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Pitch Perception Skewed By Modern Tuning
Posted by
kdawson
on Tue Sep 04, 2007 01:30 AM
from the pretty-good-pitch dept.
from the pretty-good-pitch dept.
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."
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Frist Psot? (Score:3, Insightful)
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? (Score:5, Insightful)
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.
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Re:Frist Psot? (Score:5, Interesting)
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.
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Re:Is it not more the case of losing perfect pitch (Score:3, Informative)
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.
Re:Is it not more the case of losing perfect pitch (Score:5, Informative)
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.
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Re:Is it not more the case of losing perfect pitch (Score:4, Interesting)
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Re: (Score:3, Interesting)
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 hun
Re:Frist Psot? (Score:5, Informative)
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.
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It wasn't J.S. Bach (Score:4, Informative)
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Re: (Score:3, Interesting)
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:Frist Psot? (Score:5, Informative)
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.
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Re:Frist Psot? (Score:5, Insightful)
No, no, no! Twelve-tone pitch is derrived from perfect intervals, such as perfect thirds [wikipedia.org], fourths [wikipedia.org] and fifths [wikipedia.org]. These can be defined very cleanly as the integer ratio between two frequencies (look up just intonation [wikipedia.org]). 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".
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Re: (Score:3, Informative)
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
Re:Frist Psot? (Score:5, Interesting)
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."
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No, perfect pitch is a natural talent (Score:3, Interesting)
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 tele
Re: (Score:2)
Equal tempered scales aren't perfect. If you look at early keyboard instruments, some had distinct E-flat (slashdot won't let me use unicode symbols - slashdot janitors, please note that most of the world doesn't use straight ASCII any more) and D-sharp keys (again, lack of unicode prevents me from writing this properly). On fretless stringed instruments, you don't play the "exa
Re:Frist Psot? (Score:5, Informative)
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?
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Re: (Score:3, Informative)
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.
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just just (Score:3, Interesting)
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
Mental reference pitches (Score:2, Interesting)
Re: (Score:3, Interesting)
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 na
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Re:Mental reference pitches (Score:5, Interesting)
Regards,
--
*Art
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Oboe (Score:5, Informative)
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Re:Mental reference pitches (Score:5, Informative)
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Summary is misleading (Score:4, Interesting)
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Apparently tuning forks are very accurate and do not degrade more than a few cents over hundreds of years. Typically every major hall would have its own tuning fork, owned by the master conductor or organist. Occasionally, in some traditions, the choir would have a much lower lower "A" pitch (400-415Hz was typical, even less was possible) than the orchestral or
not related to technology at all (Score:5, Informative)
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 [uk-piano.org]. 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 (Score:5, Interesting)
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.
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equal temperament also affects people... (Score:5, Informative)
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.)
Our Ears? (Score:3, Insightful)
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 (Score:3, Interesting)
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:Did anyone (Score:4, Funny)
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A435 is old standard (Score:5, Interesting)
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PS (Score:2)
Re:A435 is old standard (Score:4, Interesting)
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Re:A435 is old standard (Score:5, Informative)
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).
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Re:A435 is old standard (Score:5, Funny)
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 [superdickery.com].
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Re: (Score:3, Informative)
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 po
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something to try (Score:5, Interesting)
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.
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I know one... (Score:2)
I, on the other hand, have excellent relative pitch (I can tell you if a sequential interval is out of tune by 10 cents, wide or narrow) but only a weak sense