inharmonicity paper etc.

A fairly nice looking short investigation here (though nothing like as
comprehensive as Paul's remarks):
http://www.sea-acustica.es/WEB_ICA_07/fchrs/papers/mus-02-006.pdf

Three instruments from the RCM collection: Kirkman 1773, Broadwood
1799, Bertsche 1821. Fourier transform and an automatic analysis were
used to determine the best fit value of B in the formula
f_n = nf_0 sqrt(1 + B n^2)

in hopefully self-explanatory notation.

They look at notes from C to c'' and find a general behaviour of B
increasing fairly steeply above "middle C". The harpsichord has B
about 1/10th as large as the pianos.

They say ".. the stiffness of piano strings is much greater than in
harpsichords due to the larger string diameters and the
correspondingly high tensions (...) in order for the instrument to
produce high volumes of sound. Hence it is expected that B will also
be larger for the pianos than the harpsichords."

The standard expressions for string tension and inharmonicity are
T= pi d^2 rho f_0^2 l^2
(d= string diameter, rho= density, l= length)

and
B= pi^3 Q d^4 / (64 l^2 T)
(Q= elastic modulus).

What follows is a physicist's handwaving ("spherical cow")
explanation, but it agrees with what Paul said in basically all respects.

To simplify things we assume that rho and Q don't vary much.
Through most of the range of keyboards (the bass being an exception)
we have a 'scaling' such that f_0 x l does not vary much from note to
note, although different instruments have slightly different scaling
lengths. So T is approximately a constant (f_0 l)^2 times d^2. This
means that

B = const. x d^2 / (l^2 x (f_0 l)^2)

So we expect B to rise steeply in the treble. (Also possibly in the
low bass where f_0 l becomes smaller to prevent enormously long strings.)

Also, for a fixed pitch, sounding length and material density, both
the tension and the inharmonicity rise steeply with the string
diameter. The main difference of the piano is just this significantly
larger string diameter.

The strain (tension per cross-sectional area) goes as rho (f_0 l)^2,
so trying to lengthen the scaling is impossible if you're already near
the breaking strain. One has overwound strings in the bass which
increase the effective 'rho', but this doesn't solve the problem of
breaking strain, it only saves some space...

Pianos *could* be a lot less inharmonic if people liked how they sound
with thinner strings, but that doesn't seem to have been the case
historically, makers have chosen to prioritize (acoustic) volume.

The question of overtone content is a separate one, but it is quite
audible (from my small sample of recordings) that many pianos in the
early 19th century had weaker high overtones than most instruments of
the late 18th, for whatever reason.
Just the existence of the 5th harmonic is not problematic for ET (you
can't very well tune ET without hearing it!!) - but if 5-10-15... are
all present and warbling away persistently it can't help but become
tiresome.
~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> A fairly nice looking short investigation here (though nothing like as
> comprehensive as Paul's remarks):
> http://www.sea-acustica.es/WEB_ICA_07/fchrs/papers/mus-02-006.pdf

Interesting prodding at the topic. Wanted to go to Madrid last year
meeself, beins as it's only a hoot and holler down the road, but
couldn't get away in the end.
>
> They look at notes from C to c'' and find a general behaviour of B
> increasing fairly steeply above "middle C". The harpsichord has B
> about 1/10th as large as the pianos.

It varies from instrument to instrument, of course. Brits used
separate bass bridges from the get-go for pianos, meaning they could
keep the bottom end of the "iron" bridge longer than when it has to
meet a brass scale, which kept inharm reasonably low in the bottom.
The Wieners all tried separate bridges c.1805-10 and gave up on the
extra work, except Graf who kept on with it. Walter is a good example
of how bad it can get down there. Not only did he use a single bridge
but he was a cheap bastard who didn't want to pay anymore than
required for brass (hard stuff to make, brass, plus copper has always
been in high demand - makes such good canons when mixed with a touch
of tin!). The standard brass/steel transition point in Wiener pianos
was F, one octave above the bottom until they ran the bottom down to
CC. But good old Anton W. ran his steel down to Eb or even D
sometimes, and you really notice it when you tune these babies; things
start getting all wanky as you approach the brass, and then suddenly
the sun comes out and the birds sing for the firs few notes of brass
before it starts going all funny for the bottom few notes. Nothing
quite as interesting as the number of different solutions there are to
tuning the octave FF-F, all them of equally "wrong".
>
> They say ".. the stiffness of piano strings is much greater than in
> harpsichords due to the larger string diameters and the
> correspondingly high tensions (...) in order for the instrument to
> produce high volumes of sound. Hence it is expected that B will also
> be larger for the pianos than the harpsichords."

Lots of things missing/wrong in this little study. What kind of wire
is on these instruments currently? Most certainly NOT original.
Antiques can be strung with everything from a variety of
"reproduction" wires (of which none of them are) to modern music wire.
The use of "standard values" for E of brass, iron, and steel is about
as trustworthy as using "standard values" for modern aircraft cruising
speeds based on published airline flight times. Plus "iron" has NEVER
been used as a stringing material.

What pitch levels are the instruments tuned at?

What is the scale design like?

But yeah, the main thing is diameter, which is bigger on bangers than
pluckers, so inharmonicity is higher, (yawn) what else is new? Hope
they got there publishing requirement brownie points.

;-)

>
> What follows is a physicist's handwaving ("spherical cow")
> explanation,

Couldn't have phrased it better meeself!
>
> The strain (tension per cross-sectional area) goes as rho (f_0 l)^2,
> so trying to lengthen the scaling is impossible if you're already near
> the breaking strain. One has overwound strings in the bass which
> increase the effective 'rho', but this doesn't solve the problem of
> breaking strain, it only saves some space...

The whole point of wound strings is to create a synthetic material
with a reasonably low E but a rather high density. Works like a charm,
actually. I make wound strings myself, and I'm always amazed at how
bizarre they feel in my hands; to much mass for all that flexibility!
>
> Pianos *could* be a lot less inharmonic if people liked how they sound
> with thinner strings,

Or if someone would invent a wonder steel with high strength and low E.

> but that doesn't seem to have been the case
> historically, makers have chosen to prioritize (acoustic) volume.

That's what sells! Then and now...

Ciao,

P

> http://www.sea-acustica.es/WEB_ICA_07/fchrs/papers/mus-02-006.pdf
>
> Three instruments from the RCM collection: Kirkman 1773, Broadwood
> 1799, Bertsche 1821. Fourier transform and an automatic analysis were
> used to determine the best fit value of B in the formula
> f_n = nf_0 sqrt(1 + B n^2)
>
> in hopefully self-explanatory notation.

On second reading, I'd give it a D at best. Yet another example of
science guys flailing about at some topic while failing to realize
that their myopic viewpoint is undermining the veracity of their
results. To wit:

It's rather obvious to me why their Kirkman experimental results don't
jive with the predictions. First, they are using off-the-shelf iron
values for E and just assuming that the wire on the instrument has the
same value. Totally scientifically INVALID. Second, looks to me like
somebody changed out a few broken strings in the treble with modern
wire, whilst the rest is probably strung in Malcolm Rose "A Iron".

Actually, measuring the inharmonicity gives the value of E! Doh!
Plugging-in some generic value and thinking it is somehow valid for an
unknown material is just plain stupid.

They are also completely up the creek about tension being a cause of
increased values of B. Increased tension, if it were possible to
isolate, would REDUCE B, not increase it. The only fly in the ointment
is that short of making a string longer, which is limited by the
rupture load of the material, the ONLY way you can increase tension is
by increasing diameter (mass being pretty much a constant for all
ferrous-based steels, since anything other than Fe will always be in
trace amounts). And when you increase D, which increase rigidity, then
T also goes up. So what?

It's like these guys can juggle the numbers alright, but they don't
really UNDERSTAND what's going on in terms of real-world physics of
vibrating strings, i.e. it's the amount of rigidity-induced restoring
force relative to tension-induced restoring force that produces
inharmonicity in the first place. When the former goes up OR the
latter goes down, B goes up, but when the former goes down OR the
latter goes up, B goes down. I always thought scientists were supposed
to be trained at realizing this sort of interconnectivity between
factors and how to isolate the primary causes from other things which
just go along for the ride, but what do I know?
>
> They say ".. the stiffness of piano strings is much greater than in
> harpsichords due to the larger string diameters and the
> correspondingly high tensions (...)

There they go again. Oh well....

Ciao,

P

I haven't stopped following this thread, just struggling
for something constructive to say.

Ah, the dream of comparing old instruments to new.
Impossible of course.

Thanks Paul for your usual detailed comments. But none of
it really addresses the question as I see it, I'm afraid.
I'd already posted about the effects on harmonicity of
string length & tension vs. stiffness & thickness. If
you're taking a position on the net effect of trends in
these design factors over the ages, I didn't catch it.

And it seems nobody knows about the effects of hammer
material / placement. Naively I'd assume that the softer
the material, the greater the portion of available energy
going into antinodes, which would tend to reduce the
contribution of higher partials to the timbre. Then again,
the dynamics of a hammer of whatever material striking a
string are apparently quite involved -- not to mention the
fact that one is usually striking more than one string
at a time...

To me, the key experiment would be to go to a place like
the Harpsichord Clearing House and measure some brand-new
fortepianos from different builders, and then do the same
thing at a fine piano showroom in New York, and compare
the harmonicity and spectral balance. If anybody knows of
data like this, please share. My own hunch is that the
harmonicity of the modern designs would be better or at
least no worse. But I think Tom is probably right that
fortepianos get a greater helping of higher partials.

-Carl

Paul:
> The whole point of wound strings is to create a synthetic material
> with a reasonably low E but a rather high density. Works like a charm,
> actually. I make wound strings myself, and I'm always amazed at how
> bizarre they feel in my hands; to much mass for all that flexibility!

Tom:
>> Pianos *could* be a lot less inharmonic if people liked how they sound
>> with thinner strings,

Paul:
> Or if someone would invent a wonder steel with high strength and low E.

This I find interesting, even if it takes us off-topic. The thing is,
there are materials (polymers and composites) where the Young's
modulus is not the same in all directions. With a thread I think this
can work the way we want. The chains will be aligned along the
thread, so tension in that direction is mainly resisted by covalent
bonds. Perpendicular to this, the right polymer would be flexible,
having a low Young's modulus.

The obvious "wonder steel" is, of course, carbon fiber. A quick
Googling shows people speculating on replacing every part of a piano
bar the strings with carbon fiber. Maybe that's because it really
wouldn't work. Wikipedia says it's possible to get high tensile
strength with a low Young's modulus. But then it also says that
carbon fiber's stiffer than other composites -- that makes sense
because it's not a flexible molecule. They say Kevlar's less stiff
but has higher tensile strength, so...

Then, for the ultimate in tensile strength, we have nanotubes. Here's
the Wikipedia page:

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

Also stiff, but very, very strong. And there's a table which shows a
lower Young's modulus than stainless steel (probably not
representative for piano strings) but a massively higher tensile
strength.

Doesn't really solve the "high density" problem though. But there are
a lot of materials out there so maybe one will do the trick.

Graham

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> Ah, the dream of comparing old instruments to new.
> Impossible of course.

Quite.
>
> If
> you're taking a position on the net effect of trends in
> these design factors over the ages, I didn't catch it.

My position is that inharmonicity in modern pianos is significantly
higher than in Classical instruments, but perhaps marginally better
than c. 1840 instruments.
>
> Then again,
> the dynamics of a hammer of whatever material striking a
> string are apparently quite involved -- not to mention the
> fact that one is usually striking more than one string
> at a time...

Yes, all very complex and not really well understood. Stephen Birkett
is also doing some high-end research trying to model hammer covering
dynamics. He says all current models fail to explain what happens in
reality. But this won't change inharmoncity, only the brightness of
the tone, i.e. the amount of higher partial excitation. Inharmoncity
can be hidden by a dull tone, but it is still there.
>
> To me, the key experiment would be to go to a place like
> the Harpsichord Clearing House and measure some brand-new
> fortepianos from different builders, and then do the same
> thing at a fine piano showroom in New York, and compare
> the harmonicity and spectral balance.

I'm not sure what you mean by spectral balance; do you mean spectral
content? Furthermore, you've got your terminology turned around. Since
INharmonicity is ALWAYS present, we will never be measuring
harmonicity. Harmonicity is a subclass on the braoder concept of
congruence, which is an absolute: anything which is not congruent,
even only by a very small amount, is incongruent.

Only wind instruments and bowed strings exhibit harmonicity. And
electronics, too, of course.

> If anybody knows of
> data like this, please share. My own hunch is that the
> harmonicity of the modern designs would be better or at
> least no worse.

My experience tuning instruments tells me you would be quite wrong.
One thing the paper shows is that inharmonicity in early instruments,
including pianos, is next to nill in the lower octaves, especially the
tenor where one sets the temperament. As you move upward, it gets
worse, but it doesn't matter because the higher harmonics drop out and
you are only concerned with how the octave works looking downward. I
tune my octaves harmonically pure, i.e. no audible beats, and I can
tell you from having checked many times against electronic references
that even big 6 1/2 octave pianos require either no stretch or only
very little to keep the topmost octaves sounding pure with the rest.
When any stretch is need, it is only the highest octaves and only very
very little. Not the case with modern pianos. They require stretch
everywhere. If you tune a modern piano tenor octave perfectly note for
note by setting unisons to an electronic reference (with pure octaves
thus) I can tell you from experience the the octaves will beat. Thus,
high inharmonicity.

> But I think Tom is probably right that
> fortepianos get a greater helping of higher partials.

It depends on how they are voiced. Some builders go for what we in the
trade call the "mini-Steinway" sound. Others, like me, point to the
vast evidence that the instruments were voiced quite brightly until
after 1800, and even then there were two schools. A 5 octave FePo out
to be able to hold its own in concert in the literature written for
it, such a Mozart & Beethoven trios, or the wind quintets. I can tell
you from experience that half the modern "copies" get lost in the mix,
some of them overpowered by a single violin with gut strings! This
cannot be an authentic sound.

Ciao,

P
>
> -Carl
>

--- In tuning@yahoogroups.com, "Graham Breed" <gbreed@...> wrote:
>
> Paul:
> > The whole point of wound strings is to create a synthetic material
> > with a reasonably low E but a rather high density. Works like a charm,
> > actually. I make wound strings myself, and I'm always amazed at how
> > bizarre they feel in my hands; to much mass for all that flexibility!
>
> Tom:
> >> Pianos *could* be a lot less inharmonic if people liked how they
sound
> >> with thinner strings,
>
> Paul:
> > Or if someone would invent a wonder steel with high strength and
low E.
>
> This I find interesting, even if it takes us off-topic. The thing is,
> there are materials (polymers and composites) where the Young's
> modulus is not the same in all directions. With a thread I think this
> can work the way we want. The chains will be aligned along the
> thread, so tension in that direction is mainly resisted by covalent
> bonds. Perpendicular to this, the right polymer would be flexible,
> having a low Young's modulus.

>
> Doesn't really solve the "high density" problem though. But there are
> a lot of materials out there so maybe one will do the trick.
>

No need to go to exotic materials. Since even the treble strings of
your average modern piano are significantly understressed (about 6
semitones below rupture load as opposed to 2 for your average FePo),
one could reduce the stiffness of the a standard modern steel string
by laser etching a spiral pattern to a depth which would reduce the
core diameter to one which is bearing a higher load. The wire would
probably have to be super-cooled during the process to prevent the
heat of etching from taking out the temper and ending up with
something with no strength at all. Probably perfectly technologically
possible but also probably hideously expensive.

Ciao,

P

Paul wrote:
> > If you're taking a position on the net effect of trends
> > in these design factors over the ages, I didn't catch it.
>
> My position is that inharmonicity in modern pianos is
> significantly higher than in Classical instruments, but
> perhaps marginally better than c. 1840 instruments.

Sorry I missed it then! Is there a single trend that was
mostly responsible?

> > Then again,
> > the dynamics of a hammer of whatever material striking a
> > string are apparently quite involved -- not to mention the
> > fact that one is usually striking more than one string
> > at a time...
>
> Yes, all very complex and not really well understood. Stephen
> Birkett is also doing some high-end research trying to model
> hammer covering dynamics. He says all current models fail to
> explain what happens in reality.

Let us know if you hear about his progress.

> Inharmoncity can be hidden by a dull tone, but it
> is still there.

Just backing up, Tom's claim was twofold: that inharmonicity
is greater in modern instruments, and that a relative lack of
high partials in the timbre is used to hide it.

> > To me, the key experiment would be to go to a place like
> > the Harpsichord Clearing House and measure some brand-new
> > fortepianos from different builders, and then do the same
> > thing at a fine piano showroom in New York, and compare
> > the harmonicity and spectral balance.
>
> I'm not sure what you mean by spectral balance; do you mean
> spectral content?

Yes; in particular the rough energy balance between
low (say, 1-6) and high (> 6) partials.

> Furthermore, you've got your terminology turned around. Since
> INharmonicity is ALWAYS present, we will never be measuring
> harmonicity.

