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Location: Yorkshire, England | Pythagoras discovered the ratios of frequencies that make up the musical scale - Pressing down on a vibrating string at its centre, obviously making it 1/2 as long, plays a note an octave higher than the full string did and vibrates twice as fast.
Now, instead of holding the string in the centre, let's hold it so that it is 2/3 it's original length. The string now plays a 5th higher than the original note. The string is vibrating 3/2 as fast as it was originally.
You may know that when you have gone up a 5th, then a 4th from there, you will have gone up an octave - Lets see if that works !
Up a 5th =3/2, up a 4th = (3/2(4/3)=2 Which is an octave.
BUT!! There's a flaw in this musical scale -Let's start going up a 5th until we find another C - that is C-G-D-A-E-B-F#-C#-G#-D#-A#-F-C
This C vibrates vibrates (3/2) to the twelfth power faster than the original C.
You will all no doubt now have guessed (those of us familiar with calculus, that is) what has gone wrong. Yes, you've got it - this C is not an even number of octaves above our original C ! But it is close! Instead of vibrating 128 times as fast (7 octaves higher) it vibrates (as you all may be able to work out) 129.7463379 times as fast ! It is obvious to the ear that these notes are both not C !
As you will also be able to see, F# is not the same as Gb (going down from C) for the same reason.
I hope you've all been taking this, in as I'll be asking questions later. |
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Location: Latitude 39.56819, Longitude -105.080066 | Didn't you post this up in the "For Sale" section about 2 weeks ago? |
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Posts: 270
Location: Yorkshire, England | Nope ! This is something completely different. |
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Posts: 13303
Location: Latitude 39.56819, Longitude -105.080066 | Damn, guess I'm gonna have to read it then ;) |
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Posts: 270
Location: Yorkshire, England | Go On ! Enjoy !!! |
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Posts: 672
Location: New South Wales, Australia | Mathematics was never my strong point. Wasn't Pythagoras a Greek soccer player?
Wonder if he played guitar? |
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Posts: 1634
Location: Warren,Pa. | Stopping the string at the 12th fret doesn't make it half the length of the open string...because you are STRETCHING the string down to the fingerboard. That "half" is slightly longer than half. I truly wish my ears didn't pick up on this, but they do. Acceptable intonation is harder for some of us to achieve than it is for others.
John <>{ |
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Posts: 10777
Location: Keepin' It Weird in Portland, OR | Originally posted by Captain Black:
You will all no doubt now have guessed (those of us familiar with calculus, that is) what has gone wrong. Yes, you've got it - this C is not an even number of octaves above our original C ! But it is close! Instead of vibrating 128 times as fast (7 octaves higher) it vibrates (as you all may be able to work out) 129.7463379 times as fast!
I hope you've all been taking this, in as I'll be asking questions later. I forgot my Slide-Rule... |
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Posts: 4394
Location: East Tennessee | Wasn't there a brand of guitar where the frets aren't parallel to each other to compensate for this? |
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Posts: 11840
Location: closely held secret | Novax
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Posts: 20
| Seems to me that this guitar has a different scale for each string, you don't really need SO much difference... |
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September 2008
Posts: 20
| Originally posted by Captain Black:
As you will also be able to see, F# is not the same as Gb (going down from C) for the same reason.
This was true until the end of the XVIIth century, but since the "temperate" system was intruduced, they are the same note. Same value of pulsation, ask Bach! |
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Posts: 4996
Location: Phoenix AZ | Originally posted by The Wabbit Formerly Known As Waskel:
Novax
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Location: Cicero, NY | Didn't T28 have a git with compensating frets? Someone around these parts did... |
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Posts: 11840
Location: closely held secret | No, he frets about compensating. |
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Location: Cicero, NY | AHH! I knew it was something along those lines. |
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Posts: 2120
Location: Chicago | I've never been able to "hear" very well the difference between "well tempered" and "equal tempered" tuning on a keyboard. Never even got near a "mean tempered" or "Pythagorean". I hear they bite. |
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Location: closely held secret | Try to avoid the ill-tempered ones.
And don't worry, "Pythagoreans" don't bite. They just wrap themselves around your brain until it explodes. |
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Posts: 10777
Location: Keepin' It Weird in Portland, OR | Originally posted by The Wabbit Formerly Known As Waskel:
Novax
I guess you don't really do chords on this one.[8-string Novax $3.3K] |
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Posts: 1017
Location: Budd Lake, NJ | I'm with you, Bauerhill--
I can hear the differences, too; that's how I know when one of the girls needs tweaking a bit--when I really can't stand it.
Hmmmmm......ghosts of mathematics past coming back to haunt me. Out, out, lousy ghosts!!
But wait--wasn't a pythagorus a dinosaur that used to wrap itself around its prey and crush it?
--Karen |
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March 2007
Posts: 698
Location: Cork, Ireland | Gets interesting when you play harmonica and guitar together as different harmonicas (even different diatonic ones) use different intonation systems. Checking both against an electronic tuner doesn't always work, you have to tune the guitar to the harp (as the latter are rather hard to tune on the fly)
http://www.patmissin.com/tunings/tun5.html |
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May 2003
Posts: 4389
Location: Capital District, NY, USA Minor Outlying Islands | Some people worry too much about being in tune. Basically, when it comes down to it, as long as my adamas' on board tuner says its tune, the guitar's good to go for about an hour of flogging, then I'll hear a little something, then put it back in the green.
PS I always thought that F# was the same G flat? Just like A# was the same as Bflat. I'm no expert, but it might just be because I'm stuck in the world of the guitar fret board. |
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May 2003
Posts: 4389
Location: Capital District, NY, USA Minor Outlying Islands | I got to play a bass in david gage's shop in soho. As I recall, it was made in the early 1600's. The first person to play it was a contempory of shakespeare. To think that to this person, shakespeare was new ...
It was made before the days of tempered tuning. It had an awesomely broad sound. of course, there were no frets ....
If you guys ever get to NYC you should set up a tour. Just call in advance, and they show you around, and you try out the basses. Their luthier shop is top drawer, and top dollar. |
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November 2005
Posts: 1126
Location: Omaha, NE | The most important thing to remember from a guitar player's perspective is that there is no such thing as an "in tune" guitar, only an "in tune" player.
All tuning systems are compromises. Its up to the player to make it work. |
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February 2005
Posts: 11840
Location: closely held secret | Originally posted by Omaha:
The most important thing to remember from a guitar player's perspective is that there is no such thing as an "in tune" guitar, only an "in tune" player. Well, I'm in trouble then... |
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Location: The Great Pacific Northwest | Not as dramatic as the Novax, but http://www.microfrets.com/ is another. |
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Ahh ! Intonation. Over to you Mr Pythagoras!