Can_you_hear_the_difference.cwk

Can You Hear The Difference?

All our keyboard instruments are fixed-pitched, that is, there is no way to change the intonation to accommodate the ensemble. Yes, we can do some pitch bending, but only to lower the pitch, and only for a very limited time. Other than having your instrument retuned to a different standard, your instrument is tuned in equal temperament and probably around A=440. At least it was originally. But marimbas need tuning from time to time. Steel pans need tuning more often. Vibraphones and glockenspiels are considerably more stable, but just how well were they tuned at the factory?

There seems to be quite a controversy over what standard we should have out instruments tuned to. Many contend that the standard in the U.S. is A=440 Hz, and that in Europe the standards are higher, A=442 Hz or even more. But those standards are in a continual state of flux, and they seem to be established by some of the major orchestras. While the difference might seem minute, several of the instruments' timbal character can be significantly changed by tuning to a higher standard. All the instruments in the orchestra except for ours can be tuned to whatever note the oboist and the music director have agreed on. Just how close is everyone in the orchestra to that specific pitch? And of course, even if they are absolutely in tune with the A the oboist plays, how close are they going to be with everything else they play? Dumb question, so let's move on.

Let's start by comparing three different frequencies for A. The tones are simple sine waves.

The first is A=440 Hz

The second is A=441 Hz

The third is A=442 Hz

Yeah, by the time you've listened to and then download the next file, your ears have probably already forgotten how the previous file sounded. So the next file is each of the files in this succession: 440, 441, 442, and back to 440, each pitch lasting about 2 seconds. You might have to listen to it more than once to hear the changes, and if other sounds in the room are interfering with the sound, try using headphones.

440 Hz, 441 Hz, 442 Hz, 440 Hz

When these different frequencies are played simultaneously, you can hear the interference patterns, or "beats" that occur as the sine waves go in and out of phase with each other. The strong pulse occurs when the two waves are in sync and there is increased amplitude. The weak part of the pulse occurs when the two waves are 180 degrees out of phase with each other. In the following recordings, the strong pulse has a buzzing quality. The first file consists of 440 Hz and 441 Hz together. You should hear one beat per second. The second file is 440 Hz and 442 Hz together and you should hear two beats per second.

440 Hz and 441 Hz

440 Hz and 442 Hz

Here is another example of 440 Hz and 442 Hz. In this file, the two tones are mixed together and are then panned across the stereo field so that the buzz of the interference disappears. You should still be able to hear the beats, but without the distortion. At the end of the file, the tones are mixed again and you will hear the buzz.

440 Hz and 442 Hz pan

Harmonic Series vs. Equal Temperament

Fixed-pitch instruments use the equal temperament tuning system where the octave is divided into twelve equal semitones. Other than the octave, none of the other pitches in this particular chromatic scale are the same frequency as their natural harmonic series counterpart. That means that an equal tempered perfect fifth will be slightly flat compared to the "natural" fifth.

Here is a natural perfect fifth: 220 Hz and 330 Hz

Here is an equal tempered perfect fifth: 220 Hz and 329.628 Hz

Hardly noticeable if at all. It is easier to hear the difference if they are played in succession: two seconds each of the natural fifth, the EQ fifth, the natural, and finally the EQ.

Perfect fifths: nat, EQ, nat, EQ

That little blip in the middle of the file is where the sequence repeats.

The difference between a natural major third and an equal tempered major third is considerably more noticeable.

Here is a natural major third: 220 Hz and 275 Hz

Here is an equal tempered major third: 220 Hz and 277.183 Hz

You can hear the difference. But just to make it more graphic, this file plays the two different intervals in succession just like the previous file with fifths.

Major thirds: nat, EQ, nat, EQ

Where's the Rub?

Back to the argument about whether to have your instrument tuned to 440 Hz or something else. Since we have already explored the difference between three different frequencies for A, let's put them into context. Below are four different recordings of Chick Corea's Captain Marvel. Only one file has both the marimba and the vibes tuned to 440 Hz. Another has one instrument still at 440 Hz, while the other is tuned to 442 Hz. For the most part, it is difficult to tell that they are tuned to different standards. The most noticeable place is at 0:36 and following, where they have unison pitches. There are two files that have the two instruments even farther apart: one instrument at 440 Hz and the other at 443 Hz. This is probably more discernible but still not objectionable until the same time marker where the unison appears. I think you'll agree that it isn't anywhere near the rub as you get when playing along with steel pan, acoustic bass, or the piano in that studio that got tuned "sometime this year."

So here's a mix and match. See if you can tell which numbered file in the left column has the specific tuning scheme in the right column. While you"re at it, see if you can tell which instrument is tuned to 440 Hz.

File one	A. 440 Hz vs. 440 Hz
File two	B. 440 Hz vs. 442 Hz
File three	C. 440 Hz vs. 443 Hz
File four	D. 440 Hz vs. 443 Hz

I ordered my marimba tuned to 440. It seemed to be the thing to do at the time. Probably still does. But years later, after listening to countless examples such as the ones above, I ordered my vibes tuned to 442. Any particular reason? No, I just liked the way it sounded with most instruments, and I doubt most people can really tell the difference. If it bothers anybody, I turn on the motor.

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