I take them to be simple inverses, so I can express results
of a measurement either way.

> Harmonicity is a subclass on the braoder concept of congruence,
> which is an absolute: anything which is not congruent, even
> only by a very small amount, is incongruent.

Sorry, but this just seems like nitpicking to me.

> > If anybody knows of
> > data like this, please share. My own hunch is that the
> > harmonicity of the modern designs would be better or at
> > least no worse.
>
> My experience tuning instruments tells me you would be quite
> wrong. One thing the paper shows is that inharmonicity in early
> instruments, including pianos, is next to nill in the lower
> octaves, especially the tenor where one sets the temperament
> As you move upward, it gets worse, but it doesn't matter because
> the higher harmonics drop out and you are only concerned with
> how the octave works looking downward. I tune my octaves
> harmonically pure, i.e. no audible beats, and I can tell you
> from having checked many times against electronic references
> that even big 6 1/2 octave pianos require either no stretch or
> only very little to keep the topmost octaves sounding pure with
> the rest. When any stretch is need, it is only the highest
> octaves and only very very little. Not the case with modern
> pianos. They require stretch everywhere. If you tune a modern
> piano tenor octave perfectly note for note by setting unisons
> to an electronic reference (with pure octaves thus) I can tell
> you from experience the the octaves will beat. Thus, high
> inharmonicity.

Well, that's something. It'd be nice to have quantitative
data, based on recordings made with the same mic, etc.

I listened to some of the audio files on your site, as well
as at HCH. Unfortunately they're all of music, which is of
course useless in this context. :P And it's hard to tell the
effects of well temperament from inharmonicity differences.
But strictly from qualitative listening, I hear no evidence
for lower inharmonicity in fortepianos.

> > But I think Tom is probably right that fortepianos get
> > a greater helping of higher partials.
>
> It depends on how they are voiced. Some builders go for what
> we in the trade call the "mini-Steinway" sound. Others, like
> me, point to the vast evidence that the instruments were voiced
> quite brightly until after 1800, and even then there were two
> schools. A 5 octave FePo out to be able to hold its own in
> concert in the literature written for it, such a
> Mozart & Beethoven trios, or the wind quintets. I can tell
> you from experience that half the modern "copies" get lost in
> the mix, some of them overpowered by a single violin with gut
> strings! This cannot be an authentic sound.

I'll buy that.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

>
> I listened to some of the audio files on your site, as well
> as at HCH. Unfortunately they're all of music, which is of
> course useless in this context. :P And it's hard to tell the
> effects of well temperament from inharmonicity differences.
> But strictly from qualitative listening, I hear no evidence
> for lower inharmonicity in fortepianos.

You won't, even if your ear is well trained. I can't tell you the
number of times I have been tuning an instrument for a concert, and I
think. "This is going to be a disaster!" because the instrument just
won't go in tune, or is so inharmonic that you can't balance the
octaves and other intervals in a reasonable compromise, or there are
many false strings, or whatever. And yet, when the music starts, it
all melts away into the overpowering wash of harmony. The only way to
really get inside the sound of an instrument by ear is to sit down and
tune it.

My most recent experience was tuning for these concerts:

http://www.harmoniques.ch/index.php?menu=concerts

The Stodard was an absolute nightmare of inharmonicity and falseness,
and I suffered and sweated many bullets. But in the concerts, even I
was surprised at how it all just became part of the sound, and I
always got lots of compliments about how well-tuned it was! Go figure!

Ciao,

P

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Paul wrote:
> > > If you're taking a position on the net effect of trends
> > > in these design factors over the ages, I didn't catch it.
> >
> > My position is that inharmonicity in modern pianos is
> > significantly higher than in Classical instruments, but
> > perhaps marginally better than c. 1840 instruments.
>
> Sorry I missed it then! Is there a single trend that was
> mostly responsible?
>
No. In pre-1840-ish pianos, it is increasing diameter coupled with the
required decrease in length (fatter strings break at lower load thus
shorter length). In post-1840-ish it is both increasing diameter and
increasing values of E of Bessmer steels. Length gets longer again but
can't keep up with the double whammy of the other two.

BTW, I take it back about those science types who wrote that paper
being able to run the numbers. Their own equation 5 would tell them
that increasing tension reduces inharmonicty, if they bothered to
look. Like I said, any time l or T goes up, B goes down. Duh!

Ciao,

P

Here's some numbers to help you get a handle on the problem.
Comparison of the diameter/length ratio of a "typical" fortepiano, the
5 octave c.1800 Walter in the Germanisches National Museum (MINe109),
which is more or less used as a basis for about 85% of all modern
"copies", and a Steinway D.

Walter
l d d/l
c1 559 0,52 9,3E-04
c2 281 0,44 1,6E-03
c3 144 0,40 2,8E-03

Steinway
c1 654 1,04 1,6E-03
c2 341 0,97 2,8E-03
c3 179 0,91 5,1E-03

The Steinway is marginally longer but much more heavily-strung. The
ratio is pretty consistently 1,8 x higher. And that doesn't take into
account the increased value of E of modern steel, which will only
worsen the case.

Ciao,

P

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
> > > > If you're taking a position on the net effect of trends
> > > > in these design factors over the ages, I didn't catch it.
> > >
> > > My position is that inharmonicity in modern pianos is
> > > significantly higher than in Classical instruments, but
> > > perhaps marginally better than c. 1840 instruments.
> >
> > Sorry I missed it then! Is there a single trend that was
> > mostly responsible?
>
> No. In pre-1840-ish pianos, it is increasing diameter coupled
> with the required decrease in length (fatter strings break at
> lower load thus shorter length). In post-1840-ish it is both
> increasing diameter and increasing values of E of Bessmer steels.
> Length gets longer again but can't keep up with the double
> whammy of the other two.

OK, that makes sense. And now that I hear it this way, I think
this does sound familiar from your earlier post.

-Carl

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:

> Walter
> l d d/l
> c1 559 0,52 9,3E-04
> c2 281 0,44 1,6E-03
> c3 144 0,40 2,8E-03
>
> Steinway
> c1 654 1,04 1,6E-03
> c2 341 0,97 2,8E-03
> c3 179 0,91 5,1E-03
>
> The Steinway is marginally longer but much more heavily-strung.
> The ratio is pretty consistently 1,8 x higher. And that doesn't
> take into account the increased value of E of modern steel,
> which will only worsen the case.

Yay, data! Thanks!

The Steniway's strings are under much greater tension, though,
which should offset some of this, no? The Steinway's c1 is
not only longer, but also higher in pitch, no?

-Carl

--- In tuning@yahoogroups.com, "Graham Breed" <gbreed@...> wrote:

> The obvious "wonder steel" is, of course, carbon fiber. A quick
> Googling shows people speculating on replacing every part of a
> piano bar the strings with carbon fiber. Maybe that's because
> it really wouldn't work. Wikipedia says it's possible to get
> high tensile strength with a low Young's modulus. But then it
> also says that carbon fiber's stiffer than other composites --
> that makes sense because it's not a flexible molecule...

Are you talking about carbon fiber, or carbon fiber composite?
I've been dreaming about pianos made of the later since the
mid '90s, but I've never thought of using it for strings. The
epoxy generally makes it phenomenally stiff and brittle and I
doubt it'd work. You'd have to use ribbon instead of wire, I
suppose. I know there are bicycle wheels with spokes made of
such ribbon:
http://www.carbonsports.com/LW_Obermayer.lasso

...

> They say Kevlar's less stiff but has higher tensile
> strength, so..

Kevlar is just the fiber, which is more like thread, which
is a more natural try for strings. I wonder what Paul thinks?

> Then, for the ultimate in tensile strength, we have nanotubes.

Strings made of a single nanotube would certainly be thin!

> Doesn't really solve the "high density" problem though. But
> there are a lot of materials out there so maybe one will do the
> trick.

My money is on metallic glasses. They have phenomenally high
yield strength and low stiffness. Some can even be made into
wire quasi-economically.

-Carl

> No need to go to exotic materials. Since even the treble strings of
> your average modern piano are significantly understressed (about 6
> semitones below rupture load as opposed to 2 for your average FePo),
> one could reduce the stiffness of the a standard modern steel string
> by laser etching a spiral pattern to a depth which would reduce the
> core diameter to one which is bearing a higher load. The wire would
> probably have to be super-cooled during the process to prevent the
> heat of etching from taking out the temper and ending up with
> something with no strength at all. Probably perfectly technologically
> possible but also probably hideously expensive.

Cool idea. When I saw Tremaine Parsons talk at the local
PTG meetup, he kept repeating his preference to use wound
strings much higher in the scale than the original manufacturers.

-Carl

2008/11/26 Paul Poletti <paul@...>:

> No need to go to exotic materials. Since even the treble strings of
> your average modern piano are significantly understressed (about 6
> semitones below rupture load as opposed to 2 for your average FePo),
> one could reduce the stiffness of the a standard modern steel string
> by laser etching a spiral pattern to a depth which would reduce the
> core diameter to one which is bearing a higher load. The wire would
> probably have to be super-cooled during the process to prevent the
> heat of etching from taking out the temper and ending up with
> something with no strength at all. Probably perfectly technologically
> possible but also probably hideously expensive.

Right, so you wouldn't want to do that. More practical would be a
composite string with metal fibers in a polymer matrix (glue). I know
such materials exist, and are relatively easy to make, but I can't
find a reference. The metal carries a lot of the stress under
tension, but it's flexible much like a cable. So you get higher
tensile strength than the pure plastic with lower stiffness (where it
counts) than the pure metal. More expensive then steel no doubt. How
much do the strings contribute to the cost of a top-quality piano?

Famous materials have a high strength to weight ratio because that's
what engineers tend to want. Here you say you want a high density.
That's why I suggest the metal fibers. The density will approach that
of the metal. What you lose in tensile strength you gain in
flexibility, so where needs be you can make them thicker. And still
use conventional steel winding.

Whether this works or not, there's a wide range of modern materials
with widely different properties (and costs). If you've looked at
them and discovered they don't work I'll be interested to hear about
it. Your initial comments suggested you were overlooking them. And,
of course, nylon and gut are polymers so this isn't such a radical
departure.

Graham

2008/11/26 Carl Lumma <carl@...>:
> --- In tuning@yahoogroups.com, "Graham Breed" <gbreed@...> wrote:
>
>> The obvious "wonder steel" is, of course, carbon fiber. A quick
>> Googling shows people speculating on replacing every part of a
>> piano bar the strings with carbon fiber. Maybe that's because
>> it really wouldn't work. Wikipedia says it's possible to get
>> high tensile strength with a low Young's modulus. But then it
>> also says that carbon fiber's stiffer than other composites --
>> that makes sense because it's not a flexible molecule...
>
> Are you talking about carbon fiber, or carbon fiber composite?
> I've been dreaming about pianos made of the later since the
> mid '90s, but I've never thought of using it for strings. The
> epoxy generally makes it phenomenally stiff and brittle and I
> doubt it'd work. You'd have to use ribbon instead of wire, I
> suppose. I know there are bicycle wheels with spokes made of
> such ribbon:
> http://www.carbonsports.com/LW_Obermayer.lasso

I said it probably wouldn't work, and that goes either way. But you
can use a flexible matrix (which may or may not be an epoxy) if that's
what you want. You can also use carbon fibers to reinforce steel for
another example.

Shouldn't spokes have compressive strength with high stiffness -- the
exact opposite of what we want?

Graham

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Graham Breed" <gbreed@> wrote:
>
> > The obvious "wonder steel" is, of course, carbon fiber.
>
> Are you talking about carbon fiber, or carbon fiber composite?
> I've been dreaming about pianos made of the later since the
> mid '90s, but I've never thought of using it for strings. The
> epoxy generally makes it phenomenally stiff and brittle and I
> doubt it'd work....

http://www.newviolinfamily.org/8tet.html#anchor1351671
"TREBLE VIOLIN

The Treble Violin, tuned G-D-A-E, an octave above the violin, is the
smallest and highest member of the Octet. In England it is called the
Sopranino following the nomen datum of the recorder family. Its
dimensions are approximately those of a quarter-size violin, but in
construction it is quite different. In order to achieve the transposed
violin sound, the Treble not only has extremely thick top and back
plates, but extra large f-holes and strategically placed small holes
in the shallow ribs so that its main resonances occur at the desired
frequencies. Michael Praetorius projected an instrument in this tone
range, but without the high E-string, so that in effect there were
only three strings. Since the string length must be at least long
enough for a player to finger consecutive semitones securely, the E
string (tuned to 1320 Hz) must be extremely strong and thin. A
space-age material known as carbon rocket wire, with a tensile
strength nearly twice that of the normal violin E string wire, is used
for this purpose. Even so, this wire is close to the breaking point.
No wonder Praetorius omitted it in his tuning of high treble!"

Pic. at:
http://www.newviolinfamily.org/pdf/Newsletter%202%20Revised%20October%2021.pdf
on page 8 of the document.

"tring Strife.
We could find no material with
enough tensile strength to
withstand the tension of e"' (1325
Hz) at a length dictated by the
standard violinmaker's formula
for neck dimensions. At first we
used conventional violin strings
in all sizes and got a surprising
number of them to work, but
nothing we tried would suffice
for the E string. To keep a more
comfortable string length, we
made the neck two centimeters
longer and tuned the strings
down a step, but we still could
not find an E string that would
not break.
Finally, through the Bell
Telephone laboratories, we
located carbon "rocket wire"
manufactured by the National
Standard Company in Niles,
Michigan. Even though the wire
is only 0.007" in diameter, this
space age-material had a tensile
strength of 530,000 psi (pounds
per square inch) as compared to
350,000 psi for standard steel E
string wire. Rocket wire worked
quite well, but musicians still
complained that even if the string
did not break, the instrument was
much harder to play with strings
tuned a tone lower.
We made a longer nut, thus
shortening the string length so a
rocket-wire E could be tuned to
1325 Hz and still hold. The string
length of 8-2/3 inches continues
to pose problems for many
players, especially those with
wide fingers, and it is still difficult
to finger consecutive semitones
without sliding the fingers
around....

http://www.catgutacoustical.org/research/articles/fiddfam/fiddfam8.htm
"A string material of requisite tensile strength to reach the high E
1320 was finally found in carbon rocket wire, made by National
Standard Company. This proved suitable not only for the high E string
but for a number of others on the new instruments. "

http://www.bath.ac.uk/physics/news/archive/oktober2004.html

http://www.fiddleforum.com/fiddleforum/index.php?action=printpage;topic=8418.0
"The E string on the treble violin is particularly special in that it
is made of carbon rocket wire. Its tensile strength needs to be almost
twice as strong as a regular violin E string since the register is
much higher"

Quest:
How about to apply that substance in pianos?

http://www.newviolinfamily.org/cmh/cmh-modechart.html

bye
A.S.

2008/11/26 Andreas Sparschuh <a_sparschuh@...>:

<snip>
> only three strings. Since the string length must be at least long
> enough for a player to finger consecutive semitones securely, the E
> string (tuned to 1320 Hz) must be extremely strong and thin. A
> space-age material known as carbon rocket wire, with a tensile
> strength nearly twice that of the normal violin E string wire, is used
> for this purpose. Even so, this wire is close to the breaking point.
> No wonder Praetorius omitted it in his tuning of high treble!"
<snip>

So what is rocket wire? According to this link:

http://www.eng-tips.com/viewthread.cfm?qid=45248&page=9

it's a kind of steel, not a carbon fiber composite: "...basically
music wire (patented 1% carbon steel)with higher levels of manganese
and silicon for additional strength." That means I haven't been
proved wrong for saying I was wrong in bringing up carbon fiber, on
account of it being too stiff.

Graham

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:

http://www.violin.be/treble.htm
"At one point we thought we might have to resort to a three-stringed
instrument in this range as was indicated by Michael Praetorius in 1619.
A string material of requisite tensile strength to reach the high E
1320 was finally found in carbon rocket wire."
http://www.violin.be/Foto/treble.jpg

http://singingwoodsviolin.com/html_pages/octet_html/treble_violin.html
"...an original model treble violin by Carleen Hutchins. The string
length on this model is about 8 1/3 inches (211.6 mm). Even at that
short span, the tension on the string, tuned to E 1330 Hz, is probably
in the neighborhood of 500,000 psi. The material used for the string
is carbon rocket wire, the strongest wire we have been able to find.
Even so, the string is near to its breaking point."
http://singingwoodsviolin.com/photos/3_trebles_front.png

bye
A.S.

--- In tuning@yahoogroups.com, "Graham Breed" <gbreed@...> wrote:
> http://www.eng-tips.com/viewthread.cfm?qid=45248&page=9
>
> it's a kind of steel, not a carbon fiber composite: "...basically
> music wire (patented 1% carbon steel)with higher levels of manganese
> and silicon for additional strength." That means I haven't been
> proved wrong for saying I was wrong in bringing up carbon fiber, on
> account of it being too stiff.
>
Agreed,
sorry,
but I never intened presume that you were "wrong".
As far as I can catch by viewing from the pics of the violin,
it appears that all strings are made basically of steel
in whatsoever composition of alloy and proportion of carbon?

