Fret calculation

I was thinking more in terms of Pythagoras' theorem. When you push the string down, you stretch the vibrating part according to a formula. I want to know the formula. Maybe Manuel can help?

Oz.

----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: 05 Temmuz 2007 Perşembe 6:53
Subject: RE: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

Hi brother

I believe that in acoustic music , pitch error is an inavoidable thing because your control on instrument will change everything.
But ,an important thing to mention , as you know , is that it is mostly related to compensation as is discussed in http://www.mandolincafe.com/glossary/glossary_60.shtml and other related links.
EDL and many other measurements are for a physical ideal string but many other things have effect on these ratios: http://www.classicalandflamencoguitars.com/Compensation4.htm
My experience for fretting setar is that at first i must have compensated octave fret in its best condition due to my ear error and sound analyzer's result and then use EDL to fret other frets as compared with octave fret ( as mentioned in my EDO-EDL sheet).
So if anyone wants to fret instrument , firstly must compensate frets to delete errors as is done for guitars.
also uncertainty principle of frequency analysis http://www-gewi.uni-graz.at/staff/parncutt/PSYCHOACOUSTICS.pdf have somethings to say.
and this may be is useful for you :http://www.wellesley.edu/Physics/brown/pubs/vibPerF100P1728-P1735.pdf

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ??????

My farsi page in Harmonytalk ???? ??????? ?? ??????? ???

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ????

------------------------------------------------------------------------------
From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Ozan Yarman
Sent: Wednesday, July 04, 2007 4:42 PM
To: tuning@yahoogroups.com
Subject: Re: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

3100-EDL is a fine choice. But how do we include the error caused by the inclination of the string when fingers touch the frets?

Oz.
----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: 04 Temmuz 2007 Çarşamba 15:43
Subject: RE: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

Hi ozan
according to my EDO-EDL calculator , 3100-Edl is a good choic.3101-EDl cant satisfy you but 3102-EDL is better than 3100.

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ??????

My farsi page in Harmonytalk ???? ??????? ?? ??????? ???

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ????

----------------------------------------------------------------------------
From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Ozan Yarman
Sent: Wednesday, July 04, 2007 3:48 PM
To: tuning@yahoogroups.com
Subject: Re: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_

What is the best EDL to approximate 159-EDO? Error for each pitch should be less than 0.5 cents.

Oz.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I was thinking more in terms of Pythagoras' theorem. When
> you push the string down, you stretch the vibrating part
> according to a formula. I want to know the formula. Maybe
> Manuel can help?
>
> Oz.
>
> From: Mohajeri Shahin
> > Hi brother
>
> > I believe that in acoustic music , pitch error is an
> > inavoidable thing because your control on instrument
> > will change everything.

If you intended to calculate with high numerical precision
wouldn't you want to know how the materials deform as the
strain is raised by stretching the string, and for your
finger as well?

Clark

Download from the link near the bottom of this page, and adjust the values for your tuning and the nut to bridge distance (decimal inches or mm).

http://www.lucytune.com/guitars_and_frets/frets.html

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 6 Jul 2007, at 19:20, threesixesinarow wrote:

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > I was thinking more in terms of Pythagoras' theorem. When
> > you push the string down, you stretch the vibrating part
> > according to a formula. I want to know the formula. Maybe
> > Manuel can help?
> >
> > Oz.
> >
> > From: Mohajeri Shahin
> > > Hi brother
> >
> > > I believe that in acoustic music , pitch error is an
> > > inavoidable thing because your control on instrument
> > > will change everything.
>
> If you intended to calculate with high numerical precision
> wouldn't you want to know how the materials deform as the
> strain is raised by stretching the string, and for your
> finger as well?
>
> Clark
>
>
>

The classic frequency equation for strings states that frequency is
directly proportional to the square root of tension, and inversely
proportional to length.

If you push down (or up) on a string and the frequency increases,
then elongation of the string is not a factor because as the string
length increases, the string frequency decreases.

However, if you push down (or up) on a string and the frequency
increases, then tension is a factor because as the tension
increases, the frequency increases as well.

The "action" of strings, or their height above the frets, is the
critical determining factor with respect "bending" the frequency of
a string, or increasing the frequency of a string.

Since the height of the strings above the frets varies considerable
on a given instrument, and among different instruments of the same
kind -- among guitars, tunburs, etc. -- a practical equation that
accounts for these increases in tension is not feasible.

Cris Forster

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I was thinking more in terms of Pythagoras' theorem. When you push
the string down, you stretch the vibrating part according to a
formula. I want to know the formula. Maybe Manuel can help?
>
> Oz.
>
> ----- Original Message -----
> From: Mohajeri Shahin
> To: tuning@yahoogroups.com
> Sent: 05 Temmuz 2007 Perþembe 6:53
> Subject: RE: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was
53 drawing, as an extension of Re: pseudo-Odo _dialogus_
>
>
> Hi brother
>
> I believe that in acoustic music , pitch error is an inavoidable
thing because your control on instrument will change everything.
> But ,an important thing to mention , as you know , is that it is
mostly related to compensation as is discussed in
http://www.mandolincafe.com/glossary/glossary_60.shtml and other
related links.
> EDL and many other measurements are for a physical ideal string
but many other things have effect on these ratios:
http://www.classicalandflamencoguitars.com/Compensation4.htm
> My experience for fretting setar is that at first i must have
compensated octave fret in its best condition due to my ear error
and sound analyzer's result and then use EDL to fret other frets as
compared with octave fret ( as mentioned in my EDO-EDL sheet).
> So if anyone wants to fret instrument , firstly must compensate
frets to delete errors as is done for guitars.
> also uncertainty principle of frequency analysis http://www-
gewi.uni-graz.at/staff/parncutt/PSYCHOACOUSTICS.pdf have somethings
to say.
> and this may be is useful for
you :http://www.wellesley.edu/Physics/brown/pubs/vibPerF100P1728-
P1735.pdf
>
>
>
> Shaahin Mohajeri
>
> Tombak Player & Researcher , Microtonal Composer
>
> My web site?? ???? ????? ??????
>
> My farsi page in Harmonytalk ???? ??????? ?? ??????? ???
>
> Shaahin Mohajeri in
Wikipedia ????? ?????? ??????? ??????? ???? ????
>
>
>
>
>
> -------------------------------------------------------------------
-----------
> From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On
Behalf Of Ozan Yarman
> Sent: Wednesday, July 04, 2007 4:42 PM
> To: tuning@yahoogroups.com
> Subject: Re: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's, was
53 drawing, as an extension of Re: pseudo-Odo _dialogus_
>
>
>
> 3100-EDL is a fine choice. But how do we include the error
caused by the inclination of the string when fingers touch the frets?
>
> Oz.
> ----- Original Message -----
> From: Mohajeri Shahin
> To: tuning@yahoogroups.com
> Sent: 04 Temmuz 2007 Çarþamba 15:43
> Subject: RE: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's,
was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_
>
>
> Hi ozan
> according to my EDO-EDL calculator , 3100-Edl is a good
choic.3101-EDl cant satisfy you but 3102-EDL is better than 3100.
>
> Shaahin Mohajeri
>
> Tombak Player & Researcher , Microtonal Composer
>
> My web site?? ???? ????? ??????
>
> My farsi page in Harmonytalk ???? ??????? ?? ??????? ???
>
> Shaahin Mohajeri in
Wikipedia ????? ?????? ??????? ??????? ???? ????
>
>
>
>
>
> -------------------------------------------------------------------
---------
> From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com]
On Behalf Of Ozan Yarman
> Sent: Wednesday, July 04, 2007 3:48 PM
> To: tuning@yahoogroups.com
> Subject: Re: 612-EDL and 53-EDO ; RE: [tuning] 612 Newton's,
was 53 drawing, as an extension of Re: pseudo-Odo _dialogus_
>
>
>
> What is the best EDL to approximate 159-EDO? Error for each
pitch should be less than 0.5 cents.
>
> Oz.
>

But we already know all that... what we need is a compensator equation given
the distance the string goes down. If the inclination of the string in
regards to the fretboard changes, that should be part of the formula.

Oz.

----- Original Message -----
From: "Cris Forster" <cris.forster@comcast.net>
To: <tuning@yahoogroups.com>
Sent: 06 Temmuz 2007 Cuma 23:25
Subject: [tuning] Re: Fret calculation

The classic frequency equation for strings states that frequency is
directly proportional to the square root of tension, and inversely
proportional to length.

If you push down (or up) on a string and the frequency increases,
then elongation of the string is not a factor because as the string
length increases, the string frequency decreases.

However, if you push down (or up) on a string and the frequency
increases, then tension is a factor because as the tension
increases, the frequency increases as well.

The "action" of strings, or their height above the frets, is the
critical determining factor with respect "bending" the frequency of
a string, or increasing the frequency of a string.

Since the height of the strings above the frets varies considerable
on a given instrument, and among different instruments of the same
kind -- among guitars, tunburs, etc. -- a practical equation that
accounts for these increases in tension is not feasible.

Cris Forster

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> I was thinking more in terms of Pythagoras' theorem. When you push
the string down, you stretch the vibrating part according to a
formula. I want to know the formula. Maybe Manuel can help?
>
> Oz.

It looks very complicated when I behold it. All I'm asking for is a formula.

Oz.
----- Original Message -----
From: Charles Lucy
To: tuning@yahoogroups.com
Sent: 06 Temmuz 2007 Cuma 21:35
Subject: Re: [tuning] Re: Fret calculation - This .xls will do all the calculations for you.

Download from the link near the bottom of this page, and adjust the values for your tuning and the nut to bridge distance (decimal inches or mm).

http://www.lucytune.com/guitars_and_frets/frets.html

Charles Lucy lucy@lucytune.com

----- Original Message -----
From: "threesixesinarow" <CACCOLA@NET1PLUS.COM>
To: <tuning@yahoogroups.com>
Sent: 06 Temmuz 2007 Cuma 21:20
Subject: [tuning] Re: Fret calculation

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > I was thinking more in terms of Pythagoras' theorem. When
> > you push the string down, you stretch the vibrating part
> > according to a formula. I want to know the formula. Maybe
> > Manuel can help?
> >
> > Oz.
> >
> > From: Mohajeri Shahin
> > > Hi brother
> >
> > > I believe that in acoustic music , pitch error is an
> > > inavoidable thing because your control on instrument
> > > will change everything.
>
> If you intended to calculate with high numerical precision
> wouldn't you want to know how the materials deform as the
> strain is raised by stretching the string, and for your
> finger as well?
>
> Clark
>
>

I intend to calculate with fair precision only. What you enumerate are not
for the faint of heart!

Oz.

A formula would assume that thin strings and thick strings respond
identically to a secondary vertical (down-bearing) force, or respond
identically to "the distance the string goes down."

A formula would assume that pressing down on a string in the center
of its length has the same effect, or poses the same resistances as
pressing down a string near the nut or near the bridge.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> But we already know all that... what we need is a compensator
equation given
> the distance the string goes down. If the inclination of the
string in
> regards to the fretboard changes, that should be part of the
formula.
>
> Oz.
>
> ----- Original Message -----
> From: "Cris Forster" <cris.forster@...>
> To: <tuning@yahoogroups.com>
> Sent: 06 Temmuz 2007 Cuma 23:25
> Subject: [tuning] Re: Fret calculation
>
>
> The classic frequency equation for strings states that frequency is
> directly proportional to the square root of tension, and inversely
> proportional to length.
>
> If you push down (or up) on a string and the frequency increases,
> then elongation of the string is not a factor because as the string
> length increases, the string frequency decreases.
>
> However, if you push down (or up) on a string and the frequency
> increases, then tension is a factor because as the tension
> increases, the frequency increases as well.
>
> The "action" of strings, or their height above the frets, is the
> critical determining factor with respect "bending" the frequency of
> a string, or increasing the frequency of a string.
>
> Since the height of the strings above the frets varies considerable
> on a given instrument, and among different instruments of the same
> kind -- among guitars, tunburs, etc. -- a practical equation that
> accounts for these increases in tension is not feasible.
>
> Cris Forster
>
>
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > I was thinking more in terms of Pythagoras' theorem. When you
push
> the string down, you stretch the vibrating part according to a
> formula. I want to know the formula. Maybe Manuel can help?
> >
> > Oz.
>

The first guitars that I calculated fretting for were electric guitars with adjustable bridges.

