What is the significance of this number:

certainly does ring a bell - lol

Originally posted by sonhouse
Well if it wasn't famous before it will be now, So on a scale from 1 to 12, how many people do you think understand? I expect some sharp answers here.

it will take some clever thinking to get to the root of this, and you'll need to think inside the square... ;-)

Originally posted by xcomradex
it will take some clever thinking to get to the root of this, and you'll need to think inside the square... ;-)

don't you mean inside the circle....hehe

Originally posted by chronicman
don't you mean inside the circle....hehe

You guys need to minorly tone down the joking.

Spoiler ahead!

http://www.avdgs.org.au/nlissue05.html

Originally posted by UmbrageOfSnow
You guys need to minorly tone down the joking.

our sense of humor doesn't strike a chord with you?...

Originally posted by xcomradex
our sense of humor doesn't strike a chord with you?...

Maybe if we pitched it a different way he would appreciate it? Of course I thought we were pretty chordial already.

Of note is that most people got this quite quickly, but don't fret if you were board of this problem because I'm sure your sharp anyway!

Originally posted by AThousandYoung
Spoiler ahead!

http://www.avdgs.org.au/nlissue05.html

Hey, great article. I saved it in favorites. I went one better than all those people however. I made a VARIABLE fret ruler. Think about that one for a while. See if you can duplicate my efforts. At the dulcimer festivals when I made it, I would take it to the luthiers booths where they had their instruments made and was able to check ALL their instruments with one tool. I became known in the duclimer circles as the 'Fret nazi'🙂 It was suprising how many had the frets in the wrong place and was glaringly obvious using my tool, well my fret ruler tool anyway🙂

so what exactly is the importance of the number anyway?
i don't get it

Originally posted by sofar55
so what exactly is the importance of the number anyway?
i don't get it

Ah, I guess we have led people on long enough. Most of the dudes answering just google it in and get a rough idea but not being musicians wouldn't have a clue as to whats its about.
0.943874..... is the inversion of 1.05946... which is the 12th root of 2.
So if you multiply 1.059.... by itself 12 times you will end up with 2, EXACTLY.
That is the heart of the tempered scale. You can use that relationship to build fretboards for instance or use it with a frequency counter to figure out what the correct frequency should be of the next note in the scale, so if the first note is 1000 hertz, (the standard is A=440 hz but for clarity I will use 1000 hz) the next note would be 1000 times 1.059
or 1059 hz. So if you called that 1000 hz tone A, the 1059 hertz tone would be A sharp. multiply 1059 times 1.059 again and you have a new frequency of 1122.4 hz which in this case you would call B. Do it again and you have 1188 and change Hz which would be C, etc. etc.
In the case of building a fretboard, say for a guitar, you use the inversion which is 1/(12th root of 2) or 1/1.059... or that number I talked about first, 0.9438743.... but this time if you keep multiplying it together after 12 such multiplications you end up with exactly 0.5
(2 inverted) which is what you want if you are marking off a fretboard for a stringed instrument you are making, whatever that is and however long it is. Suppose you have a one meter long fretboard, a pretty long one but for illustration it works fine. The longest string length would be 1000 mm or exactly one meter. Now the trick is finding where to mark your fretboard for the next fret. No sweat now that you know that number, just multiply 1000 times 0.94387 and you have the distance from the bridge to that fret as 943.87 mm.
You always use the distance from the bridge (where the string is attached to the soundbox) to the fret placement. So multiplying 943.87 times 0.943874 and you come up with 890.9 mm which is the second fret distance, so thats where you mark your fretboard to cut the slot for the second fret and so forth down the board as many times as you want. You will notice if you do that the distance between frets gets progressively smaller but after the 12th time you will find yourself putting down a fret that is EXACTLY halfway between the nut (where the string starts by the tuning machine end) and the bridge. That is the octave point where in the case of the 1000 mm long string would be exactly at the 500 mm distance. So that is the first harmonic.
You do that 12 more times and you end up at the second harmonic, EXACTLY at 250 mm and so forth, the third harmonic at exactly 125 mm. At some point the frets are too close together to be able to finger so there is a practical limit but thats how you mark off the frets if you are making an instrument. BTW, that 12th root of 2 thing is not the only scale around. you can just as easily use the 5th root of 2, or 1.148698... and its inversion 0.87055.... to build a fretboard with a scale that would include just 5 notes between octaves. That scale is actually used in some tribes around the world. Or you can go up, you could if you want, use the 13th root of 2 or the 18th root of 2. One dude even built a scale using computers to make the sounds derived from the 43rd root of two which is 1.01625 and change and the inversion of 0.98400... which makes a scale with exactly 43 notes between octaves. I played with the 18th root of 2 and found it has notes that are close to the blues scale so people experiment around with alternative scales a lot!

Originally posted by sonhouse
I played with the 18th root of 2 and found it has notes that are close to the blues scale so people experiment around with alternative scales a lot!

Apparently a nineteen note is the next best after twelve. This gives a scale where the notes are separated by thirds-of-a-tone (rather than semitones) thus:

C, C#, Db, D, D#, Eb, E, E#, F, F#, Gb, G, G#, Ab, A, A#, Bb, B, B#.

Note that in this scale C# and Db (and similar pairs) are NOT enharmonic.

Amazingly, people have built instruments based on this scale and used it to compose music. See here: http://eceserv0.ece.wisc.edu/~sethares/tet19/guitarchords19.html for details of a "19 guitar"

Originally posted by howardbradley
Apparently a nineteen note is the next best after twelve. This gives a scale where the notes are separated by thirds-of-a-tone (rather than semitones) thus:

C, C#, Db, D, D#, Eb, E, E#, F, F#, Gb, G, G#, Ab, A, A#, Bb, B, B#.

Note that in this scale C# and Db (and similar pairs) are NOT enharmonic.

Amazingly, people have built instruments ba ...[text shortened]... http://eceserv0.ece.wisc.edu/~sethares/tet19/guitarchords19.html for details of a "19 guitar"

That is one interesting site! Co-incidentally, I just finished my all me CD, all original tunes plus my entry in the music competition here, john hardy which is a traditional song. Using ordinary 12 tone instruments. Actually the lap dulcimer has frets taken out to make the notes equal to the white keys of a piano. Its an interesting study in modal tunings. I wrote a tune today, I called it an Elizibethan tune for no particular reason, but what is interesting about it is when the dulcimer is capoed up the character of the scales changes completely.
So the one I used was capoed onto the 4th dulcimer fret, that is the same as capoing a guitar on the 7th fret. I am listening to that tune now, figuring out which cut needs more editing, some are too loud, some too soft so I have to go back to Wavelab or Sound forge to equalize all those tracks. When you capo on the 4th fret of the dulcimer it comes out in a minor key and I figured out a tune to play ing it pretty fast and got it recorded with two dulcimers, one mandolin and one guitar just making like a base. It was an interesting study in composition and instrumentation. Used Pro Tools LE. Great program!