Pitch Perception Skewed By Modern Tuning

The feed deliverers us news of research suggesting that the use of A as the universal tuning frequency has made our ears less discerning of the notes immediately around it. Here's the abstract from PNAS describing research with people possessing the rare quality of "absolute pitch."

Comments

Frist Psot?

[mcrbids]

It's interesting that pitches can be amalgamated by experience. Which is a basic part of human nature - the mind adapts to fit circumstances, and if the key of A is what we tune in to, why wouldn't our minds adapt to fit this reality?

It's all how it works. The article is weak on details, but this post is probably bigger. If every time you heard a sound like a jet engine, you got smacked upside the back of your head, wouldn't you get jumpy when you heard anything that sounded like a jet engine, even if it wasn't *exactly* the same?

Sometimes it's funny how Science has to prove the stuff that "Everybody Knows". (TM)

Re:Frist Psot?

[Incoherent07]

Adding to the shrug factor, the twelve-tone pitch system as a whole is a human invention. This makes perfect pitch that much stranger, because it means people have an innate ability to attune themselves to an artificial note naming scheme.

So since that scheme can vary somewhat, it would make sense that depending on "which" A your perfect pitch is tuned to, you may have trouble distinguishing G# or A# in a different tuning.

Re:Frist Psot?

[semiotec]

I am not sure whether you really understood much here.

First, the "article" is not "weak on details". It's the abstract, if you want details, read the full article (link on the right-hand side, "Full Text (PDF)".

Second, "absolute pitch" or "perfect pitch" is sort of a innate ability. You can either have it or you don't, as the article shows that pitch accuracy is best in younger people. But there's different levels of the ability. If I hear a relatively clean note, I can pretty much identify what the pitch to within a semitone. However, I have problem just singing/humming a specific note as correctly without help. but I know a few people that can sing any note accurately without help and they can tell you whether your instrument is out of tune simply by their innate ability, without having to check with another instrument or tuning fork or some other gadget.

I've heard stories that it is possible to train to have the "perfect pitch" temporarily. Someone I know sang in the Stravinsky Mass, and they practiced so much that for a few months he was able to sing a B note correctly without assistance. But this is not permanent, they lose this if they stop "training" for it.

Now, what the article is reporting is that, people with perfect pitch, are starting to have this ability blurred due to the way orchestras inaccurately tune to a wide range of A. I assume this means they would have had exposure to such "tuning sessions" at the beginning of concerts and so on.

So this sort of the reverse of what you have written. AP is not trained, not acquired from accumulated experience, but it can be degraded gradually if you keep blurring their idea of what A should be.

The interesting part is, as per the abstract, they systematically get notes around A wrong, and more frequently than other notes:

"given as a pure tone, G# is as perceived sharp far more than any other tone, whereas errors in D occur infrequently"
"Interestingly, pure A# is most often perceived as flat, not in keeping with the other pitches,"
"A statistical analysis shows that G# is uniquely error-prone."

Re:Frist Psot?

[hazem]

This makes perfect pitch that much stranger, because it means people have an innate ability to attune themselves to an artificial note naming scheme.

I don't believe perfect/absolute pitch is being born with the ability to simply hear a note and know that it's C#. Rather, you have to be trained at least once that a certain sound is Bb, but later, any time you hear it, you know it's Bb. And I doubt that they'd be limited to a 12-tone pitch system unless that was all you ever exposed them to.

I think the same thing can happen with color. Some people (tetrachromats, I think) have a very sensitive ability to discern and remember colors, such that they could see paint swab at the store and know if it matches the paint on the wall at home.

I know I don't have perfect pitch myself, but I play piano. Now suppose I sit down at the piano at the beginning of the day, having not listened to any music, I can almost always tell what the note I'm about to hit first will sound like. In fact, sometimes I'll play a game and try to hum the sound before playing the first note. Sometimes, though, I'm off by up to a whole step. Someone with perfect pitch would probably never make that mistake.

Re:Frist Psot?

[dreddnott]

The big villain in equal temperament is the sharp major thirds, perfect fifths and fourths are very close to the arbitrary ones, at 702 and 498 cents respectively. We're used to it enough to tolerate it but it's not the whole story of modern music.