The difficulty is to decide exactly what the nut to bridge distance should be counted as.

The way I handled this was to take the distance from the centre of the travel of the adjustable bridge to the nut.

I used the resulting value to calculate the fret positions using the old length(1)/freq(1) and freq(2)length(2) formula, to find the fret to bridge distances for each fret.

When marked, cut and installed by a competent luthier by measuring to the distances that I had specified from the nut,

all I had to do was to adjust the bridge position for each individual string.

I adjust the bridge position so that the pitch sounded by gently touching each string near the octave fret,

sound the same pitch as I get by playing (as cleanly as possible) by depressing the string at the octave fret.

This is the usual way that luthiers and guitarists "set their intonation", for once you have got the octave pitches right, all the other frets

(assuming your calculations and fretwork has been done correctly) should work proportionally.

This is a very pragmatic way of doing things, and for me it passes the ultimate test; i.e. it works!

I, too, had played around, in vain, with the idea of string tensions, string weight, height from fretboard, etc. etc. yet when it comes down to physical reality, I have yet to find a better method than

this pragmatic and obvious way of doing things.

There are just too many imponderable factors and variables to consider using a more mathematically complex solution.

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 6 Jul 2007, at 23:43, Cris Forster wrote:

> A formula would assume that thin strings and thick strings respond
> identically to a secondary vertical (down-bearing) force, or respond
> identically to "the distance the string goes down."
>
> A formula would assume that pressing down on a string in the center
> of its length has the same effect, or poses the same resistances as
> pressing down a string near the nut or near the bridge.
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > But we already know all that... what we need is a compensator
> equation given
> > the distance the string goes down. If the inclination of the
> string in
> > regards to the fretboard changes, that should be part of the
> formula.
> >
> > Oz.
> >
> > ----- Original Message -----
> > From: "Cris Forster" <cris.forster@...>
> > To: <tuning@yahoogroups.com>
> > Sent: 06 Temmuz 2007 Cuma 23:25
> > Subject: [tuning] Re: Fret calculation
> >
> >
> > The classic frequency equation for strings states that frequency is
> > directly proportional to the square root of tension, and inversely
> > proportional to length.
> >
> > If you push down (or up) on a string and the frequency increases,
> > then elongation of the string is not a factor because as the string
> > length increases, the string frequency decreases.
> >
> > However, if you push down (or up) on a string and the frequency
> > increases, then tension is a factor because as the tension
> > increases, the frequency increases as well.
> >
> > The "action" of strings, or their height above the frets, is the
> > critical determining factor with respect "bending" the frequency of
> > a string, or increasing the frequency of a string.
> >
> > Since the height of the strings above the frets varies considerable
> > on a given instrument, and among different instruments of the same
> > kind -- among guitars, tunburs, etc. -- a practical equation that
> > accounts for these increases in tension is not feasible.
> >
> > Cris Forster
> >
> >
> >
> >
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > I was thinking more in terms of Pythagoras' theorem. When you
> push
> > the string down, you stretch the vibrating part according to a
> > formula. I want to know the formula. Maybe Manuel can help?
> > >
> > > Oz.
> >
>
>
>

Absolutely, this minimizes the down-bearing force,
and gives empirical data for making sensitive
adjustments. Isn't imperfection wonderful?!

> I adjust the bridge position so that the pitch sounded by gently
> touching each string near the octave fret,

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> The first guitars that I calculated fretting for were electric
> guitars with adjustable bridges.
>
> The difficulty is to decide exactly what the nut to bridge
distance
> should be counted as.
>
> The way I handled this was to take the distance from the centre
of
> the travel of the adjustable bridge to the nut.
>
> I used the resulting value to calculate the fret positions using
the
> old length(1)/freq(1) and freq(2)length(2) formula, to find the
fret
> to bridge distances for each fret.
>
> When marked, cut and installed by a competent luthier by measuring
to
> the distances that I had specified from the nut,
>
> all I had to do was to adjust the bridge position for each
individual
> string.
>
> I adjust the bridge position so that the pitch sounded by gently
> touching each string near the octave fret,
>
> sound the same pitch as I get by playing (as cleanly as possible)
by
> depressing the string at the octave fret.
>
> This is the usual way that luthiers and guitarists "set their
> intonation", for once you have got the octave pitches right, all
the
> other frets
>
> (assuming your calculations and fretwork has been done correctly)
> should work proportionally.
>
> This is a very pragmatic way of doing things, and for me it
passes
> the ultimate test; i.e. it works!
>
> I, too, had played around, in vain, with the idea of string
tensions,
> string weight, height from fretboard, etc. etc. yet when it comes
> down to physical reality, I have yet to find a better method than
>
> this pragmatic and obvious way of doing things.
>
> There are just too many imponderable factors and variables to
> consider using a more mathematically complex solution.
>
>
> Charles Lucy lucy@...
>
> ----- Promoting global harmony through LucyTuning -----
>
> For information on LucyTuning go to: http://www.lucytune.com
>
> LucyTuned Lullabies (from around the world):
> http://www.lullabies.co.uk
>
> Skype user = lucytune
>
> http://www.myspace.com/lucytuning
>
>
> On 6 Jul 2007, at 23:43, Cris Forster wrote:
>
> > A formula would assume that thin strings and thick strings
respond
> > identically to a secondary vertical (down-bearing) force, or
respond
> > identically to "the distance the string goes down."
> >
> > A formula would assume that pressing down on a string in the
center
> > of its length has the same effect, or poses the same resistances
as
> > pressing down a string near the nut or near the bridge.
> >
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > But we already know all that... what we need is a compensator
> > equation given
> > > the distance the string goes down. If the inclination of the
> > string in
> > > regards to the fretboard changes, that should be part of the
> > formula.
> > >
> > > Oz.
> > >
> > > ----- Original Message -----
> > > From: "Cris Forster" <cris.forster@>
> > > To: <tuning@yahoogroups.com>
> > > Sent: 06 Temmuz 2007 Cuma 23:25
> > > Subject: [tuning] Re: Fret calculation
> > >
> > >
> > > The classic frequency equation for strings states that
frequency is
> > > directly proportional to the square root of tension, and
inversely
> > > proportional to length.
> > >
> > > If you push down (or up) on a string and the frequency
increases,
> > > then elongation of the string is not a factor because as the
string
> > > length increases, the string frequency decreases.
> > >
> > > However, if you push down (or up) on a string and the frequency
> > > increases, then tension is a factor because as the tension
> > > increases, the frequency increases as well.
> > >
> > > The "action" of strings, or their height above the frets, is
the
> > > critical determining factor with respect "bending" the
frequency of
> > > a string, or increasing the frequency of a string.
> > >
> > > Since the height of the strings above the frets varies
considerable
> > > on a given instrument, and among different instruments of the
same
> > > kind -- among guitars, tunburs, etc. -- a practical equation
that
> > > accounts for these increases in tension is not feasible.
> > >
> > > Cris Forster
> > >
> > >
> > >
> > >
> > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@>
wrote:
> > > >
> > > > I was thinking more in terms of Pythagoras' theorem. When you
> > push
> > > the string down, you stretch the vibrating part according to a
> > > formula. I want to know the formula. Maybe Manuel can help?
> > > >
> > > > Oz.
> > >
> >
> >
> >
>

Do these matter so much in the calculations? Or are their effect negligible?

----- Original Message -----
From: "Cris Forster" <cris.forster@comcast.net>
To: <tuning@yahoogroups.com>
Sent: 07 Temmuz 2007 Cumartesi 1:43
Subject: [tuning] Re: Fret calculation

> A formula would assume that thin strings and thick strings respond
> identically to a secondary vertical (down-bearing) force, or respond
> identically to "the distance the string goes down."
>
> A formula would assume that pressing down on a string in the center
> of its length has the same effect, or poses the same resistances as
> pressing down a string near the nut or near the bridge.
>
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > But we already know all that... what we need is a compensator
> equation given
> > the distance the string goes down. If the inclination of the
> string in
> > regards to the fretboard changes, that should be part of the
> formula.
> >
> > Oz.
> >

Finally, some pragmatical approach! Thank you Charles.

So, once more in terms I can understand: should I employ 1006-ADO values to tie frets to the tanbur and then adjust the bridge, using the octave fret to check for unison?

Oz.
----- Original Message -----
From: Charles Lucy
To: tuning@yahoogroups.com
Sent: 07 Temmuz 2007 Cumartesi 2:22
Subject: Re: [tuning] Re: Fret calculation - Fret positioning in the real world.

The first guitars that I calculated fretting for were electric guitars with adjustable bridges.

The difficulty is to decide exactly what the nut to bridge distance should be counted as.

The way I handled this was to take the distance from the centre of the travel of the adjustable bridge to the nut.

I used the resulting value to calculate the fret positions using the old length(1)/freq(1) and freq(2)length(2) formula, to find the fret to bridge distances for each fret.

When marked, cut and installed by a competent luthier by measuring to the distances that I had specified from the nut,

all I had to do was to adjust the bridge position for each individual string.

I adjust the bridge position so that the pitch sounded by gently touching each string near the octave fret,

sound the same pitch as I get by playing (as cleanly as possible) by depressing the string at the octave fret.

This is the usual way that luthiers and guitarists "set their intonation", for once you have got the octave pitches right, all the other frets

(assuming your calculations and fretwork has been done correctly) should work proportionally.

This is a very pragmatic way of doing things, and for me it passes the ultimate test; i.e. it works!

I, too, had played around, in vain, with the idea of string tensions, string weight, height from fretboard, etc. etc. yet when it comes down to physical reality, I have yet to find a better method than

this pragmatic and obvious way of doing things.

There are just too many imponderable factors and variables to consider using a more mathematically complex solution.

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 6 Jul 2007, at 23:43, Cris Forster wrote:

A formula would assume that thin strings and thick strings respond
identically to a secondary vertical (down-bearing) force, or respond
identically to "the distance the string goes down."

A formula would assume that pressing down on a string in the center
of its length has the same effect, or poses the same resistances as
pressing down a string near the nut or near the bridge.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> But we already know all that... what we need is a compensator
equation given
> the distance the string goes down. If the inclination of the
string in
> regards to the fretboard changes, that should be part of the
formula.
>
> Oz.
>
> ----- Original Message -----
> From: "Cris Forster" <cris.forster@...>
> To: <tuning@yahoogroups.com>
> Sent: 06 Temmuz 2007 Cuma 23:25
> Subject: [tuning] Re: Fret calculation
>
>
> The classic frequency equation for strings states that frequency is
> directly proportional to the square root of tension, and inversely
> proportional to length.
>
> If you push down (or up) on a string and the frequency increases,
> then elongation of the string is not a factor because as the string
> length increases, the string frequency decreases.
>
> However, if you push down (or up) on a string and the frequency
> increases, then tension is a factor because as the tension
> increases, the frequency increases as well.
>
> The "action" of strings, or their height above the frets, is the
> critical determining factor with respect "bending" the frequency of
> a string, or increasing the frequency of a string.
>
> Since the height of the strings above the frets varies considerable
> on a given instrument, and among different instruments of the same
> kind -- among guitars, tunburs, etc. -- a practical equation that
> accounts for these increases in tension is not feasible.
>
> Cris Forster
>
>
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > I was thinking more in terms of Pythagoras' theorem. When you
push
> the string down, you stretch the vibrating part according to a
> formula. I want to know the formula. Maybe Manuel can help?
> >
> > Oz.
>

In the world of acoustic music making, I would advise against
dictating string diameter and string-to-fret clearance (i.e., down-
bearing force) parameters to instrument builders and musicians.
State your case with respect to scales and frequencies (i.e., cent
values) and let builders and musicians exercise their years of
experience and freedom of choice. All stringed instruments,
especially the koto, rely on the illusive down-bearing force not
only for acoustic reasons (an efficient transfer of wave energy from
string, to bridge, to soundboard, to the surrounding air), but for
musically expressive reasons as well.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Do these matter so much in the calculations? Or are their effect
negligible?
>
> ----- Original Message -----
> From: "Cris Forster" <cris.forster@...>
> To: <tuning@yahoogroups.com>
> Sent: 07 Temmuz 2007 Cumartesi 1:43
> Subject: [tuning] Re: Fret calculation
>
>
> > A formula would assume that thin strings and thick strings
respond
> > identically to a secondary vertical (down-bearing) force, or
respond
> > identically to "the distance the string goes down."
> >
> > A formula would assume that pressing down on a string in the
center
> > of its length has the same effect, or poses the same resistances
as
> > pressing down a string near the nut or near the bridge.
> >
> >
> >
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > But we already know all that... what we need is a compensator
> > equation given
> > > the distance the string goes down. If the inclination of the
> > string in
> > > regards to the fretboard changes, that should be part of the
> > formula.
> > >
> > > Oz.
> > >
>

So, I have no saying in how to fret a tanbur, is that what you are saying?

