As a Frenchman, I chuckled at "In Britain, however, the French standard was interpreted in an erroneous way, due to which British orchestras commonly tuned to A = 439 Hz."
NOTE: I hope the word chuckle isn't interpreted as condescending, I only meant that this story is almost a perfect parable for our relationship with Great Britain throughout history, one of mutual defiance and refusal to acknowledge the other party as an equal even though I've always felt that there is some hidden love and respect going on at a deeper level on both sides.
'mocking' the French has been a mainstay of British humour for a very long time, including many classic Monty python caricatures.
I put mocking in quotes because it's always in good humour. There has always been a string English / French rivalry and I guess this has morphed to poking fun at each other.
It's always felt to me (a Brit) like a sort of sibling relationship. We can poke fun at each other all day long, but we'll defend each other from anyone else trying to do the same.
As a Brit, my reaction to a Frenchman is one of disgust as I reach for my insults. Yet there are few countries I would turn to so quickly in the search for a sane and good friend.
Perhaps it is easiest to say:
Where the USA has Russia, we have France. Where the USA has Canada, we have France.
Oh, England and France are entirely about the narcissism of small differences. (Also England and Scotland, hence the Auld Alliance of Scotland and France.)
And as an American, I don't know anyone who doesn't like Canada or Canadians, while simultaneously not understanding what makes it different other than basically superficial stuff (i.e. french language, metric, being polite, etc.)
So I don't think we have that England/France relationship at all either. It seems pretty special on the world stage.
From anyone familiar with it, is New Zealand and Australia's relationship at all similar to either Canada and USA or England and France?
NZ/Aus is pretty special. Most analogous to USA/Canada
The original point was that Britain/France have the superficial differences that let us be friends (USA/Canada) yet we have some deeper differences and historical differences that let us be enemies (USA/Russia).
The nice part of it is that we can carrot and stick ourselves with one neighbour, instead of making our enemy the devil incarnate.
US-Canada also has that element of small-versus-large - the US looms (I imagine) much larger in the Canadian consciousness than Canada does in the American one, just because the US isn't so defined by that one neighbor.
Maybe more like Portugal-Spain? Hard to find examples like that where there haven't been any wars in a couple hundred years, and there's also that linguistic/cultural similarity.
It's not just French/Britain. The book "How music works" describes how each country and, hell, cities, had different tunings, so an Italian singer with a perfect pitch visiting Germany cannot really perform. Maybe just the local organ builder had a different tuning fork when building the church and everyone tuned from there :)
Similar to how people didn't have standard time until relatively recently and the one clock at the town square can be off by quite a bit with the next town.
But from what I've read the British actually tried to adopt the French standard and made some conversion error, they didn't come up with their own thing independently.
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.
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 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.
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.
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!
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.
Here's the rant I posted to Facebook when someone posted about this a couple of years ago. The site that was on Facebook 404s, including the Wayback Machine, so I can't share all the craziness:
The simplest argument against this is the casual way your typical garage bands tune. Not everyone is busting out the tuners and dialing up 440 Hz, when the guitar player figures out they're out of tune with the bass they just tune up to wherever they're at. With strings stretçhing, drop D tuning, and tuning down a half step, most bands would have hit the 'magic' 432 Hz every other practice and would have stayed there if it had any special properties. And this isn't just me and my buddies in the garage but musicians of nearly every style, genre, and background around the world. We'd revolt if we found our magic 432 Hz and then some clown brought a keyboard in that was at 440 Hz. This simply doesn't happen.
The 'cymatics' demonstrations are great, even the professors I work for get excited about how these demonstrate standing waves in materials. Unfortunately for the 432 Hz people the wave patterns depend on the vibrating materials. I make music out of vibrating strings, resonating wood and digital beeps and boops instead of square plates of metal (nothing against square plates of metal, I'd use those too). So maybe they should start by making pretty pictures of sand on top of a guitar to have a point with the cymatics. Also, the tuner they keep showing for the notes in their video shows their frequencies sharp or flat. They should at least get their notes right. They're also using a modulated tone with harmonics which introduces all kinds of questions about whether they're trying to prove a point or just make cool patterns with the sand. But really, who cares if it sounds good, right? Seriously, if you like your music 'detuned' to 432, go for it.