Remark:
Mozart's "Königin der Nacht" 'Queen of the night' sings
in reference to todays a'=440 at about ~1470Hz
near to the upper limit of the female voice.

http://books.google.de/books?id=bnsxb8nXOPAC&pg=PA110&lpg=PA110&dq=k%
C3%B6nigin+der+nacht+sopran+frequenz&source=web&ots=fZxFbCvBYH&sig=-
w9Xv42RPuiCGeCzTuKx9AEffi4&hl=de&sa=X&oi=book_result&resnum=3&ct=resul
t

bye
A.S.

> Shouldn't spokes have compressive strength with high stiffness -- the
> exact opposite of what we want?

That's the miracle of bicycle wheels -- it's the rim that bears
compression. The spokes are under tremendous tension.

-Carl

> I said it probably wouldn't work, and that goes either way. But
> you can use a flexible matrix (which may or may not be an epoxy)
> if that's what you want.

Savarez does make "composite fiber" classical guitar strings, but
they don't say what's in the composite.

http://www.savarez.fr/anglais/faq.html#3

-Carl

Interesting. Having trouble finding details on the
material online. I suspect it's a steel alloy, but
it certainly does sound promising. -Carl

> So what is rocket wire? According to this link:
>
> http://www.eng-tips.com/viewthread.cfm?qid=45248&page=9
>
> it's a kind of steel, not a carbon fiber composite:

Thanks Graham. -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>

>
> Yay, data! Thanks!

Glad to be of service.
>
> The Steniway's strings are under much greater tension, though,
> which should offset some of this, no?

Some, yes, but compare the exponents which T and d carry in equation
5. Which is more significant, and by how much?

> The Steinway's c1 is
> not only longer, but also higher in pitch, no?

Not really. A typical Viennese pitch for c.1800 was probably 438-ish.
This 430 calssical pitch stuff in an invention of the modern
Histerically Unimformed Performance Practice movement.

Ciao,

p

2008/11/27 Carl Lumma <carl@...>:

> Savarez does make "composite fiber" classical guitar strings, but
> they don't say what's in the composite.
>
> http://www.savarez.fr/anglais/faq.html#3

Lordy, here we go...

I can't get that link, but I found some here:

https://www.stringsdirect.co.uk/strings/classical_guitar

Which turn out be "feature an exclusive high-tech Zyex(R)
multi-filament stranded core, which delivers gut-like tone with
extremely long life and consistency."

So what exactly is Zyex? It's got its own website, and they say they
sell polyketone fibers.

http://www.zyex.com/

Polyketone is in the mighty Wikipedia:

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

About a tenth of the tensile strength of mild steel but

Gmail has some shortcut to send a message doesn't ask you to confirm ...

2008/11/27 Graham Breed <gbreed@...>:
> 2008/11/27 Carl Lumma <carl@...>:
>
>> Savarez does make "composite fiber" classical guitar strings, but
>> they don't say what's in the composite.
>>
>> http://www.savarez.fr/anglais/faq.html#3
>
> Lordy, here we go...
>
> I can't get that link, but I found some here:
>
> https://www.stringsdirect.co.uk/strings/classical_guitar
>
> Which turn out be "feature an exclusive high-tech Zyex(R)
> multi-filament stranded core, which delivers gut-like tone with
> extremely long life and consistency."
>
> So what exactly is Zyex? It's got its own website, and they say they
> sell polyketone fibers.
>
> http://www.zyex.com/
>
> Polyketone is in the mighty Wikipedia:
>
> http://en.wikipedia.org/wiki/Polyketone

About a tenth of the tensile strength of mild steel but Young's
modulus two orders of magnitude lower.

Here's another link:

https://www.stringsdirect.co.uk/products/647-daddario_pro_arte_lightly_polished

"The Lightly Polished basses are silverplated copper wound on a
multi-filament Composite core and then polished offering greatly
reduced finger noise."

For reduced finger noise without the plating you want a low friction
material, of course. And that's exactly what you don't want for a
bowed string. So one size doesn't fit all instruments.

Another thing that came up:

https://www.stringsdirect.co.uk/products/641-savarez_520r_red_card_high_tension

Rectified nylon, so not as interesting, but I noticed that the claim
is "This grittiness contributes to a lessening of the high overtones."
Then below it a rave review says "This gives a precise, bright tone
with flamenco style finger-picking which is ideal for studio work. I
find these a league above most other dull, lifeless classical strings
I've tried."

Quite how lessening the high overtones brightens the tone is beyond me.

Graham

> >> http://www.savarez.fr/anglais/faq.html#3
> >
> > Lordy, here we go...
> >
> > I can't get that link, but I found some here:
> >
> > https://www.stringsdirect.co.uk/strings/classical_guitar
> >
> > Which turn out be "feature an exclusive high-tech Zyex(R)
> > multi-filament stranded core, which delivers gut-like tone with
> > extremely long life and consistency."

I don't think that's the same stuff. Savarez makes lots
of strings. What I pointed to was their "KF ALLIANCE plain
composite trebles monofilament"

http://www.savarez.fr/anglais/alliance-corum.html

-Carl

I want to say thanks for this very informative discussion and offer a
couple of comments from my domain:

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Savarez does make "composite fiber" classical guitar strings, but
> they don't say what's in the composite.
> -Carl

Savarez' material is "fluorocarbon" which no doubt has a more
technical name. Related to freon and introduced in the 70's by a
Japanese chemical company as fishing line under the brand name
Seaguar. It is denser than nylon by a factor of about 1.8 .

material densities

1000 Kg/m³, nylon
1276 Kg/m³, gut and nylgut
1791 Kg/m³, fluorocarbon
7800 Kg/m³, iron
8600 Kg/m³, brass

I'm half of a working "nylon-string" guitar duo, and we have replaced
our nylon trebles with Seaguar Fluoro Premier fishing leader, which
is superior to nylon in tone and volume and available in 25 meter
reels from online fishing supply houses in a variety of diameters.
The several companies packaging commercial fluorocarbon classical
guitar strings, including Savarez, have various difficulties with
quality control AND tone, but since the Japanese take their fishing
very seriously !:) the Seaguar fishing line strings are great, I
can't say enough good things about them. Vihuela and lute players who
are in the know use them for non-standard string lengths which are
not commercially available (you can buy a range of diameters and do
calculations for tension) but the early instrument folks use them at
"low" tensions around 3 - 4 kg of tension per string, whereas I like
them at around 7 kg for our purposes.

>> Graham wrote:
"Whether this works or not, there's a wide range of modern materials
with widely different properties (and costs). If you've looked at
them and discovered they don't work I'll be interested to hear about
it. Your initial comments suggested you were overlooking them. And,
of course, nylon and gut are polymers so this isn't such a radical
departure.
Graham"

Could we add a little exclamation point or an "ahem" to the idea that
gut is a polymer... :) There is however a material called "nylgut"
from the Italian string company Aquila, which is a polymer at
approximately the same density as gut. 1276 Kg/m³

>> Andreas wrote:
"The Treble Violin, tuned G-D-A-E, an octave above the violin, is the
smallest and highest member of the Octet.... Since the string length
must be at least long enough for a player to finger consecutive
semitones securely, the E string (tuned to 1320 Hz) must be extremely
strong and thin. A space-age material known as carbon rocket wire,
with a tensile strength nearly twice that of the normal violin E
string wire, is used for this purpose. Even so, this wire is close to
the breaking point. No wonder Praetorius omitted it in his tuning of
high treble!"

I can't imagine wanting to listen to this thing but appreciate the
problem. We have tried very high tunings for some experimental
instruments with our fluorocarbon strings (not that high, though) but
there is a diminishing return because it seems (sorry, no hard data
here) that the smallest diameters will not accept as much tension as
I calculated. There's a guy who set up an online string tension /
diameter calculator which has been useful for approximations
preceding experiments:
http://www.cs.helsinki.fi/u/wikla/mus/Calcs/wwwscalc.html

--- jack

--- In tuning@yahoogroups.com, "Graham Breed" <gbreed@...> wrote:
> >
> >> Savarez does make "composite fiber" classical guitar strings, but
> >> they don't say what's in the composite.

> > Lordy, here we go...
> > I can't get that link, but I found some here:
> > https://www.stringsdirect.co.uk/strings/classical_guitar
> > Which turn out be "feature an exclusive high-tech Zyex(R)
> > multi-filament stranded core, which delivers gut-like tone with
> > extremely long life and consistency."
> > So what exactly is Zyex? It's got its own website, and they say
> > they sell polyketone fibers.
> > http://www.zyex.com/
> > Polyketone is in the mighty Wikipedia:
> > http://en.wikipedia.org/wiki/Polyketone
> About a tenth of the tensile strength of mild steel but Young's
> modulus two orders of magnitude lower.

This is news to me, thanks, have to look into this.

> Here's another link:
> https://www.stringsdirect.co.uk/products/647-
daddario_pro_arte_lightly_polished
>
> "The Lightly Polished basses are silverplated copper wound on a
> multi-filament Composite core and then polished offering greatly
> reduced finger noise."
> For reduced finger noise without the plating you want a low friction
> material, of course. And that's exactly what you don't want for a
> bowed string. So one size doesn't fit all instruments.

Guitar player chimes in: Polished basses don't sound very good, they
have no character. They are only for studio musicians who need squeak-
free first takes (and amateurs who have no idea of tone
anyway... :)). Regular basses with round-wire windings make a lot of
squeaks when shifting positions, but an experienced player learns to
minimize those through superior technique (although you can't get rid
of all.) Lots of people remove them digitally now, of course.

By the way, the modern standard for classical guitar basses is silver
plated bronze alloy wound on a nylon core, costing about 5 bucks USD
for a set of 3. However, the Aquila company makes "pure" (?) silver
wound basses ($15 USD a set) which make me "remember" what the bass
strings on a guitar are really supposed to sound like! Oh yeah baby.

> Another thing that came up:
> https://www.stringsdirect.co.uk/products/641-
savarez_520r_red_card_high_tension
> Rectified nylon, so not as interesting, but I noticed that the claim
> is "This grittiness contributes to a lessening of the high
overtones."
> Then below it a rave review says "This gives a precise, bright
tone
> with flamenco style finger-picking which is ideal for studio work. I
> find these a league above most other dull, lifeless classical
strings
> I've tried."
>
> Quite how lessening the high overtones brightens the tone is beyond
me.
> Graham

Beyond me too :)

"precise, bright tone with flamenco style finger-picking which is
ideal for studio work."

Complete word salad... written by the marketing department.
All string industry hype, all too common nowadays. They have to tell
some kind of marketing story to sell strings, and the stories are all
in competition with each other - because the strings are very
similar. Facts are few and fancy phrases are
many!

Rectified nylon has been first extruded and then run through a
controlled polishing process which reduces the diameter to a uniform
result perhaps better than some extrusion processes. They have a
little different feel under the fingers but there is really no
significant difference to me. (Since I switched to fluorocarbon and
THAT's a significant difference.) Most guitar string companies have
both rectified and plain nylon models to give the appearance of
variety. Savarez was first on the scene about 20 years ago with
fluorocarbon (their "Alliance" line) but the high E strings are
frequently false.

Nylon has never sounded as good as gut, although it has been much
improved since WWII when it was introduced. However, it is much
easier to get quality control than with gut. Gut being an organic
material is very variable, temperature and humidity sensitive, prone
to breakage and fraying, and so on. Nylon is very temperature
sensitive and goes up and down in pitch with slight changes.
Fluorocarbon is much more stable and doesn't sound as much like
"plastic strings".

Hi Jack,

> > Savarez does make "composite fiber" classical guitar strings,
> > but they don't say what's in the composite.
> > -Carl
>
> Savarez' material is "fluorocarbon" which no doubt has a more
> technical name. Related to freon and introduced in the 70's by
> a Japanese chemical company as fishing line under the brand
> name Seaguar.

Sure, I fished with it all the time when I was a kid.
Fluorocarbons are a class of compounds that include any
hydrocarbon with fluorine in it, including teflon, etc.
I don't know which particular polymers are used for fishing
line or guitar strings, but I don't the KF Alliance strings
I'm talking about are fluorocarbon. At least, fluorocarbon
isn't a "composite", as the KF Alliance material claims
to be. Players are calling these strings "carbon fiber",
but Savarez seems to discourage this terminology.

-Carl

I wrote:
> Sure, I fished with it all the time when I was a kid.
> Fluorocarbons are a class of compounds that include any
> hydrocarbon with fluorine in it, including teflon, etc.
> I don't know which particular polymers are used for fishing
> line or guitar strings, but I don't the KF Alliance strings
> I'm talking about are fluorocarbon. At least, fluorocarbon
> isn't a "composite", as the KF Alliance material claims
> to be. Players are calling these strings "carbon fiber",
> but Savarez seems to discourage this terminology.

Hello again, Jack. I'm getting an education here. I think
I'm seeing your posts over on the classical guitar forums.
Apparently fluorocarbon strings are called "carbon" strings
in the guitar world. And Savarez's Alliance strings are
apparently known for being one of the first to market them
to guitarists. But I still want to believe the KF Alliance
material is different. Have you actually seen these strings?
Do they look like fluorocarbon?

It's really depressing me that terms like "carbon", "carbon
fiber", and "composite" are tossed around in the guitar
string world with complete disregard for their meanings.

-Carl

I know that Cris Forster winds his own strings for his piano because he could not find the right gauge for the length he wanted. This being another consideration.
I am surprised we don't have more guitar players filling us in on these different strings.
--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> ... to guitarists. But I still want to believe the KF Alliance
> material is different. Have you actually seen these strings?
> Do they look like fluorocarbon?

I used Savarez Alliance strings on and off from the early nineties
until last year. The trebles (not the basses) are distinctly
different from nylon. They are significantly louder than nylon, and
the Savarez ones also have much more treble response, which, on some
spruce top guitars, makes them unbearably shrill (this is worst with
Savarez as opposed to other brands). Also, the high E strings, as I
wrote, are frequently uneven and therefore don't play in tune,
ruining the whole set, because they don't mix well with nylon tonally
and you can't just replace the E string without buying another set.
The high E strings also show a characteristic "shredding"
delamination after about 5 to 6 weeks, which is not a problem since
that's a normal lifespan.

Last year I embarked on a series of new string experiments (to find
optimal strings for a pair of new guitars) and tested the
"carbon" strings from Galli and Oasis. The Galli strings sounded
great but deteriorated very rapidly, with the same characteristic
shredding pattern as the Savarez high E, both the high E and the B
sometimes in only 4 HOURs of playing time, so I found them un-usable.
The Oasis strings were better, but not satisfactory because they were
not even enough for consistent intonation, and also showed the
characteristic delamination at about 3 weeks of use. (Last summer,
after I started using the Seaguar, Oasis announced free beta sets of
a new formula and sent me two sets with two B strings each and no
High E. The B delaminated.) Then somebody turned me on to the Seaguar
strings, last March and I was sold.

Although I can't say for certain that the commercial carbon strings
and the Seaguar strings are the same material - and the Seaguar
strings mercifully do NOT delaminate in the characteristic pattern -
the materials are much more similar to each other than either is to
nylon, and they use the same approximate diameters (significantly
thinner than nylon) and therefore must have the same density, and
they all make the same general type of tone, different from nylon.
Clearly there are different formulas floating around since the
several brands of commercial strings have varying degrees of the same
common flaws.

> Carl wrote:
> > ... I don't [think(?)] the KF Alliance strings
> > I'm talking about are fluorocarbon. At least, fluorocarbon
> > isn't a "composite", as the KF Alliance material claims
> > to be. Players are calling these strings "carbon fiber",
> > but Savarez seems to discourage this terminology.
> ...
> It's really depressing me that terms like "carbon", "carbon
> fiber", and "composite" are tossed around in the guitar
> string world with complete disregard for their meanings.

Marketing! "composite" "new polymer" "KF" etc., but no specs
available. Don't believe anything any of them say even if they say
something different, the guitar string industry is very competitive
and they are always trying like heck to distinguish mostly identical
products from the competition, so it has become a habit with them to
hype even a legitimately new product with buzzwords and phrases.
Yes, the "carbon" strings are different from nylon, but all the
commercial brands I've tried have problems, hence it's amazing to me
that the Seaguar material is even and true and sounds great. I admit
I have not tried Hannabach's carbon strings, which have a good
reputation so far. I slowed down my experiments after I found the
Seaguars (which of course are treble strings only), and turned my
attention to finding some compatible basses to go with them.

-- jack

--- In tuning@yahoogroups.com, "Jack" <gvr.jack@...> wrote:

> > ... to guitarists. But I still want to believe the KF Alliance
> > material is different. Have you actually seen these strings?
> > Do they look like fluorocarbon?
>
> I used Savarez Alliance strings on and off from the early nineties
> until last year.

