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Topic: BEATS (tuning), where do they come from? |
J D Sauser
From:
Wellington, Florida
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Posted 20 Sep 2003 1:23 am |
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Since Carl has brought the subject back up (it's your fault, Carl  ) and in order to try to keep his thread "clean" and free of any "beats"  , I'd like to go back a little and open a new can of worms here and talk about what provokes these beats and/or where they (may) come from (maths or physics or what ever).
Just like Carl's thread, this thread has not been started with the intention to provide some of you with space to start your little thing about how you tune and why your approach is better than every body elses, but well, I'm told this is still a free country...
I would just like to find out if some of us have a clear idea what makes an ET tuned interval "beat" or "wobble", sound unbearable or what ever you want to call it and why or what makes JT sound "clean", "sweet" or "beat-free".
To make it easier I would suggest we'd start out only taking apart one particular interval:
A major third interval using the notes A and C#:
In ET this would be; A (440Hz) and it's major third interval C# (ET 554.3652619537Hz), as calculated using a logarhithm, producing harmony with "beats".
In JT; A (440Hz) and it's major third interval C# (550Hz), as calculated using a system of fractions resulting in a flattened (tweaked?) major third which in turn creates harmony that sounds "clean" with no "beats".
Thank you. ... J-D.
[This message was edited by J D Sauser on 20 September 2003 at 02:35 AM.] |
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Donny Hinson
From:
Glen Burnie, Md. U.S.A.
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Posted 20 Sep 2003 4:35 am
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It's quite simple, actually. Whenever you combine two different frequencies, what you wind up with is four frequencies. You, of course, still have the two original frequencies. You also wind up with two new frequencies. One is the sum of the original frequencies, and the other is the difference of those two frequencies.
Foe example, when you combine (beat) a 500hz wave and a 600hz wave, you get a complex wave that consists of 500hz, 600hz, 1100hz (the sum of the original waves) and 100hz (the difference between the two original waves). So, "beating" 500 against 600 equals 100, 500, 600, and 1100.
Now, if you "beat" two frequencies that are close together (say 498hz and 500hz), one of the waves produced would be 2hz. While you couldn't hear the individual vibrations that comprise either the 498hz or the 500hz sound wave, you can easily hear the individual vibrations that comprise the 2hz sound wave.
So, you say, what good is this? Well, for one thing, it gives us a means of easily discerning the difference between two very close frequencies. Let's take the preceding example of 498 plus 500. That gives us a "beat" frequency of two. Now let's take 497 and 500. That gives us a "beat" frequency of 3. So, combining 498 plus 500 would gives us a "beat" of 2 two times a second, and combining 497 and 500 would give us a "beat" of 3 times a second. This difference is significant! Even though we've changed the frequency of one of the original waves by only 1hz (497 vs. 498, or .2%), the "beat frequency" has been changed by 50% (2 vs. 3)! While our ears have trouble detecting the difference between 497 and 498, they have no problem detecting the difference between 2 and 3. (Note: The same thing happens when you combine electrical waves, too!)
[This message was edited by Donny Hinson on 20 September 2003 at 06:30 AM.] |
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Joey Ace
From:
Hamilton, Ontario, Canada
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Posted 20 Sep 2003 5:17 am
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It's a physical thing.
Two tones at almost the same frequency have a reoccuring point where their sum adds and creates a stronger signal that we hear as a beat.
In this o'scope example the top and bottom are two tuning forks at near, but not quite, the same frequency.
The middle trace is the two signals added.
The beats can be clearly seen.
For more info, and to see the lab experiment procedure that this is taken from click here. [This message was edited by Joey Ace on 20 September 2003 at 06:19 AM.] |
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Donny Hinson
From:
Glen Burnie, Md. U.S.A.
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Posted 20 Sep 2003 5:23 am
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Excellent example, Joey! You can actually see the "warbling" effect JD mentions. Where the "beat" is 2, you would hear 2 "warbles" a second, and so on.
Thanks!  |
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Rick Aiello
From:
Berryville, VA USA
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Rick Aiello
From:
Berryville, VA USA
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Rick Aiello
From:
Berryville, VA USA
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Posted 20 Sep 2003 12:43 pm
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| Here's another ... less math ... more animation |
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Joey Ace
From:
Hamilton, Ontario, Canada
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Posted 20 Sep 2003 12:48 pm
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Great animations, Rick.
THey got the point across, but made me seasick! |
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John Hawkins
From:
Onalaska, Tx. on Lake Livingston * R.I.P.
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Posted 20 Sep 2003 3:24 pm
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J.D . or Donny ,
I can hear beats very easily and tune them out but it is impossible ,at least for me , on stage --too much noise ! I use Jeff Newmans' tuning chart through my tuner. While it ( the chart cents per string + or - 440 ) will not tune out beats, it is acceptable during live gigs .