Oz.

----- Original Message -----
From: "Cris Forster" <cris.forster@comcast.net>
To: <tuning@yahoogroups.com>
Sent: 07 Temmuz 2007 Cumartesi 18:10
Subject: [tuning] Re: Fret calculation

> In the world of acoustic music making, I would advise against
> dictating string diameter and string-to-fret clearance (i.e., down-
> bearing force) parameters to instrument builders and musicians.
> State your case with respect to scales and frequencies (i.e., cent
> values) and let builders and musicians exercise their years of
> experience and freedom of choice. All stringed instruments,
> especially the koto, rely on the illusive down-bearing force not
> only for acoustic reasons (an efficient transfer of wave energy from
> string, to bridge, to soundboard, to the surrounding air), but for
> musically expressive reasons as well.
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Do these matter so much in the calculations? Or are their effect
> negligible?
> >
> > ----- Original Message -----
> > From: "Cris Forster" <cris.forster@...>
> > To: <tuning@yahoogroups.com>
> > Sent: 07 Temmuz 2007 Cumartesi 1:43
> > Subject: [tuning] Re: Fret calculation
> >
> >
> > > A formula would assume that thin strings and thick strings
> respond
> > > identically to a secondary vertical (down-bearing) force, or
> respond
> > > identically to "the distance the string goes down."
> > >
> > > A formula would assume that pressing down on a string in the
> center
> > > of its length has the same effect, or poses the same resistances
> as
> > > pressing down a string near the nut or near the bridge.
> > >
> > >
> > >
> > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > > >
> > > > But we already know all that... what we need is a compensator
> > > equation given
> > > > the distance the string goes down. If the inclination of the
> > > string in
> > > > regards to the fretboard changes, that should be part of the
> > > formula.
> > > >
> > > > Oz.
> > > >
> >
>

Since when do string diameters and string-to-fret clearances
constitute frets or placements of frets?

Say and do whatever you want.

Know this, there is nothing negligible about the
down-bearing force: ask any koto or sitar player.

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> So, I have no saying in how to fret a tanbur, is that what you are
saying?
>
> Oz.
>
> ----- Original Message -----
> From: "Cris Forster" <cris.forster@...>
> To: <tuning@yahoogroups.com>
> Sent: 07 Temmuz 2007 Cumartesi 18:10
> Subject: [tuning] Re: Fret calculation
>
>
> > In the world of acoustic music making, I would advise against
> > dictating string diameter and string-to-fret clearance (i.e.,
down-
> > bearing force) parameters to instrument builders and musicians.
> > State your case with respect to scales and frequencies (i.e.,
cent
> > values) and let builders and musicians exercise their years of
> > experience and freedom of choice. All stringed instruments,
> > especially the koto, rely on the illusive down-bearing force not
> > only for acoustic reasons (an efficient transfer of wave energy
from
> > string, to bridge, to soundboard, to the surrounding air), but
for
> > musically expressive reasons as well.
> >
> >
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > Do these matter so much in the calculations? Or are their
effect
> > negligible?
> > >
> > > ----- Original Message -----
> > > From: "Cris Forster" <cris.forster@>
> > > To: <tuning@yahoogroups.com>
> > > Sent: 07 Temmuz 2007 Cumartesi 1:43
> > > Subject: [tuning] Re: Fret calculation
> > >
> > >
> > > > A formula would assume that thin strings and thick strings
> > respond
> > > > identically to a secondary vertical (down-bearing) force, or
> > respond
> > > > identically to "the distance the string goes down."
> > > >
> > > > A formula would assume that pressing down on a string in the
> > center
> > > > of its length has the same effect, or poses the same
resistances
> > as
> > > > pressing down a string near the nut or near the bridge.
> > > >
> > > >
> > > >
> > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@>
wrote:
> > > > >
> > > > > But we already know all that... what we need is a
compensator
> > > > equation given
> > > > > the distance the string goes down. If the inclination of
the
> > > > string in
> > > > > regards to the fretboard changes, that should be part of
the
> > > > formula.
> > > > >
> > > > > Oz.
> > > > >
> > >
> >
>

We are after all trying to determine the pitch change caused by the
down-bearing force.

----- Original Message -----
From: "Cris Forster" <cris.forster@comcast.net>
To: <tuning@yahoogroups.com>
Sent: 07 Temmuz 2007 Cumartesi 19:59
Subject: [tuning] Re: Fret calculation

> Since when do string diameters and string-to-fret clearances
> constitute frets or placements of frets?
>
> Say and do whatever you want.
>
> Know this, there is nothing negligible about the
> down-bearing force: ask any koto or sitar player.
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > So, I have no saying in how to fret a tanbur, is that what you are
> saying?
> >
> > Oz.
> >
> > ----- Original Message -----
> > From: "Cris Forster" <cris.forster@...>
> > To: <tuning@yahoogroups.com>
> > Sent: 07 Temmuz 2007 Cumartesi 18:10
> > Subject: [tuning] Re: Fret calculation
> >
> >
> > > In the world of acoustic music making, I would advise against
> > > dictating string diameter and string-to-fret clearance (i.e.,
> down-
> > > bearing force) parameters to instrument builders and musicians.
> > > State your case with respect to scales and frequencies (i.e.,
> cent
> > > values) and let builders and musicians exercise their years of
> > > experience and freedom of choice. All stringed instruments,
> > > especially the koto, rely on the illusive down-bearing force not
> > > only for acoustic reasons (an efficient transfer of wave energy
> from
> > > string, to bridge, to soundboard, to the surrounding air), but
> for
> > > musically expressive reasons as well.
> > >
> > >

From my unpublished book
"Musical Mathematics."

"In vibrating bars, there are two restoring forces: a bending
moment ( M ) that induces rotation about a given point in the bar,
and a shear force ( V ) that induces translation in a direction
perpendicular to the bar's horizontal axis. That is, M causes
bending motion in a circular direction, and V causes linear motion
in a vertical direction. In vibrating bars, these two forces act
as a single restoring force. Note, however, that M and V do not
appear as variables in frequency Equations 6.1 and 6.11. The reason
for this omission is that both forces vary with space (or a given
location in the bar) and time (or a given instant in the period of
vibration). Therefore, it is not possible to quantify M and V for
use in frequency equations. Since both forces are directly
proportional to the bending stiffness ( B ) of a bar, we may
interpret an increase or decrease in B as an increase or decrease in
M and V."

This general principle also applies to strings. There are two
restoring forces at work: A tension force ( T ) and acts in a
horizontal direction, and a shear force ( V [string] ) that acts in
a vertical direction. The latter down-bearing force varies with
space (or a given location in the string). Therefore, it is not
possible to quantify ( V [string] ) for use in frequency equations.

Imagine a trampoline or a board supported at the ends by bricks. As
you jump up and down, where do you suppose the greatest amount of
motion is: in the center or at the ends? The same applies to bars
and strings: rates of vertical deflection and the down-bearing
forces required to produce these deflections vary with space, or at
given locations in vibrating systems.

All of these observations and conclusion arise from solutions to
partial differential equations, some of which took several
generations of mathematicians to solve. I am not one of them.

Cris Forster

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> We are after all trying to determine the pitch change caused by the
> down-bearing force.
>
>
> ----- Original Message -----
> From: "Cris Forster" <cris.forster@...>
> To: <tuning@yahoogroups.com>
> Sent: 07 Temmuz 2007 Cumartesi 19:59
> Subject: [tuning] Re: Fret calculation
>
>
> > Since when do string diameters and string-to-fret clearances
> > constitute frets or placements of frets?
> >
> > Say and do whatever you want.
> >
> > Know this, there is nothing negligible about the
> > down-bearing force: ask any koto or sitar player.
> >
> >
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > So, I have no saying in how to fret a tanbur, is that what you
are
> > saying?
> > >
> > > Oz.
> > >
> > > ----- Original Message -----
> > > From: "Cris Forster" <cris.forster@>
> > > To: <tuning@yahoogroups.com>
> > > Sent: 07 Temmuz 2007 Cumartesi 18:10
> > > Subject: [tuning] Re: Fret calculation
> > >
> > >
> > > > In the world of acoustic music making, I would advise against
> > > > dictating string diameter and string-to-fret clearance (i.e.,
> > down-
> > > > bearing force) parameters to instrument builders and
musicians.
> > > > State your case with respect to scales and frequencies (i.e.,
> > cent
> > > > values) and let builders and musicians exercise their years
of
> > > > experience and freedom of choice. All stringed instruments,
> > > > especially the koto, rely on the illusive down-bearing force
not
> > > > only for acoustic reasons (an efficient transfer of wave
energy
> > from
> > > > string, to bridge, to soundboard, to the surrounding air),
but
> > for
> > > > musically expressive reasons as well.
> > > >
> > > >
>

And where does this lead us?

----- Original Message -----
From: "Cris Forster" <cris.forster@comcast.net>
To: <tuning@yahoogroups.com>
Sent: 07 Temmuz 2007 Cumartesi 21:17
Subject: [tuning] Re: Fret calculation

