It’s time to tackle the most complicated aspect of the guitar, the fretboard.
Have you ever asked yourself:
Why are the frets located in the location that they are located?
Do you know who you need to thank?
Ever hear of Pythagoras?
The same guy that brought you a2 + b2 = c2 (the triangle thing) also brought you the 12th root of 2. The 12th root of 2, which I’ll refer to as the “magic number” is 17.817.
The overall scale of 25.5 is divided by the magic number, and the number you get is the placement of the first fret in relation to the nut. What is left over becomes a new fret scale, for this example, the number is 24.069. That number would then be divided by the magic number and so on and so forth. If you do the math, you see that the 5th fret is numerically equal to 75%, the 7th is 66.666% and the 12th fret is 50% of the original scale of 25.5. These ratios divide the string up into quarters, thirds and in half, the places where you might play harmonics.
Assignment: Do the fret scale for a 25.5 scale. Turn your papers into me by the end of the week for grading. All papers will be graded and returned. Hint use excel
Filed under: Even Tempered Scale, Fret Scales, Guitar, Pythagoras, The Fretboard | Tagged: Guitar Building, Technical Stuff
I’ll do a fret scale for a 25.5 scale, if you paint a picture for me of what life must have been like for the average musician before we had this method of universal tuning, I suppose generally called the well tempered system.
IG
I learned to label it as the even tempered scale. back in school they had us literally solve for the 12th root of 2 then do the calculations, and again with a different divisor if we wanted to use some different strings.
The basics remain, well tempered or even tempered, they are both better than a bad temper.