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I was wondering why are the white dots in the fretboard usually placed in frets number 3,5,7,9,12,15,17,19 and 21.

I know that their general purpose is for counting, but what I wonder is why are they placed on precisely those frets, and not different ones?

For Example: Why are there two frets between the dots on 7 and 9, and three frets between the dots on 9 and 12?

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I have guitars with a marker on the first fret as well ! Is that for the hard of thinking? –  Tim Apr 17 at 17:04

8 Answers 8

The frets that are highlighted are the equal-tempered equivalents of the basic fractions, as seen in the table below. (The first column is the fraction, the second column is the corresponding number of half-tones):

 1      0      = 0
 6/5    3.156  ~ 3
 4/3    4.980  ~ 5
 3/2    7.020  ~ 7
 5/3    8.844  ~ 9
 2      12     = 12 (from now on, it's simply an octave up, i.e.,
 12/5   15.156 ~ 15     times 2 for the fractions and +12 for the frets)
 8/3    16.980 ~ 17
 3      19.020 ~ 19
 10/3   20.844 ~ 21

One can ask why 6/5 and not 7/5, 8/5 or 9/5. I don't know exactly, but the fractions used have the lowest possible sum of numer+denom in the interval [1,2]. (I'm not 100% precise here, we omit 5/4 which gives 3.863 ~ 4, but you wouldn't place two dots adjacent since it would only confuse people, would you?)

This as well explains why 9 got there and not 10: It corresponds to a very low-entry fraction. One can as well notice that you can try flajolets on bars 12, 7 and 5 easily, and with some adjustments on 3, 4 and 9 as well, but these don't sound quite strong. Flajolets on other positions are even more difficult.

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Please let me know what exactly is wrong with my answer, so that I can do better next time. Thanks. –  yo' Dec 8 at 22:24
    
Not sure where the downvote is from, but one really specific thing I notice is that technically speaking, fretboards are (typically) equal-tempered, not well-tempered. –  NReilingh Dec 9 at 4:31
    
@NReilingh Ah thanks, that's lost in (my bad) translation from Czech to English. My fault, I'll correct it. –  yo' Dec 9 at 9:19

I always thought the ninth fret marker was simply aesthetics. Being that the marker after the twelth is three frets away, the marker before the the twelth is the same distance away. It centers the twelve marker. Practically speaking, the twelve marker is also more noticeable.

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After 45 minutes or so reading people's answers to the ninth fret question, then 15 minutes of pondering, I came up with a crappy answer:

The NINTH FRET is a position of all flatted notes:

Db Ab Fb Cb Gb Db --or-- Db Gb Cb Fb Ab Db

(The order depending upon whether You look at the notes from first string to sixth or vice-versa.) But then, the fourth fret is also a position of all flatted notes. I know we aren't supposed to call B a Cb or F an Eb, though there are exceptions. Yeah, somebody, please come up with the answer to this ninth fret conundrum! In any case I won't stop thinking about this.

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Cb is actually B –  Dom Nov 29 at 23:48
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@Dom - depends what key it's in !! However, F can never be Eb... –  Tim Nov 30 at 8:08
    
Maybe you wanted to write "or E an Fb"? Because F can truly never be an Eb ;) –  yo' Dec 9 at 9:24

They are at important intervals: minor third, fourth, fifth, major sixth, octave.

Then they repeat for the second octave: minor third, fourth, fifth, major sixth.

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Maybe lost to history, the dots are references for the Fibonacci series, which when harmonics are considered, give a pure major chord with octave and perfect fifth redundancies. The dot at the 9th fret marks 2/5ths the string length. The harmonic there is of the 5th partial (the major third) -- this is the one that throws you off.

This is my observation, and it is so easy once seen, that I have little doubt that many people have stumbled across it. Nonetheless, Gibson and Martin guitars had nothing to say about it, and so far as I could see, nothing to see in google searches. THE DOTS MARK THE HARMONICS COMPRISING A PURE MAJOR CHORD.

Are the dots an atavism from pre-equal tempered tuning? In historical paintings of fretted instruments, or in museums, when are the earliest dots seen in their modern location??

string
open = 1 = do
dots
12 = 2nd partial = do (octave over root)
7 = 3rd partial = sol (perfect 5th + octave over root)
5 = 4th partial = do (double octave over root)
9 = 5th partial = mi (double octave + major third over root)
3 = 6th partial = sol (double octave + perfect 5th over root)

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Ok, I found other way to explain the ninth fret. When I was starting learning music teacher have shown me solmization sounds (do, re, mi, fa, sol, si); which was most basic major scale; sounds in it are c, d, e ,f, g, a, b(in my country h). And I was thinking how I would mark fretboard if I did it by myself.

First string tuned to e. How to map any sound from these with rule: do not mark adjacent frets? The easiest way is to put a dot between c and d.

  • e - 0 fret
  • f - adjacent do not mark
  • g - first dot
  • a - second dot
  • b - third dot
  • c - adjacent do not mark
  • it is easy to remember that fourth dot is between c and d
  • d - adjacent do not mark
  • e - double dot octave
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The spacing is designed to offer useful milestones on the fretboard. Take the notes on the 6th string (in standard tuning), for example:

  • Open (0th fret) is E.
  • The F is only 1 fret away, why put a marker on the 1st fret? It's already marked by being the first fret
  • The G is on fret 3, so put a marker there.
  • The A is on fret 5, which is a perfect 4th from the open string, so it deserves a marker.
  • B follows on fret 7, which is a perfect 5th from the open string, so another marked fret.
  • Why there's a mark on fret 9, I'll never know, I wish it was on 10 for D instead of 9 for C#
  • But you need a marker on 12, for certain - it's the octave!
  • The 15, 17, and 19 are just 3, 5, and 7 + 12 (an octave), respectively.
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6  
"The A is on fret 5, so it deserves a marker" is p4th of the root. "B follows on fret 7, another marked fret" and is the p5th of the root. Quite important intervals. –  Anonymous Apr 4 '11 at 23:27
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I own a very old russian made guitar with the marker on the 10th fret. And boy, is it hard to play because of that, even though I usually don't watch the markers... –  mrbuxley Apr 5 '11 at 5:42
    
@ledfloyd - You're obviously much more of a theory guru than I am. Would you please edit this answer to include your insights? @mrbuxley - I wouldn't want to play that guitar now, either. I'm used to the 9th fret mark by now. I just wish it were the other way. However, ledfloyd's answer explains why it is where it is. –  gomad Apr 5 '11 at 17:48
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I'd guess that the 9th fret has a marker and not the 10th because the 9th fret is a member of the major scale while the 10th is not. But then, the same logic would put a marker on the second fret and not the third, so I don't know. –  Alex Basson Apr 5 '11 at 19:05
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Nice breakdown. With regards to the 9th fret, my suggestion would be that it marks the position of the relative minor to an open-string major scale. Having said that, however, I think the reason is more prosaic: the flanking two-fret intervals make the octave immediately stand out, even if the markers are bars or some such (i.e. no special double dot symbol or similar). The remaining seven frets are divided in the most efficient way for easy recognition: four marks, three spaces. –  Faza May 24 '11 at 9:08

I think it's to signify intervals as much as anything else. The 12th fret is the most obvious - it's the octave. The 3rd fret is pretty obvious because it gives you some general orientation for most open chords. The 5th and 7th frets are valuable because they signify the 4th and 5th interval of the open strings.

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protected by Dom Dec 8 at 20:25

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