> From my unpublished book
> "Musical Mathematics."
>
> "In vibrating bars, there are two restoring forces: a bending
> moment ( M ) that induces rotation about a given point in the bar,
> and a shear force ( V ) that induces translation in a direction
> perpendicular to the bar's horizontal axis. That is, M causes
> bending motion in a circular direction, and V causes linear motion
> in a vertical direction. In vibrating bars, these two forces act
> as a single restoring force. Note, however, that M and V do not
> appear as variables in frequency Equations 6.1 and 6.11. The reason
> for this omission is that both forces vary with space (or a given
> location in the bar) and time (or a given instant in the period of
> vibration). Therefore, it is not possible to quantify M and V for
> use in frequency equations. Since both forces are directly
> proportional to the bending stiffness ( B ) of a bar, we may
> interpret an increase or decrease in B as an increase or decrease in
> M and V."
>
> This general principle also applies to strings. There are two
> restoring forces at work: A tension force ( T ) and acts in a
> horizontal direction, and a shear force ( V [string] ) that acts in
> a vertical direction. The latter down-bearing force varies with
> space (or a given location in the string). Therefore, it is not
> possible to quantify ( V [string] ) for use in frequency equations.
>
> Imagine a trampoline or a board supported at the ends by bricks. As
> you jump up and down, where do you suppose the greatest amount of
> motion is: in the center or at the ends? The same applies to bars
> and strings: rates of vertical deflection and the down-bearing
> forces required to produce these deflections vary with space, or at
> given locations in vibrating systems.
>
> All of these observations and conclusion arise from solutions to
> partial differential equations, some of which took several
> generations of mathematicians to solve. I am not one of them.
>
> Cris Forster
>
>
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > We are after all trying to determine the pitch change caused by the
> > down-bearing force.
> >
> >
> > ----- Original Message -----
> > From: "Cris Forster" <cris.forster@...>
> > To: <tuning@yahoogroups.com>
> > Sent: 07 Temmuz 2007 Cumartesi 19:59
> > Subject: [tuning] Re: Fret calculation
> >
> >
> > > Since when do string diameters and string-to-fret clearances
> > > constitute frets or placements of frets?
> > >
> > > Say and do whatever you want.
> > >
> > > Know this, there is nothing negligible about the
> > > down-bearing force: ask any koto or sitar player.
> > >
> > >
> > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > > >
> > > > So, I have no saying in how to fret a tanbur, is that what you
> are
> > > saying?
> > > >
> > > > Oz.
> > > >
> > > > ----- Original Message -----
> > > > From: "Cris Forster" <cris.forster@>
> > > > To: <tuning@yahoogroups.com>
> > > > Sent: 07 Temmuz 2007 Cumartesi 18:10
> > > > Subject: [tuning] Re: Fret calculation
> > > >
> > > >
> > > > > In the world of acoustic music making, I would advise against
> > > > > dictating string diameter and string-to-fret clearance (i.e.,
> > > down-
> > > > > bearing force) parameters to instrument builders and
> musicians.
> > > > > State your case with respect to scales and frequencies (i.e.,
> > > cent
> > > > > values) and let builders and musicians exercise their years
> of
> > > > > experience and freedom of choice. All stringed instruments,
> > > > > especially the koto, rely on the illusive down-bearing force
> not
> > > > > only for acoustic reasons (an efficient transfer of wave
> energy
> > > from
> > > > > string, to bridge, to soundboard, to the surrounding air),
> but
> > > for
> > > > > musically expressive reasons as well.
> > > > >
> > > > >
> >
>
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>

Having just endured three hours of traffic jams in central London, thanks to le Tour de France, I return to the tranquility of the tuning list.

I heard where Cris is travelling with this, yet I am very sceptical about all the traditional models for vibrating strings.

As far as I have seen/heard/read/observed most string models seem to consider only longitudinal and transverse wave patterns.

If you watch a vibrating string very carefully you will see that having been displaced from the central stable position by being hit or plucked,

the movement cross-section becomes oval and eventually circular, as the whole string returns to its resting position.

The patterns are so mathematically complex that no-one seems yet to have been able to describe them very accurately.

So, for example, you begin looking at the patterns as you would a pendulum, or a dozen other potential comparisons.

You read all the books you can find about sine waves, and the traditional models of harmonics; and the "old" models are still incomplete, and fail make practical, and logical sense.

There is always this enticing hint that there is something subtle and even more fundamental underlying the simplistic and obvious traditional models.

Certainly you need to consider three dimensions plus time, yet do you do this for each theoretical point on the string, for the general shape of the string?

How does the resonator, other strings, the striking method, and a thousand other factors influence the sound that you hear?

How do your ears perceive the sound?

How does your brain process it?

How do you perceive the extremely complex actions and reactions that are happening so rapidly?

We can look at the visual patterns on our computer screens using this week's latest audio analysis applications.

We can reprocess the audio files through every filter, effect, and enhancement: sample, resample, emulate and (re)synthesise it; yet there is always "something" missing.

The more carefully you listen, the more sounds you heard, the more you get "hooked";-)

So we continue experimenting, continue archiving sounds, melodies, harmonies, and other patterns, which appeal to us;

and gradually we allow them to filter out into the collective consciousness via performances, recordings, radio, TV, films, commercials, and sound files on the net.

Some sell very well; some not at all; yet the universe somehow allows and enables us to continue across the generations.

We must be doing something right;-)

Charles Lucy lucy@lucytune.com

----- Promoting global harmony through LucyTuning -----

For information on LucyTuning go to: http://www.lucytune.com

LucyTuned Lullabies (from around the world):
http://www.lullabies.co.uk

Skype user = lucytune

http://www.myspace.com/lucytuning

On 7 Jul 2007, at 19:17, Cris Forster wrote:

> From my unpublished book
> "Musical Mathematics."
>
> "In vibrating bars, there are two restoring forces: a bending
> moment ( M ) that induces rotation about a given point in the bar,
> and a shear force ( V ) that induces translation in a direction
> perpendicular to the bar's horizontal axis. That is, M causes
> bending motion in a circular direction, and V causes linear motion
> in a vertical direction. In vibrating bars, these two forces act
> as a single restoring force. Note, however, that M and V do not
> appear as variables in frequency Equations 6.1 and 6.11. The reason
> for this omission is that both forces vary with space (or a given
> location in the bar) and time (or a given instant in the period of
> vibration). Therefore, it is not possible to quantify M and V for
> use in frequency equations. Since both forces are directly
> proportional to the bending stiffness ( B ) of a bar, we may
> interpret an increase or decrease in B as an increase or decrease in
> M and V."
>
> This general principle also applies to strings. There are two
> restoring forces at work: A tension force ( T ) and acts in a
> horizontal direction, and a shear force ( V [string] ) that acts in
> a vertical direction. The latter down-bearing force varies with
> space (or a given location in the string). Therefore, it is not
> possible to quantify ( V [string] ) for use in frequency equations.
>
> Imagine a trampoline or a board supported at the ends by bricks. As
> you jump up and down, where do you suppose the greatest amount of
> motion is: in the center or at the ends? The same applies to bars
> and strings: rates of vertical deflection and the down-bearing
> forces required to produce these deflections vary with space, or at
> given locations in vibrating systems.
>
> All of these observations and conclusion arise from solutions to
> partial differential equations, some of which took several
> generations of mathematicians to solve. I am not one of them.
>
> Cris Forster
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > We are after all trying to determine the pitch change caused by the
> > down-bearing force.
> >
> >
> > ----- Original Message -----
> > From: "Cris Forster" <cris.forster@...>
> > To: <tuning@yahoogroups.com>
> > Sent: 07 Temmuz 2007 Cumartesi 19:59
> > Subject: [tuning] Re: Fret calculation
> >
> >
> > > Since when do string diameters and string-to-fret clearances
> > > constitute frets or placements of frets?
> > >
> > > Say and do whatever you want.
> > >
> > > Know this, there is nothing negligible about the
> > > down-bearing force: ask any koto or sitar player.
> > >
> > >
> > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > > >
> > > > So, I have no saying in how to fret a tanbur, is that what you
> are
> > > saying?
> > > >
> > > > Oz.
> > > >
> > > > ----- Original Message -----
> > > > From: "Cris Forster" <cris.forster@>
> > > > To: <tuning@yahoogroups.com>
> > > > Sent: 07 Temmuz 2007 Cumartesi 18:10
> > > > Subject: [tuning] Re: Fret calculation
> > > >
> > > >
> > > > > In the world of acoustic music making, I would advise against
> > > > > dictating string diameter and string-to-fret clearance (i.e.,
> > > down-
> > > > > bearing force) parameters to instrument builders and
> musicians.
> > > > > State your case with respect to scales and frequencies (i.e.,
> > > cent
> > > > > values) and let builders and musicians exercise their years
> of
> > > > > experience and freedom of choice. All stringed instruments,
> > > > > especially the koto, rely on the illusive down-bearing force
> not
> > > > > only for acoustic reasons (an efficient transfer of wave
> energy
> > > from
> > > > > string, to bridge, to soundboard, to the surrounding air),
> but
> > > for
> > > > > musically expressive reasons as well.
> > > > >
> > > > >
> >
>
>
>

You did not distinguish between traveling waves and standing waves.

In vibrating systems such as musical instruments, longitudinal
traveling waves and transverse traveling waves are never visible to
the naked eye.

In musical instruments, longitudinal traveling waves and transverse
traveling never produce sound.

The superposition of longitudinal traveling waves causes
longitudinal standing waves. In musical instruments, only
longitudinal standing waves produce musical (periodic) sound.

The superposition of transverse traveling waves causes transverse
standing waves. In musical instruments, only transverse standing
waves produce musical (periodic) sound.

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Having just endured three hours of traffic jams in central
London,
> thanks to le Tour de France, I return to the tranquility of the
> tuning list.
>
> I heard where Cris is travelling with this, yet I am very
sceptical
> about all the traditional models for vibrating strings.
>
> As far as I have seen/heard/read/observed most string models seem
to
> consider only longitudinal and transverse wave patterns.
>
> If you watch a vibrating string very carefully you will see that
> having been displaced from the central stable position by being
hit
> or plucked,
>
> the movement cross-section becomes oval and eventually circular,
as
> the whole string returns to its resting position.
>
> The patterns are so mathematically complex that no-one seems yet
to
> have been able to describe them very accurately.
>
> So, for example, you begin looking at the patterns as you would a
> pendulum, or a dozen other potential comparisons.
>
> You read all the books you can find about sine waves, and the
> traditional models of harmonics; and the "old" models are still
> incomplete, and fail make practical, and logical sense.
>
> There is always this enticing hint that there is something subtle
and
> even more fundamental underlying the simplistic and obvious
> traditional models.
>
> Certainly you need to consider three dimensions plus time, yet do
you
> do this for each theoretical point on the string, for the general
> shape of the string?
>
> How does the resonator, other strings, the striking method, and a
> thousand other factors influence the sound that you hear?
>
> How do your ears perceive the sound?
>
> How does your brain process it?
>
> How do you perceive the extremely complex actions and reactions
that
> are happening so rapidly?
>
> We can look at the visual patterns on our computer screens using
this
> week's latest audio analysis applications.
>
> We can reprocess the audio files through every filter, effect,
and
> enhancement: sample, resample, emulate and (re)synthesise it; yet
> there is always "something" missing.
>
> The more carefully you listen, the more sounds you heard, the
more
> you get "hooked";-)
>
> So we continue experimenting, continue archiving sounds,
melodies,
> harmonies, and other patterns, which appeal to us;
>
> and gradually we allow them to filter out into the collective
> consciousness via performances, recordings, radio, TV, films,
> commercials, and sound files on the net.
>
>
> Some sell very well; some not at all; yet the universe somehow
allows
> and enables us to continue across the generations.
>
> We must be doing something right;-)
>
>
> Charles Lucy lucy@...
>
> ----- Promoting global harmony through LucyTuning -----
>
> For information on LucyTuning go to: http://www.lucytune.com
>
> LucyTuned Lullabies (from around the world):
> http://www.lullabies.co.uk
>
> Skype user = lucytune
>
> http://www.myspace.com/lucytuning
>
>
> On 7 Jul 2007, at 19:17, Cris Forster wrote:
>
> > From my unpublished book
> > "Musical Mathematics."
> >
> > "In vibrating bars, there are two restoring forces: a bending
> > moment ( M ) that induces rotation about a given point in the
bar,
> > and a shear force ( V ) that induces translation in a direction
> > perpendicular to the bar's horizontal axis. That is, M causes
> > bending motion in a circular direction, and V causes linear
motion
> > in a vertical direction. In vibrating bars, these two forces act
> > as a single restoring force. Note, however, that M and V do not
> > appear as variables in frequency Equations 6.1 and 6.11. The
reason
> > for this omission is that both forces vary with space (or a given
> > location in the bar) and time (or a given instant in the period
of
> > vibration). Therefore, it is not possible to quantify M and V for
> > use in frequency equations. Since both forces are directly
> > proportional to the bending stiffness ( B ) of a bar, we may
> > interpret an increase or decrease in B as an increase or
decrease in
> > M and V."
> >
> > This general principle also applies to strings. There are two
> > restoring forces at work: A tension force ( T ) and acts in a
> > horizontal direction, and a shear force ( V [string] ) that acts
in
> > a vertical direction. The latter down-bearing force varies with
> > space (or a given location in the string). Therefore, it is not
> > possible to quantify ( V [string] ) for use in frequency
equations.
> >
> > Imagine a trampoline or a board supported at the ends by bricks.
As
> > you jump up and down, where do you suppose the greatest amount of
> > motion is: in the center or at the ends? The same applies to bars
> > and strings: rates of vertical deflection and the down-bearing
> > forces required to produce these deflections vary with space, or
at
> > given locations in vibrating systems.
> >
> > All of these observations and conclusion arise from solutions to
> > partial differential equations, some of which took several
> > generations of mathematicians to solve. I am not one of them.
> >
> > Cris Forster
> >
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > We are after all trying to determine the pitch change caused
by the
> > > down-bearing force.
> > >
> > >
> > > ----- Original Message -----
> > > From: "Cris Forster" <cris.forster@>
> > > To: <tuning@yahoogroups.com>
> > > Sent: 07 Temmuz 2007 Cumartesi 19:59
> > > Subject: [tuning] Re: Fret calculation
> > >
> > >
> > > > Since when do string diameters and string-to-fret clearances
> > > > constitute frets or placements of frets?
> > > >
> > > > Say and do whatever you want.
> > > >
> > > > Know this, there is nothing negligible about the
> > > > down-bearing force: ask any koto or sitar player.
> > > >
> > > >
> > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@>
wrote:
> > > > >
> > > > > So, I have no saying in how to fret a tanbur, is that what
you
> > are
> > > > saying?
> > > > >
> > > > > Oz.
> > > > >
> > > > > ----- Original Message -----
> > > > > From: "Cris Forster" <cris.forster@>
> > > > > To: <tuning@yahoogroups.com>
> > > > > Sent: 07 Temmuz 2007 Cumartesi 18:10
> > > > > Subject: [tuning] Re: Fret calculation
> > > > >
> > > > >
> > > > > > In the world of acoustic music making, I would advise
against
> > > > > > dictating string diameter and string-to-fret clearance
(i.e.,
> > > > down-
> > > > > > bearing force) parameters to instrument builders and
> > musicians.
> > > > > > State your case with respect to scales and frequencies
(i.e.,
> > > > cent
> > > > > > values) and let builders and musicians exercise their
years
> > of
> > > > > > experience and freedom of choice. All stringed
instruments,
> > > > > > especially the koto, rely on the illusive down-bearing
force
> > not
> > > > > > only for acoustic reasons (an efficient transfer of wave
> > energy
> > > > from
> > > > > > string, to bridge, to soundboard, to the surrounding
air),
> > but
> > > > for
> > > > > > musically expressive reasons as well.
> > > > > >
> > > > > >
> > >
> >
> >
> >
>

