pitch and frets

[Emibass]

How did Leo measured where the frets had to be placed when he designed the first P-bass???

Was it by ear or he had something like an osciloscope to see the note/frequencie???

[Ed Fuqua]

It's a pretty precise mathematical formula, you set how long you want the string to be, the strings dimensions and tension and then apply the formula for the pitch "location".

[megadan]

It was basic math.

[Emibass]

Originally Posted by Ed Fuqua

It's a pretty precise mathematical formula, you set how long you want the string to be, the strings dimensions and tension and then apply the formula for the pitch "location".

but if you diferent gauge, tension...etc than??? Maybe it has more to do with lenght??

Sorry for the silly questions. It´s just curiosity

[ggunn]

Originally Posted by Emibass

but if you diferent gauge, tension...etc than??? Maybe it has more to do with lenght??

Sorry for the silly questions. It´s just curiosity

It has only to do with fractions of scale length (the distance from bridge to nut). Fine adjustments for string gauge, etc. are taken care of by adjustable bridge saddles. Here's some info: http://liutaiomottola.com/formulae/fret.htm

[ninepoundjammer]

Frequency (pitch) and wavelength (string length) are inversely proportional. If you halve the wavelength you double the frequency -- this is why the first octave or 12th fret is at half the scale length. The rest of the fret positions also follow from application of this principle.

The above holds as long as the string tension is held constant. Of course, when you fret the string you change the tension slightly, how much depends on the action, strings, etc. Fretting also changes the geometry of things a bit. You adjust the intonation to compensate for this.

No magic involved.

[uethanian]

each semitone in 12-tone equal temperament has the value of 1:12th-root-of-2. (sorry, can't type radicals and math symbols). to find the first fret, measured from the nut, you'd do this

34" - 34"(1/12-root-of-2)^1 = 1.91"

then the second fret

34" - 34"(1/12-root-of-2)^2 = 3.71"

third

34" - 34"(1/12-root-of-2)^3 = 5.41"

and so on. you can do this with any scale length (just change the 34" to any number, works for centimeters too), and any equal division of the octave (change the 12 in '12-root-of-2' to any number).

[vibhas_2310]

Originally Posted by uethanian

each semitone in 12-tone equal temperament has the value of 1:12th-root-of-2. (sorry, can't type radicals and math symbols). to find the first fret, measured from the nut, you'd do this

34" - 34"(1/12-root-of-2)^1 = 1.91"

then the second fret

34" - 34"(1/12-root-of-2)^2 = 3.71"

third

34" - 34"(1/12-root-of-2)^3 = 5.41"

and so on. you can do this with any scale length (just change the 34" to any number, works for centimeters too), and any equal division of the octave (change the 12 in '12-root-of-2' to any number).

can u explain this formula for finding out where the frets should go ?? Sorry I could not understand anything from what u just typed there .

Thanks,
Vibhas

[GianGian]

I don't know if this is right, but I remember I once heard that the fret distance(from one fret to the next) is always 1/8 shorter than the distance between this fret and the previous one..

[uethanian]

Originally Posted by vibhas_2310

can u explain this formula for finding out where the frets should go ?? Sorry I could not understand anything from what u just typed there .

Thanks,
Vibhas

sorry, i was probably a bit vague...first know that frets should be calculated from the nut, rather than from the bridge...both work mathematically, but the nut is a more accurate reference point. the basic formula is as such:

(scale length) - (scale length)*(interval)

the 'interval' in this case is really just the proportion of the string that is stopped by a fret.

if my scale length was standard bass guitar - 34 inches, and i want to find the octave fret, i'd plug this in

(34 inches) - (34 inches)*(1/2) = 17 inches from the nut

because the octave is always 1/2 of the total scale length. now things get more complicated for intervals other than octaves, but the basic principle is the same. why we use the '12th-root-of-2' as the basis for our scale system is a huge subject that kind of goes beyond what you're asking. but to put it as briefly as i can:

there are two main philosophies with regards to musical intonation. one is just intonation, or pure harmony, in which intervals maintain the simple mathematical relationships that are found in the natural harmonic series. just intonation scales have inherently unequally sized steps, so while the harmony is perfectly in tune, it's problematic modulating to different keys. classical indian music is the best example of this; there are no chord changes, just a drone to which all intervals are perfectly tuned. the other philosophy is equal temperament, which means artificially adjusting intervals so that all steps in a scale are of equal size. this permits modulation to any key, but harmony is no longer pure. for the last 200 years, western music has been primarily in 12-tone equal temperament.

phew. so to calculate fret positions in 12-tone equal temperament, the basic interval (the semitone or minor 2nd) is 1/12th-root-of-2. if i wanted to do 19-tone equal temperament, it would be 1/19th-root-of-2. 31-tone equal temperament, 1/31st-root-of-2...and so on. to calculate successive frets, you have to raise the interval an exponent, like (1/12th-root-of-2)^1,^2,^3, etc.

GianGian - you are probably thinking of the 'rule of 18/17.' historically, guitarists/lutenists were not doing the above calculations (hard to do without calculators), so they used 18/17 as the semitone, and made each successive fret 18/17 away from the next. i believe it was galileo who first proposed this, or maybe it was his son...in any case, it's a pretty close approximation to 12-equal.

[JohnMCA72]

^^^ Strongest case yet for going fretless!!!!

[GianGian]

Originally Posted by uethanian

GianGian - you are probably thinking of the 'rule of 18/17.' historically, guitarists/lutenists were not doing the above calculations (hard to do without calculators), so they used 18/17 as the semitone, and made each successive fret 18/17 away from the next. i believe it was galileo who first proposed this, or maybe it was his son...in any case, it's a pretty close approximation to 12-equal.

Yeah, it probably is. But man, it is close to equal temperament, which is already "out of tune", it must hurt to hear that!

[uethanian]

Originally Posted by GianGian

Yeah, it probably is. But man, it is close to equal temperament, which is already "out of tune", it must hurt to hear that!

yea i know what u mean...i've worked in just intonation, 31-equal, and 19-equal, and 12-equal thirds/sixths are very unpleasant for me. in any case, historically i doubt many musicians took the trouble to move their frets to calculated spots, it was more 'by ear' in that era.

[Droot]

Originally Posted by Emibass

but if you diferent gauge, tension...etc than??? Maybe it has more to do with lenght??

Sorry for the silly questions. It´s just curiosity

Yes the length, no to the rest. The formula is straight forward and predates anything Leo did by centuries.

Droot