I've got a theory that altering familiar music is a great way to get us in different moods. We like remixes, right? So a 432 Hz retune might be just the thing to mellow out to. Likewise, a 448 Hz retune might be just the kick in the ass I need in the morning to get going. So retune all you like.
I do have a technical quibble with the suggested method in Audacity, the resample will do bad things to the high end of the music, all those harmonics and partials and stuff (of course, some feel all that is lost in digital music anyway so YMMV). The Audacity wiki talks about better ways to do frequency shifts. I definitely wouldn't do this to anything that has been digitally compressed at any point, your mp3 folders and itunes collection will lose even more when you start pitch shifting them. Rip the original CDs and mess with the .wav files or get the FLAC files if you're serious about retuning your music collection.
The real way to test their idea would be to blind test a bunch of music you've never heard before, some that has been pitch shifted to a variety of frequencies including 432 Hz and some that is unaltered. Score the music and your emotions after each song and see if there is a pattern to the pitch shifting. Now do this to a bunch of people and see if there are patterns in cultures, age groups, musical preferences, etc.
> The simplest argument against this is the casual way your typical garage bands tune. Not everyone is busting out the tuners and dialing up 440 Hz, when the guitar player figures out they're out of tune with the bass they just tune up to wherever they're at. With strings stretçhing, drop D tuning, and tuning down a half step, most bands would have hit the 'magic' 432 Hz every other practice and would have stayed there if it had any special properties. And this isn't just me and my buddies in the garage but musicians of nearly every style, genre, and background around the world. We'd revolt if we found our magic 432 Hz and then some clown brought a keyboard in that was at 440 Hz. This simply doesn't happen.
I don't really understand what you're saying here. If you tune casually by ear, then of course when a digital keyboard comes in at 440 you will be off. Maybe higher, maybe lower. But you will be off. Unless you're saying 440 has some "special properties"...
They're saying that if 432 Hz had special properties, then they'd randomly hit upon it because of the random drift of tuning, and notice that it was better than other tunings; if the keyboardist then came along and insisted on 440 Hz, they'd revolt because it was worse.
But they DON'T revolt, because 432 Hz is no better or worse than 440, 450, 429, 490, or anything else in that range.
"So a 432 Hz retune might be just the thing to mellow out to."
I occasionally like to pitch-shift my music by up to a minor third. It's not enough to introduce much distortion and it can make it, if not fresh, at least something you listen to again.
(Unfortunately, the intersection of music players that make that easy and music players I want to use seems to be empty.)
Last I checked keyboards default to 440hz, and most crappy tuning tools default to 440hz too.
So it is normal for everyone to drift towards 440hz... to use 432hz in current era, it is necessary to purpusefully tune for it, including retuning digital instruments (keyboards, synths, etc...)
>"So a 432 Hz retune might be just the thing to mellow out to. Likewise, a 448 Hz retune might be just the kick in the ass I need in the morning to get going. So retune all you like."
I have no idea why my speculations here* seem to be controversial (as judging by the votes), but have you considered that the preferred fundamental pitch actually varies with season, latitude, and time of year? That would explain why no one has settled on a specific pitch for all circumstances. It is ultimately controlled by the length of day. Perhaps time of day as well, if we split the day into sun up and sun down.
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).
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.
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.
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.
> 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?
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.
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.
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."
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?
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.
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.
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).
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.
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.
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")
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.
> 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.
> 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.
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.
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.
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.
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. :)
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.
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.
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.
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.
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).
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...)
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).
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.
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.
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.
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.
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).
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.
> 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!
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!
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.
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!
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.
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...
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.
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.
Fascinating stuff. I have never pondered the arbitrariness of musical tunings (probably because I am not a musician).
However, if these tunings and notes vary so much, what does it mean when one claims that they have 'perfect pitch'? Is it an ability that uses the relative distance between notes? That is, given an A they can identify the C?
> what does it mean when one claims that they have 'perfect pitch'
someone starting before 6 years old (better chance of things sticking) and being sung "bah-bah-black sheep" with a piano at the correct pitch. So they manage to remember the starting pitch as well as the relative up/down of the melody.
Interestingly, more common in "tonal" language speakers, e.g. Mandarin, where the pitch can make a difference in the meaning of the same word. Apparently "ma" can mean mom, horse, lazy... depending on the pitch and its direction.