Alliance or **KF** Alliance? If you have seen KFs, are
they translucent or opaque? Clear/white or colored?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Alliance or **KF** Alliance? If you have seen KFs, are
> they translucent or opaque? Clear/white or colored?
> -Carl

You're squeezing me here... I am unaware of any distinction between
"Alliance" and "**KF** Alliance". I have a set on the desk here,
unopened. As always, I believe, the trebles are "KF". Savarez also
makes nylon strings which are not called "Alliance" at all. (Yes,
I've used those too.)

Verbage from the package:
"Alliance KF treble strings: Manufactured from a high technology
composite synthetic fiber and produced exclusively for Savarez..."

The strings are clear and translucent. As I said, they also are very
close to the same diameters as the Seaguars I use
(.52mm, .66mm, .91mm are the Seaguar specs; at the moment I don't
want to open these Alliances to measure them but I will if you want
the info.)

http://www.economist.com/science/displaystory.cfm?story_id=12630225

Might this also work for strings?

On 28 Nov 2008, at 15:07, Jack wrote:

....regarding strings......

Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

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

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Not sure how the thermoacoustic effect is an advantage for strings
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: Charles Lucy <lucy@harmonics.com>

Date: Fri, 28 Nov 2008 15:30:04
To: <tuning@yahoogroups.com>
Subject: [tuning] Nanotubes for speakers?

http://www.economist.com/science/displaystory.cfm?story_id=12630225

Might this also work for strings?

On 28 Nov 2008, at 15:07, Jack wrote:

.....regarding strings......

Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

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

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

So Zyex is already being used for violin strings...

https://www.stringsdirect.co.uk/products/1649-
d_addario_dz310a_zyex_violin

"Zyex is a new composite fiber core that is the closest man-made
equivalent to gut, with better recovery, less tension loss, and a
much higher resistance to climatic changes. Unanimously praised by
violinists and makers around the world."

A monofilament is available according to the manufacturer's website,
so the potential is there for treble guitar strings. http://
www.zyex.com/ - at least for an experiment.

And how about tennis rackets...
Revolutionize Your Tennis Game!
Play with Ashaway's championship Dynamite® strings made with Zyex®,
which tests show has the dynamic stiffness most similar to natural
gut. Players of all levels will benefit from the amazing bite on the
ball produced by this revolutionary fiber.
http://www.ashawayusa.com/

The density...
http://www.zyex.com/basics.htm
is 1.3 g/cm3 = 1,300 Kg/m³
which is very close to "Nylgut"

http://stringsbymail.com/serselect.asp?tCat=1&tMan=43&dMan=Aquila

1000 Kg/m³, nylon
1276 Kg/m³, gut and nylgut
1791 Kg/m³, fluorocarbon

So possibly Zyex = Nylgut ??
Nylgut has a reputation for being very brittle and breaking at the
nut or saddle, or when crossed over itself on the winding post.

-- jack

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> I wrote:
> > Sure, I fished with it all the time when I was a kid.
> > Fluorocarbons ... Players are calling these strings "carbon
fiber",
> > but Savarez seems to discourage this terminology.

> It's really depressing me that terms like "carbon", "carbon
> fiber", and "composite" are tossed around in the guitar
> string world with complete disregard for their meanings.
>
> -Carl
>

--- In tuning@yahoogroups.com, "Jack" <gvr.jack@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > Alliance or **KF** Alliance? If you have seen KFs, are
> > they translucent or opaque? Clear/white or colored?
> > -Carl
>
> You're squeezing me here... I am unaware of any distinction
> between "Alliance" and "**KF** Alliance". I have a set on the
> desk here, unopened. As always, I believe, the trebles
> are "KF". Savarez also makes nylon strings which are not
> called "Alliance" at all. (Yes, I've used those too.)
>
> Verbage from the package:
> "Alliance KF treble strings: Manufactured from a high
> technology composite synthetic fiber and produced exclusively
> for Savarez..."
>
> The strings are clear and translucent.

Thanks for reporting! Another dream shattered. I'm
flabergasted they're calling fluorocarbon a composite, and
I have no idea how they can say it's exclusive to them!

> As I said, they also are
> very close to the same diameters as the Seaguars I use
> (.52mm, .66mm, .91mm are the Seaguar specs; at the moment I don't
> want to open these Alliances to measure them but I will if you want
> the info.)

No need, but thanks for the offer.

-C.

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> http://www.economist.com/science/displaystory.cfm?story_id=12630225
>
>
> Might this also work for strings?

No, because the sound was produced thermally, not mechanically.

-Carl

Graham wrote:

> >> http://www.savarez.fr/anglais/faq.html#3
> >
> > Lordy, here we go...
> >
> > I can't get that link, but I found some here:
> > https://www.stringsdirect.co.uk/strings/classical_guitar
> > Which turn out be "feature an exclusive high-tech Zyex(R)
> > multi-filament stranded core, which delivers gut-like tone with
> > extremely long life and consistency."
> >
> > So what exactly is Zyex? It's got its own website, and they
> > say they sell polyketone fibers.
> >
> > http://www.zyex.com/
> >
> > Polyketone is in the mighty Wikipedia:
> >
> > http://en.wikipedia.org/wiki/Polyketone
>
> About a tenth of the tensile strength of mild steel but Young's
> modulus two orders of magnitude lower.

So you think KF Alliance strings are Zyex, and Jack thinks
they're fluorocarbon.

Zyex is polyketone, in particular, it's something called PEEK:

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

I don't see support for your claim that the Young's modulus
is lower than steel. According to Wikipedia and some other
sources, we have

yield E
piano wire 2350 MPa 3100 MPa
PEEK ~ 90 MPa 3700 MPa

It's strength is an order of magnitude lower, but it's stiffness
is slightly greater (according to this). Which means it'd be
much more inharmonic than piano wire.

-Carl

--- In tuning@yahoogroups.com, "Jack" <gvr.jack@...> wrote:

> 1000 Kg/m³, nylon
> 1276 Kg/m³, gut and nylgut
> 1791 Kg/m³, fluorocarbon
>
> So possibly Zyex = Nylgut ??
> Nylgut has a reputation for being very brittle and breaking at the
> nut or saddle, or when crossed over itself on the winding post.

According to wikipedia, the density of PEEK is 1300 Kg/m^3,
so that would be spot-on for nylgut.

-Carl

2008/11/29 Carl Lumma <carl@...>:

> Zyex is polyketone, in particular, it's something called PEEK:
>
> http://en.wikipedia.org/wiki/PEEK
>
> I don't see support for your claim that the Young's modulus
> is lower than steel. According to Wikipedia and some other
> sources, we have
>
> yield E
> piano wire 2350 MPa 3100 MPa
> PEEK ~ 90 MPa 3700 MPa
>
> It's strength is an order of magnitude lower, but it's stiffness
> is slightly greater (according to this). Which means it'd be
> much more inharmonic than piano wire.

For Zyex, I used the Polyketone figure of 1500 MPa for Young's
modulus. If it's PEEK then, yes, it's a bit stiffer.

I didn't know the modulus for piano wire, which is why I quoted mild
steel instead. This site agrees:

http://www.sr.bham.ac.uk/xmm/structures3.html

200 GPa. It also gives 3100 MPa for the tensile strength of piano wire.

Young's modulus of piano wire is given here:

http://www.mmdigest.com/Archives/Digests/200204/2002.04.02.08.html

Unfortuately, not in MPa. So we have to convert 1.92 x 10^12 dynes/cm
sq. According to Wikipedia, a dyne is 10^-5 newtons. So the modulus
is 1.92 x 10^7 newtons per square centimeter or 19.2 meganewtons per
square centimeter. There are 10,000 square centimeters per square
meter and the force will go up, so that's 19.2 x 10000 megapascals or
192 Gpa.

Did I get that right? Very close to the mild steel figure from
Wikipedia, and nothing like the 3.1Gpa you quoted.

Incidentally, this site says gut strings are mostly collagen:

http://web.mit.edu/3.082/www/team1_f02/collagen.htm

But we've also been told that gut isn't a polymer, so who knows?
Anyway, I found an article that says 4.8 GPa (4800 Mpa) for Young's
modulus of a collagen molecule (a string made of collagen will be
different).

http://linkinghub.elsevier.com/retrieve/pii/S0021929004003550

Probably your PEEK figure is pretty close to gut strings.

Graham

--- In tuning@yahoogroups.com, "Graham Breed" <gbreed@...> wrote:

> Young's modulus of piano wire is given here:
>
> http://www.mmdigest.com/Archives/Digests/200204/2002.04.02.08.html
>
> Unfortuately, not in MPa. So we have to convert 1.92 x 10^12
> dynes/cm sq. According to Wikipedia, a dyne is 10^-5 newtons.
> So the modulus is 1.92 x 10^7 newtons per square centimeter
> or 19.2 meganewtons per square centimeter. There are 10,000
> square centimeters per square meter and the force will go up,
> so that's 19.2 x 10000 megapascals or 192 Gpa.
>
> Did I get that right? Very close to the mild steel figure from
> Wikipedia, and nothing like the 3.1Gpa you quoted.

You're right, I think I flipped the yield and E values
in my table. But either way, steel is blowing away PEEK.

And I've thought about it some more, and I stand by my claim
that amorphous metal would be the ultimate piano string
material by a mile. Hard to find figures on the web to
corroborate that, alas.

-Carl

--- In tuning@yahoogroups.com, "Graham Breed" <gbreed@...> wrote:

>
> Young's modulus of piano wire is given here:
>
> http://www.mmdigest.com/Archives/Digests/200204/2002.04.02.08.html
>
> Unfortuately, not in MPa. So we have to convert 1.92 x 10^12 dynes/cm
> sq. According to Wikipedia, a dyne is 10^-5 newtons. So the modulus
> is 1.92 x 10^7 newtons per square centimeter or 19.2 meganewtons per
> square centimeter. There are 10,000 square centimeters per square
> meter and the force will go up, so that's 19.2 x 10000 megapascals or
> 192 Gpa.
>
> Did I get that right? Very close to the mild steel figure from
> Wikipedia, and nothing like the 3.1Gpa you quoted.
>
There is something funky about the whole bunch of figures given in the
link. 2 x 10^7 PSI is about 138 GPa according to a number of on-line
pressure converters. This is way too low. Good way/Odell in The
Metallurgy of 17th and 18th Century Music Wire cite 219 GPa for modern
piano wire. Stephen Birkett has tested all the modern "reproduction"
wires, which run from a low of about 170 GPa up to 210 GPa for Voss
wire. So I would think 219 is pretty believable for modern steel.

Ciao,

p

--- In tuning@yahoogroups.com, "Graham Breed" <gbreed@...> wrote:

> For Zyex, I used the Polyketone figure of 1500 MPa for Young's
> modulus. If it's PEEK then, yes, it's a bit stiffer.

I have to try this stuff to satisfy my curiosity. Probably buying a
set of "Nylgut" guitar strings is first. It will be interesting to
see what kind of intonation issues it has, and if comparing the
stiffness and density of 3 synthetic materials - nylgut/zyex(?),
nylon, "fluorocarbon" - with their various intonation issues shows
any significant pattern. I know empirically that fluorocarbon has a
different pattern of intonation issues than nylon, but so far I'm in
the dark about how to actually quantify that and make use of the
information for intelligent intonation compensations rather than my
empirical ones. Intonation adjustments on the guitar are made by
changing the string length by fractions of a mm at either the nut or
saddle or both. Stiffness (of the material) and stretch (from
fretting) are the variables... with a huge variable introduced by the
height of the action at each end of the string.

A luthier named Greg Byers wrote "the" paper on guitar intonation
issues, based on nylon, merely mentioning in passing that his results
might not be applicable to Savarez Alliance (i.e., "fluorocarbon").

http://www.byersguitars.com/research/Intonation.pdf

Byer's math is a stretch for me, sorry. Not for some of you cats. I
follow the logic generally in a sort of layman's way, and accept the
conclusions as reasonable. My intonation tweaks to my own guitars are
done more by guess and by golly, and vary quite a bit from one guitar
to the next - according to how much time I want to spend bothering
with it, mostly! And because I sit with the results for long periods
of time before deciding to proceed further.

> Incidentally, this site says gut strings are mostly collagen:
> http://web.mit.edu/3.082/www/team1_f02/collagen.htm
> But we've also been told that gut isn't a polymer, so who knows?
> Probably your PEEK figure is pretty close to gut strings.
> Graham

Am I unclear on what a polymer is?

"Polymer - Any of numerous natural and synthetic compounds of usually
high molecular weight consisting of up to millions of repeated linked
units, each a relatively light and simple molecule."

http://www.pacpkg.com/glossary.htm#P

"Collagen: an insoluble fibrous protein of vertebrates that is the
chief constituent of the fibrils of connective tissue (as in skin,
tendons, and vitreous humor) and of the organic substance of bones
and yields gelatin and glue on prolonged heating with water"

http://www.tedmontgomery.com/the_eye/glossary/C.html

I think I just made an uninformed assumption that polymers are a
general class of petroleum derivatives.

-- jack

--- In tuning@yahoogroups.com, "Jack" <gvr.jack@...> wrote:

>
> A luthier named Greg Byers wrote "the" paper on guitar intonation
> issues, based on nylon, merely mentioning in passing that his results
> might not be applicable to Savarez Alliance (i.e., "fluorocarbon").
>
> http://www.byersguitars.com/research/Intonation.pdf
>
> Byer's math is a stretch for me, sorry. Not for some of you cats. I
> follow the logic generally in a sort of layman's way, and accept the
> conclusions as reasonable.

That's your big mistake. Most of what he says is utter bollocks. I
didn't bother to check his math 'cause his basic approach is an
example of the old adage that "a little bit of learning is a dangerous
thing". His assertion that an increased inharmonicity raises the
perceived pitch is quite true, but I seriously doubt it is a factor in
guitar intonation. The guitar is normally so poor in overtone content
and the change in inharmonicty between open and stopped at the octave
is so small that it's just not going to be an issue.

He's so off on a search for the esoterical that he completely misses
the obvious; intonation problems on ALL stopped stopped string
instruments, fretted or no, are caused by one thing and thing alone:
inequalities of load on the different strings. All you need to
understand it is to remember Hooke's Law: force (tension) is linear to
extension, and vice versa. Thus when we stretch a string between two
fixed points to bring it up to pitch, we are really extending it until
there is a certain force applied to its entire length. If we increase
its length by deflecting it by pushing it against the fingerboard, we
increase the extension, which increases the force, i.e. raises the
tension.

Upt o that point, he's more or less OK, but this is where he
completely misses the critical factor. Actually, we can think of
extension and force as being the same, since they are linearly
related. The increased extension for any given extra displacement will
always be the same, BUT... and here's the cause of all the trouble...
the change in pitch will depend upon the ratio between extension
increased by deflection and the ambient extension (the extension when
the string is not stopped). The greater the ambient extension, the
less significant with be the increased tension, and the smaller the
rise in pitch.

The fly in the ointment comes because the strings of a guitar or
violin or tar or oud or whatever all have the same length, though they
all sound different notes. Diameters are different of course, but this
is a balance of tone issue and has nothing to with the mechanics.
Recall that theoretically all diameters break at the same pitch,
because load for all diameters with a given pitch and length is the
same, the tension increasing or decreasing with diameter in exact
proportion to the cross sectional area. And since load is defined as
force applied over an area, if load is always the same, this means
that EXTENSION is also always the same for any given pitch/length
combination regardless of diameter. ERGO: because the strings are all
of the same length but sound different notes, if the material is the
same, they MUST be at different extensions. That means that when they
are depressed by the same distance against the fingerboard, the added
extension is always the same, but it has a different proportion to the
ambient extension and therefore produces a different change in pitch.
The higher the open string pitch, the greater the ambient extension,
and the less pitch change when fingering any stopped note. Naturally,
the reverse is true, the lower the open string pitch, the less the
ambient extension, and the greater the relative increase in extension
introduced by fingering, and the greater the rise in pitch for any
stopped note. Thus the same fret position *cannot* serve for all
strings, nor can the same finger position serve for the same interval
on all strings in unfretted instruments.

Fingering it all out is a bit tricky but requires no fancy pants math.
However, you MUST have a reliable value for E for each type of
stringing material, because THAT is what will tell you how much
extension is need to arrive at any pitch, and also how much force will
be introduced by any deflection. Recall also that the extension must
be calculated as percentages of the ENTIRE string length, from tuning
pin to point of fixation, be it bridge or tailpiece, and NOT just the
sounding length as in the models presented in the paper.

Ciao,

P

Thank you, Paul. I'm very interested to read a different point of
view on this. As a matter of practical experience, the different
gauges and materials of strings respond differently to being fretted,
and each string therefore has its own "intonation pattern". Just
taking Byer's recommendations as a general guide to the
possibilities, my own intonation tweaks are generally like this: If a
string is fretting sharp or flat in the area of the octave, I
lengthen or shorten the string at the bridge. If it's fretting sharp
in the first four frets, I shorten it at the nut. Sometimes I
discover that with different strings, or even one different string, I
need to re-adjust. I don't do this intensively - I usually think
about it for quite a while, then make one small adjustment and sit
with it to make sure I'm clear that this is making a definite change
for the better. Typically shortening the B string at the nut makes
the single most noticeable change for the better, because there is
typically a wide split between the open B tuned to the E strings, and
the D on the B string's third fret tuned against the open D string
(the B in tune, the D will be sharp.)

