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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."
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.
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.)
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).
I may make you feel, but I can't make you think.
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.
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
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
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.
America, Home of the Brave.
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.
I read the script, and I think it would help my character's motivation if he was on fire. -Bender
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.
America, Home of the Brave.
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%
ID: the nose did not occur naturally, how would we wear glasses otherwise? (apologies to Voltaire)
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.
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.
Tom Swiss | the infamous tms | my blog
You cannot wash away blood with blood
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).