We hear just-temperament tuning all the time. Consider that the overtones of resonant instruments are tuned perfectly (C-octave, G-fifth, C-fourth, E-major third, G-minor third, then that weird flat-seven Bb interval that still manages to be in tune, then C-major second) and you'll see that it really does get beaten into us all the time. Barbershop and even high school or college choirs end up with perfectly-tuned chords, often by accident, but it's natural. Really only modern keyboard instruments (organ, piano, glockenspiel, whatever) and electronic music (although some of the experimental stuff is just-toned) are based on equal temperament. Most other instruments are flexible enough (lipping, slides, fretless, half-holed, embouchure, whatever) to play tuned chords in whatever key.

Setting up a Yamaha electronic piano to play in one of the various unequal temperaments was quite an eye-opening experience for me, and it confirmed everything my music teacher had already been telling me. How good the pure chords sounded was almost as striking as how bad chords out of the key center sounded (Ab in Pure C, blech). I've become curious about studio pitch-correctors that seem to be so common in modern, over-produced 'music' - I know they are set up for analysing and correcting pitches to fit in certain keys, but are they equal- or just-tempered?

Re:Frist Psot?

[iangoldby]

The twelve tone pitch system may well be a human invention, but it is based very closely (but not exactly) on the natural harmonics of a string (or open pipe).

If you take a string whose fundamental frequency is 440 Hz (an A) then harmonics are produced at twice, three times, four times, etc. that frequency. The notes corresponding to these are:

A (fundamental)
A one octave above (first harmonic)
E one octave and a fifth above (second harmonic)
A two octaves above
C# two octaves and a third above
E two octaves and a fifth above
G two octaves and a seventh above - slightly flat
A three octaves above

Beyond that the notes you get approximate less closely to the even-tempered western scale.

The pitch ratios for the even-tempered scale are given by a power-relationship:

p'/p = 2^(n/12)

where n is the number of semitones above p.

So for example, the closest even-tempered note to the second harmonic of A 440, E which is 19 semitones above, would have a pitch of

p' = 2.9966 * 440 Hz

which is slightly flatter than the natural harmonic 3 * 440 Hz.

What is interesting (to me at least) is that this means that if you follow a cycle of fifths from a starting note using natural pitches rather than even-tempered pitches, you never exactly get back to the note you started on. (Apparently Pythagoras was one of the first to record this observation.)

This caused no end of problems for early musicians. Instruments used to be tuned with systems based on natural pitches. This meant that instruments with fixed tunings (that the musicians could not easily alter as they played) would sound more in-tune in some keys than in others.

J S Bach was one of those who worked on a solution to this, and he came up with the modern even-tempered scale, which averages out the intervals so that all keys are equally in-tune (or out-of-tune).

If you have a well-trained ear then you can hear the slight beating that indicates this slight out-of-tuneness when you strike an open fifth on an even-tempered instrument (such as a piano). String and wind players are of course able to make the slight adjustments to overcome this tuning compromise, and if you listen to a really good string quartet you can sometimes hear the difference.

Re:Frist Psot?

[cybereal]

I think you misunderstand what perfect pitch is. It's not the ability to associate a note name with a pitch. Though, that may be a side effect given proper practice. Perfect pitch is the ability to recognize a given tone/pitch without relationship to a previous tone. Most people don't know if they hear an A or an E without something before it that is identified.

More practically, most people could listen to a song's melody played in a specific key, then hear the same melody in another key the next day, and never know there was a difference. Those with perfect pitch would know there was a difference even if they weren't musicians and didn't know the letters assigned to those pitches. The fact that most of these people don't care plays into the perceived rarity of the ability. I, however, having perfect pitch, have made it a point to discover this quality in people I know. I find many people can do this and it's not as rare as often stated.

Re:Frist Psot?

[El Jynx]

not entirely. The doubling of pitch is the difference in an octave; the complementary pitches in the octave (in other words, the sounds that sound happy, so no minors or sharps) are directly related (e.g. half of the doubling, 1/4, etc).

And on the side, I think anybody who has a mom with a voice as loud as my mom's learns absolute pitch as a natural defense mechanism.

Re:Frist Psot?

[Stooshie]

Good post (don't have mod points just now).

Natural/Just temperements have some interesting side effects. Bach (and some other composers) always claimed that if you played the same piece in a higher or lower key (even a semi-tone) that the whole mood changed. This would make sense as the beats between A and C# (key of A) and the beats between C and E (key of C) would be different in Natural Temperement.

Re:Frist Psot?

[plams]

No, no, no! Twelve-tone pitch is derrived from perfect intervals, such as perfect thirds, fourths and fifths. These can be defined very cleanly as the integer ratio between two frequencies (look up just intonation). The ratios are mathematically beautiful and simple, and also sound particularly good. The temperated (12 note) scale used by nearly all instruments today is an attempt to fit these intervals into a common scale. You may say that this approximation is a human invention (even though it's cleanly defined as freq = 440hz * 2^(n / 12), where n is the semi-note distance from A4), but as a whole? No.

