not at all surprised if the BBC decades earlier found it more complicated to handle 439Hz given whatever clock signals they had available to create it from and/or wanted to be able to match it against.

> However this falls flat

Pun intended?

A friend of mine is a professional mix engineer in NYC. He's worked with several large artists, you've probably heard of. He strongly believes in setting numerically interesting values for things like eq, gain reduction, song length, delay time in ms, etc.

A not-insubstantial part of the engineer's job is to impress the artists. Mastering engineers even more so.

Directional audio cables are another example of such "making impressions" business.

(Technically nonsense, of course.)


I would take it a step further. I'd make up my own units based on seemingly natural things and then tune to numerically interesting values of those.

"This next song's beat is 432 times faster than a cricket chirping at 50 degrees C."

A lot of those are significant though, EQ maintains relationship to pitch and tone, delay is directly related to rhythm, etc. The main issue is that most of these are relative to inputs, etc, with a few exceptions.

Edit: An exception would be trying to 'fatten' the sound of an acoustic guitar and using a 25-35ms delay, which puts it close enough that it's not perceivable as a delay, but will provide a noticeable effect on the tone of the guitar.

Like I said, I try to exploit interesting numerical properties all the time. I really am a mystic, I've made major life decisions based on a tarot reading and am glad I did so as such methods seem to work better for me than purely analytical ones. On the other hand, I'm analytical enough to not want to bullshit people with unreproducible results.

Coming from a more "bottom up" perspective it's likely that the derivation of these numbers are related to the implementation rather than anything to do with the musical theory. Digital technology makes working with arbitrary numbers quite straightforward but often times certain number patterns simply "emerge" as a result of characteristics of components, integration with other legacy technologies or even just ease of calculation. Then these numbers just become legacy themselves and you're stuck with them!

> But unless the music also contains some 1Hz modulation (or a power-of-two multiple thereof) then the 432 base frequency isn't related to anything fundamental in musical terms.

Presumably the music's timing is based on seconds, though, right? That might conceivably mean that primeness could potentially matter. I don't really think that it does, mind. But I'm not so quick to think that it doesn't, either.

Well, I'm not a sound engineer, but I think it's conceivable that 432Hz tuning might sound better due to entirely non-mystical reasons. From the perspective of harmonic entropy, or at least I think so, the tighter differences between each notes' frequencies and that makes the problem of fitting intervals into ratios harder.

I recognize that this bit is entirely personal, but I think that can make otherwise "simple" music more enjoyable. But my enjoyment of music is almost entirely dependent on the careful management of the "Wall of Sound" effect and by how much noise (in the form of timbre, attacks, number of different voices) is introduced or removed from the track. And I think that's the key difference between, say: a library piece, or a movie score; and pieces meant to be listened on their own.

Also, the expression "cargo cult numerology" pretty much made my day.



Tighter differences between each notes' frequencies??

Please explain this thought.

Well, I'm assuming that the ease or difficulty of recognizing the difference between two notes bears some proportion to difference between their frequencies (the frequency of one minus that of the other), and not just their relative frequencies. The intervals in the 432Hz are "tighter" in the sense that, because the interval they correspond to in 440Hz is smaller for every possible interval, there are more notes in 432Hz tuning in any given arbitrary frequency range (say, from 100Hz to 1,000,000Hz) than in 440Hz tuning. And this makes the problem of recognizing them harder. I should've made this out clearer.

For instance, a half-tone from 432Hz is 457.69Hz, which gives out a difference of 25.69Hz; but a half-tone from 440Hz is 446.16Hz, which gives out a difference of 26.16Hz. Between 432Hz and 864Hz we can fit a whole scale, while in the same frequency range we'd be missing a note with 440Hz tuning.

Of course, this is a slight difference and it might not be noticeable at all. I personally don't hear much difference between the two tuning. Instead, I'm playing devil's advocate.

I don't follow you. Are you saying that if I detune my guitar enough, then it will grow an extra fret?

If I understand correctly, he's guessing that pitch discrimination is finer at lower frequencies, so tuning at 432Hz would allow our ears to be more 'exact'. Of course, this advantage would be negligible, and pitch discrimination decreases past a certain point. The songwriter intended their piece to be heard by human ears at A=440Hz, knowing the various propensities of human hearing at various levels.

Ok, I see what you mean.

Then most songs would sound 'better' a half-step down, etc.

Look at it like Celsius vs Fahrenheit (this isn't a perfect analogy because both scales measuring the same value, where we're discussing different values, but it'll do).

The boiling point of water in Celsius is 100 degrees, and the freezing point is 0 degrees; in Fahrenheit, 212 and 32, respectively. What's significant is the scale of each unit. 99C is colder than 211 Fahrenheit.

In the case of music, which is all about relative frequencies, establishing A determines the size of the steps. The above poster is proposing that A=432 yields more interesting frequency relationships than A=440. I have no idea.

Well... It doesn't. The same ratios exist for A=440:A=440 * 3/2 and A=432:A=432 : 3/2, for example

I wouldn't say that's the case for most songs, but rather only for simple melodies. But yeah, a graver voice would sound better in most cases.

Consider the beggining of Bach's "Little" Fugue in G Minor (BWV 578), where the subject of the fugue is first introduced by a soprano voice and then repeated by an alto voice, while the soprano voice does the coutersubject. I'd say that, played in isolation, the melody sounds better when sung by the alto voice. But lowering the whole Fugue by a half-step wouldn't make it much better.

