Why isn't the 8th harmonic right over a guitar fret?

This is starting to bug me. If the 8th harmonic is some multiple of
100 cents, why doesn't it occur right over the 2nd fret of a guitar?
(like the 7th harmonic is about 31 cents before the 3rd fret, and the
5th harmonic is 15 cents before the 4th and 9th frets)

Btw, this is the article that inspired this question:
http://www.guitarplayer.com/article/just-desserts/Nov-05/15212

Joe

Here is one theory: As you press down the string you are stretching it a bit so the fret needs to be somewhat farther away from the bridge to make up for that stretch. This would be especially prominent near the bridge.

I don't have a guitar to test what you are talking about but I have noticed the effect on (fretless) violin and erhu. Playing the harmonic by lightly touching a string and by pressing down the string require slightly different positions.

Magnus

On Fri, 14 Dec 2007, Joe wrote:

> This is starting to bug me. If the 8th harmonic is some multiple of
> 100 cents, why doesn't it occur right over the 2nd fret of a guitar?
> (like the 7th harmonic is about 31 cents before the 3rd fret, and the
> 5th harmonic is 15 cents before the 4th and 9th frets)
>
> Btw, this is the article that inspired this question:
> http://www.guitarplayer.com/article/just-desserts/Nov-05/15212
>
> Joe
>
>
>

Joe wrote:
> This is starting to bug me. If the 8th harmonic is some multiple of
> 100 cents, why doesn't it occur right over the 2nd fret of a guitar?
> (like the 7th harmonic is about 31 cents before the 3rd fret, and the
> 5th harmonic is 15 cents before the 4th and 9th frets)
> > Btw, this is the article that inspired this question: > http://www.guitarplayer.com/article/just-desserts/Nov-05/15212

You need to touch the string at 1/8 of its length. If you had a fret there, it would shorten the length of the string to 7/8 of its length, and it would vibrate at 8/7 of the open string's pitch (231 cents).

Thanks. The patterns start to emerge (this should be in courier
font)...

harmonic actual note ratio cents fret
4+ 11/1 M2 11/10 10:1 165 1.65
M3 10/1 m3 10/9 9:1 182 1.82
M2 9/1 M2 9/8 8:1 203 2.03
oct 8/1 M2 8/7 7:1 231 2.31
m7 7/1 m3 7/6 6:1 267 2.67
5 6/1 m3 6/5 5:1 316 3.16
M3 5/1 M3 5/4 4:1 386 3.86
oct 4/1 4 4/3 3:1 498 4.98
5 3/1 5 3/2 2:1 702 7.02
oct 2/1 oct 2/1 1:1 1200 12
fun 1/1 fun 1/1 1:1 0 0

--- In MakeMicroMusic@yahoogroups.com, Herman Miller <hmiller@...>
wrote:
>
> You need to touch the string at 1/8 of its length. If you had a fret
> there, it would shorten the length of the string to 7/8 of its length,
> and it would vibrate at 8/7 of the open string's pitch (231 cents).
>

[Non-text portions of this message have been removed]

It appears that I misread the question, so please ignore this.

On Fri, 14 Dec 2007, Magnus Jonsson wrote:

> Here is one theory: As you press down the string you are stretching it a
> bit so the fret needs to be somewhat farther away from the bridge to make
> up for that stretch. This would be especially prominent near the bridge.
>
> I don't have a guitar to test what you are talking about but I have
> noticed the effect on (fretless) violin and erhu. Playing the harmonic by
> lightly touching a string and by pressing down the string require slightly
> different positions.
>
> Magnus
>
> On Fri, 14 Dec 2007, Joe wrote:
>
>> This is starting to bug me. If the 8th harmonic is some multiple of
>> 100 cents, why doesn't it occur right over the 2nd fret of a guitar?
>> (like the 7th harmonic is about 31 cents before the 3rd fret, and the
>> 5th harmonic is 15 cents before the 4th and 9th frets)
>>
>> Btw, this is the article that inspired this question:
>> http://www.guitarplayer.com/article/just-desserts/Nov-05/15212
>>
>> Joe
>>
>>
>>
>

On Dec 15, 2007 2:00 AM, Joe <tamahome02000@...> wrote:
> Thanks. The patterns start to emerge (this should be in courier
> font)...
>
> harmonic actual note ratio cents fret
> 4+ 11/1 M2 11/10 10:1 165 1.65
> M3 10/1 m3 10/9 9:1 182 1.82
> M2 9/1 M2 9/8 8:1 203 2.03
> oct 8/1 M2 8/7 7:1 231 2.31
> m7 7/1 m3 7/6 6:1 267 2.67
> 5 6/1 m3 6/5 5:1 316 3.16
> M3 5/1 M3 5/4 4:1 386 3.86
> oct 4/1 4 4/3 3:1 498 4.98
> 5 3/1 5 3/2 2:1 702 7.02
> oct 2/1 oct 2/1 1:1 1200 12
> fun 1/1 fun 1/1 1:1 0 0

For most of these there's actually more than one place on the string
you can touch to get the same harmonic. The number of places is
Euler's totient function of the harmonic number. For example, there
are 4 places to get the 8th harmonic (1/8, 3/8, 5/8, and 7/8 of the
string length), and only the first is very far off from a 12-equal
fret.

Keenan