In other words, it proabbly wouldn't make any sense to use a 16 note scale or something like that. The 12 note scale has roots in something very mathematical, not something random or "human".

Re:Frist Psot?

[Anonymous Coward]

The most common studio (and live, these days, they're rack mountable) pitch corrector is the Antares Auto-Tune...it can be tuned to a wide variety of scales (all your regular scales, plus a few chromatic variants) but as far as I know all the Automatic mode ones are equal tempered. However, it can be set up with manual pitch correction, and so it is possible for a skilled producer with an unskilled vocalist to produce vaguely authentic music in unusual keys.

Re:Frist Psot?

[Jay L]

I've used Antares AutoTune and Celemony Melodyne, two of the popular pitch-correctors, and both default to equal-tempered. I never looked to see if they'd support alternate tunings, since it wasn't relevant to the music I was working on.

Re:Frist Psot?

[bidule]

Exactly! Try with any K note scale and see how well 3:2, 4:3 and 5:4 fit in that scale. My father has been rambling about this for more than 30 years, at least twice a year. I have this thing etched in my brain so deep that I'll prolly remember this after my death.

So try it:
- 3 * 2^(a/K) ~= 2 * 2^(b/K)
- 4 * 2^(c/K) ~= 3 * 2^(d/K)
- 5 * 2^(e/K) ~= 4 * 2^(f/K)

And you won't find any other K with less error.
- 3:2 -> 19 vs 12 = 1.498 -> 0.113%
- 4:3 -> 24 vs 19 = 1.335 -> 0.113%
- 5:4 -> 28 vs 24 = 1.260 -> 0.794%

Re:Frist Psot?

[Brad Eleven]

What about the touchstones for B flat found in nature?

From http://www.npr.org/templates/story/story.php?story Id=7442915

• B Flats and Alligators: Alligators respond by bellowing, alone/in groups to a Bb tone.
  
• B Flat and Glenway Fripp the Piano Tuner: Fripp hums Bb on a stairway landing and the tone persists
  
• B Flat and Black Holes: Waves passing through gas near the black hole resonate at Bb, 57 octaves below middle C.
  

Mental reference pitches

[ihuntrocks]

I have pretty good pitch (not sure if you'd qualify it as "perfect"). Tuning to A (440 Hz) didn't really distort this ability though while I've been a musician. I do have a set of "reference pitches" that I can internalize and I can determine pitches relative to them. A440 is one of those pitches, but not the first one I use for reference, even though it is the "universal" tuning note. Could have something to do with it not being one of the notes I tuned my instrument to,and that I had a transposing instrument relative to concert pitches though.

Re:Mental reference pitches

[u38cg]

Most people with a bit of training can produce and recognise various reference pitches - it's often made easier in that most instruments' tone varies with pitch, so people can learn to recognise the in-tune tone of their instrument. If you have that ability, naming other pitches by recognising the interval is not that far behind.

What is rare is true perfect pitch, and if you have real perfect pitch you will have no problem distinguishing a G# from an A. Not only that, you would most likely be able to nail it down to a few cents.

Re:Mental reference pitches

[ihuntrocks]

I don't have a problem differentiating chromatic pitches either. It's just a half step interval after all. Tuning I'm fairly good on by ear, though I tend to be a few cents flat by ear, but nothing bad. I find this to be true on all of the instruments I play also, as well as when I try to sing pitches (I may have a terrible singing voice, but I can sing the correct pitches).

Re:Mental reference pitches

[arth1]

A440 is important because an orchestra is supposed to follow the first violin, and the main string on a violin is the A string, tuned at 440. The fine tuning cacophony you hear before a concert starts quite often has a plain A repeated at intervals throughout it -- this being the first violin letting others know what to tune against, if it isn't a standard 440. Sometimes it isn't, due to other instruments that might be hard to tune, like a concert piano (which can be 440, 442 or 452 Hz depending on where you are) or an old pipe organ (in which case all bets are off). Luckily, a violin is relatively easy to tune, and it's (in theory) the job of the first violinist to ensure he has a working A, which others then can tune their instruments to.

