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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."
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.
Too lazy to create a sig...
The oboe, not the worthless violinist. Violins a dime a dozen. You only get two oboists (generally).
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.
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."
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.
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.)
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?
I may make you feel, but I can't make you think.
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.
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.
God said, "div D = rho, div B = 0, curl E = -@B/@t, curl H = J + @D/@t," and there was light.