Here comes the stupid question : Is there a way to set my tuner to compensate and take out the beats automatically ? I think I know the answer but you guys have the knowledge that I wish I had so I thought I would ask the question anyway . If there are suggestions , please pass them on .
I know tuning out beats soundbetter --especially during my recording sessions, but I cannot do this all the time and if there is a way to set a tuner to do it automatically, it sure would be nice .
Sorry to take up your time with stupid questions !!
John [This message was edited by John Hawkins on 20 September 2003 at 04:29 PM.] [This message was edited by John Hawkins on 20 September 2003 at 04:33 PM.] [This message was edited by John Hawkins on 20 September 2003 at 04:35 PM.] |
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Ron Randall
From:
Dallas, Texas, USA
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Posted 20 Sep 2003 6:27 pm
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Great topic. Thanks for the animation Rick.
I learn something new everyday on this Forum.
Donny, Joey, great "splaining".
Thank you all. |
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Joey Ace
From:
Hamilton, Ontario, Canada
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Posted 21 Sep 2003 4:32 am
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John,
It's a fact that you usually can't hear enough on stage to tune by ear.
The JN chart is a good start, but every guitar is a bit different.
I suggest you tune by ear in a quiet room when you have a lot of time. Then make your own chart from these notes. Probably all you have to do is pencil in some changes to the JN chart.
There are some expensive tuners that allow you to save these changes, so when they read a note it's actually + or - your preprogrammed offsets.
That works well, so does a small chart taped to a cheap tuner. I use both at different times. [This message was edited by Joey Ace on 21 September 2003 at 05:34 AM.] |
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JB Arnold
From:
Longmont,Co,USA (deceased)
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Posted 21 Sep 2003 9:25 am
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Here's what you can do.
Get one of the Peterson Strobe tuners-I got one at St Louis. It has 2 user adjustable presets.
Get your axe tuned exactly the way you like it by ear in a quiet, stable environment.
You can then tune the tuner to your guitar-it will remember exactly what frequency each string is at in your own tuning. One preset for each neck. You save those, and then onstage it attaches to your steel leg and you can use it visually and know that you are getting your ear tuning from the tuner.
JB
------------------
Fulawka D-10 9&5
Fessenden D-10 8&8
"All in all, looking back, I'd have to say the best advice anyone ever gave me was 'Hands Up, Don't Move!"
www.johnbarnold.com/pedalsteel
www.buddycage.net
http://www.nrpsmusic.com/index.html
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John Hawkins
From:
Onalaska, Tx. on Lake Livingston * R.I.P.
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Posted 21 Sep 2003 11:46 am
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Joey and J.B ,
Thanks guys ! I'll look into both your recommendations . Sounds like good ideas !
John |
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J D Sauser
From:
Wellington, Florida
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Posted 22 Sep 2003 8:02 am
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Gentlemen, thank you very much for your answers.
It is is refreshing not to say positively surprinsing to experience in what a civilized manner we have eventually been able to take this oh so controversial issue, that has raised the heats only to be topped by the fellow down there, to a higher level of understanding. No, I mean it, I was scared when I saw Carl start it and I was not so sure of the outcome when I followed up on it.
Anyway, I agree we most of what I can understand of the posted.
I especially liked that it has been pointed out that overtones of a "single" note are JI, which affirms that it is a natural phenomenom which will eventually find/create a formula, and that JI doesen't only reflect what our ears want or like to hear.
Still, we are lacking one key response:
While we agree that the two frequencies A and C# tuned ET will create a third fequency that we commonly will identfy as (nasty) beats, and how or better why they occur, no one (sorry if I overlooked it) so far has been able to tell us here why A and C# tuned JI won't produce beats. There is still a difference in frequencies, a sum too... there's (almost) every thing there was in ET, every thing but... beats. WHY?
Thanks! ... J-D. |
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Rick Aiello
From:
Berryville, VA USA
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Posted 22 Sep 2003 8:25 am
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When the A string is sounded ... it produces an array of harmonics .... A,E,A,C#... etc.
If the C# string is tuned to the harmonic produced by the A string ... i.e. JI ... there will be no difference in frequency ... no beats.
In ET tuning ... the C# harmonic of A "clashes" (diff frequency) with the C# string ... beats. |
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Earnest Bovine
From:
Los Angeles CA USA
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Posted 22 Sep 2003 11:14 am
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| Quote: |
| why A and C# tuned JI won't produce beats. There is still a difference in frequencies, a sum too... there's (almost) every thing there was in ET, every thing but... beats. WHY? |
Right you are. Of course there will be beats there too. There are 2 reasons you don't usually notice them:
1. Consider the low harmonics (1,2,3,4,5) of the 2 strings. There are no two whose frequencies are very close together; i.e. within, say, 1 Hz of each other. So all the beats are faster than that, and you don't even notice. In other words you don't hear the beats unless the frequencies of 2 overtones (from 2 strings) almost coincide.