Regards,
--
*Art

Re:Mental reference pitches

[The -e**(i*pi)]

The oboe is the instrument that stays in tune the best, and is the one a Symphony Orchestra tunes too. Most, if not all professional orchestras are Symphony's. So most professionals tune to the Oboe, not the first violin. Tuning starts where all the woodwinds and brass tune, then the oboe plays another A and the strings tune, and the percussion tune somewhere . Of course the woodwinds have to keep using their instruments or they will get cold and be out of tune so they keep playing until the start, while strings only need to warm up their fingers.

Re:Did anyone

[Adambomb]

Yes, but it was delivered orally in the key of A, so the discrepancy was not noticed.

Summary is misleading

[piojo]

The article summary leaves out the important part. The summary:

the use of A as the universal tuning frequency has made our ears less discerning of the notes immediately around it. It's not the use of A that distorts perfect pitch, it's the use of "alternate A's". A is accepted to be 440Hz. Some orchestras use other pitches, sometimes for a more Baroque feel--the pitch of the accepted A has changed over time (don't ask me how we know that), and on some instruments, it may sound more authentic to use the pitch a piece was originally composed for. So when people use different pitches for A (specifically, when the orchestra tunes), it messes up the perfect pitch that some people have just a little bit.

Re:Summary is misleading

[GomezAdams]

It's not the use of different A's that make it authentic but rather the use of alternate scales. The modern tempered scale allows us to play music in any key. Older scales having different relationships among the 4ths, 5ths, 3rds, 6ths, minor 3rds, etc within the octave, was what many composers used to make the music have certain charateristics they wanted to bring out in the music. Mozart's "Requiem in D Minor" is a much different creature using the scales of Mozart's time vs the modern tempered scales. J.S. Bach popularized the modern scale with his "Well tempered Clavier" series - teaching pieces in all the scales to train pianist to play in any key. Before this time all instruments were scaled to meet the existing standard meaning differnt length of tubing on brass instruments than modern horns.

Re:Summary is misleading

[Discoflamingo13]

I would like to think I'm not alone in wanting to have something to show for nine years of getting beaten up for keeping my books in my band locker ;-)

A435 is old standard

[GomezAdams]

About 1939 A440 was adapted instead of the "French" A435 standard. In recent history some orchestras went to A445 but they are the exception. Modern piano scales are designed for A440. The length, diameter, and tension of the strings are all taken into the scale calculations. To raise pitch on a piano 5 CPS(Hz) is quite an undertaking and can add several hundreds of pounds of tension to the back (wooden part) and plate (big harp looking thingee made of cast iron and usually painted brass color) of a piano, A standard piano can have 11 tons, or more for grands, up to 20 tons of combined tension on the frame. The whole of the piano is designed to handle a certain amount of tension and can be stressed if too much tension is added. Same as letting a piano fall way below in pitch (pitch = tension) and bringing it up to pitch in one sitting. It must be done carefully & quickly to be effective. It isn't pretty to see a piano with the plate bolts sheared off and the plate bowing out from the rim. I'm a former piano technicain with 25+ years of piano tuning and rebuilding behind me so I've yanked strings on more than a few pianos, raising pitch and doing battle with aged instrments not kept in repair. Also have done complete restringing and rebuilding of all sorts of pianos.

Re:A435 is old standard

[alyosha1]

A guitar has several tons of tension on its neck No it doesn't. Each string has a few kilograms of tension, depending of course on string thickness and mass per unit length. Total tension can typically be in the range of around 50 kg.

Re:A435 is old standard

[dreddnott]

Piano strings are certainly not very slack, and a guitar cannot EVER have several tons of tension on its neck (or at the bridge, or anywhere). Assuming the guitar was made of cast iron instead of wood (which is typically solid, and steel-bar-reinforced at best) and did not instantly collapse from the tension, you wouldn't even be able to pluck the strings. Assuming you were Superman and could actually pluck a string, the pitch would be hypersonic and inaudible to all (except your Super-hearing I suppose).

Classical guitars have an average of about 25 pounds of tension per string. Of course it's slightly more for steel-stringed abominations (hence the neck reinforcement).

Re:A435 is old standard

[demi]

I have an enormous desire to see a comic book cover of Superman giving a concert with his superguitar and taunting us all with how we can't hear his beautiful music, like the dick he is.

Re:A435 is old standard

[leenks]

It depends. It could be completely screwed if it hasn't had a humidifier fitted, or is one of the earlier Kawai imports that suffered from not having suitably dried wood.

That said, if it hasn't suffered too badly, then it's tuning will have dropped quite a bit (even though it is in tune with itself) and you will need a course of 2-4 tunings at say 4 month intervals to bring it back up. I usually pay between 35 and 50 GBP per tuning, but no idea what the US rates are (probably 70-100 US assuming $2 to the pound).