Perfect pitch is mostly a curse than a blessing as many notes in the world are off, e.g. a school bell, and hurt the person with the perfect pitch. I hear :)
I'd say perfect pitch = relative pitch + internal pitch reference (i.e. A=440). You cannot be born with the latter pre-programmed in your brain because that's an arbitrary number.
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[ 4.2 ms ] story [ 284 ms ] threadhttp://www.schillerinstitute.org/music/revolution.html
I can never find the right spoon.
NOTE: I hope the word chuckle isn't interpreted as condescending, I only meant that this story is almost a perfect parable for our relationship with Great Britain throughout history, one of mutual defiance and refusal to acknowledge the other party as an equal even though I've always felt that there is some hidden love and respect going on at a deeper level on both sides.
I put mocking in quotes because it's always in good humour. There has always been a string English / French rivalry and I guess this has morphed to poking fun at each other.
Perhaps it is easiest to say:
Where the USA has Russia, we have France. Where the USA has Canada, we have France.
Can't imagine Anglo-French culture works quite like that.
So I don't think we have that England/France relationship at all either. It seems pretty special on the world stage.
From anyone familiar with it, is New Zealand and Australia's relationship at all similar to either Canada and USA or England and France?
The original point was that Britain/France have the superficial differences that let us be friends (USA/Canada) yet we have some deeper differences and historical differences that let us be enemies (USA/Russia).
The nice part of it is that we can carrot and stick ourselves with one neighbour, instead of making our enemy the devil incarnate.
- At one point New Zealand was part of the colony of New South Wales (until 1841, while the nation of Australia came into being in 1901)
- Australia and New Zealand have fought a number of wars together as close allies.
- Special visas available for New Zealanders in Australia (and vice versa I believe)
- Arch-rivals in sporting matches.
Maybe more like Portugal-Spain? Hard to find examples like that where there haven't been any wars in a couple hundred years, and there's also that linguistic/cultural similarity.
I've been watching some episodes of "Yes Minister", a British comedy show from about 30 years ago, and it's weird how much is still relevant.
https://www.youtube.com/watch?v=37iHSwA1SwE&t=027s
Similar to how people didn't have standard time until relatively recently and the one clock at the town square can be off by quite a bit with the next town.
Worth noting that today's strings are made from steel and nylon, as opposed to gut.
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.
Not at all, there are nylon wrapped strings for electric now too! [1]
[1] http://www.daddario.com/DADProductFamily.Page?ActiveID=3768&...
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'd definitely be more inclined to trust in his musical intuition than his scientific aptitude though.
The simplest argument against this is the casual way your typical garage bands tune. Not everyone is busting out the tuners and dialing up 440 Hz, when the guitar player figures out they're out of tune with the bass they just tune up to wherever they're at. With strings stretçhing, drop D tuning, and tuning down a half step, most bands would have hit the 'magic' 432 Hz every other practice and would have stayed there if it had any special properties. And this isn't just me and my buddies in the garage but musicians of nearly every style, genre, and background around the world. We'd revolt if we found our magic 432 Hz and then some clown brought a keyboard in that was at 440 Hz. This simply doesn't happen.
The 'cymatics' demonstrations are great, even the professors I work for get excited about how these demonstrate standing waves in materials. Unfortunately for the 432 Hz people the wave patterns depend on the vibrating materials. I make music out of vibrating strings, resonating wood and digital beeps and boops instead of square plates of metal (nothing against square plates of metal, I'd use those too). So maybe they should start by making pretty pictures of sand on top of a guitar to have a point with the cymatics. Also, the tuner they keep showing for the notes in their video shows their frequencies sharp or flat. They should at least get their notes right. They're also using a modulated tone with harmonics which introduces all kinds of questions about whether they're trying to prove a point or just make cool patterns with the sand. But really, who cares if it sounds good, right? Seriously, if you like your music 'detuned' to 432, go for it.
I've got a theory that altering familiar music is a great way to get us in different moods. We like remixes, right? So a 432 Hz retune might be just the thing to mellow out to. Likewise, a 448 Hz retune might be just the kick in the ass I need in the morning to get going. So retune all you like.