With respect to recorded music it tends to be the opposite: if you pitch up a track then the rhythm feels tighter and the vocals more steady, because the differences between the intent and the performance are relatively smaller. Hence an old studio trick dating at least back to the Chipmunks was to record in a lower key. Listener discrimination seems relatively less important in practice, on the other hand.

Love this post. If you're ever in Austin you have a fellow mystic to jam with. Keep on with the good vibes man.

Did you read the whole article?

Analogy: it would be difficult to explain that being born Capricorn might give you specific properties, knowing that the definitions of the constellations are completely arbitrary.

Decided to try searching this and found this lovely site:

> A=432 Hz, known as Verdi’s ‘A’ is an alternative tuning that is mathematically consistent with the universe. Music based on 432Hz transmits beneficial healing energy, because it is a pure tone of math fundamental to nature https://attunedvibrations.com/432hz/

Oh new age pseudo science. My mom loves this stuff and I never fully understood why. My sister gets angry at me when I point things out or level any criticism because "it makes her happy". This apathy to the issue from people who should know better is likely why nonsense like this keeps spreading in an age of Snopes and Google.

Eh-- pick your battles.

If family members get a positive placebo effect from listening to "5 Hours High Quality BEST 432hz Meditation Healing Chakra" on YouTube...Who cares?

Because it requires a core assumption of anti-intellectualism.

It doesn't bother you when friends and family are sold on something that is baseless and are completely opposed to actually researching it and at the very least becoming more skeptical about it?

Nah. We evolved to be superstitious. It's evolutionarily advantageous. Why? Because it's much less costly to develop a random incorrect superstition than it is to miss an important correlation.

How harmful is it to meditate to 432Hz compared to... well maybe without that superstition they wouldn't even meditate at all. It's probably advantageous, even though it's bullshit.

As long as they aren't engaging in harmful behaviors (e.g. anti-vax), best to let it go.

I would argue that "not letting it go" is equally harmless and to be permitted to the same degree that you propose otherwise.

Sorry for the late response, but correcting someone often has social costs. It takes time and energy, and can cause people discomfort and can weaken friendships.

It can also make them stronger, I'm not proposing you always ignore superstitions. Just ignore them when there's a cost and minimal payoff.

I think the problem is the mindset. And it's slowly spreading because it's considered rude to challenge it. It's this mindset that leads to unvaccinated children and the use of amber jewelry[0] that's a choking and strangulation hazard on infants and toddlers because amber has supposed magical healing properties. That article is from late 2013 and if anything it's more prevalent.

[0] http://well.blogs.nytimes.com/2013/10/11/amber-teething-neck...

It's fine. But I'm not going to pretend it's not BS when they try to talk to me about it. Now my mom no longer talks to me about homeopathy.

That sounds like typical libra talk. I'm an Aries so I don't do that.

The one whose inheritance is next squandered on highly priced meditation chakra recordings and excessively expensive hoax high-end audio equipment? (From Youtube to purchasing mail order junk...)

Until that person dies or is otherwise ruled incapacitated, it's their money to spend however they like.

No it isn't. Spending is very clearly regulated, and you are only allowed to spend it on sufficiently 'normal' things.

Who's to say you're going to inherit anything anyway? Maybe they've willed it all to charity.

And I might not even care so much about the inheritance, but I might want the old parents to have something saved up for the old age so they're not completely at the mercy of the welfare system...

(Not something I worry about personally, parents long gone).

Ha! I thought you were making that up...

It's the same reasoning behind Steve Jobs choosing quackery over medicine to treat his cancer.

Tunings (whether by key shift or by reference frequency or whatever other means) can evoke a different sort of feeling and mood in music IMHO. Music is such a personal thing in so many ways, so even though the "beneficial healing energy" / "pure tone of math fundamental to nature" thing is kind of BS, I'll allow a little out there mystical pseudobabble. :) It's just a pity in a way that the mystical BS focuses only on one number.

Personal example: As a musician, A=432 doesn't sound that different to me, not enough to make that much of a difference in tone. However I do like A=425, an arbitrary "in between" tuning on the flat side of the middle between A and Ab in A=440 tuning. It adds an entire new mood set for each key that is rather different than A=440, distinct enough to me where the moods don't overlap (whereas with A=432 it does).

There is no science that can explain this sort of thing that I know of, and I fully expect that others would have different interpretations.

Yea, I don't like this idea of belittling people because they got pulled into this idea.

Tuning is arbitrary. I've listened to some comparisons between A=432 vs 440 and I think the 440 actually sounds better. But then again, like this article even states, it depends so much on the piece. If you're listening to stuff from the 1700s/1800s, it would make sense to try to use the tuning they used at the time, if only to try to get the sense of emotion intended by the originally composers/arrangers/musicians (even then it's a best guess).

But yes, it is pretty arbitrary. It's the tuning of a note depended on the number of cycles per some arbitrary time unit we defined.

If you're listening to a song today, with all our sound precision technology, you're hearing it the way the original author/musicians wanted it to sound (depending on your equalizers, speakers and various other audio setup).

> 440 actually sounds better

I'm curious how you can tell. A double-blind test spaced a few minutes apart (enough for you to forget the frequency so you couldn't tell if what you were hearing was tuned higher or lower than what you heard on the previous trial) would be interesting.

In that place between physical frequencies and brains there is some appreciation that different tuning standards feel different.