Oboe

[nyet]

The oboe, not the worthless violinist. Violins a dime a dozen. You only get two oboists (generally).

not related to technology at all

[mateomiguel]

There is no mention of modern tuning methods in the first article. The article simply says that different orchestras use different frequencies roughly around the same pitch for A. This is not a new thing.

You would expect modern tuning methods to make the official definition of A more exact, thus eliminating the problem spoken about in the article. That's what I thought, and I'm a musician. In fact the standard A4 frequency has been defined as 440 Hz. That means that if you hear the London Philharmonic Orchestra they should be tuned to A4=440 Hz, and the Timbuktu Traditional Blowpipe Ensemble should also be tuned to A4=440Hz, because its easy to carry around a pocket piece of electronics to make a perfect 440 Hz sound.

BUT

This article does not say that. In fact it says that different orchestras all over the world still are not in sync, which has been the case for ALL OF RECORDED HISTORY. The article says that because of this phenomenon, even those who can hear absolute pitch are confused as to what name they should give the frequencies immediately around 440Hz because of the variations. This is not new, or news, or related to technology in any way. Its just a fact of life.

Re:not related to technology at all

[uglyduckling]

Thank-you, well said. I've heard a few musicians say that 'perfect' pitch is actually a curse - due to equal temperament and the fact that concert pitch is a variable concept, those with that gift are likely to hear most of the music they listen to as out of tune.

Some studios change the speed of recordings without correcting pitch because it sounds better (apparently) - I'm a musician (rock, not classical) and I often have to retune my guitar to play along with recordings even though I have a decent electronic tuner set to A4=440. I've often wondered (maybe because I don't have that gift) who gets to say what 'perfect pitch' is: is it just people who happen to have an inbuilt sense of A4=440; should be people with an inbuilt sense of A4=415 be called 'perfect dystonics' or something ?!

Far more useful is a very good relative pitch - being able to instantly recognise all the intervals and sing/play harmonies without thinking about it will make a far better musician than someone who happens to be able to tune their instrument to concert pitch without a reference note.

No, perfect pitch is a natural talent

[TheMCP]

Thereminists discuss perfect pitch frequently, because a number of noted Thereminists have had it, and it's (falsely) rumored that perfect absolute pitch is required to play the instrument. (Actually, you just need very good relative pitch.)

People who have perfect absolute pitch tend to have always had it: it's a natural talent, or curse as the case may be. They find it painful to listen to tones that are "off key" - indeed, the family of the great Clara Rockmore tells us that she even hated touch tone telephones because the tones were not on-key notes and she didn't want to hear them.

While it is possible to train someone who has a pretty good sense of absolute pitch in the first place to refine it to become extremely good, they'll never reach that level of perfect absolute pitch which some have, in which they can't stand to even hear off key pitches. And someone who has a poor sense of absolute pitch may easily be able to develop their sense of relative pitch, but is unlikely to ever reach the level of being extremely good at it.

equal temperament also affects people...

[rivaldufus]

especially string players (with no frets.) It's very difficult, if not impossible, for them to play continually in equal temperament (unless playing with an equal temperament instrument such as piano.) The usual definition of Equal temperament is that octave is (usually) divided into 12 evenly spaced pitches. Modern day keyboard instruments are all tuned like this. It's fairly effective compromise, as all the keys (C Major, F minor, Eb minor, etc.) all sound the same. Unfortunately, a fifth or even a third for a given key is slightly out of tune (the half step and the octave are the only perfectly in tune intervals on a modern day piano.) In the other systems, there may be a perfectly tuned fifth and third for a given key, but other keys may sound horribly out of tune. Certainly, equal temperament is a more practical solution than constantly retuning a piano to a different pitch each time you drastically change keys.

Unrelated - My wife has perfect pitch - and I sometime "detune" my clavinova to D mean tone or some other system and play something in Eb minor. I certainly notice the difference, but it drives her crazy. She also has great difficulty when required to tune her violin for Baroque music (A 415.)

Tetrachromats (OT)

[jhdevos]

I think the same thing can happen with color. Some people (tetrachromats, I think) have a very sensitive ability to discern and remember colors, such that they could see paint swab at the store and know if it matches the paint on the wall at home.

This is completely off-topic, but tetrachromacy is something else: it is when the eye has not three but four different types of color-discerning cells. That means the number of 'dimensions' in the visible color-space goes up by one -- the result is that tetrachromats can see some color-pairs as being completely different, while we normal people see them as completely the same.