However, this entire approach (of mine) is perhaps fatally flawed by
the (obvious?) fact that the actual layout of the frets would have to
be different for each string for true accuracy. And then that opens
another can of worms. Merely changing the string length at one end or
another of a fixed fret system still leaves problem areas of the
fretboard. (No, I have no plans to go fretless any time soon.)

Your comments on this are welcome, including suggestions for
different ways to look at it or possible different practical
procedures.

I appreciate your argument that the different responses of the
different strings are due to the different ratios between "ambient
extension" and the added extension by fretting. This seems clear
enough. So you are also saying that inharmonicity is a red herring,
correct?

I think that inharmonicity is dealt with by the common saddle setback
for all six strings, which can be individually adjusted to some
extent, and that the stretch or extension issue is what's being dealt
with by nut adjustments. Do I have that right or do you have a
comment?

You (Paul) wrote:
" Figuring it all out is a bit tricky but requires no fancy pants
math. However, you MUST have a reliable value for E for each type of
stringing material, because THAT is what will tell you how much
extension is need to arrive at any pitch, and also how much force
will be introduced by any deflection. Recall also that the extension
must be calculated as percentages of the ENTIRE string length, from
tuning pin to point of fixation, be it bridge or tailpiece, and NOT
just the sounding length as in the models presented in the paper."

Ok, so Byer's model need revision. The model disregards the portions
of the string that are under load but not part of the sounding
length. Hmm, where do I come by "a reliable value of E for each type
of string"? I'll chew on it.

Thanks a lot, I really think it's worth it to me to make an effort to
understand this, and I have copied your note to my file on strings &
intonation issues.

-- jack

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> --- In tuning@yahoogroups.com, "Jack" <gvr.jack@> wrote:

> > A luthier named Greg Byers wrote "the" paper on guitar intonation
> > http://www.byersguitars.com/research/Intonation.pdf
> > ...I follow the logic generally in a sort of layman's way, and
> > accept the conclusions as reasonable.
>
> That's your big mistake. Most of what he says is utter bollocks. I
> didn't bother to check his math 'cause his basic approach is an
> example of the old adage that "a little bit of learning is a
dangerous thing". His assertion that an increased inharmonicity
raises the perceived pitch is quite true, but I seriously doubt it is
a factor in guitar intonation. The guitar is normally so poor in
overtone content and the change in inharmonicty between open and
stopped at the octave is so small that it's just not going to be an
issue.
>
> He's so off on a search for the esoterical that he completely misses
> the obvious; intonation problems on ALL stopped stopped string
> instruments, fretted or no, are caused by one thing and thing alone:
> inequalities of load on the different strings. All you need to
> understand it is to remember Hooke's Law: force (tension) is linear
to extension, and vice versa. Thus when we stretch a string between
two fixed points to bring it up to pitch, we are really extending it
until there is a certain force applied to its entire length. If we
increase its length by deflecting it by pushing it against the
fingerboard, we increase the extension, which increases the force,
i.e. raises the tension.
>
> Up to that point, he's more or less OK, but this is where he
> completely misses the critical factor. Actually, we can think of
> extension and force as being the same, since they are linearly
> related. The increased extension for any given extra displacement
will always be the same, BUT... and here's the cause of all the
trouble...
> the change in pitch will depend upon the ratio between extension
> increased by deflection and the ambient extension (the extension
when the string is not stopped). The greater the ambient extension,
the less significant with be the increased tension, and the smaller
the rise in pitch.
>
> The fly in the ointment comes because the strings of a guitar or
> violin or tar or oud or whatever all have the same length, though
they all sound different notes. Diameters are different of course,
but this is a balance of tone issue and has nothing to with the
mechanics.
> Recall that theoretically all diameters break at the same pitch,
> because load for all diameters with a given pitch and length is the
> same, the tension increasing or decreasing with diameter in exact
> proportion to the cross sectional area. And since load is defined as
> force applied over an area, if load is always the same, this means
> that EXTENSION is also always the same for any given pitch/length
> combination regardless of diameter. ERGO: because the strings are
all of the same length but sound different notes, if the material is
the same, they MUST be at different extensions. That means that when
they are depressed by the same distance against the fingerboard, the
added extension is always the same, but it has a different proportion
to the ambient extension and therefore produces a different change in
pitch. The higher the open string pitch, the greater the ambient
extension, and the less pitch change when fingering any stopped note.
Naturally, the reverse is true, the lower the open string pitch, the
less the ambient extension, and the greater the relative increase in
extension introduced by fingering, and the greater the rise in pitch
for any stopped note. Thus the same fret position *cannot* serve for
all strings, nor can the same finger position serve for the same
interval on all strings in unfretted instruments.
>
> Figuring it all out is a bit tricky but requires no fancy pants
math. However, you MUST have a reliable value for E for each type of
> stringing material, because THAT is what will tell you how much
> extension is need to arrive at any pitch, and also how much force
will be introduced by any deflection. Recall also that the extension
must be calculated as percentages of the ENTIRE string length, from
tuning pin to point of fixation, be it bridge or tailpiece, and NOT
just the sounding length as in the models presented in the paper.
>
> Ciao
> P

--- In tuning@yahoogroups.com, "Jack" <gvr.jack@...> wrote:
>
> And then that opens another can of worms. Merely changing the
> string length at one end or another of a fixed fret system
> still leaves problem areas of the fretboard. (No, I have no
> plans to go fretless any time soon.)

Don't forget the other option -- fanned frets. -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> --- In tuning@yahoogroups.com, "Jack" <gvr.jack@> wrote:
> > And then that opens another can of worms. ... (No, I have no
> > plans to go fretless any time soon.)

> Don't forget the other option -- fanned frets. -Carl

Claro. A very reasonable theoretical suggestion, Carl.
There are these branch points where I could move into experimental
areas where I either work with funky instruments that I have adapted
myself, or expensive custom jobs like Paul Galbraith's fanned-fret 8
string (if I wanted what I might consider to be a professional
instrument). Were I experimentally driven, as I think many of the
microtonalists are, then I would passionately pursue those avenues
without regard for practical commercial application.

My interest in playing "in tune" is bound by my limiting assumptions
about commercial applicability. (Yeah, yeah, how bourgeois.) So for
commercial and artistic marketability, I want to play "in tune" on a
fairly conventional instrument. That's made a little more complex by
NOT having the assumption that 12-ET is the best model. (Why I
dislike playing with keyboard players generally, at least of the
usual stripe.) We (my duo partner and I) have made major steps
forward by finding better strings than the usual, and a nice matched
set of work guitars that are very loud and sweet, for our un-
amplified act in a hotel restaurant.

Naturally I'm aware that the convention of 12 frets per octave is
extremely limiting, particularly in the upper registers where there
are potential "microtonal" (what a clumsy word, so conditioned by
19th century 12-ET assumptions, no?) upper extensions to chords that
are very attractive... but as I say, that's a whole 'nother can of
worms. Maybe I should just have a chromatic set of jaw harps.

I had a luthier set up one of my guitars a few years ago with his own
system of "just intonation" as he conceived it. Great, but it would
only play in D. Disaster otherwise. I'm doing much better with my own
experiments. Talking to you guys on this list, and reading about all
of the various other issues that you are into (many of which don't
have direct application for me) is definitely feeding my own process,
and I appreciate it.

I've been going back and re-reading Paul P's posts about piano string
inharmonicity. Paul recently said that the effects of inharmonicity
should be neglible on the guitar, contrary to the assumptions of Greg
Byers in his paper on adjusting guitar intonation by changing the
string length at both ends.

> > http://www.byersguitars.com/research/Intonation.pdf

With piano strings, inharmonicity is a major problem with the short,
stiff upper treble strings mostly? Are the wound bass-side piano
strings not stiff enough to cause a problem? Does the 20th century
trend toward bigger and louder in classical guitars, as well as
pianos, mean that at some point in the trend toward higher tension
guitar strings, inharmonicity in the trebles could theoretically
become more of an issue? I gather that Paul thinks not, because the
modern piano suffers inharmonicity at another order of magnitude.
Just a look at the mechanical contraption with its cast-iron frame
indicates this. Even modern steel-string guitars which are made for
10x the amount of string tension as a nylon-string classical don't
require steel frames.

I did play on one of Byer's guitars once (not mine) and they do play
noticeably better "in tune" than your usual un-compensated guitar. A
non-compensated guitar has a number of predictably bad chord
positions, and Byers' compensations did make them better. Bridge-end-
only compensations, which are very common nowadays, don't do nearly
as well as his method of adjusting bridge and nut both. So, if his
assumptions about inharmonicity are wrong, we have a case of somewhat
accidental practical good results. I think I'm going to have to print
out a bunch of Paul's posts, along with Byers' paper, and get away
from the computer and chew on it.

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > The Steinway's strings are under much greater tension, though,
> > which should offset some of this, no?
>
> Some, yes, but compare the exponents which T and d carry in equation
> 5. Which is more significant, and by how much?
>
> > The Steinway's c1 is
> > not only longer, but also higher in pitch, no?
>
> Not really. A typical Viennese pitch for c.1800 was probably 438-ish.
> This 430 classical pitch stuff in an invention of the modern
> Histerically Uninformed Performance Practice movement.
>
> Ciao,
>
> p

Pitch/tension can be accounted for anyway from the standard relation
for the fundamental frequency. If we assume that the string density
and pitch are about the same between Walther and Steinway, then
T = constant * d^2 l^2 (for any given note)

- substituting this in the inharmonicity coefficient we get
B = constant * Q d^2 / l^4

I assume that what the authors called Q is the Young modulus, normally
E...

So here's my revised table (lengths in metres)

Walter
----l---d----d^2/l^4
c1 .559 0.52 2.8
c2 .281 0.44 31
c3 .144 0.40 372

Steinway
c1 .654 1.04 5.7
c2 .341 0.97 70
c3 .179 0.91 807

-> even with the 4th power of increased length & still without
accounting for 'Q', the Steinway-scaling inharmonicity is slightly
more than 2x the Walter.

I'm curious what Paul takes as a definition of 'stretch' in tuning by
ear. Eliminating audible beats needn't imply that octaves are (very
close to) 2:1. It is possible, though unlikely, that the inharmonicity
would be such as to allow (the first few) inharmonic partials to
coincide well enough in an octave.
- Is it 'stretch' when one chooses to make an octave a bit wider than
the minimum of beating; or when one does try to minimise beating, but
the octave comes out wider than 2:1 anyway (checked electronically)?

I'm thinking back to the Bremmer article where he was talking about
either '2:1' or '4:2' or '6:3' octaves in the middle range (numbers
refer to upper partials, not to mathematical ratio!) which are checked
in different ways by demanding that different partials be coincident.
He says that the '4:2' and '6:3' types may sound more 'active', to
paraphrase.