I play a lot at A=440, but I also play a lot at A=415 - mostly on the viola da gamba. A=415 is roughly one semitone lower, and it changes the way the instruments resonate. My viol happens to sound good at either pitch, but as an ensemble we find that when we're playing at A=440 the whole sound doesn't blend in quite the same satisfying way. This is due to the construction of the instruments themselves, but also just how those slightly lower pitches sound.

Oh and recorders built to A=415 just sound great. I think that slightly bigger body gives them the chance to produce a richer resonance, but then again you also don't find cheap plastic recorders (or cheap wooden ones) built at A=415 because only "serious" players go looking for those instruments.

One nitpick on the article though - historical tunings don't range from A=415, my recorder teacher has two flutes at what is sometimes called "French baroque pitch" - that's A=392!

> There is no science that can explain this sort of thing that I know of, and I fully expect that others would have different interpretations.

The article had a pretty good explanation: that strings sound different at different tensions. Musical instruments tuned lower would sound darker, mellower, and "looser" than those tuned higher. The instruments would probably feel a little different to the musicians, who would probably play differently, especially if they'd just heard somebody expound on the mystical properties of a certain tuning. I'm not at all surprised that it would sound different.

This is exactly it. If you have two identical pianos, both precisely equally tempered, but one tuned a half step lower, and then you played notes of the same pitch on both pianos (the notes are a half step apart, the pitch is not), they will sound different. Disregarding all the differences surrounding the natural wood and other materials, and the fact that it's impossible to use the same velocity, and the pianos aren't in the same exact position relative to the room, and everything like that -- you will be left with just the differences that have to do with tension.

On an FFT graph, you'll have the same fundamental and a very similar next few partials, but eventually you'll see (and hear) the results of the different tensions. Those differences represent what people like and don't like about different tunings -- nothing to do with the slightly different pitch between 440/442/438/432/etc!

Star Wars is nonsense too but it makes people happy.

Nonsense spreads not just because of apathy.

Star Wars isn't interpreted as a cure though, which is where new age stuff can be borderline dangerous sometimes.

Every work of fiction is "nonsense", but they still have value as entertainment and story-telling. The difference is that fictional works are understood by the reader/viewer to be fictional.

The problem with nonsense that purports to be true is that there's usually a scam attached to it, to separate people from their money. Fictional stories don't have this: everyone knows they're fictional before they spend their money on it, and they know what to expect from it (i.e. pure entertainment, not a cure for whatever ails you).

You leave my space wizards out of this!

And you actually pointed out why those two things are different.

We understand Star Wars is space wizards. New-agers do not understand that their beliefs are mostly bogus.

Luckily for us software development is a completely rational discipline, and is immune to fads, fashions, rhetoric, snake oil, and beliefs with no empirical foundation.

There's a difference between the practice of software development and the effects of software on the world.

She's right to get angry. There's nothing special about 432Hz (see my comment above on it's absolutely arbitrary nature), BUT the numerology that falls out of musical harmony is is indeed special and makes most of human race happy because of the aesthetic satisfaction that Pythagorean harmony (or even it's equal-tempered cousin) delivers to people.

Science is very good at describing things and why they're interesting, but science can't tell you what's beautiful or how to live. I understand your desire to point out the meaningless nature of setting up 432hz as some gold standard and agree with you that it's nonsense, but a spoonful of sugar helps the medicine go down' you could invest more time in exclaiming over the beauty and meaning of the relative pitch relationships in music, the most popular of which happen to nicely (albeit slightly inaccurately) mirror the ratios of planetary orbital periods. Your sister has the right idea in the wrong context, and you're missing out on some aesthetic insights by overlooking this.

> science can't tell you what's beautiful or how to live.

Yes it can. If you feel otherwise, it is because you're ignorant of how science actually works and how general its base principles are.

Not sure if serious, but if so no it can't except in the most primitive way (like describing harmony vs dissonance in musical notes). Art is far more complex than that, and as for prescribing philosophies of living, forget it.

Thats a very flippant comment.

I have no idea why this laughable article/idea persists, but the actual answer about 440 Hz is completely commercial and mundane.

Decisions made by the J.C. Deagan mallet instrument company at 1770 W. Berteau in Chicago are the sole reasons why A=440. I once worked in this building, still called the Deagan building.

The company made chimes and xylophones and instruments. They had customers all over the US. Each symphony in each city used a slightly different reference tuning. Philadelphia used 442, New York 438, etc.

This fact forced Deagan to retool their machinery every time a different order came in. This cut into profits. The owner, J.C. Deagan urged his customers to standardize on one reference tuning. One reference tuning meant one set of machine tools for his machines and no time or money spent retooling.

Deagan got results only when he contacted James Petrillo, the President of the AFM - the national musicians' union. Petrillo made it a work rule that A=440, overriding the conductors local preferences.

This was in 1910. Therefore there are no nazis involved.


Hey internet: don't be so goddamn gullible all the time, okay?

Maybe you should read the article first:

"Why do we use A = 440 Hz? (spoiler: no Nazis)"

I would think you'd be getting more upvotes, since the Deagan work is so completely rational and reasonable, and makes this whole thing such a non-story...

For another example: http://www.mmdigest.com/Archives/Digests/199804/1998.04.05.0...

(And by the way, the Deagan building is awesome! Glad the whole Ravenswood corridor is getting redone and readapted.)

Where did the article that nazis were involved?

Second sentence.