I do have a technical quibble with the suggested method in Audacity, the resample will do bad things to the high end of the music, all those harmonics and partials and stuff (of course, some feel all that is lost in digital music anyway so YMMV). The Audacity wiki talks about better ways to do frequency shifts. I definitely wouldn't do this to anything that has been digitally compressed at any point, your mp3 folders and itunes collection will lose even more when you start pitch shifting them. Rip the original CDs and mess with the .wav files or get the FLAC files if you're serious about retuning your music collection.
The real way to test their idea would be to blind test a bunch of music you've never heard before, some that has been pitch shifted to a variety of frequencies including 432 Hz and some that is unaltered. Score the music and your emotions after each song and see if there is a pattern to the pitch shifting. Now do this to a bunch of people and see if there are patterns in cultures, age groups, musical preferences, etc.
I don't really understand what you're saying here. If you tune casually by ear, then of course when a digital keyboard comes in at 440 you will be off. Maybe higher, maybe lower. But you will be off. Unless you're saying 440 has some "special properties"...
But they DON'T revolt, because 432 Hz is no better or worse than 440, 450, 429, 490, or anything else in that range.
I occasionally like to pitch-shift my music by up to a minor third. It's not enough to introduce much distortion and it can make it, if not fresh, at least something you listen to again.
(Unfortunately, the intersection of music players that make that easy and music players I want to use seems to be empty.)
So it is normal for everyone to drift towards 440hz... to use 432hz in current era, it is necessary to purpusefully tune for it, including retuning digital instruments (keyboards, synths, etc...)
I have no idea why my speculations here* seem to be controversial (as judging by the votes), but have you considered that the preferred fundamental pitch actually varies with season, latitude, and time of year? That would explain why no one has settled on a specific pitch for all circumstances. It is ultimately controlled by the length of day. Perhaps time of day as well, if we split the day into sun up and sun down.
*https://news.ycombinator.com/item?id=12781437
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?
So, nope his claim doesn't make sense.
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."
I wonder if there is some easy way of figuring out the simplest base number-multiplier-divisor chains for getting certain numbers?
Or perhaps seconds are relevant in the way sound was broadcast.
> 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.
If the choice is between a custom crystal and two custom boards, the custom crystal is going to be the far less painful choice.
Having all the broadcast frequencies controlled by a single reference crystal would have some obvious advantages (and a few disadvantages too, of course).
http://www.network54.com/Forum/27140/message/1296951241/More....
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.
In the digital domain it's not an issue at all.
It is electronic gating to bring down a 1khz signal. Division and multiplication to a prime number is pretty hard...
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)
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...
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.
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.
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.
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.
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.
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.
Personally I prefer singing at A=415 since my voice is lower set. :)
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.
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.
> 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.
Nonsense spreads not just because of apathy.
We understand Star Wars is space wizards. New-agers do not understand that their beliefs are mostly bogus.
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).
If family members get a positive placebo effect from listening to "5 Hours High Quality BEST 432hz Meditation Healing Chakra" on YouTube...Who cares?
(Not something I worry about personally, parents long gone).
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?
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.
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.
[0] http://well.blogs.nytimes.com/2013/10/11/amber-teething-neck...
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.
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.
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.
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).
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.
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.
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!
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!
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.
https://en.wikipedia.org/wiki/Great_Highland_Bagpipe
(As a "bonus track" on the album, she included a realization of "Toccata and Fugue in D Minor." Especially appropriate for the season!)
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
However, if these tunings and notes vary so much, what does it mean when one claims that they have 'perfect pitch'? Is it an ability that uses the relative distance between notes? That is, given an A they can identify the C?
this is relative pitch
> what does it mean when one claims that they have 'perfect pitch'
someone starting before 6 years old (better chance of things sticking) and being sung "bah-bah-black sheep" with a piano at the correct pitch. So they manage to remember the starting pitch as well as the relative up/down of the melody.
Interestingly, more common in "tonal" language speakers, e.g. Mandarin, where the pitch can make a difference in the meaning of the same word. Apparently "ma" can mean mom, horse, lazy... depending on the pitch and its direction.
Perfect pitch is mostly a curse than a blessing as many notes in the world are off, e.g. a school bell, and hurt the person with the perfect pitch. I hear :)