On 7/8/07, Cris Forster <cris.forster@comcast.net> wrote:
> You did not distinguish between traveling waves and standing waves.
>
> In vibrating systems such as musical instruments, longitudinal
> traveling waves and transverse traveling waves are never visible to
> the naked eye.

I beg to differ. If you get a quickly flickering light source such as
an old fluorescent light and play a note on a string instrument close
to its frequency (60 Hz in the US), you can clearly see the transverse
waves. If you pluck it in the middle you'll get mostly fundamental,
but if you pluck it near the end you'll excite many harmonics and the
actual shape of the string will be a traveling wave. If the pitch is
slightly different from 60 Hz you can see it move up and down the
string.

> In musical instruments, longitudinal traveling waves and transverse
> traveling never produce sound.
>
> The superposition of longitudinal traveling waves causes
> longitudinal standing waves. In musical instruments, only
> longitudinal standing waves produce musical (periodic) sound.
>
> The superposition of transverse traveling waves causes transverse
> standing waves. In musical instruments, only transverse standing
> waves produce musical (periodic) sound.

I don't understand what this is supposed to mean. You can describe any
excitation of a string (or bar or pipe or whatever) as the actual
motion of the vibrating element (traveling waves), or as the
magnitudes and phases of all the eigenmodes (standing waves). These
two descriptions describe the same physical phenomenon, so I don't
understand how you can say one "produces sound" and the other doesn't.
They're just two different ways of looking at it, whose implications
are mathematically equivalent.

Keenan

A transverse "wave" is nothing more than a pulse, or a "bump", if
you will. These pulses are either in the shape of troughs, or in
the shape of crests.

An incident crest -- upon encountering an obstacle such as a nut or
bridge -- changes direction AND position, and thus becomes a
reflected trough; vice versa.

Transverse waves or pulses do NOT compress air; therefore, they do
not make sound. Transverse waves push air in front of their leading
surfaces, like your car pushes air in front of its leading surface
(hood or trunk) as it rolls forward or backward.

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...>
wrote:
>
> On 7/8/07, Cris Forster <cris.forster@...> wrote:
> > You did not distinguish between traveling waves and standing
waves.
> >
> > In vibrating systems such as musical instruments, longitudinal
> > traveling waves and transverse traveling waves are never visible
to
> > the naked eye.
>
> I beg to differ. If you get a quickly flickering light source such
as
> an old fluorescent light and play a note on a string instrument
close
> to its frequency (60 Hz in the US), you can clearly see the
transverse
> waves. If you pluck it in the middle you'll get mostly fundamental,
> but if you pluck it near the end you'll excite many harmonics and
the
> actual shape of the string will be a traveling wave. If the pitch
is
> slightly different from 60 Hz you can see it move up and down the
> string.
>
> > In musical instruments, longitudinal traveling waves and
transverse
> > traveling never produce sound.
> >
> > The superposition of longitudinal traveling waves causes
> > longitudinal standing waves. In musical instruments, only
> > longitudinal standing waves produce musical (periodic) sound.
> >
> > The superposition of transverse traveling waves causes transverse
> > standing waves. In musical instruments, only transverse standing
> > waves produce musical (periodic) sound.
>
> I don't understand what this is supposed to mean. You can describe
any
> excitation of a string (or bar or pipe or whatever) as the actual
> motion of the vibrating element (traveling waves), or as the
> magnitudes and phases of all the eigenmodes (standing waves). These
> two descriptions describe the same physical phenomenon, so I don't
> understand how you can say one "produces sound" and the other
doesn't.
> They're just two different ways of looking at it, whose
implications
> are mathematically equivalent.
>
> Keenan
>

For this reason, a traveling wave or pulse never has a frequency;
it "only" has a speed. One always speaks of the speed (velocity) of
a traveling wave; never of the frequency of a traveling wave.

For this reason, a standing wave never has a speed; it "only" has a
frequency. One always speaks of the frequency of a standing wave;
never of the speed of a standing wave.

> They're just two different ways of looking at it, whose
>implications are mathematically equivalent.

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...>
wrote:
>
> On 7/8/07, Cris Forster <cris.forster@...> wrote:
> > You did not distinguish between traveling waves and standing
waves.
> >
> > In vibrating systems such as musical instruments, longitudinal
> > traveling waves and transverse traveling waves are never visible
to
> > the naked eye.
>
> I beg to differ. If you get a quickly flickering light source such
as
> an old fluorescent light and play a note on a string instrument
close
> to its frequency (60 Hz in the US), you can clearly see the
transverse
> waves. If you pluck it in the middle you'll get mostly fundamental,
> but if you pluck it near the end you'll excite many harmonics and
the
> actual shape of the string will be a traveling wave. If the pitch
is
> slightly different from 60 Hz you can see it move up and down the
> string.
>
> > In musical instruments, longitudinal traveling waves and
transverse
> > traveling never produce sound.
> >
> > The superposition of longitudinal traveling waves causes
> > longitudinal standing waves. In musical instruments, only
> > longitudinal standing waves produce musical (periodic) sound.
> >
> > The superposition of transverse traveling waves causes transverse
> > standing waves. In musical instruments, only transverse standing
> > waves produce musical (periodic) sound.
>
> I don't understand what this is supposed to mean. You can describe
any
> excitation of a string (or bar or pipe or whatever) as the actual
> motion of the vibrating element (traveling waves), or as the
> magnitudes and phases of all the eigenmodes (standing waves). These
> two descriptions describe the same physical phenomenon, so I don't
> understand how you can say one "produces sound" and the other
doesn't.
> They're just two different ways of looking at it, whose
implications
> are mathematically equivalent.
>
> Keenan
>

A traveling "wave" is nothing more than a pulse, or a "bump", if you
will. These pulses are either in the shape of troughs, or in the
shape of crests.

An incident crest -- upon encountering an obstacle such as a nut or
bridge -- changes direction AND position, and thus becomes a
reflected trough; vice versa.

Traveling waves or pulses do NOT compress air; therefore, they do
not make sound. Traveling waves push air in front of their leading
surfaces, like your car pushes air in front of its leading surface
(hood or trunk) as it rolls forward or backward.

Sorry for the confusion!

--- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@...>
wrote:
>
> A transverse "wave" is nothing more than a pulse, or a "bump", if
> you will. These pulses are either in the shape of troughs, or in
> the shape of crests.
>
> An incident crest -- upon encountering an obstacle such as a nut
or
> bridge -- changes direction AND position, and thus becomes a
> reflected trough; vice versa.
>
> Transverse waves or pulses do NOT compress air; therefore, they do
> not make sound. Transverse waves push air in front of their
leading
> surfaces, like your car pushes air in front of its leading surface
> (hood or trunk) as it rolls forward or backward.
>
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@>
> wrote:
> >
> > On 7/8/07, Cris Forster <cris.forster@> wrote:
> > > You did not distinguish between traveling waves and standing
> waves.
> > >
> > > In vibrating systems such as musical instruments, longitudinal
> > > traveling waves and transverse traveling waves are never
visible
> to
> > > the naked eye.
> >
> > I beg to differ. If you get a quickly flickering light source
such
> as
> > an old fluorescent light and play a note on a string instrument
> close
> > to its frequency (60 Hz in the US), you can clearly see the
> transverse
> > waves. If you pluck it in the middle you'll get mostly
fundamental,
> > but if you pluck it near the end you'll excite many harmonics
and
> the
> > actual shape of the string will be a traveling wave. If the
pitch
> is
> > slightly different from 60 Hz you can see it move up and down the
> > string.
> >
> > > In musical instruments, longitudinal traveling waves and
> transverse
> > > traveling never produce sound.
> > >
> > > The superposition of longitudinal traveling waves causes
> > > longitudinal standing waves. In musical instruments, only
> > > longitudinal standing waves produce musical (periodic) sound.
> > >
> > > The superposition of transverse traveling waves causes
transverse
> > > standing waves. In musical instruments, only transverse
standing
> > > waves produce musical (periodic) sound.
> >
> > I don't understand what this is supposed to mean. You can
describe
> any
> > excitation of a string (or bar or pipe or whatever) as the actual
> > motion of the vibrating element (traveling waves), or as the
> > magnitudes and phases of all the eigenmodes (standing waves).
These
> > two descriptions describe the same physical phenomenon, so I
don't
> > understand how you can say one "produces sound" and the other
> doesn't.
> > They're just two different ways of looking at it, whose
> implications
> > are mathematically equivalent.
> >
> > Keenan
> >
>

On 7/8/07, Cris Forster <cris.forster@comcast.net> wrote:
> A traveling "wave" is nothing more than a pulse, or a "bump", if you
> will. These pulses are either in the shape of troughs, or in the
> shape of crests.

Or in other more complex shapes. There's no reason it has to be a
trough or a crest. (The only limitation is that the strain should be
everywhere small enough that the material responds linearly. If it
becomes significantly nonlinear then our basic assumptions are
violated and we need a more sophisticated model.)

> An incident crest -- upon encountering an obstacle such as a nut or
> bridge -- changes direction AND position, and thus becomes a
> reflected trough; vice versa.
>
> Traveling waves or pulses do NOT compress air; therefore, they do
> not make sound. Traveling waves push air in front of their leading
> surfaces, like your car pushes air in front of its leading surface
> (hood or trunk) as it rolls forward or backward.
>
> Sorry for the confusion!

What do you mean they don't compress air? Why not?

More importantly, since a traveling pulse and a linear combination of
standing waves with different phases are *exactly the same physical
phenomenon*, how can one compress air and not the other?