The second sentence makes no such claim. If you scroll further down you'll see

> Why do we use A = 440 Hz? (spoiler: no Nazis)

Right, the second sentence describes a conspiracy theory, and the end of the article dismisses this theory. The person you were replying to concurs with this dismissal, and presents additional evidence.

No I think the person I was replying doesn't know that the article dismisses the conspiracy theory. I might be wrong

> I have no idea why this laughable article/idea persists

You are wrong about that. This is the third or fourth time I've seen this dippy nonsense in print, and I wish it did not persist. Its central sin is that it obscures the mundane, industrial-based reasons for the tuning standard's emergence.

I'm sorry for being wrong then, but I'm still a bit confused - which part of the article is inaccurate?

> Its central sin is that it obscures the mundane, industrial-based reasons for the tuning standard's emergence.

The article claims that tuning standards emerged because pitch inflation lead to problems for singers, is that inaccurate?

No apology needed!

And yes, the tuning standard emerged from the wishes of the owner of a single mallet instrument factory in Chicago named Deagan.


> orchestras specializing in older music may sometimes tune in the tuning close to the one for which the piece was originally written, which may range from 415 Hz to 470 Hz).

I can say as someone who performs a lot of Baroque music (c. 1600 - 1750) that there is a relatively common standard of A=415 for music of this period. A=415 is often referred to as "Baroque pitch."

This mainly applies to ensembles that specialize in Baroque music, and use historical instruments. If you see your local symphony orchestra play Bach on modern instruments, they will probably play at A=440.

I have never performed at a pitch higher than 440. I'm sure it happens sometimes, but I think it's more of a niche thing.

Opera singer here - you must be playing in North America. In Germany tunings range from 436 to 444, depending on what you're playing. Most theaters tune to 442.

One thing that gets opera singers (like me) up in a knot about this, is that the human voice is not a tune-able instrument. There are registration issues in fixed frequency ranges, which we can't change. At A440, a register shift happens a quarter tone lower than where Mozart and Verdi expected it. That creates a sound difference that an audience can hear, and a big difference technically.

As a classically trained but relatively amateur singer, and professional audio engineer, this fascinates me because I would've thought such breaks vary enough from person to person that it wouldn't be possible for a composer/conductor to expect it to be somewhere with anything like quarter-tone precision. Cool!

Thank you. This is the part of the conversation that gets drowned out by the taoy-wowy numerology crap.

If memory serves, a number of opera singers, including Pavoratti, were lobbying for a change of the international standard to 432. I thought this was a bit foolish, as the problem is better addressed by simply agreeing to adopt an alternate tuning for those pieces that would benefit from it.

Yes I am in North America (Seattle area). However I've also noticed this on recordings of international groups. For example, both Bach Collegium Japan and Taverner Choir (England) have recorded Handel's Messiah at A=415. I didn't realize Germany favored higher pitch.

Personally I prefer singing at A=415 since my voice is lower set. :)

You are an opera singer and a computer programmer? That's pretty cool.

it also depends if you are performing in ensembles together with historical instruments that can't change their pitch, or on those instruments on their own, for example for organs you can find examples up to A=465

This said I think it's more fun to talk about temperaments than absolute pitch, after all unless you have absolute pitch I don't think you can hear much of a difference between something played at 432 or 440, but going from equal temperament to something else is a lot more noticeable and makes a lot more impact to the music if it's written taking that into account.

Yes, but temperament is really only a part of the discussion when we are talking about instruments that can actually be tuned to different temperaments: pianos, harpsichords, organs, etc. Strings and woodwinds, for example, cannot.

> I have never performed at a pitch higher than 440. I'm sure it happens sometimes, but I think it's more of a niche thing.

In addition to varying by era of music, as you mention, this also varies by country. My violin teacher had done a lot of traveling and performing in different countries. She told me that, in one country[0], she was given criticism that her tuning was off in her solos. She realized that they were using A=445, and their ears were trained on that, so everything she played solo sounded flat to them[1]. Once she discovered this, it was an easy "problem" to fix!

[0] I wish I remember which countries - I think Austria and Germany? I can't be sure. I'm almost postive it's not Russia, because I think A=435/438 is more common there - or at least was at the time.

[1] It's only really relevant for solos, because for a trained violinist playing in an orchestra, tuning is done by ear. So a professional violinist would adjust to the tuning used by the group without really thinking about it.

(Finally something I can contribute to, on HN)

My father plays in a baroque orchestra (the Amsterdam Baroque Orchestra), and I know that when they play a repertory, e.g. Dieterich Buxtehude, the orchestra tunes to 465 meantone.

I suspect the temperament makes a dramatically larger difference than shifting every note sharper by a bit less than (95.7% on a log scale) a semitone compared to A440.

Mainland europe non-opera orchestras generally tunes 442, with some regional exceptions. Apart from germany that is. Last time I played in the germanosphere (the Cologne radio symphony orchestra a couple of weeks as co-principal bassoon in the early 00s), they _started_ at 443 or 444 and ended up somewhere around 446-447. That was _hell_ for us woodwinds.

The regional variations depends a lot on orchestra politics. For example, when I played the munich phil in the late 90s they started at 443, but concert heat be damned, if the last chord wasn't 443 there were some yelling at the first violins and brass section for striving to much upwards.

The Swedish radio decided to play 441 for political reasons (it was a compromise that stuck), and I think still does.

