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"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.

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.

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.

https://www.youtube.com/watch?v=z6i1VVikRu0

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.

USA network used to do this.

"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.

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.

Stanley Kubrick would have hated this. ;)

http://www.cinemablend.com/new/Message-From-Stanley-Kubrick-...

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.)

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

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?

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?

That seems like a logical conclusion

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...

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

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

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.

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.

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%.

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.

https://www.lynda.com/Pro-Tools-tutorials/Understanding-vide...

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

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?

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 :-)

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 :)

I LOLed

> 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.

https://frinklang.org/frinkdata/units.txt

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.

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.

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.

That is good to know.

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

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 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.

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

All our music would sound wrong.

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

XD

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
[(1,1),(9,8),(5,4),(4,3),(3,2),(5,3),(15,8),(2,1)]

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

[432.0,486.0,540.0,576.0,648.0,720.0,810.0,864.0]

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

[432.0,460.8,480.0,486.0,518.4,540.0,576.0,607.5,648.0,691.2,720.0,810.0,777.6,810.0,864.0]

..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

https://en.wikipedia.org/wiki/Highly_composite_number

https://en.wikipedia.org/wiki/Superior_highly_composite_numb...

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/

Edit:

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

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.

> 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:

https://en.wikipedia.org/wiki/Sunrise_equation

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

https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/FORTRAN/req/...

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.

http://news.harvard.edu/gazette/story/1999/07/human-biologic...

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

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.

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.)

https://xkcd.com/670/

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.

http://sethares.engr.wisc.edu/paperspdf/HarmonicEntropy.pdf

What???

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.