Keenan

Keenan Pepper schrieb:
> On 7/8/07, Cris Forster <cris.forster@comcast.net> wrote:
>> A traveling "wave" is nothing more than a pulse, or a "bump", if you
>> will. These pulses are either in the shape of troughs, or in the
>> shape of crests.
> > Or in other more complex shapes. There's no reason it has to be a
> trough or a crest. (The only limitation is that the strain should be
> everywhere small enough that the material responds linearly. If it
> becomes significantly nonlinear then our basic assumptions are
> violated and we need a more sophisticated model.)
> >> An incident crest -- upon encountering an obstacle such as a nut or
>> bridge -- changes direction AND position, and thus becomes a
>> reflected trough; vice versa.
>>
>> Traveling waves or pulses do NOT compress air; therefore, they do
>> not make sound. Traveling waves push air in front of their leading
>> surfaces, like your car pushes air in front of its leading surface
>> (hood or trunk) as it rolls forward or backward.
>>
>> Sorry for the confusion!
> > What do you mean they don't compress air? Why not?

Isn't it more important to move the soundboard before compressing air?

For an electric pickup, I can see that logitudinal waves in the string don't affect it. For a bridge, I'd have assumed the opposite, but I have no idea how a bridge works - and I have my doubts that a violin type middle-of-the-string bridge works the same as the bar-holding-the-string guitar type.

klaus

> > More importantly, since a traveling pulse and a linear combination of
> standing waves with different phases are *exactly the same physical
> phenomenon*, how can one compress air and not the other?
> > Keenan

These will be my last comments on this subject. I gladly yield the
floor…

Go to a rubber supply store, or to a well-stocked hardware store,
and buy a round rubber cord approximately 20 feet long, with a
diameter of approximately 1/4 inch. A rope may also do; however,
because it is not flexible like a rubber cord, it is more difficult
to control.

Tie this cord to a wall (doorknob) and walk until the cord is fairly
tight. Give the cord one up-and-down flick with your hand and watch
as a traveling wave, a pulse, travels to the doorknob, reflect
there, and returns to your hand. If you hold still, the traveling
wave will continue its journey to the doorknob and back to your
hand. Every time it returns to your hand, you will actually feel a
pulse, very much like the pulse of your heart.

Now, here is the critical moment which requires some experience,
practice, and skill. If you move the cord with a rapid succession of
flicks, a whole bunch of traveling waves will begin traveling to the
doorknob and back, etc. When the timing of the flicks is just
right, these traveling waves will begin to collide. This is called
superposition. Suddenly, the traveling waves or pulses are no
longer moving in a horizontal direction, but the whole cord begins
to move in a vertical direction between the floor and the ceiling.
The cord now has the shape of an elongated oval; i.e., the shape of
the fundamental mode of vibration. When the cord moves in a
vertical motion, it is called a standing wave. (It just "stands"
there and "waves" up and down.)

Now, if you move the cord in an even more rapid succession of
flicks, a node will appear at its center! The cord now has the
shaped of two (shorter) elongated ovals; i.e., the shape of the
second harmonic, or the second mode of vibration.

When the cord begins moving in the vertical direction, in the
standing wave direction, you will begin hearing a rush of air.
Because the large surface area of the cord is vibrating up and down
within the confines of its entire length, it now begins to compress
the air at its leading surface, and it begins to rarefy the air at
its trailing surface. This marks the beginning of the production of
humanly audible sound. When the standing wave vibrates at 440
cycles per second (when it compresses and rarefies the air at such a
rate) we identify the produced sound as the A above middle C, hence
A-440.

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...>
wrote:
>
> On 7/8/07, Cris Forster <cris.forster@...> wrote:
> > A traveling "wave" is nothing more than a pulse, or a "bump", if
you
> > will. These pulses are either in the shape of troughs, or in the
> > shape of crests.
>
> Or in other more complex shapes. There's no reason it has to be a
> trough or a crest. (The only limitation is that the strain should
be
> everywhere small enough that the material responds linearly. If it
> becomes significantly nonlinear then our basic assumptions are
> violated and we need a more sophisticated model.)
>
> > An incident crest -- upon encountering an obstacle such as a nut
or
> > bridge -- changes direction AND position, and thus becomes a
> > reflected trough; vice versa.
> >
> > Traveling waves or pulses do NOT compress air; therefore, they do
> > not make sound. Traveling waves push air in front of their
leading
> > surfaces, like your car pushes air in front of its leading
surface
> > (hood or trunk) as it rolls forward or backward.
> >
> > Sorry for the confusion!
>
> What do you mean they don't compress air? Why not?
>
> More importantly, since a traveling pulse and a linear combination
of
> standing waves with different phases are *exactly the same physical
> phenomenon*, how can one compress air and not the other?
>
> Keenan
>

The algorithm of Eduardo Sábat that John Chalmers mentioned is
implemented in Scala, see Analyse:Show string lengths.
It takes care of the increment in string tension when it's pressed
down, as well as the increment in length. It assumes a linear
relationship between stretch and tension, and it doesn't take
stiffness into account so it works best for thin strings.

Manuel

On 7/9/07, Cris Forster <cris.forster@comcast.net> wrote:
> Tie this cord to a wall (doorknob) and walk until the cord is fairly
> tight. Give the cord one up-and-down flick with your hand and watch
> as a traveling wave, a pulse, travels to the doorknob, reflect
> there, and returns to your hand. If you hold still, the traveling
> wave will continue its journey to the doorknob and back to your
> hand. Every time it returns to your hand, you will actually feel a
> pulse, very much like the pulse of your heart.

Right, and you would also hear a sound if the cord were shorter, or
stiffer, or if you could hear sounds below a few hertz. The reason you
can't hear it has nothing to do with traveling waves versus standing
waves, it's simply because the frequency is too low.

> When the cord begins moving in the vertical direction, in the
> standing wave direction, you will begin hearing a rush of air.
> Because the large surface area of the cord is vibrating up and down
> within the confines of its entire length, it now begins to compress
> the air at its leading surface, and it begins to rarefy the air at
> its trailing surface. This marks the beginning of the production of
> humanly audible sound. When the standing wave vibrates at 440
> cycles per second (when it compresses and rarefies the air at such a
> rate) we identify the produced sound as the A above middle C, hence
> A-440.

The trick is getting a 20-foot-long rubber cord to resonate well at
440 Hz, when its fundamental is down near 1 Hz.

You completely ignored what I said about traveling waves and
superpositions of standing waves being different ways of looking at
the same phenomenon.

Keenan

At high speeds, the compression of large volumes of air at the
leading surfaces of a jet causes a sonic boom. A sonic boom has
nothing to do with compression/rarefaction cycles that cause musical
(periodic) frequencies.

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...>
wrote:
>
> On 7/9/07, Cris Forster <cris.forster@...> wrote:
> > Tie this cord to a wall (doorknob) and walk until the cord is
fairly
> > tight. Give the cord one up-and-down flick with your hand and
watch
> > as a traveling wave, a pulse, travels to the doorknob, reflect
> > there, and returns to your hand. If you hold still, the
traveling
> > wave will continue its journey to the doorknob and back to your
> > hand. Every time it returns to your hand, you will actually
feel a
> > pulse, very much like the pulse of your heart.
>
> Right, and you would also hear a sound if the cord were shorter, or
> stiffer, or if you could hear sounds below a few hertz. The reason
you
> can't hear it has nothing to do with traveling waves versus
standing
> waves, it's simply because the frequency is too low.
>
> > When the cord begins moving in the vertical direction, in the
> > standing wave direction, you will begin hearing a rush of air.
> > Because the large surface area of the cord is vibrating up and
down
> > within the confines of its entire length, it now begins to
compress
> > the air at its leading surface, and it begins to rarefy the air
at
> > its trailing surface. This marks the beginning of the
production of
> > humanly audible sound. When the standing wave vibrates at 440
> > cycles per second (when it compresses and rarefies the air at
such a
> > rate) we identify the produced sound as the A above middle C,
hence
> > A-440.
>
> The trick is getting a 20-foot-long rubber cord to resonate well at
> 440 Hz, when its fundamental is down near 1 Hz.
>
> You completely ignored what I said about traveling waves and
> superpositions of standing waves being different ways of looking at
> the same phenomenon.
>
> Keenan
>

Fascinating.

----- Original Message -----
From: "Cris Forster" <cris.forster@comcast.net>
To: <tuning@yahoogroups.com>
Sent: 09 Temmuz 2007 Pazartesi 18:09
Subject: [tuning] Re: Fret calculation and string motions - "hooked" on
sound.

These will be my last comments on this subject. I gladly yield the
floor�

Go to a rubber supply store, or to a well-stocked hardware store,
and buy a round rubber cord approximately 20 feet long, with a
diameter of approximately 1/4 inch. A rope may also do; however,
because it is not flexible like a rubber cord, it is more difficult
to control.

Tie this cord to a wall (doorknob) and walk until the cord is fairly
tight. Give the cord one up-and-down flick with your hand and watch
as a traveling wave, a pulse, travels to the doorknob, reflect
there, and returns to your hand. If you hold still, the traveling
wave will continue its journey to the doorknob and back to your
hand. Every time it returns to your hand, you will actually feel a
pulse, very much like the pulse of your heart.

Now, here is the critical moment which requires some experience,
practice, and skill. If you move the cord with a rapid succession of
flicks, a whole bunch of traveling waves will begin traveling to the
doorknob and back, etc. When the timing of the flicks is just
right, these traveling waves will begin to collide. This is called
superposition. Suddenly, the traveling waves or pulses are no
longer moving in a horizontal direction, but the whole cord begins
to move in a vertical direction between the floor and the ceiling.
The cord now has the shape of an elongated oval; i.e., the shape of
the fundamental mode of vibration. When the cord moves in a
vertical motion, it is called a standing wave. (It just "stands"
there and "waves" up and down.)

Now, if you move the cord in an even more rapid succession of
flicks, a node will appear at its center! The cord now has the
shaped of two (shorter) elongated ovals; i.e., the shape of the
second harmonic, or the second mode of vibration.

When the cord begins moving in the vertical direction, in the
standing wave direction, you will begin hearing a rush of air.
Because the large surface area of the cord is vibrating up and down
within the confines of its entire length, it now begins to compress
the air at its leading surface, and it begins to rarefy the air at
its trailing surface. This marks the beginning of the production of
humanly audible sound. When the standing wave vibrates at 440
cycles per second (when it compresses and rarefies the air at such a
rate) we identify the produced sound as the A above middle C, hence
A-440.

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...>
wrote:
>
> On 7/8/07, Cris Forster <cris.forster@...> wrote:
> > A traveling "wave" is nothing more than a pulse, or a "bump", if
you
> > will. These pulses are either in the shape of troughs, or in the
> > shape of crests.
>
> Or in other more complex shapes. There's no reason it has to be a
> trough or a crest. (The only limitation is that the strain should
be
> everywhere small enough that the material responds linearly. If it
> becomes significantly nonlinear then our basic assumptions are
> violated and we need a more sophisticated model.)
>
> > An incident crest -- upon encountering an obstacle such as a nut
or
> > bridge -- changes direction AND position, and thus becomes a
> > reflected trough; vice versa.
> >
> > Traveling waves or pulses do NOT compress air; therefore, they do
> > not make sound. Traveling waves push air in front of their
leading
> > surfaces, like your car pushes air in front of its leading
surface
> > (hood or trunk) as it rolls forward or backward.
> >
> > Sorry for the confusion!
>
> What do you mean they don't compress air? Why not?
>
> More importantly, since a traveling pulse and a linear combination
of
> standing waves with different phases are *exactly the same physical
> phenomenon*, how can one compress air and not the other?
>
> Keenan
>

You can configure your subscription by sending an empty email to one
of these addresses (from the address at which you receive the list):
tuning-subscribe@yahoogroups.com - join the tuning group.
tuning-unsubscribe@yahoogroups.com - leave the group.
tuning-nomail@yahoogroups.com - turn off mail from the group.
tuning-digest@yahoogroups.com - set group to send daily digests.
tuning-normal@yahoogroups.com - set group to send individual emails.
tuning-help@yahoogroups.com - receive general help information.

