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| WFret Question http://www-.luthiersforum.com/forum/viewtopic.php?f=10102&t=8583 |
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| Author: | Shane Neifer [ Sun Sep 24, 2006 4:31 am ] |
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I am curious about fret calculatoins and am hoping that some of you guys/gals that fully understand this stuff can enlighten the dark cavities of my small brain. WFret allows the option to calculate using the 12th root of 2, rule of 18's and custom temperment. I just did a quick check and could find no differnece between the results of 12th of 2 and rule of 18's using 25.4" scale length and 24 frets. Is there a difference? What do each of the rules refer too? Is there any advantage in using one rule over the other? When would you want to customize your spacing and why? Although these are not really critical questions I am quite curious about this. Thanks Shane |
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| Author: | Serge Poirier [ Sun Sep 24, 2006 4:52 am ] |
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Shane, not sure if i understand your question well, my brain might just be smaller than yours! 
To me, what mattered most was to have the drawing itself so i could transfer it to a template but i'm guessing you want to double check with a read out of the measurements? |
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| Author: | Shane Neifer [ Sun Sep 24, 2006 5:10 am ] |
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Not really Serge, I don't have a problem laying everything out, I am just wandering why there are two mathematical models that seem to give the same results and just want to make sure that I am not missing an advantage of one method over the other. And I am wondering what effect either would have on the finished instrument as far intonation would have. The same illogic follows for my question of why would you want to use a custom temperment. I am just curious about the theories here..... |
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| Author: | Serge Poirier [ Sun Sep 24, 2006 5:14 am ] |
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Ok bud, i'll go take a couple of aspirins now, you made my brain work too hard!
Good luck with the answers on this one! 
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| Author: | Lillian F-W [ Sun Sep 24, 2006 5:48 am ] |
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I haven't looked at it, but I'm willing to bet that the farther down the fretboard you go, you could see a difference, abit, small, but a difference. |
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| Author: | Dave White [ Sun Sep 24, 2006 6:56 am ] |
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Shane, Others (like Al C) who know more of the maths will pitch in but I'll quote here from Cumpiano & Natleson (pp.267 in my version): ". . . a number must be found which, when divided into the scale length will increase the string's pitch by one semi-tone. Since the pitch frequency doubles at the twelfth fret, that number will be divided by a factor of two. Thus, the string's pitch will be increased by one semi-tone when the string is shortened by dividing the scale length by the twelfth root of two which equals 1.0594631. This means that the scale length will be 1.0594631 times the distance from the first fret to the end of scale. The relationship of the scale length to the first fret interval is therefore: 1.0594631/0.0594631 which equals 17.817152. This constant when divided into any scale length, will provide the distance from the nut to the first fret and, when successively divided into the remaining scale length, will produce the remaining fret spacing intervals." The "rule of 18" came, apparently from rounding this constant up to 18 and using it as an approximation for the twelfth root of two. Modern spreadsheets have more decimal places and so using the twelfth root of two and this constant to a sufficient number of decimal places I suspect give you the same result. Now this gives you the equal tempered scale which, as I'm sure you know, is a compromise. It is possible to determine the fret placings for a scale that is "perfect" but the catch is you have to do this for one key. Play in another key and you are s*****d - to use the technical term.
Hope your brain is hurting as much as it should |
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| Author: | Shane Neifer [ Sun Sep 24, 2006 8:02 am ] |
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Thanks Dave!! A great explanantion and consequently, also on page 267 of my copy of C&N!! That also explains why the two rules are the same...because they are really then just the same rule, two names! Which is why the results are the same when calculated by either method. I was well aware of the process for determining fret spacing using the 17.817152 constant. Kinkead discusses it also but was just uncertain why there were two methods in WFret that came to the same results. You have cleared that up for me..... Thanks again my freind! Shane |
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| Author: | Shane Neifer [ Sun Sep 24, 2006 9:01 am ] |
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Thanks Todd, I actually recently bought a ruler from the Wholesale Tool Company that Michael McBroom had recommended. It is scaled in 1/100th's of an inch over its 24 inch length. So I will just use that. I have printed the layout and have checked for accuracy and they appear pretty accurate from my printer but I will be making templates out of acrylic products so I will probably just use the rule and thick glasses! Shane |
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| Author: | Michael McBroom [ Mon Sep 25, 2006 2:29 am ] |
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Shane, The nice thing about that ruler is the graduations are engraved. So you can do like Cumpiano shows in his book: clamp the ruler to a piece of flat material with a good right angle, clamp this setup atop your template, insuring the ruler is parallel with the template's edge, and then take an X-acto blade (or equiv), insert it into the graduation, and transfer a mark exactly where it should be. I made a template out of lexan for a 640mm scale using this method. I cut the slots on a milling machine, confirming their accuracy as I went along (the ruler measures only to the nearest 0.01" but I can get +/-0.001" with the mill). Best, Michael Best, Michael |
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