2. Consider the higher harmonics, the overtones that are 3,4,5 octaves above the fundamental. Here the overtone frequencies are very close together, and they do produce slow beats, but you don't hear them because the amplitudes of these high overtones are so small. (too quiet to hear) |
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Rick Aiello
From:
Berryville, VA USA
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J D Sauser
From:
Wellington, Florida
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Posted 23 Sep 2003 6:36 am
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Rick, I start to like you
Thanks for your answer. And thanks to everybody elso too.
I have been braining over the porblem the whole night and, although I know that natural harmonics are JI I overlooked the obvious.
Yesterday night I came up with a different theory, or better suspicion:
Given that we have two basic sines (spelling?) or waves. Both of similar amplitude but of a different frequency, they could be regarded as running paralel to each other, just like on that O'scope picture. We can assume that every x-number of cicles they will altenately do one of the following:
Bottoming out TOGETHER.
Peaking out TOGETHER.
One peaking out while the other bottoms out, canceling all sound for a spitt second (right?).
Well, I thought that this might be the origin of beats, but on the other hand it would more be like a tremolo, wouldn't.
I thought that it could be possible, as this phenomenom would altern between simultaneous peak and bottom outs and oposits, that this would explain the "wuawuuaawuuuaaa." sound of slower beats when aproximating JI.
Then again, I asked myself, well, why does it stop beating? And then I suggested to myself (yeah, I really did ) that there could be a mathmatical point where the two frequencies would never find together, or almost, just like there's no number that can divide 3, 7, 11, 17, 19, 23 and so forth... by then It was 3AM and I can seem drunk when I get too tired talking to myself... so I wont tell you the rest I came up with
Yours makes sense, and it seems plausible (I mean, I understand the reasoning behind it), so, I like it.
Thanks! ... J-D.
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Rick Aiello
From:
Berryville, VA USA
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Posted 23 Sep 2003 6:51 am
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| Quote: |
| Yours makes sense, and it seems plausible (I mean, I understand the reasoning behind it), so, I like it |
As much as I'd like to ... I can't take credit for the Laws of Physics governing wave superposition. 
I just try to explain them the best I can ...
Here's a paper that does a nice job explaining what happens beyond the point where beats can no longer be detected as individual "entities" ...
Wobbling |
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Earnest Bovine
From:
Los Angeles CA USA
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Posted 23 Sep 2003 8:30 am
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quote:
they will altenately do one of the following:
Bottoming out TOGETHER.
Peaking out TOGETHER.
One peaking out while the other bottoms out, canceling all sound for a spitt second (right?).
Yes, that's exactly what the audible beats are. |
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J D Sauser
From:
Wellington, Florida
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Posted 24 Sep 2003 9:52 am
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So, huh... Rick and Ernest...
We now have two theories?
Beats from the mismatch of naturally occuring harmonics and the similar second string.
And/or (?) beats from sine waves catching up on each other?
Rick I was not trying to give you credit for the phenomenom... just for taking the time and being able to lay it out before us so nicely.
Tahnks! ... and the beat goes on... J-D. |
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Rick Aiello
From:
Berryville, VA USA
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Posted 24 Sep 2003 10:29 am
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Just one explaination ....
The description you gave (that Earnest quoted) basically sums up what happens when the superposition of waves occurs.
If the two waves are close enough in frequency ... say 10 Hz or less ... you will hear distinct beats with a beat frequency that equals the difference of the two parent waves.
If the two waves are relatively close in frequency ... say in the range of 10 to 30 Hz (depending on the listener)... you will not hear distinct beats ... more of a fast wobble or what some folks call a "roughness" ... a rather annoying, uneasy sensation.
If there is a difference of more than say ... 20 - 30 Hz between the two waves ... you will perceive the summation as a "new" tone.
As in the A 220 example I gave earlier ... it is the superposition of the 5th harmonic of A with the 4th harmonic of C# that results in the "beats" you hear ... All other frequencies (fundamentals and other overtones) are too distant to be involved in producing audible beats.
In my classes we used wave generators, oscilloscopes and "ears" (some kids could differentiate beats at 10 b/s ... most could at 7 b/s) to observe and quantify this particular acoustic phenomenon ... it was the best series of labs we did all year.
The kids really enjoyed it (especially the band and chorus students) ... it was a great "real life" application of algebra, trig and calculus ... and it "ate up" a good week and a half of the school year. [This message was edited by Rick Aiello on 24 September 2003 at 12:32 PM.] |
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Caution ... Calculus involved 
will produce a beat frequency of 8.8 b/s ....