Yahoo! Groups Links

Like those of tanbur. Excellent. What is the algorithm?

----- Original Message -----
From: "Manuel Op de Coul" <manuel.op.de.coul@eon-benelux.com>
To: <tuning@yahoogroups.com>
Sent: 09 Temmuz 2007 Pazartesi 18:48
Subject: [tuning] Re: Fret calculation

The algorithm of Eduardo S�bat that John Chalmers mentioned is
implemented in Scala, see Analyse:Show string lengths.
It takes care of the increment in string tension when it's pressed
down, as well as the increment in length. It assumes a linear
relationship between stretch and tension, and it doesn't take
stiffness into account so it works best for thin strings.

Manuel

http://www.kettering.edu/~drussell/Demos/superposition/superposition.
html

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...>
wrote:
>
> On 7/9/07, Cris Forster <cris.forster@...> wrote:
> > Tie this cord to a wall (doorknob) and walk until the cord is
fairly
> > tight. Give the cord one up-and-down flick with your hand and
watch
> > as a traveling wave, a pulse, travels to the doorknob, reflect
> > there, and returns to your hand. If you hold still, the
traveling
> > wave will continue its journey to the doorknob and back to your
> > hand. Every time it returns to your hand, you will actually
feel a
> > pulse, very much like the pulse of your heart.
>
> Right, and you would also hear a sound if the cord were shorter, or
> stiffer, or if you could hear sounds below a few hertz. The reason
you
> can't hear it has nothing to do with traveling waves versus
standing
> waves, it's simply because the frequency is too low.
>
> > When the cord begins moving in the vertical direction, in the
> > standing wave direction, you will begin hearing a rush of air.
> > Because the large surface area of the cord is vibrating up and
down
> > within the confines of its entire length, it now begins to
compress
> > the air at its leading surface, and it begins to rarefy the air
at
> > its trailing surface. This marks the beginning of the
production of
> > humanly audible sound. When the standing wave vibrates at 440
> > cycles per second (when it compresses and rarefies the air at
such a
> > rate) we identify the produced sound as the A above middle C,
hence
> > A-440.
>
> The trick is getting a 20-foot-long rubber cord to resonate well at
> 440 Hz, when its fundamental is down near 1 Hz.
>
> You completely ignored what I said about traveling waves and
> superpositions of standing waves being different ways of looking at
> the same phenomenon.
>
> Keenan
>

If you throw punches with both arms at high speeds while
shouting "Sonic Boom!", you can move a large volume of hot
air and create a sonic boom. These sonic booms have
nothing to do with whether you can defeat the evil crime
lord, M. Bison. -C.

--- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@...> wrote:
>
> At high speeds, the compression of large volumes of air at the
> leading surfaces of a jet causes a sonic boom. A sonic boom has
> nothing to do with compression/rarefaction cycles that cause
> musical (periodic) frequencies.
>

The only thing more interesting than personalized actualizations are
very personalized actualizations.

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> If you throw punches with both arms at high speeds while
> shouting "Sonic Boom!", you can move a large volume of hot
> air and create a sonic boom. These sonic booms have
> nothing to do with whether you can defeat the evil crime
> lord, M. Bison. -C.
>
>
> --- In tuning@yahoogroups.com, "Cris Forster" <cris.forster@>
wrote:
> >
> > At high speeds, the compression of large volumes of air at the
> > leading surfaces of a jet causes a sonic boom. A sonic boom has
> > nothing to do with compression/rarefaction cycles that cause
> > musical (periodic) frequencies.
> >
>

Hi Charles Lucy,

you might want to take into consideration that "traditional
models" do not claim to describe more than an IDEAL string. And any
text more than utterly elementary is surely not going to
mislead anyone into thinking that sound is a travelling wave
shooting out from the end of a string like a laser beam, or
some such thing: there is a mechanism translating to the air that
which is happening in the string.

Judging from your post, I'd say that things are far better
understood than you believe, check out for example:

http://en.wikipedia.org/wiki/Almost_periodic_function

Nobody (I hope) believes that an ideal string is "what we hear",
although it seems certain that there is something along the lines of
an "ideal string" wired into us, otherwise electronic disco "bass
phatteners" wouldn't work. Let's see... yes,

http://en.wikipedia.org/wiki/Missing_fundamental

and of course you can verify all these things for yourself with
additive synthesis.

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Having just endured three hours of traffic jams in central
London,
> thanks to le Tour de France, I return to the tranquility of the
> tuning list.
>
> I heard where Cris is travelling with this, yet I am very
sceptical
> about all the traditional models for vibrating strings.
>
> As far as I have seen/heard/read/observed most string models seem
to
> consider only longitudinal and transverse wave patterns.
>
> If you watch a vibrating string very carefully you will see that
> having been displaced from the central stable position by being
hit
> or plucked,
>
> the movement cross-section becomes oval and eventually circular,
as
> the whole string returns to its resting position.
>
> The patterns are so mathematically complex that no-one seems yet
to
> have been able to describe them very accurately.
>
> So, for example, you begin looking at the patterns as you would a
> pendulum, or a dozen other potential comparisons.
>
> You read all the books you can find about sine waves, and the
> traditional models of harmonics; and the "old" models are still
> incomplete, and fail make practical, and logical sense.
>
> There is always this enticing hint that there is something subtle
and
> even more fundamental underlying the simplistic and obvious
> traditional models.
>
> Certainly you need to consider three dimensions plus time, yet do
you
> do this for each theoretical point on the string, for the general
> shape of the string?
>
> How does the resonator, other strings, the striking method, and a
> thousand other factors influence the sound that you hear?
>
> How do your ears perceive the sound?
>
> How does your brain process it?
>
> How do you perceive the extremely complex actions and reactions
that
> are happening so rapidly?
>
> We can look at the visual patterns on our computer screens using
this
> week's latest audio analysis applications.
>
> We can reprocess the audio files through every filter, effect,
and
> enhancement: sample, resample, emulate and (re)synthesise it; yet
> there is always "something" missing.
>
> The more carefully you listen, the more sounds you heard, the
more
> you get "hooked";-)
>
> So we continue experimenting, continue archiving sounds,
melodies,
> harmonies, and other patterns, which appeal to us;
>
> and gradually we allow them to filter out into the collective
> consciousness via performances, recordings, radio, TV, films,
> commercials, and sound files on the net.
>
>
> Some sell very well; some not at all; yet the universe somehow
allows
> and enables us to continue across the generations.
>
> We must be doing something right;-)
>
>
> Charles Lucy lucy@...
>
> ----- Promoting global harmony through LucyTuning -----
>
> For information on LucyTuning go to: http://www.lucytune.com
>
> LucyTuned Lullabies (from around the world):
> http://www.lullabies.co.uk
>
> Skype user = lucytune
>
> http://www.myspace.com/lucytuning
>
>
> On 7 Jul 2007, at 19:17, Cris Forster wrote:
>
> > From my unpublished book
> > "Musical Mathematics."
> >
> > "In vibrating bars, there are two restoring forces: a bending
> > moment ( M ) that induces rotation about a given point in the
bar,
> > and a shear force ( V ) that induces translation in a direction
> > perpendicular to the bar's horizontal axis. That is, M causes
> > bending motion in a circular direction, and V causes linear
motion
> > in a vertical direction. In vibrating bars, these two forces act
> > as a single restoring force. Note, however, that M and V do not
> > appear as variables in frequency Equations 6.1 and 6.11. The
reason
> > for this omission is that both forces vary with space (or a given
> > location in the bar) and time (or a given instant in the period
of
> > vibration). Therefore, it is not possible to quantify M and V for
> > use in frequency equations. Since both forces are directly
> > proportional to the bending stiffness ( B ) of a bar, we may
> > interpret an increase or decrease in B as an increase or
decrease in
> > M and V."
> >
> > This general principle also applies to strings. There are two
> > restoring forces at work: A tension force ( T ) and acts in a
> > horizontal direction, and a shear force ( V [string] ) that acts
in
> > a vertical direction. The latter down-bearing force varies with
> > space (or a given location in the string). Therefore, it is not
> > possible to quantify ( V [string] ) for use in frequency
equations.
> >
> > Imagine a trampoline or a board supported at the ends by bricks.
As
> > you jump up and down, where do you suppose the greatest amount of
> > motion is: in the center or at the ends? The same applies to bars
> > and strings: rates of vertical deflection and the down-bearing
> > forces required to produce these deflections vary with space, or
at
> > given locations in vibrating systems.
> >
> > All of these observations and conclusion arise from solutions to
> > partial differential equations, some of which took several
> > generations of mathematicians to solve. I am not one of them.
> >
> > Cris Forster
> >
> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > We are after all trying to determine the pitch change caused
by the
> > > down-bearing force.
> > >
> > >
> > > ----- Original Message -----
> > > From: "Cris Forster" <cris.forster@>
> > > To: <tuning@yahoogroups.com>
> > > Sent: 07 Temmuz 2007 Cumartesi 19:59
> > > Subject: [tuning] Re: Fret calculation
> > >
> > >
> > > > Since when do string diameters and string-to-fret clearances
> > > > constitute frets or placements of frets?
> > > >
> > > > Say and do whatever you want.
> > > >
> > > > Know this, there is nothing negligible about the
> > > > down-bearing force: ask any koto or sitar player.
> > > >
> > > >
> > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@>
wrote:
> > > > >
> > > > > So, I have no saying in how to fret a tanbur, is that what
you
> > are
> > > > saying?
> > > > >
> > > > > Oz.
> > > > >
> > > > > ----- Original Message -----
> > > > > From: "Cris Forster" <cris.forster@>
> > > > > To: <tuning@yahoogroups.com>
> > > > > Sent: 07 Temmuz 2007 Cumartesi 18:10
> > > > > Subject: [tuning] Re: Fret calculation
> > > > >
> > > > >
> > > > > > In the world of acoustic music making, I would advise
against
> > > > > > dictating string diameter and string-to-fret clearance
(i.e.,
> > > > down-
> > > > > > bearing force) parameters to instrument builders and
> > musicians.
> > > > > > State your case with respect to scales and frequencies
(i.e.,
> > > > cent
> > > > > > values) and let builders and musicians exercise their
years
> > of
> > > > > > experience and freedom of choice. All stringed
instruments,
> > > > > > especially the koto, rely on the illusive down-bearing
force
> > not
> > > > > > only for acoustic reasons (an efficient transfer of wave
> > energy
> > > > from
> > > > > > string, to bridge, to soundboard, to the surrounding
air),
> > but
> > > > for
> > > > > > musically expressive reasons as well.
> > > > > >
> > > > > >
> > >
> >
> >
> >
>

Dear Cameron,

You are right.

The standing-wave surface (or profile) of a vibrating string is
extremely irregular (bumpy); it is extremely complex.

Superposition (of traveling waves) not only explains the occurrence
of a given standing wave, but it also explains simultaneous
occurrences of many standing waves (or modes of vibration) in a
single vibrating string. Consequently, we hear many simultaneously
occurring harmonics form a single string.

In his great book, _The Science of Musical Sounds_, p. 66, Dayton
C. Miller was the first scientist to successfully photograph the
complex standing-wave surfaces of vibrating strings.