I have met some very competent musicians who have found 432 tuning to be powerfully effective. When I dug into this, I discovered they were tuning the other notes in the scal to frequencies in whole numbered cycles per second, using tables being passed around. So the real change was in the qualities of intervals; many of these became far more resonant than the compromised resonant qualities we get with equal tempered tuning. This trade-off was once well known in the musical world, but it is now long forgotten. I consider "432" to be a symbol that suggests the restoration of forgotten methods for tuning scales, rather than a literal value to be used to proportionally change the frequency of every note.

If you're interested in this sort of thing, look for Wendy Carlos' album Switched-On Bach 2000. She revisits the material of her classic electronic music album with modern synthesizer equipment, and uses authentic Bach tunings for the pieces as well. The liner notes for the album explain the tuning systems used, and how they differ from the modern, mathematically-perfect equal temperament. She notes that Bach was himself a first-rate tuner and theorist, and was not above retuning "on the fly" to improve the sound of various compositions. Of course, with synthesizers, a tuning is just a block of data, which can be reloaded as needed.

(As a "bonus track" on the album, she included a realization of "Toccata and Fugue in D Minor." Especially appropriate for the season!)

Wendy Carlos is awesome! I didn't know about the 2000 version, I will check that out.

Tuning is just a block of data on a digital synthesizer, but on an analog synthesizer it's not. If you use a keyboard controller, it's generating pitch control voltages with a fixed 2^(1/12) ratio between notes (or logarithm thereof). It would be challenging to convert this into a just intonation.

On the other hand, if the pitch control voltages are generated by potentiometers on an analog sequencer [1] and the musician is setting those potentiometers by ear, the musician will probably end up tuning to a just intonation because it sounds more correct to the ear.

[1] https://en.wikipedia.org/wiki/Analog_sequencer

Just intonation is a system of getting beautiful pythagorean intervals for rich harmonies as the expense of modulation from one key into another (a staple of the western musical tradition for several centuries). It's what makes barbershop quartets enjoyable to listen to. High end electronic instruments let you switch between equal-tempered or other tuning schemas.

could also be about the instruments, say a violin built in the olden times tuned differently so the tension of the strings is different and the body accentuates certain harmonics in a certain way...

On the subject, here's an interesting song that starts out at A432hz and makes its way up to A440hz by the end.

Hideaway – Jacob Collier https://www.youtube.com/watch?v=4v3zyPEy-Po

I did not explicitly notice this the first time hearing it, but I certainly felt it. When I discovered the change it made sense to me. The mood is lifted over the course of the song as the tuning is also lifted.

There are so many elements of music that are routinely varied within a song — dynamics, texture, timbre, rhythm, key, and tempo (though less frequently during this age of the click track). I don't think I'd noticed tuning used prior to this.

I sometimes vary the tuning in subtle ways in my piano music (using a software piano).

> the BBC required their orchestras to tune to 440 Hz instead of 439 Hz because 439 is a prime number, and the corresponding frequency is hard to generate electronically.

I followed, until this. Earlier he debunks the significance of 432 per second (including that it's a sum of four consecutive primes), because a second is an arbitrary length of time. But now he says that 439 per second is difficult to generate electronically, because it's prime.

I'm not an EE. I'm willing to believe, but could a knowledgeable someone help us out here?

From other sources it doesn't seem clear if this actually was considered in the decision, but it describes how they got the tone:

> The B.B.C. tuning-note is derived from an oscillator controlled by a piezo-electric crystal that vibrates with a frequency of one million Hz. This is reduced to a frequency of 1,000 Hz by electronic dividers; it is then multiplied eleven times and divided by twenty-five, so producing the required frequency of 440 Hz. As 439 Hz is a prime number a frequency of 439 Hz could not be broadcast by such means as this (http://www.wam.hr/sadrzaj/us/Cavanagh_440Hz.pdf)

Since 1000 Hz also was (is?) a broadcasted test tone, it makes sense that it is much easier to get perfectly matching 440 and 1000 Hz from the same high-frequency source than it is to get 439 and 1000 Hz. A more precise way of describing the problem is then that it's hard to generate since it doesn't share any divisors with other desired test frequencies.

If they only required 439 Hz they could have just used a slightly differently tuned source oscillator, yes.

I wonder why they decided it was better to design and build an 11x multiplier and a 25x divider rather than cut a 440 kHz crystal and run it with a copy of the 1000x divider electronics they already had.

Because 1MHz crystals are common off-the-shelf items, 440kHz are not?

In order for that explanation to make sense, one has to assume that 11x multipliers and 25x dividers were common off-the-shelf items during the time period in question.

If the choice is between a custom crystal and two custom boards, the custom crystal is going to be the far less painful choice.

I would bet that the BBC was using the 1 MHz crystal and the associated division/multiplication circuitry for other frequency control purposes, not just the musical test tone. 1 MHz is smack-dab in the middle of the medium wave band usually used for AM broadcasting, and the BBC has always broadcast on many different frequencies at the same time.

Having all the broadcast frequencies controlled by a single reference crystal would have some obvious advantages (and a few disadvantages too, of course).

Arbitrary dividers and multipliers are fairly easy to design in a circuit. Certainly far easier than cutting a custom crystal.

The world is so ... physical. :) Thanks.

To common ways to produce precise oscillating signals are tuned crystals or RC oscilators. In both cases, you're looking at common parts (i.e. standardised to x Hz), and then multiplying or dividing by integer multiples to get to the frequency you want. With a prime number, you'd need a component specifically tuned to that or a multiple of it.

I found a plausible explanation here:


tl;dr: The BBC reference pitch was generated by dividing and multiplying a 1MHz crystal oscillator. A440 was achievable by this means; A439 was not.