See wikipedia: http://en.wikipedia.org/wiki/Tetrachromacy

Jan

Re:Tetrachromats (OT)

[TeknoHog]

That means the number of 'dimensions' in the visible color-space goes up by one -- the result is that tetrachromats can see some color-pairs as being completely different, while we normal people see them as completely the same.

I think the grandparent makes a sensible point about tetrachromats having an enhanced sensory response to different colors, which probably translates to better cognitive abilities related to color.

In terms of spectroscopy, normal human vision divides the whole spectrum of visible light into three bands, while tetrachromats have four bands. So I wouldn't call it an extra dimension (though it's true in a way), but rather simply increased resolution. Compare this to spectrometers, which usually have hundreds of bands.

From what I've read, tetrachromats have the extra band in addition to the usual three of RGB, so the four are not equally spaced. IIRC, the fourth is usually very close to R or G, so the extra sensitivity is not spread throughout the spectrum.

It wasn't J.S. Bach

[jenik]

Modern equal tempering was not even developed until about 70 years after J.S. Bach's death. In his Well-tempered Clavier he made use of 'well tempering', which was an older technology. He didn't develop that one either though. http://www.jimloy.com/physics/scale.htm http://en.wikipedia.org/wiki/Well_temperament

Re:Is it not more the case of losing perfect pitch

[Stooshie]

... we may all be born with perfect pitch but the vast majority of us soon lose this ...

I think the point the GP is making is that no-one can be born with it as the 12-tone system is a man-made invention. Very experienced musicians are aware of what A is because over time they have learned what A is through the constant use when tuning instruments.

something to try

[v1]

You can demonstrate perfect pitch to a bystander that's butchering something if you can whistle a good solid tone and so can they.

Not sure if it's uncommon or not, but I can match another person's whistle to the cycle, and it has an interesting effect. Ask them to whistle a good pure solid tone and not waver or drift. Be sure to tell them to NOT STOP whistling, even if they feel they're not whistling anymore.

If you can lock onto their whistle quickly, (before you run outa breath!) you can beat them cycle for cycle, and it has the effect of zeroing out the tone. When you are near perfect, the sound where the whistle originates will change. Instead of hearing it from yourself and your friend, it will appear to be coming from somewhere between where the two of you stand. (be sure you're a good 5 ft apart) This is very unsettling because for a time during the duration you can't hear yourself or the other person whistling and it tends to influence one or both of you "move" a little bit up or down just so you can hear yourself again.

People standing off to the side will get the weirdest look on their face as they can hear the whistle slowly drifting back and forth between the two of you, as your pitch is 1/8 cycle or so off from each other, causing it to nearly zero beat. You can of course perfectly match them but that's no fun as the perceived origin of the sound does not drift between the two of you, it merely stops somewhere in between.

Re:Er.... still artificial.

[iangoldby]

I'm not sure what your point is, but I don't think we're really in major disagreement. Of course A 440 Hz is an arbitrary standard. Come to that, 440 Hz as a number is dependent on an arbitrary definition of the length of a second, the use of the base ten number system, etc.

What isn't arbitrary is the relative pitches of notes in the Western scale - that is the ratio between pitches - which as I was trying to explain above, is related to real physics and is not at all arbitrary.

Re:Octave?

[Mode_Locrian]

There are plenty of alternative tuning systems, though I don't know if a "metric" tuning has been done (though I wouldn't be surprised at all if someone had already tried it). Just as an example, Javanese Gamelan music uses two different tuning systems, both of which (iirc) divide the octave unevenly between five pitches. In any event, I think that our current tuning system is really quite a reasonable one. Ignoring the fact that A is the note commonly tuned (this, I think, is more of a historical accident based on the fact that this is an open string on a violin) the frequencies of the "home note", C, are actually all powers of 2. Middle C is 512Hz, an octave above it is 1024Hz, an octave below it is 256Hz etc. That strikes me as being a lot neater than a "metric" system anyway. Oh, and I think that the reason it's called an octave has to do with the fact that the eighth note of the traditional Western scale is the repeated one. E.g. C D E F G A B C

Harder time discerning notes around A?

[soulexposed]

This may just be me, but if you use A to tune all the time wouldn't you become more accustomed to its pitch and therefore notice more often if it was sharp or flat?