Cris Forster

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...>
wrote:
>
> Hi Charles Lucy,
>
> you might want to take into consideration that "traditional
> models" do not claim to describe more than an IDEAL string. And
any
> text more than utterly elementary is surely not going to
> mislead anyone into thinking that sound is a travelling wave
> shooting out from the end of a string like a laser beam, or
> some such thing: there is a mechanism translating to the air that
> which is happening in the string.
>
> Judging from your post, I'd say that things are far better
> understood than you believe, check out for example:
>
> http://en.wikipedia.org/wiki/Almost_periodic_function
>
> Nobody (I hope) believes that an ideal string is "what we hear",
> although it seems certain that there is something along the lines
of
> an "ideal string" wired into us, otherwise electronic disco "bass
> phatteners" wouldn't work. Let's see... yes,
>
> http://en.wikipedia.org/wiki/Missing_fundamental
>
> and of course you can verify all these things for yourself with
> additive synthesis.
>
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@> wrote:
> >
> > Having just endured three hours of traffic jams in central
> London,
> > thanks to le Tour de France, I return to the tranquility of the
> > tuning list.
> >
> > I heard where Cris is travelling with this, yet I am very
> sceptical
> > about all the traditional models for vibrating strings.
> >
> > As far as I have seen/heard/read/observed most string models
seem
> to
> > consider only longitudinal and transverse wave patterns.
> >
> > If you watch a vibrating string very carefully you will see
that
> > having been displaced from the central stable position by being
> hit
> > or plucked,
> >
> > the movement cross-section becomes oval and eventually circular,
> as
> > the whole string returns to its resting position.
> >
> > The patterns are so mathematically complex that no-one seems yet
> to
> > have been able to describe them very accurately.
> >
> > So, for example, you begin looking at the patterns as you would
a
> > pendulum, or a dozen other potential comparisons.
> >
> > You read all the books you can find about sine waves, and the
> > traditional models of harmonics; and the "old" models are still
> > incomplete, and fail make practical, and logical sense.
> >
> > There is always this enticing hint that there is something
subtle
> and
> > even more fundamental underlying the simplistic and obvious
> > traditional models.
> >
> > Certainly you need to consider three dimensions plus time, yet
do
> you
> > do this for each theoretical point on the string, for the
general
> > shape of the string?
> >
> > How does the resonator, other strings, the striking method, and
a
> > thousand other factors influence the sound that you hear?
> >
> > How do your ears perceive the sound?
> >
> > How does your brain process it?
> >
> > How do you perceive the extremely complex actions and reactions
> that
> > are happening so rapidly?
> >
> > We can look at the visual patterns on our computer screens using
> this
> > week's latest audio analysis applications.
> >
> > We can reprocess the audio files through every filter, effect,
> and
> > enhancement: sample, resample, emulate and (re)synthesise it;
yet
> > there is always "something" missing.
> >
> > The more carefully you listen, the more sounds you heard, the
> more
> > you get "hooked";-)
> >
> > So we continue experimenting, continue archiving sounds,
> melodies,
> > harmonies, and other patterns, which appeal to us;
> >
> > and gradually we allow them to filter out into the collective
> > consciousness via performances, recordings, radio, TV, films,
> > commercials, and sound files on the net.
> >
> >
> > Some sell very well; some not at all; yet the universe somehow
> allows
> > and enables us to continue across the generations.
> >
> > We must be doing something right;-)
> >
> >
> > Charles Lucy lucy@
> >
> > ----- Promoting global harmony through LucyTuning -----
> >
> > For information on LucyTuning go to: http://www.lucytune.com
> >
> > LucyTuned Lullabies (from around the world):
> > http://www.lullabies.co.uk
> >
> > Skype user = lucytune
> >
> > http://www.myspace.com/lucytuning
> >
> >
> > On 7 Jul 2007, at 19:17, Cris Forster wrote:
> >
> > > From my unpublished book
> > > "Musical Mathematics."
> > >
> > > "In vibrating bars, there are two restoring forces: a bending
> > > moment ( M ) that induces rotation about a given point in the
> bar,
> > > and a shear force ( V ) that induces translation in a direction
> > > perpendicular to the bar's horizontal axis. That is, M causes
> > > bending motion in a circular direction, and V causes linear
> motion
> > > in a vertical direction. In vibrating bars, these two forces
act
> > > as a single restoring force. Note, however, that M and V do not
> > > appear as variables in frequency Equations 6.1 and 6.11. The
> reason
> > > for this omission is that both forces vary with space (or a
given
> > > location in the bar) and time (or a given instant in the
period
> of
> > > vibration). Therefore, it is not possible to quantify M and V
for
> > > use in frequency equations. Since both forces are directly
> > > proportional to the bending stiffness ( B ) of a bar, we may
> > > interpret an increase or decrease in B as an increase or
> decrease in
> > > M and V."
> > >
> > > This general principle also applies to strings. There are two
> > > restoring forces at work: A tension force ( T ) and acts in a
> > > horizontal direction, and a shear force ( V [string] ) that
acts
> in
> > > a vertical direction. The latter down-bearing force varies with
> > > space (or a given location in the string). Therefore, it is not
> > > possible to quantify ( V [string] ) for use in frequency
> equations.
> > >
> > > Imagine a trampoline or a board supported at the ends by
bricks.
> As
> > > you jump up and down, where do you suppose the greatest amount
of
> > > motion is: in the center or at the ends? The same applies to
bars
> > > and strings: rates of vertical deflection and the down-bearing
> > > forces required to produce these deflections vary with space,
or
> at
> > > given locations in vibrating systems.
> > >
> > > All of these observations and conclusion arise from solutions
to
> > > partial differential equations, some of which took several
> > > generations of mathematicians to solve. I am not one of them.
> > >
> > > Cris Forster
> > >
> > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@>
wrote:
> > > >
> > > > We are after all trying to determine the pitch change caused
> by the
> > > > down-bearing force.
> > > >
> > > >
> > > > ----- Original Message -----
> > > > From: "Cris Forster" <cris.forster@>
> > > > To: <tuning@yahoogroups.com>
> > > > Sent: 07 Temmuz 2007 Cumartesi 19:59
> > > > Subject: [tuning] Re: Fret calculation
> > > >
> > > >
> > > > > Since when do string diameters and string-to-fret
clearances
> > > > > constitute frets or placements of frets?
> > > > >
> > > > > Say and do whatever you want.
> > > > >
> > > > > Know this, there is nothing negligible about the
> > > > > down-bearing force: ask any koto or sitar player.
> > > > >
> > > > >
> > > > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@>
> wrote:
> > > > > >
> > > > > > So, I have no saying in how to fret a tanbur, is that
what
> you
> > > are
> > > > > saying?
> > > > > >
> > > > > > Oz.
> > > > > >
> > > > > > ----- Original Message -----
> > > > > > From: "Cris Forster" <cris.forster@>
> > > > > > To: <tuning@yahoogroups.com>
> > > > > > Sent: 07 Temmuz 2007 Cumartesi 18:10
> > > > > > Subject: [tuning] Re: Fret calculation
> > > > > >
> > > > > >
> > > > > > > In the world of acoustic music making, I would advise
> against
> > > > > > > dictating string diameter and string-to-fret clearance
> (i.e.,
> > > > > down-
> > > > > > > bearing force) parameters to instrument builders and
> > > musicians.
> > > > > > > State your case with respect to scales and frequencies
> (i.e.,
> > > > > cent
> > > > > > > values) and let builders and musicians exercise their
> years
> > > of
> > > > > > > experience and freedom of choice. All stringed
> instruments,
> > > > > > > especially the koto, rely on the illusive down-bearing
> force
> > > not
> > > > > > > only for acoustic reasons (an efficient transfer of
wave
> > > energy
> > > > > from
> > > > > > > string, to bridge, to soundboard, to the surrounding
> air),
> > > but
> > > > > for
> > > > > > > musically expressive reasons as well.
> > > > > > >
> > > > > > >
> > > >
> > >
> > >
> > >
> >
>

Ozan wrote:
> Like those of tanbur. Excellent. What is the algorithm?

Here's the code. There isn't a formula in closed form. The algorithm
converges asymptotically to the result.

procedure Fret_Position (Str_Length : in Long_Float;
Hfret : in Long_Float;
Hnut : in Long_Float;
Hbridge : in Long_Float;
Del01 : in Long_Float;
Lin_Pitch : in Long_Float;
Result : out Long_Float;
Bridge_Dis : out Long_Float) is
Hb : constant Long_Float := Hbridge - Hfret;
Hn : constant Long_Float := Hnut - Hfret;
Incold : Long_Float := 1.0E9;
Lh, Lns, L2, Fr, Inc : Long_Float;
begin
if Hb = 0.0 and Hn = 0.0 then
Result := Str_Length / Lin_Pitch;
Bridge_Dis := Str_Length - Result;
return;
elsif Hb = Hn then
Lh := Str_Length;
else
Lh := Sqrt(Str_Length ** 2 - (Hb - Hn) ** 2);
end if;
Result := abs Hn;
loop
Lns := Sqrt(Result * Result + Hn * Hn);
Bridge_Dis := Sqrt((Lh - Result) ** 2 + Hb * Hb);
L2 := Bridge_Dis + Lns;
Fr := Sqrt(Str_Length * L2 * (Del01 + L2 - Str_Length)) /
(Sqrt(Del01) * Bridge_Dis);
Inc := Str_Length * (Fr - Lin_Pitch) / (Lin_Pitch * Lin_Pitch);
exit when abs Inc < 1.0E-10 * Str_Length;
Result := Result - Inc;
if Inc > Incold or Result > Str_Length then
raise Argument_Error;
end if;
Incold := abs Inc;
end loop;
end Fret_Position;

Manuel

Aie, I'm not a programmer, is there no way to put all this into a tiny
formula?

----- Original Message -----
From: "Manuel Op de Coul" <manuel.op.de.coul@eon-benelux.com>
To: <tuning@yahoogroups.com>
Sent: 10 Temmuz 2007 Sal� 18:53
Subject: [tuning] Re: Fret calculation

> Ozan wrote:
> > Like those of tanbur. Excellent. What is the algorithm?
>
> Here's the code. There isn't a formula in closed form. The algorithm
> converges asymptotically to the result.
>
> procedure Fret_Position (Str_Length : in Long_Float;
> Hfret : in Long_Float;
> Hnut : in Long_Float;
> Hbridge : in Long_Float;
> Del01 : in Long_Float;
> Lin_Pitch : in Long_Float;
> Result : out Long_Float;
> Bridge_Dis : out Long_Float) is
> Hb : constant Long_Float := Hbridge - Hfret;
> Hn : constant Long_Float := Hnut - Hfret;
> Incold : Long_Float := 1.0E9;
> Lh, Lns, L2, Fr, Inc : Long_Float;
> begin
> if Hb = 0.0 and Hn = 0.0 then
> Result := Str_Length / Lin_Pitch;
> Bridge_Dis := Str_Length - Result;
> return;
> elsif Hb = Hn then
> Lh := Str_Length;
> else
> Lh := Sqrt(Str_Length ** 2 - (Hb - Hn) ** 2);
> end if;
> Result := abs Hn;
> loop
> Lns := Sqrt(Result * Result + Hn * Hn);
> Bridge_Dis := Sqrt((Lh - Result) ** 2 + Hb * Hb);
> L2 := Bridge_Dis + Lns;
> Fr := Sqrt(Str_Length * L2 * (Del01 + L2 - Str_Length)) /
> (Sqrt(Del01) * Bridge_Dis);
> Inc := Str_Length * (Fr - Lin_Pitch) / (Lin_Pitch * Lin_Pitch);
> exit when abs Inc < 1.0E-10 * Str_Length;
> Result := Result - Inc;
> if Inc > Incold or Result > Str_Length then
> raise Argument_Error;
> end if;
> Incold := abs Inc;
> end loop;
> end Fret_Position;
>
> Manuel
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Aie, I'm not a programmer, is there no way to put all this into a tiny
> formula?

Probably not, what's the problem with using Scala?

Manuel

There is no problem with Scala, I just wanted to see the formula.

Oz.

----- Original Message -----
From: "Manuel Op de Coul" <manuel.op.de.coul@eon-benelux.com>
To: <tuning@yahoogroups.com>
Sent: 11 Temmuz 2007 �ar�amba 12:00
Subject: [tuning] Re: Fret calculation

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Aie, I'm not a programmer, is there no way to put all this into a tiny
> > formula?
>
> Probably not, what's the problem with using Scala?
>
> Manuel
>