You raise a good point. a second is an arbitrary length, so nothing universally significant about 439 Hz or 432 Hz or etc.

However, when you are trying to build a device that oscillates at x Hz, there are engineering-ly sigificant values. For example (as already mentioned) a 1kHz oscillator might be easier to come by. As an additional example, the AC power in the UK is at 50 Hz, a factor of 440 Hz. So there is a free 50 Hz reference available everywhere, that can be multiplied (with a PLL, which is more robust to, say, temperature differences, than say, building a 50 Hz or 440 Hz reference yourself).

(50 Hz is just an example. AC line frequency probably is not stable enough in the short term to be a useful pitch reference)

AC line frequency has been recognized as a preferred reference for pitch. This is what made Hammond electric clocks the first reliable AC powered timekeepers.

Later, Hammond famously produced electro-mechanical organs referenced to line frequency.

Well, what do you expect from somebody simply following in the creative footsteps of Leonardo DaVinci & Thos. Edison?


I don't think it's a particularly stable reference in the short term. It's true that the power companies adjust it to hit exactly the nominal frequency over a period of many hours, but not at any one instant.

In fact: https://en.wikipedia.org/wiki/Utility_frequency#Time_error_c...

439 being a prime would be an issue if you were up multiplying a lower frequency to generate it, for example using a PLL. However it is such a slow signal that it would be generated by dividing down a higher frequency. For example you can divide it down from an 18 MHz clock.

So, nope his claim doesn't make sense.

439 from 18M requires a divisor of 41, which does sound trivial. Meanwhile 440 from 1M requires only dividing by 5 and 2 when first multiplied by 11, which might have been significantly simpler than dividing by 41.

I wonder if there is some easy way of figuring out the simplest base number-multiplier-divisor chains for getting certain numbers?

Dividing a frequency by a large prime, like 41, is somewhat difficult without digital electronics. Smaller factors are easier.

I imagine historic gearmakers for watches and clocks would have worked out such a system.

PLL's have been around since the 1920's. They could easily divide by n. The actual value of n didn't matter (within some bounds).

Would it not just have been created natively using an appropriate osciallator, given that the reference was from 1939?

A truly decent audio oscillator was only available after 1939, when Hewlett & Packard issued their first instrument.

In a 1985 letter, Dave [Packard] described Hewlett's audio oscillator as "the foundation on which Hewlett-Packard Company was able to grow into the largest manufacturer of electronic instruments in the world, the keystone that allowed four and one-half decades of major contributions to electronic measurement technology and equipment."

Maybe but it'd have been significantly more complex, here they could take a MHz piezo-electric crystal and tack on a few electronic multipliers and dividers (/1000 *11 /25) to get the desired frequency.

Quartz oscillators are usually made in at leas 10th of kHz range, for whatever reason. Second most stable oscillators are LC and would require large coils for lower frequencies.

It would still have been divided down. There aren't many "Hz" oscillators. They're all usually in KHz/MHz range.

Perhaps he meant to say the BBC made that choice for that reason. Not that they're necessarily right to do so.

Or perhaps seconds are relevant in the way sound was broadcast.

And that doesn't even make sense.

An instrument will go ever so slightly out of tune by the time the orchestra is done playing. Temperature and humidity play a large role in how an instrument is tuned.

Sibling comments have the explanation, but good catch. It so happens 439 Hertz = 1000 Diddly (a just-now-invented unit defined as "cycles per 2.277904328 seconds")

Maybe if your "electronics" are vacuum tubes and relays.

In the digital domain it's not an issue at all.

Electronic =/= digital.

It is electronic gating to bring down a 1khz signal. Division and multiplication to a prime number is pretty hard...

But there's nothing special about the 1k signal either, because a second is arbitrary. The original signal might have been 878 Hz instead (or equivalently 1000 cycles / 1.139 seconds which is no more or less privileged than 1000 cycles / 1.000 seconds) and then the gating to 439 is easy.

What do you think they were using in 1939.

I spent three months in meditation retreat some years ago. I'd never heard of this phenomenon. At some point, I started hearing various tones that weren't coming from outside. They eventually became quite loud. I noticed three tones in particular, and wrote some code to pin down their frequencies.

I discovered that they were C, E, and G, where the A would have been 432 Hz (or very close to it; certainly much closer than to 440). Some internet searching turned up this phenomenon. Apparently ancient Hindus and Buddhists heard similar tones during meditation, and related them to various points in the body.

Maybe there is something to the notion that it's related to our neurology or physiology in some way.

> I noticed three tones in particular, and wrote some code to pin down their frequencies.

What kind of code does one write to get the exact frequency of a sound in your head?

Haha yeah I could have explained better. I wrote code to play a solid tone where I could adjust the frequency via keyboard input. I played around until it matched what I heard internally. I have some musical training and know I can do that pretty well.

Thanks for sharing that. I think that the article's author missing the point here:

> and I think that if 432 Hz were some kind of a sweet spot, someone would have noticed by now.

because that's exactly what people who talk about 432 Hz are saying, that it's a sweet spot!

Wasn't the 432 Hz thing started by Lyndon Larouche?


He basically popularized it, and I was surprised someone wrote an entire article on this without mentioning that fact.

The article mentions pitch inflation and it reminds me of something I learned about symphony orchestras.