Also, in listening to our institute's new Yamaha cheap electro-beast,
there is probably a symptom of modern inharmonicity in that the notes
are sampled from a real Yamaha, but seem to have been re-pitched to
some sort of idealized tempered scale ... result is that a few
octaves, some indeed around the tenor range, beat rather obviously. At
least that's the only explanation I can find, since they can't have
sampled the notes from a real but badly/electronically-tuned piano.
(Can they?)
~~~T~~~

don't have a lot of time this evening, have to finishing correcting
last Friday's exam papers. But a few quick comments...

--- In tuning@yahoogroups.com, "Jack" <gvr.jack@...> wrote:

> With piano strings, inharmonicity is a major problem with the short,
> stiff upper treble strings mostly?

Yeah, it's the short string coupled with the thick diameter that makes
it worse than lower regions.

> Are the wound bass-side piano
> strings not stiff enough to cause a problem?

This bass is where inharmonicity is most audible. The problem down
there is that the scale is sooooo much too short (about 2 octaves or
4x length too short) that you just cannot get the tension up to where
it reduces stiffness to an inconsequential restoring force - even with
the synthetic material which is a wrapped string.

> as the Does the 20th century
> trend toward bigger and louder in classical guitars, as well as
> pianos, mean that at some point in the trend toward higher tension
> guitar strings, inharmonicity in the trebles could theoretically
> become more of an issue?

Not likely. The sound of the guitar is rather short and in the upper
octaves rather poor in harmonics, so we neither have the time nor that
material to perceive inharmonicty.

> I gather that Paul thinks not,

You gather correctly.

> because the
> modern piano suffers inharmonicity at another order of magnitude.

That's an understatment!
>
> I did play on one of Byer's guitars once (not mine) and they do play
> noticeably better "in tune" than your usual un-compensated guitar.

Beyer's mehtods WILL improve fret placement, he's more or less barking
up the right tree. It's just that he does it in such a ridiculously
obtuse and obfuscating manner. He could lay it out plain and simple,
giving the basic cause (Hooke's Law). But he seems to be a math brain,
one of those guys who can't tell you how to get to the train station
without using differential equations and caluclus.

More later...

Ciao,

p

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

Hi Tom,
>
> I'm curious what Paul takes as a definition of 'stretch' in tuning by
> ear. Eliminating audible beats needn't imply that octaves are (very
> close to) 2:1.
The human ear deviates from 2:1

http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/octstretch.html
" Formally, octave stretch - or, in a more general term, octave
deviation - then is suitably defined by

W = (f2-2f1)/(2f1)

where f1 < f2 is presumed. Octave stretch is indicated by W > 0. "

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JASMAN0000720000S1000S45000003&idtype=cvips&gifs=yes
"Ascending and descending digitally synthesized pure-tone melodic
octaves in the range 250–1500 Hz, varying width from 1180¢ to 1220¢
were presented to nine highly musical subjects who were asked to judge
(1) degree of octave mistuning, and
(2) whether the second tone of the pair was sharp or flat. Results
confirm the existence of so-called "octave stretch" previously
reported in the literature. However, the two tasks were found to be
perceptually dissimilar in degree of octave stretch, variability, and
dependence on register. Consistent with results of Lindqvist and
Sandberg preferred "octave stretch" for the "sense of mistuning"
judgments was very small (about 2.5¢) for low register octaves.

http://www.skytopia.com/music/theory/scale-dissertation.html#octavestretch
"Therefore, one would need to stretch all of the intervals by
approximately +10 to +20 cents per physical octave to compensate
(around frequency^1.0125 for any arbitrary interval)..."

http://www.musikforskning.se/stm/STM1974/STM1974_1FranssonSundbergTjernlund.pdf

Test yourself:
http://eamusic.dartmouth.edu/~book/MATCpages/applethtml/ch1_octave_stretch.html

> It is possible, though unlikely, that the inharmonicity
> would be such as to allow (the first few) inharmonic partials to
> coincide well enough in an octave.

Also in the ear there's an likewise effect,
due to the stiffness of the basilar-membrane.
http://en.wikipedia.org/wiki/Basilar_membrane

> - Is it 'stretch' when one chooses to make an octave a bit wider than
> the minimum of beating; or when one does try to minimise beating, but
> the octave comes out wider than 2:1 anyway (checked electronically)?
>
http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/scalestretch.html

As this explanation of piano-scale stretch makes occurrence or absence
of scale stretch dependent on whether or not the individual tones of
the instrument are true harmonic complex tones, one should expect that
instruments whose tones are truly harmonic should not have a stretch
of the tone scale. True harmonic complex tones emerge from steady
periodic oscillations such as those of bowed strings, wind
instruments, organ pipes, and the singing voice. The only keyboard
type of instrument (i.e. with a fixed tuning) that produces steady
periodic tones is the organ (pipe or electronic). Indeed, the
intonation of pipe organs exhibits very little stretch, if any. (Yet
pipe-organ experts say that it is much better to tune pipes of the
high region sharp than to tune flat.) And in most types of electronic
organ (beginning with the classical electro-mechanical Hammond organ)
there cannot be any stretch at all, because the technique of tone
production is such that octaves are exactly in a 1:2 frequency ratio.

....

Rather, the role of the piano among the other musical instruments is
elucidated. The inharmonicity of piano strings which as such enforces
stretched tuning turns out to be beneficial, as it enables
reconciliation of two phenomenomena that with truly harmonic complex
tones can hardly be reconciled: The preference of the ear for
stretched successive pitch intervals on the one hand, and the
occurrence of beats from the simultaneous sounding of simultaneous
tones in stretched intonation, on the other. It is only the piano on
which you can have both stretched and beat-free octaves.

bye
A.S.

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote:

> The human ear deviates from 2:1

Ooohh, I'd be real careful about making blanket statements like this.
It depends on whether you are talking harmonically or melodically.
>
> > - Is it 'stretch' when one chooses to make an octave a bit wider than
> > the minimum of beating; or when one does try to minimise beating, but
> > the octave comes out wider than 2:1 anyway (checked electronically)?

I call stretch anything that is not 2:1. That could be a "Pure"
octave-like thing with mild inharmonicity, i.e. a beatless non-octave.
This is ostensibly the reason why modern piano octaves are stretched,
but many tuners go beyond that and make them even bigger, Lord only
knows why. Probably to resolve their won melodic non-linearity.

>
> Rather, the role of the piano among the other musical instruments is
> elucidated. The inharmonicity of piano strings which as such enforces
> stretched tuning turns out to be beneficial, as it enables
> reconciliation of two phenomenomena that with truly harmonic complex
> tones can hardly be reconciled: The preference of the ear for
> stretched successive pitch intervals on the one hand, and the
> occurrence of beats from the simultaneous sounding of simultaneous
> tones in stretched intonation, on the other.

I'd be a bit careful about pushing it that far as well. Meldoic
stretched octave preference is different for different people,
registers, volume levels, tone colors, etc etc etc, whereas
non-beating octaves on any specific instrument is an inflexible
objectively verifiable solution to an acoustic reality. Rarely would
the two coincide. I, for example, know that in the upper octaves I
hear a pure octave played melodically as something almost as small as
a major 7th. obviously there is no piano in the world with so much
inharmonicity that I could kill both birds with one stone in my case.

> It is only the piano on
> which you can have both stretched and beat-free octaves.

What about bells?

Ciao,

p

> This bass is where inharmonicity is most audible. The problem
> down there is that the scale is sooooo much too short (about 2
> octaves or 4x length too short) that you just cannot get the
> tension up to where it reduces stiffness to an inconsequential
> restoring force - even with the synthetic material which is a
> wrapped string.

Are the walter bass strings wound? If not, the diameters
aren't directly comparable, correct?

But no doubt the inharmonicity of modern instruments is
worse in the bass. I've often thought the first movement
of the Waldstein sonata must only make sense on a period
instrument.

-Carl

Andreas wrote:
> "Ascending and descending digitally synthesized pure-tone melodic
> octaves in the range 250–1500 Hz, varying width from 1180¢ to 1220¢
> were presented to nine highly musical subjects who were asked to
> judge
> (1) degree of octave mistuning, and
> (2) whether the second tone of the pair was sharp or flat.
> Results confirm the existence of so-called "octave stretch"
> previously reported in the literature.

Experiment used pure tones. Irrelevant for music contexts.

-Carl

2008/12/2 Jack <gvr.jack@...>:

>> > http://www.byersguitars.com/research/Intonation.pdf
>
> With piano strings, inharmonicity is a major problem with the short,
> stiff upper treble strings mostly? Are the wound bass-side piano
> strings not stiff enough to cause a problem? Does the 20th century
> trend toward bigger and louder in classical guitars, as well as
> pianos, mean that at some point in the trend toward higher tension
> guitar strings, inharmonicity in the trebles could theoretically
> become more of an issue? I gather that Paul thinks not, because the
> modern piano suffers inharmonicity at another order of magnitude.
> Just a look at the mechanical contraption with its cast-iron frame
> indicates this. Even modern steel-string guitars which are made for
> 10x the amount of string tension as a nylon-string classical don't
> require steel frames.

I looked at a sample of a steel-string guitar (a cheap strat copy) in
a spectrogram once. It was definitely inharmonic, the 3:1 being a few
cents off. I know this is only one data point but, still, I assume
steel-string guitars are inharmonic until being convinced otherwise.
It's less famous than with pianos because steel-string guitars don't
play in orchestras (except sometimes with other steel-string guitars)
and you can add any required stretch by ear.

I reckon bass guitars are even more harmonic but don't make a big
point of it because I don't want to make bass players angry. Maybe
there is a tendency to reduce the higher partials. Rock guitars are
usually played with the bridge pickups, where the sound is brightest.

I'm sure classical guitars are much more harmonic. We've seen the
figures for the modulus of steel compared to nylon and related
thermoplastics.

> I did play on one of Byer's guitars once (not mine) and they do play
> noticeably better "in tune" than your usual un-compensated guitar. A
> non-compensated guitar has a number of predictably bad chord
> positions, and Byers' compensations did make them better. Bridge-end-
> only compensations, which are very common nowadays, don't do nearly
> as well as his method of adjusting bridge and nut both. So, if his
> assumptions about inharmonicity are wrong, we have a case of somewhat
> accidental practical good results. I think I'm going to have to print
> out a bunch of Paul's posts, along with Byers' paper, and get away
> from the computer and chew on it.

This has been on the list before. The basic theory (which I
confirmed) is that stopping a string stretches it by about the same
amount wherever you stretch it. So there will be a difference between
stopped and open strings. The answer, then, is to adjust the length
of open strings without affecting the fret placements. Hence you need
nut adjustments. But bridge adjustments are still good enough for
most people.

I don't think inharmonicity has anything to do with nut-adjustment.
All you need to do is stretch the scale a bit. Moving the bridge will
do that. Mostly you only care about intervals between strings, so you
adjust the open string tuning a bit (still within the "good" range of
an electronic tuner).

The systematic out-of-tune-ness of equal temperament is still an order
of magnitude more significant than these tuning optimizations.
Putting the frets in different places will make triads sound
noticeably purer even if you don't get it quite right. Of course, we
all know the drawbacks.

Graham

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Andreas wrote:
> [...]> Results confirm the existence of so-called "octave stretch"
> > previously reported in the literature.
>
> Experiment used pure tones. Irrelevant for music contexts.
>
> -Carl
>

I have a friend that plays viola and violin (as well as other
instruments). He says that stretched octaves are required in doubled
octaves in pieces of the Romanticism (e.g. Paganini) in order to
*sound as octaves* (with volume). He reserves pure octaves for antique
music (e.g. Baroque music), when the octave pitches need do merge as
only one sound.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > This bass is where inharmonicity is most audible. The problem
> > down there is that the scale is sooooo much too short (about 2
> > octaves or 4x length too short) that you just cannot get the
> > tension up to where it reduces stiffness to an inconsequential
> > restoring force - even with the synthetic material which is a
> > wrapped string.
>
> Are the walter bass strings wound?

No. The first few notes are usually "red" brass (90 Cu, 10 Z) and the
rest up to D or D# are brass. Wound strings don't appear in the
Viennese tradition until around 1825, and then only some makers and
only the four bottom notes (CC-EE). Entire wound basses start
appearing in the mid-30's.

> If not, the diameters
> aren't directly comparable, correct?

Any time yo have different stringing materials you cannot compare
diameters in regards to inharmonicity. Even different wound string
solution for the same note on the same instrument will have different
inharmonicty. The stiffness of a wound string is 99% the fault of the
core, and there is a pretty wide variety of core/wrap diameters that
will work.
>
> But no doubt the inharmonicity of modern instruments is
> worse in the bass.

Anything from CC down is hardly a tone in any normal sense. It is a
collection of vaguely related tones that we have learned to accept as
a bass note.

> I've often thought the first movement
> of the Waldstein sonata must only make sense on a period
> instrument.

There is so much more. As someone who absolutely worshiped Beethoven
long before I discovered the fortepiano, I can honestly say the one
cannot begin to fathom his true genius as a composer until you know
the literature on the proper instrument. The modern piano is so...
"other".

Ciao,

p

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

>
> Experiment used pure tones. Irrelevant for music contexts.
>
Right on right on Brother Carl!! So true of so much psychoacoustic
research.

In this particular aspect, the critical factor is of course tonal
memory. When the lower tone has some harmonic content, we actually
hear the upper octave (i.e. fundamental x2) when the lower note is
sounded. Regardless of whether or not we are conscious of it, that
information goes into the bin and if the second tone appears within a
short space of time, we've still got the first sound in the the memory
to use as a comparison. Then it ceases to become an octave comparison
study and shifts more to a JND study. I'm sure they realized this,
which is why they used pure tones, but as you point out, it
essentially invalidates the conclusion for the vast majority of real
world situations.

That's why I say it is very misleading to go around making statements
like "The human ear prefers wide octaves." It's only true in limited
contexts which rarely exist outside the laboratory.

Ciao,

P

Paul wrote:
> > If not, the diameters
> > aren't directly comparable, correct?
>
> Any time yo have different stringing materials you cannot compare
> diameters in regards to inharmonicity.

Presumably Tom's taking care of that by including
the Young's modulus. Or rather, he didn't, and that
can only be good for modern instruments.

> The stiffness of a wound string is 99% the fault of the
> core, and there is a pretty wide variety of core/wrap
> diameters that will work.

Right, so my point being that he shouldn't have compared
the diameter of a wound to an unwound string.

-Carl

--- In tuning@yahoogroups.com, "hfmlacerda" <hfmlacerda@...> wrote:

> I have a friend that plays viola and violin (as well as other
> instruments). He says that stretched octaves are required in doubled
> octaves in pieces of the Romanticism (e.g. Paganini) in order to
> *sound as octaves* (with volume).

Ah-ha! Maybe that's why oh so much modern double-stopped playing
sounds so hideously out-of-tune to me.

;-)

Reminds me of the time that a friend of mine, a modern cellist, asked
what my opinion was on whether vibrato should be centered around the
proper frequency of the note, move from there only downward, or move
from there only upward. I said the answer was obvious because the ear
always takes the center of the movement as "the" pitch. She assured me
that there were proponents of all three in the modern string playing
world.

Honestly, I have to say that what passes for intonation in the modern
string world is so often so absolutely hideously malformed in any real
acoustic sense that I am unable to listen to most modern playing, let
alone the other problems with modern interpretation (no awareness of
rhetoric, too much bow all the time, too much vibrato, etc etc etc).
Like modern voice, I think it is an art form which has long passed
beyond any sense of natural expression and has gone off into the
stratosphere of inbred decadence. Both modern string playing and
modern singing have about as much to do with any sort of natural
musical expression as Kabuki has to do with story telling.

> He reserves pure octaves for antique
> music (e.g. Baroque music), when the octave pitches need do merge as
> only one sound.

I would add that in this case the lack of vibrato also allows the ear
to actually JUDGE the quality of the octave rather than simply have to
rely on some artificial acquired sense of what is the sound of an
octave. Also, modern instruments are so loud that we run into the
problem of volume distorting the pitch perception. To say nothing of
the damage it does to the musicians hearing!

Ciao,

P

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:

> > Experiment used pure tones. Irrelevant for music contexts.
>
> Right on right on Brother Carl!! So true of so much psychoacoustic
> research.
>
> In this particular aspect, the critical factor is of course tonal
> memory. When the lower tone has some harmonic content, we actually
> hear the upper octave (i.e. fundamental x2) when the lower note is
> sounded. Regardless of whether or not we are conscious of it, that
> information goes into the bin and if the second tone appears within
> a short space of time, we've still got the first sound in the the
> memory to use as a comparison.

That's one point, which is probably valid, and there's another
as well. The presence of more than one partial 'activates'
the brain's virtual pitch processor, and this is a much stronger,
or at any rate very different, type of pitch perception on which
results from tests with pure tones may not bear.

I note that Terhardt claims stretched octaves were also observed
with real musical instruments, but the abstract of the paper he
cites is less than impressive. His explanation of octave stretch
for complex tones is that the intervals between consecutive
harmonics will be stretched by pitch shifts (which are known to
be due to the response of the basilar membrane as Andreas seems
to mention), and thus fit best to a harmonic template with a
virtual f0 slightly higher than the actual partial sounding at f0.
That's a seductive explanation but I doubt it's correct.

> Then it ceases to become an octave comparison
> study and shifts more to a JND study. I'm sure they realized this,
> which is why they used pure tones, but as you point out, it
> essentially invalidates the conclusion for the vast majority of
> real world situations.

They also clearly chose melodic intervals because the desire
to eliminate beating can be completely over-riding in harmonic
contexts. Melodic jumps of an octave aren't terribly common
in music.

-Carl

> Ah-ha! Maybe that's why oh so much modern double-stopped playing
> sounds so hideously out-of-tune to me.
>
> ;-)

I could never stand most orchestral string sections, even as
a kid. My Dad was a fan of early music, which I liked
immediately. That some modern orchestra string sections
can and do play in tune and without excessive vibrato... but
it's relatively rare. -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Paul wrote:
> > > If not, the diameters
> > > aren't directly comparable, correct?
> >
> > Any time yo have different stringing materials you cannot compare
> > diameters in regards to inharmonicity.
>
> Presumably Tom's taking care of that by including
> the Young's modulus. Or rather, he didn't, and that
> can only be good for modern instruments.

Difficult to say. The modern piano is such a different beast in its
design. When he was talking about notes in the tenor, it really
depends on where in the tenor: top of the bass bridge or bottom of the
treble bridge? The break in the modern piano is always a troublesome
area, something the majority of Viennese instruments does not have to
deal with, having only a single bridge.
>
> > The stiffness of a wound string is 99% the fault of the
> > core, and there is a pretty wide variety of core/wrap
> > diameters that will work.
>
> Right, so my point being that he shouldn't have compared
> the diameter of a wound to an unwound string.

He didn't. He was redoing my comparison of notes above c1 (middle c).
We are both using museum organology nomenclature (Helmholtz derived),
not modern piano tuner's terminology:

AAA - bottom note
CC
C
c
c1 - middle c
c2
c3
c4
c5 - top note modern piano

It has the added advantage of being similar to the terminology found
in most historical (17th and 18th century) German texts, so when
reading about temperament and all we are comfortable with concepts
such as "one-lined c".

Ciao,

P

> He didn't. He was redoing my comparison of notes above
> c1 (middle c). We are both using museum organology
> nomenclature (Helmholtz derived), not modern piano tuner's
> terminology:
>
> AAA - bottom note
> CC
> C
> c
> c1 - middle c
> c2
> c3
> c4
> c5 - top note modern piano
>
> It has the added advantage of being similar to the terminology found
> in most historical (17th and 18th century) German texts, so when
> reading about temperament and all we are comfortable with concepts
> such as "one-lined c".

Ah; thanks. -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>

> I note that Terhardt claims stretched octaves were also observed
> with real musical instruments, but the abstract of the paper he
> cites is less than impressive. His explanation of octave stretch
> for complex tones is that the intervals between consecutive
> harmonics will be stretched by pitch shifts (which are known to
> be due to the response of the basilar membrane as Andreas seems
> to mention), and thus fit best to a harmonic template with a
> virtual f0 slightly higher than the actual partial sounding at f0.
> That's a seductive explanation but I doubt it's correct.

If I follow you correctly, it seems like a classic example of circular
reasoning.

In any case, one of the thing that plagues the modern acoustic world
is that acousticians are often so abysmally ignorant of anything
outside the tiny world of modern Western classical musical style. Not
too long back, for example, I had a very unproductive exchange with
the guy who runs the acoustics website at the University of New South
Wales:

http://www.phys.unsw.edu.au/music/

... which is mostly a really good source. I suggested that his flute
sound samples should be recorded without vibrato so that it didn't
muck up the works when doing spectral analysis and such. I also said
that in the spirit of science it would be better to isolate factors of
an instruments tone, and vibrato is only a stylistic overlay which has
nothing to do with how the flute functions. He replied that vibrato
was an inherent part of the sound of the flute and therefore it
wouldn't be proper to present straight tones! Really, I am NOT making
this up!!! Funny thing is, this guy also does a lot with digeridoo;
you'd think he would have an awareness of the fact that vibrato in
flute playing is only "inherent" in certain styles, and that even a
lot of jazz players play straight (as do a lots of "pop" singers, who
use vibrato mostly as an ornament on long sustained notes).
Personally, I think he was just too damn lazy to do them over again
and was just reaching for an excuse.

Reminds me of the singers how go around talking about "the natural
vibrato"!

But yeah, always take EVERYTHING you read with a grain of salt.

>
> They also clearly chose melodic intervals because the desire
> to eliminate beating can be completely over-riding in harmonic
> contexts. Melodic jumps of an octave aren't terribly common
> in music.

You mean unaccompanied octave jumps. Amen to that!

Ciao,

P

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> --- In tuning@yahoogroups.com, "hfmlacerda" <hfmlacerda@> wrote:
>
> > I have a friend that plays viola and violin (as well as other
> > instruments). He says that stretched octaves are required in doubled
> > octaves in pieces of the Romanticism (e.g. Paganini) in order to
> > *sound as octaves* (with volume).
>
> Ah-ha! Maybe that's why oh so much modern double-stopped playing
> sounds so hideously out-of-tune to me.
>
> ;-)
>
> Reminds me of the time that a friend of mine, a modern cellist, asked
> what my opinion was on whether vibrato should be centered around the
> proper frequency of the note, move from there only downward, or move
> from there only upward. I said the answer was obvious because the ear
> always takes the center of the movement as "the" pitch. She assured me
> that there were proponents of all three in the modern string playing
> world.
>
> Honestly, I have to say that what passes for intonation in the modern
> string world is so often so absolutely hideously malformed in any real
> acoustic sense that I am unable to listen to most modern playing,
>

What I read from Hans Keller in his book on Haydn quartets: octaves
played by a soloist shouldn't be absolutely in tune, otherwise how
would you know they were octaves?

Slightly more seriously, the beating does enhance *perceived* volume
(as does vibrato of course).

To hear pure octaves and excellent tuning in a Romantic violin solo,
you need to go back to Alfredo Campoli in about 1950 playing the
Mendelssohn concerto. This is really worth hearing (reissued on CD by
Beulah). Before that you have interesting things such as Josef
Wolfsthal playing the Beethoven in about 1928...
~~~T~~~

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
> (Helmholtz derived),
> not modern piano tuner's terminology:
>
> AAA - bottom note
> CC
> C
> c
> c1 - middle c
> c2
> c3
> c4
> c5 - top note modern piano
>
en detail:
/tuning-math/message/17411

bye
A.S.

