a question (TIA

Could someone give me the exact math on multiple/movable bridges--for
example, say you slide a pencil under the 5th or 7th or 12th (etc) fret
of a guitar, I want to know pitches/math specifics of the notes that
would sound to the left and to the right of the pencil?

http://zebox.com/daniel_anthony_stearns/

Hi
As your question is related to string length , this may help you:
http://240edo.googlepages.com/equaldivisionsoflength(edl)

Shaahin mohajeri , Tombak player and microtonalist
 
My microtonal web site
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Irandrumz ensemble

If the string full length is "l" and its frequency is "f" then for length "m" the frequency will be "f*l/m".
For the string at the distance "m" from one bridge frequencies are "f*l/m" and "f*l/(l-m)".
The calculation is not absolutely exact, it does not include possible string tension changed by the pencil, effective string length which is little shorter than bridge distance, etc.
Milan

daniel_anthony_stearns wrote:
> Could someone give me the exact math on multiple/movable bridges--for > example, say you slide a pencil under the 5th or 7th or 12th (etc) fret > of a guitar, I want to know pitches/math specifics of the notes that > would sound to the left and to the right of the pencil?
>
> http://zebox.com/daniel_anthony_stearns/ >
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>
>
>

Hi Dan,

--- In tuning-math@yahoogroups.com, aum <aum@...> wrote:
>
> If the string full length is "l" and its frequency is "f"
> then for length "m" the frequency will be "f*l/m". For
> the string at the distance "m" from one bridge frequencies
> are "f*l/m" and "f*l/(l-m)". The calculation is not absolutely
> exact, it does not include possible string tension changed
> by the pencil, effective string length which is
> little shorter than bridge distance, etc.
> Milan
>
> daniel_anthony_stearns wrote:
> > Could someone give me the exact math on multiple/movable
> > bridges--for example, say you slide a pencil under the 5th
> > or 7th or 12th (etc) fret of a guitar, I want to know
> > pitches/math specifics of the notes that would sound to
> > the left and to the right of the pencil?
> >
> > http://zebox.com/daniel_anthony_stearns/

Right after i took my last math course, a year ago, Brink
asked me about this, and my knowledge of logarithms was
fresh enough that i was able to make a spreadsheet with
all the calculations.

Assuming that the frets give an EDO (equal-temperament),
what happens is that with a moveable bridge but stationary
frets, you get exactly that EDO with the bridge at only
one spot, but as the bridge is moved closer to or farther
from the nut, the notes deviate from other EDOs symmetrically
around a certain point.

For each EDO, frets on one side of that point give notes
that are progressively too low, and frets on the other side
give notes that are progressively too high. The closest
match to the given EDO is for the 2 frets which are closest
to the "magic" point.

I don't remember the formula now, otherwise i'd post it here.
I'll look around for the spreadsheet and email it to you
when i find it.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software