I dated an symphony oboe player for a few years. Oboes players play the note used to tune the orchestra before performances because the oboe has a penetrating sound and has very limited tuning capability (due to their construction) so other instruments are tuned to the oboe.

She said that the string players often wanted a higher "brighter" pitch than the true pitch for middle C. She had to carry an electronic tuner (about the size of a smart phone) to verify her pitch and resolve disputes with the some of the string players.

Moral of the story is that numbers with dimensions totally arbitrary. In theoretical physics you often want to find a small parameter to do a Taylor expansion and make some mathematical expression simpler. A small parameter is a number much less than one, but if we have a quantity with the units of metres for example, we cannot say "r is much less than 1" because you can't compare a number with dimensions to one. You could always pick your units such that the number is much less than 1. What you instead do is find some _ratio_ of quantities that is much less than one, because then the units cancel and you have a dimensionless quantity that you can then compare to 1.

One proposed pitch standard that was never widely used set C at 256 hz just to make the math slightly easier.


I use all different sizes of strings and tensions and tunings for my basses and guitars. ALL of the Western 12 note musical system is a social construct, not something innate to music, and other than what audiences and musicians are accustomed to, it makes no difference what tuning you use. Just like bands can play songs slightly faster or slower live, they can also transpose the pitch a half step or two, or a semitone in whatever direction, without most people consciously noticing. And it could have a beneficial effect on a song, or not. Exact tuning just doesn't matter to people without perfect pitch - relative pitch matters.

    An equilateral triangle whose area and perimeter are
    equal has the area of exactly the square root of 432.
Let's say we have an equilateral triangle with a perimeter of 3x units. Then each side is x units, and the area is sqrt(3) * x^2 / 4 square units. So we set:

            3x = sqrt(3) * x^2 / 4
             3 = sqrt(3) * x / 4
   3*4/sqrt(3) = x
    12/sqrt(3) = x
Then the area is:

    sqrt(3) * (12/sqrt(3))^2 / 4
    sqrt(3) * 144 / 12
    sqrt(3) * 12
    sqrt(3) * sqrt(144)

I saw that in the article, too, but it didn't make sense to me. One has units of area and the other has units of length. How can they possibly be equal? That's like saying a 700 foot wall is the same size as a 700 square foot apartment.

That's what made it jump out to me too! But the key thing is that one number is in linear units and the other is in square units. So for any linear unit you choose (mm, in, km, furlongs, ...) an equilateral triangle with perimeter sqrt(432) units will have area sqrt(432) square units.

It is the intersection between a line and a parabola.

Prince was also big into the 432 Hz thing vs. 440. 432 on guitar feels a little nicer overall but I like to play along to radio / DJ mixes for fun & practice and being at 432 feels off to me, so I stick with 440. 432 is good on acoustic, but then again open tuning sounds good on acoustic no matter if using 432 or 440.

I like playing bass tuned slightly flat because I have tiny hands and it's easier to play with less tension.

Neat! I can understand. Also like how some guitarists who sing prefer to tune to Eb. I think it's more of a sonic fit for some registers.

I've always wanted to play heavy strings, so I also explored tuning down. Imagine my surprise seeing what Dimebag Darrell was tuning to for "Floods" on 'Great Southern Trendkill' - C# F# B E G# C. I had trouble getting intonation that worked well for me, so I went ahead and got a Les Paul style Baritone. Definitely a workout, and the opposite of going lighter, but I really dig the tone it puts out. Worth the hand cramps to practice on the 27" scale.

I recently switched to nylon wrapped strings... they also have lower tension. But I mostly did it because I play a lot of americana / folk / rockabilly / blues / jazz and wanted a better slap sound.

Unfortunately they sound terrible arco so now I have to play cello when I play in my wife's orchestra. :(

[edit] it occurs to me that you're talking about electric bass... in which case nylon strings would be a bit strange ;) sorry about that.

I was talking about electric. But thanks for reminding me to play my upright now and then! Poor thing needs some TLC... and a much lower bridge.

> in which case nylon strings would be a bit strange ;)

Not at all, there are nylon wrapped strings for electric now too! [1]

[1] http://www.daddario.com/DADProductFamily.Page?ActiveID=3768&...

Like the article says, just getting lighter gauge strings is just as easy and keeps you in tune. I play guitar, and the Ernie Ball Slinkys work well for me.

Fair, although this is something I discovered mostly through picking up and playing my bass without bothering to tune it, or than something I do on purpose.

If electric bass (or maybe even if not) try Thomastik-Infeld strings, especially the flatwound strings.

Never heard of this brand. DR has been my go-to for years and recently gave Rotosound a try after going on a Yes bender. Thanks for the tip.

All of their strings are fairly mellow sounding. If Rotosound/Yes is your style, you might not like the Thomastik sound. But they are very low-tension and flexible!

Prince also believed in chemtrails, there's youtube videos of him talking about them. He comes off as a massive tinfoil hat-wearer.

I'd definitely be more inclined to trust in his musical intuition than his scientific aptitude though.

Just wait until the conspiracy nuts learn about the tunings that affect the distance between notes, not just the shift! (I'm surprised my double music major is useful somewhere).

See dragonshine's post above which addresses that. I'm not calling dragonshine a 'nut', just saying that you'll need to speak further on it to make your point.

Just curious - what exactly is a double music major? (I always have heard of double majors as being separate subjects.)

Cost him twice as much, with the added benefit that it gives the person the right to mention their double major twice in every sentence they speak/write.

I think they mean that chose to major in <X>, with music as a second (additional) major.