Also, as someone who has been told they have perfect pitch (I haven't done any official tests so I'm not 100% sure), when I'm listening to music that may not be precisely on-key it doesn't bother me or sound "wrong", it just sounds different. That is, as long as the instruments are all tuned together; if it's just one instrument that's out of key from the rest of them, it does bother me. :P

Re:Is it not more the case of losing perfect pitch

[locofungus]

12-tone system is a man-made invention

Not really.

The (perfect) octave, fourth and fifth are natural harmonics. So natural, infact, that if you silently hold down a G and then strike the C an octave and a half below the G will start to audibly resonate (even though on the piano the G is slightly out of tune compared to the C)

Twelve consecutive fifths (and I'm using consecutive here to mean going up a fifth, then another fifth etc rather than it's musical meaning) will (almost) bring you back to the original note but 7 octaves higher.
Twelve consecutive fourths will (almost) bring you back to the original note but 5 octaves higher.

Other intervals also have rational ratios.

Major third = 5/4

And if you look at the harmonics of the fundamental:

1 - Fundamental
2 - Octave
3 - Fifth (3/2)
4 - Octave
5 - Major third (5/4)

And as an aside, the clarinet only has odd harmonics, therefore the upper register is an octave and a fifth above for the same fingering.

A bell has a resonance a minor third (6/5) below the fundamental.

(The minor third is the interval between the major third and the dominant: 3/2 / 5/4 = 6/5)

Tim.

Re:Is it not more the case of losing perfect pitch

[Mr. Slippery]

The (perfect) octave, fourth and fifth are natural harmonics.

Except that the perfect fourth and fifth are not what are used in the modern well-tempered 12 note scale.

Our scale is based on the twelth root of two. (Thus the octave, a factor of two, is broken up into twelve steps.) It's a convenience to let us have instruments that can play in many different keys without needing to be re-tuned.

Re:Physics of Music

[agg-1]

I'm surprised that there are so many knowlegable folks on slash here that can discuss music and the physics of music

Me too. :) Myself I'm a mathematician who happens to lead a computer music department, so I guess I'm supposed to know this stuff.

One thing that I'm lacking is a good reference on the theory. For example, I know that "no sharps of flats" is the key of C-major/A-minor. Why? Is it by definition?

Basically, yes. But the details are surprisingly complicated. I've also noticed time and again that many musicians know zilch about this, as it involves a good deal of mathematics and physics and many musicians abhor these subjects. If you're looking for online materials, it might be worth to take a look at the Just Intonation Network which has a wealth of information on different kinds of tunings and the rationale behind them, as well as links to the literature. And then there's the Tuning & temperament bibliography. Last but not least, if you want to get really serious about learning the mathematics behind music, I'd recommend Mazzola's tome Topos of Music.

just just

[dickens]

There is arguably no one alive today in the west that is culturally conditioned to prefer just intonation. Just intonations is "just", meaning it's mathematically correct - intervals are the ratios of small integers. Other intonations are not. I'm sure peoples' ears can be conditioned to expect anything.

I'm a barbershop singer, and we have to deal with oddities such as having to sing an ascending third sharper than we think it should be when the melody is moving up by that interval, yet when singing the third as part of a harmony, it will have to be flatter to be in tune.

If you want to hear a correct third, just get 50 guys in a room and have them all sing the same vowel, in the intervals root/fifth/root. The third will just jump out and wail away without anyone singing it.

Re:Is it not more the case of losing perfect pitch

[Incoherent07]

Since about six people have all responded to this in the same way, I'll point out that while there is a mathematical basis for a twelve tone system, there's nothing intrinsic about the idea of only twelve tones. If you extend the idea of harmonics beyond the 12 tones most people stop at, you end up with different numbers of tones, like 19 or 31. See also: microtonal music, which a music composition friend of mine in college was really into.

Our Ears?

[DynaSoar]

I don't see anything in TwholeFA that says anything about "modern" tuning as opposed to non-modern. The choice of A is arbitrary. Until this is replicated using different notes as the target, they've got too much confluence of musical memory and their theoretical genetics to do more than use the conclusions as the basis for more work. (And what good grant-using researcher doesn't; a PNAS publication makes that very easy for them).

The use of "none were musically naive" is a poor operational definition because it's too vague. Better to use "professionally trained performers with X years performance experience". Those with a lot of listening exposure and only enough performance experience (even if just by themselves) makes it likely that those with true AP and those with relative pitch (RP; being able to tell a pitch compared to another) are mixed together. The latter can have an extensive musical memory and be able to compare a presented tone with a song in memory that they know is in a certain key. They may well have done so, because they included at least one subject with skewed scores that were very consistent in their skewing (always one sharp off) as an AP subject.

