In the spirit of modern experimentation, I thought I would build a guitar to try see what happens -
As you can see, it is built from exotic timbers and is minimalist in form, having just one string (9 thou). The action is normal to low, and requires pressing the string down. (9 is our best selling gauge by the way)
First I set the bridge and nut 650mm apart (- they are both fixed), and tuned it to E, using the tuner in the picture.
Next I slid the movable frets to about halfway, and moved back and forth, until I hit E again. Nut to fret distance 323.8mm
Up another octave, nut to fret 486mm
Next I wrote a php program <a href="http://www.rockfactory.co.uk/fretcalculator.php">fret calculate</a>
results here -
Scale is 650mm
divisor is 17.91
1 36.2926 36.293
2 34.2662 70.559
3 32.3529 102.912
4 30.5465 133.458
5 28.841 162.299
6 27.2306 189.53
7 25.7102 215.24
8 24.2747 239.515
9 22.9193 262.434
10 21.6396 284.074
11 20.4314 304.505
12 19.2906 323.796
13 18.2135 342.009
14 17.1966 359.206
15 16.2364 375.442
16 15.3299 390.772
17 14.4739 405.246
18 13.6658 418.912
19 12.9027 431.815
20 12.1823 443.997
21 11.5021 455.499
22 10.8599 466.359
23 10.2535 476.612
24 9.681 486.294
As you can see a divisor of 17.91 seems to provide a fairly close match to my experimental results
Here is the php if anyone needs to check
“
<p>
<?php
$scale=650;
$divisor=17.91;
echo "Scale is " . $scale ."mm" . "<br /> <br />";
echo "divisor is " . $divisor . "<br /><br />";
for ($counter=1; $counter<25; $counter++)
{
$fret=$scale/$divisor;
$total=$total+$fret;
if ($counter==12)
print "<br />";
echo $counter . " ";
print round($fret,4). " ";
print round($total,3) . "<br />";
$scale=$scale-$fret;
}
?>
</p>
“
Loads of potential errors here, - new string, maybe more elastic than a used one - measuring equipment (cheap tuner and steel rule) a bit primitive - but nevertheless I will be going with this until convinced otherwise.
Still working on this when I have the time - will post if any more insights.