Possible also they got to different music degrees, in say, Composition/Theory and Trombone Performance.

I can only presume, but I believe they meant they graduated with a 'main' major (possibly something technical, like engineering or CS, since we're in HN), but also double majored (i.e. also majored) in music.

A guy I met at a party this weekend was explaining this to me (as something he believed) and I was trying to keep the "WTF" off my face. Thanks for posting this.

For those wondering, 432 Hz is about 32 cents below 440 Hz, or nearly a quartertone flat.

There has been a "hertz" war in the bagpipe world for the past 200 years with the pitch raising steadily higher over the decades. Ancient pipes' "A" were historically tuned at 440hz, but modern pipes are tuned around 476-480hz!


A cool video on "music temperament" as well: https://www.youtube.com/watch?v=VRlp-OH0OEA

Interestingly, his argument for dismissing the conspiracy theory basically boils down to type theory.

It's not legal to "convert" Hertz to other units willy-nilly, especially because Hertz is tagged with an attribute that says "this relies on arbitrary constants", meaning you would have to multiply 432 by some conversion factor before you can compare it to pure numbers.

Thinking about things in terms of types (in a fuzzy, intuitive way) like this is a very powerful mental shortcut that is useful surprisingly often.

I helped do a lot of costumer relations for a music instrument maker who makes fixed-tuning instruments (which cannot be retuned by players, it's a fine art).

By nature of the instrument, we had a lot of relatively mystical-minded customers, and a solid subset inquired about the availability of instruments tuned to a 432 Hz reference.

What was interesting is that there is indeed a difference in 'feel' (character, vibe...) for most acoustic instruments when you tune them down e.g. to an alternative, lower, pitch reference. (Because most aspects of the system are either non-linear e.g. our sensitivity to various pitches, and maybe some sort of psychoacoustic quasi-significance assignment... ... or because simply they are changing one term in a function, e.g. given a fixed thickness of vibrating membrane, tuning it to a different pitch yields a different relationship to the many 'modes' in the system akin to standing waves... etc etc etc)

There's nothing mystical about it all of course... but the vibe changes, and many people prefer a slightly lower pitch, and now it is 'carried' by the instruments.

Then you get fuzzy thinking... I like this better, it feels better, QED an alternative pitch reference is the key to life itself.

What's funny in my experience is that our specific instrument did not have a fixed equal tempered tuning anyway, for technical reasons... so even with a 432 Hz A reference, the pitch values for say C# or F# were not === what they 'should' be according to 432 Hz adherents.

But try explaining that gently to an adherent... especially in the context of kindly debunking their mysticism around this topic... <wince>

However, in the 19th century, obtaining thicker strings was not that easy. Manufacturing of strings was a complicated procedure, so rather than changing the manufacturing process, it was much easier to tune the same strings to a higher pitch to increase tension and thus improve the sound.

Worth noting that today's strings are made from steel and nylon, as opposed to gut.

[Posted on my blog](http://www.krisconstable.com/432-hz-vs-440-hz-conspiracy-the...)

While I appreciate Jakub’s breakdown for the reader to get to explaining why the 432 number itself is effectively fabricated for convenience, he eventually states: “_The 432 Hz tuning, the divine tuning of nature itself, is ultimately defined as one vibration per 21279240.2083 periods of radiation of an uncommon chemical element_” however he’s missing the critical argument.

What is missing from the argument is the irrelevance of the number. For example, if 432 Hz resonates with I don’t know, the neocortex, there is no relevance what the number is or that we’ve associated with what we humans currently call a time second — that’s just a standard way of identifying the number.

What needs to be done is validation or invalidation of this frequency in terms of “healing and soothing properties.” It’s also important to not do so defensively, otherwise you’re arguing against organized religion or Santa Claus or Unicorns — it’s a useless effort to argue against something that has no scientific evidence. If someone is making a claim without evidence in the first place, you’re arguing irrationally already and you’ve already lost. Reason requires logic.

“Here is my repeatable scientific evidence why I feel the world is flat” is different than “I have a feeling the reason the sky is blue is from unicorn tears — prove to me it’s not”.

It is my suggestion that if someone feels that 432 Hz has healing and soothing properties, they take this hypothesis and run it through the scientific method. It will be these published results that can be responded to, directly. A quick search on plosone doesn’t show that there’s any documented research in this area currently, a new opportunity for those interested.

This can be difficult because everybody has been overexposed to 440, which is nearly impossible to control for. Even if you log an effect it can be argued that the effect is not of 432 but of a certain deviation from a norm.

Eh, try it across a range of different tunings and see if there's a peak in the effect around 432. If there were, it would be easier for me to believe it's the 432 that's significant rather than "normal - 8Hz"

Thank you! My thoughts exactly - glad to see someone else with the same sentiment

When I first heard of this I was really messing around with different tunings and such for writing music on guitar/bass. I didn't buy the whole new science schtick, but I did give it a try and I believe recorded and "produced" (as a hobbyist) an entire song in 432 hz to see if it'd be more interesting to work it. The only real noticeable thing to me was my strings were a bit more floppy than usual (due to it being in between E and Eflat tuning). It was an interesting experiment, but I've stuck to 440hz ever since, except for one time when I tried to do a rock cover/adaptation of a song from the 1920s that was in some crazy mystery temperament that I could never properly match (probably because every instrument section was different, horns were like 435+, double bass was 432, some strings were flat at like 430 or 431.. it was a difficult thing I never accomplished)


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