The memory problem will probably also come out if they replicate this (as they suggest) with people from other cultures. Those who come from cultures with tonal based languages are going to have a very good tonal memory and discrimination from any given starting note and so good RP.

I'm highly suspect of a 44% sample of AP. I used the more rigorous definition of musical experience in brain imaging experiments and had about 15% true AP among them. Many of those claiming AP had good RP, and their EEG showed more memory than auditory activation, just as those claiming and having only RP. I'm also suspect of getting the same results from sinusoidal tones vs. piano tones. The latter has multiple overtones, providing multiple cues for the pitch. I used only sinusoidal for that reason.

Having the tones presented via web transmission gives no control over the actual output. Despite having as little as 0.01% total harmonic distortion in the amplifiers, output devices such as speakers and headphone or ear buds have around 1% to 3% THD, all of the different kinds having different harmonic distortion profiles.

Their description of aging causing "sharping" due to hair cell stiffening with age is very good. But the possibility remains that the documented time distortion due to perceptual slowing with age can be involved. That needs prying apart with other perceptual testing for time distortion per subject. A longitudinal study with the same "true" AP subjects decades later would be wonderful for the aging/sharpening problem, but figure the odds.

All that aside, good AP and RP probably have the same genetic source for auditory perception (minus auditory memory). I think they're on to something.

Frequency shifting

[compwizrd]

My hearing aids frequency shift everything down to around 1000hz, the range I can actually somewhat hear in.

The brain gradually learns what high pitch and low pitch is. With hearing aids, I can hear the 8khz band being tweaked on an equalizer, whereas without the hearing aids I can't tell the difference when the 1khz or higher is adjusted.

With a cochlear implant, with time the brain learns to adjust and distinguish frequencies, but never has the same degree of sensitivity.

Re:Blame.

[UnknownSoldier]

Yeah, the bastards should of used the 256 Hz Scientific Scale

Re:Blame.

[DupleMeter]

Many practitioners of early music tune to an A415 (hence the term 'Baroque Standard' for such a thing). Antonio Stradivari, builder of the famed Stradivarius violins, was known to tune to A415 (actually A414.97 was what his reference fork measured when found). Most owners/players of Stradivarius violins tune to an A415 and claim it is like having a completely different instrument, in term sof how the violin responds at the tuning it was designed for.

You'll also find that many guitarists (acoustic guitarists particularly, but others too) tune to A415 (or 'a half step down' as you'll hear it referred to). It tends to open up the instrument and also seems to 'sit' better key wise (at least IMO).

The A440 is a new standard, only nearing 70 years now. When decided upon very little was taken into account, though the story goes that the string section was pleased at being noticeably louder at A440 than at lower 'A's. A415 has a much longer history and several heavy hitters backing it up (the entire Bach family, Vivaldi, Mozart, Scarlatti, et al).

Amusingly, some from the Romantic period were fond of tuning up for a more 'intense' timbre...sometimes as high an A462 (which comes out to be about a half step higher than A440)!

Back on topic...I think the inexcusable lack of music education is the reason people have trouble with pitch recognition, not an arbitrary reference for musicians. For example, if you went through life never being trained to discern colors you'd be a visual moron - painting (as it were) is very broad strokes ('it's reddish') rather than having the subtlety to see real differences in similar colors (bright red, brick red, maroon). It's even worse for music, since we are not necessarily penalized for not being astute listeners (in the sense of pitch and timbre). I mean, how many times has someone said "is that a major or minor chord?" to you, or what you thought of a chord grouping in an arrangement? Now when was the last time someone asked your visual opinion? Sadly this is even true for musicians...being trained from a young age to hone sight and speech, but not listening. Hell, I know "musicians" who cannot solfege a simple major scale (you know - do re mi fa sol la ti do) & hit all the notes. Just starting from a note and moving up in a major scale pattern relative to the starting note. And man, relative pitch is so much more important than perfect pitch.

Re:Is it not more the case of losing perfect pitch

[onion_joe]

And as an aside, the clarinet only has odd harmonics, therefore the upper register is an octave and a fifth above for the same fingering.

tell me about it. For anyone learning woodwinds out there, I highly recommend learning the clarinet first. Master it and every other woodwind is a transposition and/or embouchure adjustment only.

After learning the clarinet, the saxophone or (for you Jethro Tull fans out there) flute is a cakewalk.

Not to mention you can play some bitchin' klezmer!