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:

> > The human ear
can
> > deviate from 2:1
>
> Ooohh, I'd be real careful about making blanket statements like this.
> It depends on whether you are talking harmonically or melodically.
That both aspects can differ also individually.
> >
> This is ostensibly the reason why modern piano octaves are
> stretched,
> but many tuners go beyond that and make them even bigger, Lord only
> knows why.

Eventually because that laypersons got trained their ears mainly on:
http://de.wikipedia.org/wiki/Fl%C3%BCgel_(Musikinstrument)

"Flügel werden in vielen verschiedenen Größen gebaut. Eine nicht
normierte Einteilung lautet:

* Stutzflügel (Länge: etwa 1,4 m bis 1,8 m)
* Baby-grand (length: about 1.4m up to 1.8m)
"
Grands are built in different seizes.
An not (yet) normed classification sounds:

* Studioflügel (Länge: etwa 1,9 m)
* Salonflügel (Länge: etwa 1,8 m bis 2,1 m)
* Halbkonzertflügel (Länge: etwa 2,1 m bis 2,4 m)
* Konzertflügel (Länge: etwa 2,4 m bis 3,06 m, die „klassische"
Konzertflügellänge ist etwa 2,75 m)

Conjecture:
I guess that tuners simply overview to adopt properly
the values of the short and thick strings in baby-grands to
the longer and thinner ones in concert-grands
in the correct manner, by aptly reducing the over-broadening?

Die Bezeichnung „Stutzflügel" für einen kurzen Flügel kommt übrigens
aus dem 19. Jahrhundert, als das Musizieren zunehmend auch im
Bürgertum üblich wurde und ein großer Bedarf an Instrumenten gegeben
war. In den Schlössern der Adeligen war genug Platz für bis zu 3 m
lange Hammerflügel, in den kleineren Wohnräumen der Bürger nicht. So
wurden alte lange Instrumente kurzerhand abgeschnitten, gekürzt -
„gestutzt". Damit war natürlich auch eine Änderung der Besaitung –
kürzere aber dickere Saiten – in der unteren Mittellage und im Bass
notwendig. Der erste "Stutzflügel" wurde von der Firma Ernst Kaps
Klavierfabrik AG im Jahr 1865 gebaut. Breite von Flügeln: ca. 150 cm

The labeling "baby-grand" for a short grand comes form the 19th
century, when making music became more usual in the middle-class.
In the castels of the lords was enough space for the up to 3m long
forte-pianos, but no so in the smaller flats of the bourgeoisie.
Hence the long old instruments became simply cut down shortened
to "baby" (degree). By that changed the stringing towards
shorter and thicker, in the middle and bass position.
The first "babies" were built by Kaps in 1865 of ca. 150cm.

http://de.wikipedia.org/wiki/Ernst_Kaps_Klavierfabrik_AG

> Probably to resolve their won melodic non-linearity.
as they had acosutemed as habit on "babies" or low uprights.

Therhard claims:
> > The preference of the ear for
> > stretched successive pitch intervals on the one hand, and the
> > occurrence of beats from the simultaneous sounding of simultaneous
> > tones in stretched intonation, on the other.
>
> I'd be a bit careful about pushing it that far as well. Meldoic
> stretched octave preference is different for different people,
> registers, volume levels, tone colors, etc etc etc, whereas
> non-beating octaves on any specific instrument is an inflexible
> objectively verifiable solution to an acoustic reality.
Simply by counting beats.

> Rarely would
> the two coincide.
Agreed.
The divergence of that both can be wide,
depending on the individual disposition.

> I, for example, know that in the upper octaves I
> hear a pure octave played melodically as something almost as small as
> a major 7th. obviously there is no piano in the world with so much
> inharmonicity that I could kill both birds with one stone in my
> case.
Which piano-sacling(mensur) would you personally prefer at soonest?
>
> What about bells?
http://www.speedylook.com/Inharmonicity.html
".... For this reason this effect is all the more important as the
cords are short, and thus will be much more important on a small
upright piano than on a large grand piano. This has as a consequence
which it is in general impossible to obtain a correct agreement
between two piano very different. If one correctly grants them for
central C, the two pianos will be all the more désaccordés in the
extremes which they are different.

The bell

The case of the Cloche is an extreme case, where the deviation
compared to the harmonic model can reach Intervalle S of a third, even
more. All the art of the Fondeur of bells thus consists in producing a
bell whose harmonics are granted, in order to obtain most beautiful
sonority. Certain current type-setters used this provision of
harmonics in their works, in order to recreate, for example with an
orchestra, a sonority which evokes that of the bell...."

bye
A.S.

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> ... I suggested that his flute
> sound samples should be recorded without vibrato so that it didn't
> muck up the works when doing spectral analysis and such.
Good idea.
All to much vibrato results often from poor intonation of pitch.

> I also said
> that in the spirit of science it would be better to isolate factors
> of an instruments tone,
Right,
In order to reduce the number of disturbing interference factors.

> and vibrato is only a stylistic overlay which has
> nothing to do with how the flute functions.
Vibrato got often applied in oder to coat lacking precision
of proper pitch.

> He replied that vibrato
> was an inherent part of the sound of the flute and therefore it
> wouldn't be proper to present straight tones!
An typical dabbler's specious lame-excuse,
for fluctual see-saw detuning
that won't hold water
nor earwax at least in my ears.

> Really, I am NOT making
> this up!!!
Presumably not even able to transfer and adopt
a'=440Hz from an ordinary tuning fork.

> Funny thing is, this guy also does a lot with digeridoo;
For him probably sooner fitting instrument than the flute.

> you'd think he would have an awareness of the fact that vibrato in
> flute playing is only "inherent" in certain styles, and that even a
> lot of jazz players play straight (as do a lots of "pop" singers, who
> use vibrato mostly as an ornament on long sustained notes).
....if at all.

> Personally, I think he was just too damn lazy to do them over again
> and was just reaching for an excuse.
In deed, an silly lame excuse.
>
> Reminds me of the singers how go around talking about "the natural
> vibrato"!

http://notsosynonymous.tripod.com/sing/vibrato/othervoices.html
some idiot teached that so to
"Anthony:
I have just read why you should never use a vibrato. I am a
barritone and the vibrato which i produce is natural (according to my
vocal trainer) and should be used."

and bungeled by that his pupils formerly clear voice.
In contrast to:
"Nicole....
.... Some people do it, but only because they haven't had any vocal
training and do not know any better.
There are places where singing without vibrato is good. Choral singing
is such a place. But, the straight tone must be produced freely, and
not be forced."

> But yeah, always take EVERYTHING you read with a grain of salt.

>
> >
> > They also clearly chose melodic intervals because the desire
> > to eliminate beating can be completely over-riding in harmonic
> > contexts. Melodic jumps of an octave aren't terribly common
> > in music.
>
> You mean unaccompanied octave jumps. Amen to that!
http://www.geocities.com/februsmax/phrasing.html
"A 'dramatic' interval is a jump of a 5th or more in a contiguous
melodic phrase. In the love song from 'Titanic', Miss Dion displays
her awesome range with a jump of an octave. The verse lays back and is
very linear, almost lulling you to rest, then the chorus hits
you-'near, far, where[octave]ever you are' and blows you away. The
octave jump is very powerful and can produce hit songs like 'Somewhere
Over the Rainbow', Aerosmith's 'Dream On', which actually uses a 9th
and dozens more...."

bye
A.S.

>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> The presence of more than one partial 'activates'
> the brain's virtual pitch processor, and this is a much stronger,
> or at any rate very different, type of pitch perception on which
> results from tests with pure tones may not bear.
Because incompareable, due to different spectra.

>
> I note that Terhardt claims stretched octaves were also observed
> with real musical instruments, but the abstract of the paper he
> cites is less than impressive. His explanation of octave stretch
> for complex tones is that the intervals between consecutive
> harmonics will be stretched by pitch shifts (which are known to
> be due to the response of the basilar membrane as Andreas seems
> to mention), and thus fit best to a harmonic template with a
> virtual f0 slightly higher than the actual partial sounding at f0.
> That's a seductive explanation but I doubt it's correct.
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2230936
http://www.patentstorm.us/patents/7398204/description.html
"in the case of a harmonic masker the
modulation rate for each filter output signal is the fundamental
frequency. When inharmonicity is introduced by perturbing the
frequencies of the partials, a variation of the modulation rate across
filters is noticeable. The variation increases with
increasing inharmonicity. In general, the harmonicity nature of a
complex masker is characterized by the variance calculated from the
envelope modulation rates across a plurality of auditory filters."

ou of:
http://www.bioportfolio.com/indepth/Basilar_Membrane/patents.html

even implemented in C_sound:
"...bringing the threshold too low would allow harmonically unrelated
partials into the analysis algorithm and this will compromise the
method's accuracy. These initial steps emulate the response of the
basilar membrane by identifying physical characteristics of the input
sound....

bye
A.S.

How great to see these heresies in print! (I almost wrote, "to hear
these heresies spoken aloud" - well that would be nice, too.) The
emperor's musicians have no clothes, Paul P. says. I would not have
dared mention it myself - (re modern voice & string playing, also the
low notes of the piano.)

It was once my karma to spend several years in a yoga ashram chanting
ancient texts in a semi-monotone, and my spiritual tempering usually
took the form of somebody sitting behind me who couldn't sing to
pitch. While I amused myself, on a good day, by listening to them and
comparing pitches, a friend of mine smacked the lady behind him one
day, apparently out of the blue, for singing off key...
(Those chanting sessions were sometimes enlivened, BTW, by a once-
famous composer of pop songs who sat in the back of the hall and
accompanied himself softly on the guitar with 9th and 13th chords. In
front, a harmonium to keep the pitch, and in the middle, a large
group of people singing a step or two below.)

(The real reason I came to this list, I needed more tuning jokes.
Guitar players cannot pick on violists like everybody else does. But
maybe I can get a few more good one-liners from Paul.)

The tuning group: land of the curmudgeons with ears.

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
"Honestly, I have to say that what passes for intonation in the modern
string world is so often so absolutely hideously malformed in any real
acoustic sense that I am unable to listen to most modern playing, ...

Like modern voice, I think it is an art form which has long passed
beyond any sense of natural expression and has gone off into the
stratosphere of inbred decadence. Both modern string playing and
modern singing have about as much to do with any sort of natural
musical expression as Kabuki has to do with story telling."

--- jack interjects: Arts which are over-ripe become self-
referential, and the audience is expected to appreciate the mere
reference to the original art, because it would be un-cool to just
state the original object of reference. New arts, however, are
subject to the rule that "it is every generation's responsibility to
create a new musical style unacceptable to their parents."

"Also, modern instruments are so loud that we run into the
problem of volume distorting the pitch perception. To say nothing of
the damage it does to the musicians hearing!"

">> But no doubt the inharmonicity of modern instruments is worse in
the bass.<<
--- Anything from CC down is hardly a tone in any normal sense. It is
a collection of vaguely related tones that we have learned to accept
as a bass note."

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> > ... a modern cellist, asked
> > what my opinion was on whether vibrato should be centered around the
> > proper frequency of the note, move from there only downward, or move
> > from there only upward. I said the answer was obvious because the ear
> > always takes the center of the movement as "the" pitch....
>
> Hans Keller in his book on Haydn quartets:
> octaves
> played by a soloist shouldn't be absolutely in tune, otherwise how
> would you know they were octaves?
>
> Slightly more seriously, the beating does enhance *perceived* volume
> (as does vibrato of course).

Hi Paul & Tom,

Peter van Poucke wrote in
http://www.bsz-bw.de/depot/media/3400000/3421000/3421308/95_0110.html
" Encyclopedia of keyboard instruments / ed. by Robert Palmieri. -
New York ; London : Garland. -
Vol. 1. The piano. - 1994. - XIII, 521 S. ; 27 cm. - (... ; 1131).
- ISBN 0-8240-5685-X
"
on p. 412 article 'TUNING':
'Sometimes tuners tend to widen even more the high octaves
for the sake of brilliancy and because of the tendency of treble
strings to lose their tension more quickly than bass strings.
Tthe same degree of mathematical inaccuracy is present in tuning in
general.
One has to
[p.413]
bear in mind that experienced tuners work empirically,
and that the resulting irregularities are favored by both piano
players and audiences.
This explains also why the impure tuning of trichords
(the 3 strings are "mistuned" ca. ~0.09% compared to each other,
in order to strenghten the sound) has never porvoked any protest.
the mistuning of trichords is done by inserting a strip of felt
inbetween the strings. the middle string is tuned pure. The right and
left strings are then tuned till about one beat per 3 seconds appears..."

That results about in the range of
1200Cents * ln(1.0009) / ln(2) = ~1.56...Cents

and for a'=440cps

1200Cents * ln(440.3/440) / ln(2) = ~1.18...Cents

bye
A.S.

Wow - this is eye opening. Thanks I never knew pianos were so complex!
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: "Andreas Sparschuh" <a_sparschuh@yahoo.com>

Date: Fri, 05 Dec 2008 20:43:37
To: <tuning@yahoogroups.com>
Subject: [tuning] How much vibrato inbetween piano-strings? was: Re: octave stretch in the ear....

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> > ... a modern cellist, asked
> > what my opinion was on whether vibrato should be centered around the
> > proper frequency of the note, move from there only downward, or move
> > from there only upward. I said the answer was obvious because the ear
> > always takes the center of the movement as "the" pitch....
>
> Hans Keller in his book on Haydn quartets:
> octaves
> played by a soloist shouldn't be absolutely in tune, otherwise how
> would you know they were octaves?
>
> Slightly more seriously, the beating does enhance *perceived* volume
> (as does vibrato of course).

Hi Paul & Tom,

Peter van Poucke wrote in
http://www.bsz-bw.de/depot/media/3400000/3421000/3421308/95_0110.html
" Encyclopedia of keyboard instruments / ed. by Robert Palmieri. -
New York ; London : Garland. -
Vol. 1. The piano. - 1994. - XIII, 521 S. ; 27 cm. - (... ; 1131).
- ISBN 0-8240-5685-X
"
on p. 412 article 'TUNING':
'Sometimes tuners tend to widen even more the high octaves
for the sake of brilliancy and because of the tendency of treble
strings to lose their tension more quickly than bass strings.
Tthe same degree of mathematical inaccuracy is present in tuning in
general.
One has to
[p.413]
bear in mind that experienced tuners work empirically,
and that the resulting irregularities are favored by both piano
players and audiences.
This explains also why the impure tuning of trichords
(the 3 strings are "mistuned" ca. ~0.09% compared to each other,
in order to strenghten the sound) has never porvoked any protest.
the mistuning of trichords is done by inserting a strip of felt
inbetween the strings. the middle string is tuned pure. The right and
left strings are then tuned till about one beat per 3 seconds appears..."

That results about in the range of
1200Cents * ln(1.0009) / ln(2) = ~1.56...Cents

and for a'=440cps

1200Cents * ln(440.3/440) / ln(2) = ~1.18...Cents

bye
A.S.

I cannot tolerate the mistuning of trichords. Seems like an ol' wives' tale.

Oz.

