Pitch Perception Skewed By Modern Tuning 253
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."
Oboe (Score:5, Informative)
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:Mental reference pitches (Score:5, Informative)
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.)
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).
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?
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.
Tetrachromats (OT) (Score:2, Informative)
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 [wikipedia.org]
Jan
It wasn't J.S. Bach (Score:4, Informative)
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: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.
Re:Frist Psot? (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.
Re:Frist Psot? (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 = 1.260 -> 0.794%
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.
Re:Is it not more the case of losing perfect pitch (Score:2, Informative)
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:A435 is old standard (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 pound).