On Dec 5, 2008, at 11:24 PM, chrisvaisvil@... wrote:

> Wow - this is eye opening. Thanks I never knew pianos were so complex!
> Sent via BlackBerry from T-Mobile
>
>
> From: "Andreas Sparschuh"
> Date: Fri, 05 Dec 2008 20:43:37 -0000
> To: <tuning@yahoogroups.com>
> Subject: [tuning] How much vibrato inbetween piano-strings? was: Re: > octave stretch in the ear....
>
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> > > ... a modern cellist, asked
> > > what my opinion was on whether vibrato should be centered around > the
> > > proper frequency of the note, move from there only downward, or > move
> > > from there only upward. I said the answer was obvious because > the ear
> > > always takes the center of the movement as "the" pitch....
> >
> > Hans Keller in his book on Haydn quartets:
> > octaves
> > played by a soloist shouldn't be absolutely in tune, otherwise how
> > would you know they were octaves?
> >
> > Slightly more seriously, the beating does enhance *perceived* volume
> > (as does vibrato of course).
>
> Hi Paul & Tom,
>
> Peter van Poucke wrote in
> http://www.bsz-bw.de/depot/media/3400000/3421000/3421308/95_0110.html
> " Encyclopedia of keyboard instruments / ed. by Robert Palmieri. -
> New York ; London : Garland. -
> Vol. 1. The piano. - 1994. - XIII, 521 S. ; 27 cm. - (... ; 1131).
> - ISBN 0-8240-5685-X
> "
> on p. 412 article 'TUNING':
> 'Sometimes tuners tend to widen even more the high octaves
> for the sake of brilliancy and because of the tendency of treble
> strings to lose their tension more quickly than bass strings.
> Tthe same degree of mathematical inaccuracy is present in tuning in
> general.
> One has to
> [p.413]
> bear in mind that experienced tuners work empirically,
> and that the resulting irregularities are favored by both piano
> players and audiences.
> This explains also why the impure tuning of trichords
> (the 3 strings are "mistuned" ca. ~0.09% compared to each other,
> in order to strenghten the sound) has never porvoked any protest.
> the mistuning of trichords is done by inserting a strip of felt
> inbetween the strings. the middle string is tuned pure. The right and
> left strings are then tuned till about one beat per 3 seconds > appears..."
>
> That results about in the range of
> 1200Cents * ln(1.0009) / ln(2) = ~1.56...Cents
>
> and for a'=440cps
>
> 1200Cents * ln(440.3/440) / ln(2) = ~1.18...Cents
>
> bye
> A.S.
>
>
>

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>
> I cannot tolerate the mistuning of trichords. Seems like an ol' wives'
> tale.
>
> Oz.

I'm with you 100% on that one! I don't know any modern tuners who do
this. I think Oz is right that it is a poodle/microwave story.

BTW, I keep seeing posts about Oz's work on macam intonation, but a
quick search of the archives didn't turn up a link. Is it available
for download? I would dearly love to read it.

Thanx,

p

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> Pitch/tension can be accounted for anyway from the standard
> relation for the fundamental frequency. If we assume that
> the string density and pitch are about the same between
> Walther and Steinway, then T = constant * d^2 l^2 (for any
> given note)
>
> - substituting this in the inharmonicity coefficient we get
> B = constant * Q d^2 / l^4
>
> I assume that what the authors called Q is the Young
> modulus, normally E...
>
> So here's my revised table (lengths in metres)
>
> Walter
> ----l---d----d^2/l^4
> c1 .559 0.52 2.8
> c2 .281 0.44 31
> c3 .144 0.40 372
>
> Steinway
> c1 .654 1.04 5.7
> c2 .341 0.97 70
> c3 .179 0.91 807
>
> even with the 4th power of increased length & still without
> accounting for 'Q', the Steinway-scaling inharmonicity is
> slightly more than 2x the Walter.

http://i30.photobucket.com/albums/c348/mireut/sandersonB.png

For the old "international pitch" with B calculated with the
formula used by http://www.goptools.com/ps_screen.htm,
http://www.accu-tuner.com/

--- In tuning@yahoogroups.com, chrisvaisvil@... wrote:
>
> Wow - this is eye opening.
> Thanks I never knew pianos were so complex!

> > the middle string is tuned pure. The right and
> > left strings are then tuned till about one beat per 3 seconds
> > appears..."

http://www.speech.kth.se/music/5_lectures/weinreic/mistuned.html

The last figure, Fig. 8, shows some theoretical curves of the history
of the vertical force exerted on the soundboard when driven by two
strings, initially excited by a perfectly symmetric hammer blow. The
different curves correspond to different "mistunings," and the bridge
impedance is assumed such as to allow the "locking together" of the
frequencies (which is not always the case in practice). In calculating
these curves, we have assumed parameters more or less typical of the
middle range of a piano keyboard. For this case, there are no beats
unless the "mistuning" is more than about 0.3 Hz; more correctly, for
smaller "mistunings" there is just a single "beat null," followed by a
beatless aftersound whose level depends on the "mistuning." Above
about 0.3 Hz beats do appear, as exemplified by the curve drawn for a
"mistuning" of 0.64 Hz; even here, however, the time between beats is
a bit larger than the 1.6 seconds which would be naively predicted
(1/0.64 Hz = 1.6 s). The importance of Fig. 8 is that it indicates how
an excellent tuner can, under some circumstances, use very fine tuning
control in order to adjust the aftersound of each note to a more
uniform level than if it were due entirely to imperfections in the
hammer or the string mountings.

Fig. 8 Calculated vertical force on the soundboard when driven by two
strings with different mistuning ( f). In this example beats occur
only when the mistuning is larger than 0.3 Hz, illustrated by the
curve for f = 0.64 Hz. For smaller values the strings lock to a common
frequency, and the effect of the mistuning is to control the level of
the aftersound (cf. the curves for f = 0.22 Hz and 0.06 Hz). Fig. 8
Calculated vertical force on the soundboard when driven by two strings
with different "mistuning" ( f). In this example beats occur only when
the "mistuning" is larger than 0.3 Hz, illustrated by the curve for f
= 0.64 Hz. For smaller values the strings lock to a common frequency,
and the effect of the "mistuning" is to control the level of the
aftersound (cf. the curves for f = 0.22 Hz and 0.06 Hz).

Reference:
Kirk, R. (1959): "Tuning preferences for piano unison groups,"
Journal of the Acoustical Society of America 31(12), pp. 1644-1648.

In fact, it was observed by Kirk in 1959 that a carefully and
competently tuned piano had the strings of the trichords tuned
slightly differently by an amount that appeared to vary randomly from
note to note. This randomness may, however, hide an underlying
regularity. If, for example, you take a sheet of paper and tear it,
examination of one of the pieces will reveal an irregular and
seemingly random rough edge; yet comparison with the other piece will
show that one irregularity exactly matches the other. Our hypothesis
here is that, in the same way, the seeming "randomness" of the tuning
comes from the fact that the skilful tuner was adjusting this quantity
to another randomness, namely the randomness of hammer imperfections,
in such a way that the result is not random. It would be interesting
to test this hypothesis by investigating, for example, whether good
tuners are consistent in the "mistuning" of the individual trichords
when tuning the same piano over and over again.

Reference:
Kirk, R. (1959): "Tuning preferences for piano unison groups,"
Journal of the Acoustical Society of America 31(12), pp. 1644-1648.
that is also quoted in:

Arthur H. Benade's
FUNDAMENTALS OF MUISCAL ACOUSTICS
Oxford Univ. Press 1976
Lib. of. Congr: 75-25460
p.335
'...In 1959 Roger Kirk of the
Baldwin-Piano-Company reported the preferecnes of a large group
of people for tuning reloationship among the 3 strings of each so
called unison of a piano: He found that:
"...the most preferred tuning conditions...
are 1 and 2 Cents maximum deviation among the strings of each note in
the scale. Musically trained subjects prefer less deviation...
than do untrained subjects. Close agreement was found beteween the
subjects' tuning preferences and the way artist tuners acutually tune
piano strings."
....
p.336
....
'Kirk found that piano tuners and musicians are unanimous in their
verdict that too-close tuning gives a tone that not only sounds dead
but dies away to rapidly. Laboratory measurments confirms the auditory
impression we gained...'
....
p.338
....
'....We seem by now to have left the slightly detuned strings of a
real piano in a sort of unexplained limbo intbetween the single string
and a perfectly tuned triplet....'

Further literature:
https://www.wiley-vch.de/publish/dt/AreaOfInterestME00/availableTitles/0-471-80465-7/?sID=
"Crocker, Malcolm J. (Editor/Hrsg.)
*Encyclopedia of Acoustics*
ISBN-10: 0-471-80465-7 NY 1997
ISBN-13: 978-0-471-80465-9 - John Wiley & Sons
Volume 1: General Linear Acoustics; Non-Linear Acoustics and
Cavitation; Aeroacoustics and Atmospheric Sound; Underwater Sound
Volume 2: Ultrasonics; Quantum Acoustics and Physical Effects of
Sound; Mechanical Vibrations and Shock; Statistical Methods in
Acoustics; Noise: Its Effects and Control
Volume 3: Architectural Acoustics; Acoustical Signal Processing;
Physiological Acoustics; Psychological Acoustics
Volume 4: Speech Communication; Music and Musical Acoustics;
Bioacoustics; Animal Bioacoustics; Acoustical Measurements and
Instrumentation; Transducers; Index."

Quote
p.1667-1669 in Volume 4 (Chapter 136: about pianos...)
".....When the two strings are not tuned identically,
there will be still two coupled modes with different decay rates,
but they will no longer be exactly symmetric or exactly
antisymmetric. It has been suggested that this fact allows
a skilled tuner to adjust the LEVEL of aftersound,
making it appropriately even from note to note,
insted of depending on accidential factors
as irregularirities of the hammer...."

Further literature deeper en detail:
D.E. Hall & A Askenfeldt,
"Piano string Excitation
V. Spectra for Real Hammers and Strings."
J. Acoust. Soc. Am. Vol.83, 1988, pp. 1627-1638
(This reference lists also earlier articles in hte same series.)

http://portal.acm.org/ft_gateway.cfm?id=1289424&type=pdf&coll=GUIDE&dl=GUIDE&CFID=13790618&CFTOKEN=59840225

But personally I do prefer ~1 Cents less vibrato than
D.E.Hall und his coauthor Mark Lindley:
http://www.bfg-muenchen.de/lind3_e.htm
"The musical doughnut" (with D. E. Hall)"

http://listserv.albany.edu:8080/cgi-bin/wa?A2=ind0605&L=HPSCHD-L&P=R611&I=-3
"The best (!) alternative is a small upright with all but 49 strings
muted out, which fulfils the important criterion of fitting
unobtrusively into a small corner at the front of the lecture hall."

Probably it was the fault of the poor piano,
the adverse conditions in seminar and other awkward circumstances
that caused Mark Lindley's decision for more vibrato inbetween
the 3 strings than usual on better scaled instruments.

in order to get rid of:
http://www.amarilli.co.uk/academic/acoustics/false_beats.pdf

bye
A.S.

Eid Mubarek Paul! I'm glad you think the same way about mistuning of unisons. I have the impression that eliminating beats in the tricordi is what makes them unisons in the first place. Does that imply any "mistuning" at all?

I understand you are searching for my published article here:

http://www.musicstudies.org/Abjad_JIMS_071203.pdf

Happy reading and season's greetings!
Oz.

On Dec 6, 2008, at 9:13 AM, Paul Poletti wrote:

> --- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:
>>
>> I cannot tolerate the mistuning of trichords. Seems like an ol' >> wives'
>> tale.
>>
>> Oz.
>
> I'm with you 100% on that one! I don't know any modern tuners who do
> this. I think Oz is right that it is a poodle/microwave story.
>
> BTW, I keep seeing posts about Oz's work on macam intonation, but a
> quick search of the archives didn't turn up a link. Is it available
> for download? I would dearly love to read it.
>
> Thanx,
>
> p
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
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>
>

> I understand you are searching for my published article here:
>
> http://www.musicstudies.org/Abjad_JIMS_071203.pdf

Ozan! Did I miss the original announcement of this article
here? Anyway, congratulations!!

-Carl

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> --- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@> wrote:
> >
> > I cannot tolerate the mistuning of trichords.
>
Try out:
http://www.amarilli-books.co.uk/ecom/index1.html
For seeing the index:
Click there on the button <more-details>

> I don't know any modern tuners

Probaly you asked only among the adherents:
"5 - "Traditional" piano tuning theory and elementary practice"

> who do
> this.

But never mind,
many other tuners are also not yet aware of the 1959:
"
15 - The Kirk Experiment

nor about the from that resulting:

Part 3 - Advanced Theory

16 - The single piano string in one plane
17 - The Weinreich Model
18 - Two strings, two planes
19 - The Trichord
20 - Furrher comments on false partials
21 - Inharmonicity
"

Here some more online-stuff:
/tuning/topicId_79284.html#79429

>I think Oz is right that it is a poodle/microwave story.

http://www.smecc.org/microwave_oven_legends.htm
"It happened in 1970 in a
suburb on the south side of Fort Worth, Texas
......
However, they told her to use a towel the
next time the dog got caught in the rain!
Glen Zook, K9STH
"
http://urbanlegends.about.com/od/dogs/a/microwaved_pet.htm
http://www.snopes.com/horrors/techno/microwavedpet.asp

But those story is barely fairy "old-wives-tale"
alike the claims about the alleged perfect piano-wire
without the slightest 'false-partials' deviations.

http://www.zainea.com/piano%20sound.htm
"17.3. The Effect of Multiple Stringing on the Sound of the Piano

We will introduce ourselves to some of the consequences of multiple
stringing on a piano with the help of experiments you can easily try.
Repeatedly strike the C4 key of a piano while alternately pressing and
releasing a finger (or pencil eraser) against two of the three
strings, so that part of the time only one string is free to vibrate
and the rest of the rime all three strings are sounding. With any
reasonably well-tuned piano, the perceived loudness at your ears
(expressed in sones) should be roughly 40 percent higher when three
strings are active than when only one is producing a sound (see curve
B of fig. 13.5), which is a quite significant change. The next
experiment con­sists in verifying in a crude and informal way that the
total audibility time of the decaying tone is roughly the same whether
three strings are active or only one. So far everything appears to be
in accordance with our expectations. We also notice that the tone is a
little thinner and perhaps less interesting when only one string is
allowed to sound than it is when all three are set into vibration. To
be sure, if the piano is badly out of tune the three strings will beat
against one another to give the jangling sound conventionally
associated with a barroom piano, while on a freshly tuned instrument
there is only a hint of beats among the lower partials and a
pleasantly shimmering suggestion of beating among the higher ones.

In 1959 Roger Kirk of the Baldwin Piano Company reported the
preferences of a large group of people for the tuning relationship
among the three strings of each so-called unison of a piano.' He found
that :
the most preferred tuning conditions . . . are 1 and 2 cents maximum
deviation among the strings of each note in the scale. Musically
trained subjects prefer less deviation . . . than do untrained subjects.
Close agreement was found between the subjects' tuning pref­erences
and the way artist tuners actually tune piano strings.

He also found that a piano tuned so that the group of strings for each
note of the scale covered a spread of 8 cents was acceptable to many
listeners, and that the overall spread between the lowest and highest
frequency strings was of more importance than the tuning of the
intermediate string. The beat frequencies between the first five
components (partials) of two C., strings tuned 2 cents and 8 cents
apart are: )s 335 Hz beat that one uses in setting the
equal-temperament fifth to G., (see sec. 16.6, part D). Note that
partial 2 of the G., strings will have a similar bearing rate to
obscure further the departure from just tuning. With the 8-cent
interstring spread, on the other hand, the fifths be­come pretty diffuse.

Let us turn now to the interval of a major third in equal temperament.
Using a 2-cent detuning, the fifth component group of Ca has within it
a 1.5-Hz maximum beating frequency, as does the fourth component group
of the note E., if its strings similarly have a 2-cent detuning
spread. Taking these together we see the possibility of beat
frequencies as high as 1.5 + 1.5 = 3 Hz among the components upon
which the interval is chiefly based. In section 16.7, we learned that
the beating rate for a piano tuner's third in equal temperament is
about 8 Hz, a little more than twice the smearing produced by the
detuned unison. If the spread among members of a three-string "unison"
were increased to 8 cents, the beating would become rapid enough to

Component: 1 2 3 4 5

2-cent difference: 0.30 0.61 0.91 1.20 1.50 Hz

8-cent difference: 1.21 2.42 3.53 4.80 6.10 Hz

Notice first of all that with the 2-cent detuning the beating rate for
the first pair of partials is quite slow, as are those for the second
and third pair of partials. As a result the tone sounds reasonably
smooth when played by itself. The 8-cent spread gives a rather
brighter sound, but it is not yet the sort of jangle one gets with a
spread of 15 to 20 cents.

When we use a 2-cent detuning between strings, the 0.91-Hz beat
frequency belonging to its set of 3rd components is just able to cover
up the 0.89­ Hz beat that one uses in setting the equal-temperament
fifth to G4 (see sec 16.6, part D). Note that partial 2 of the G4
strings will have a similar bearing rata to obscure further the
departure from just tuning. With the 8-cent inter string spread, on
the other hand, the fifths be come pretty diffuse.

Let us turn now to the interval of a major third in equal temperament.
Using a 2-cent detuning, the fifth component group of C4 has within it
a 1.5-Hz maximum bearing frequency, as does the fourth component group
of the note E4 if its strings similarly have a 2-cent detuning spread.
Taking these together we se, the possibility of beat frequencies as
high as 1.5 + 1.5 = 3 Hz among the components upon which the interval
is chiefly based. In section 16.7, we learned that the beating rate
for a piano tuner's third in equal temperament is about 8 Hz, little
more than twice the smearing produced by the detuned unison. If the
spread among members of a three-string "unison" were increased to 8
cents, the bearing would become rapid enough to drown the temperament
error completely. Clearly there is a trade-off of musical virtues
between the two kinds of unison spread as one compares various musical
intervals. In any event we have provided ourselves with another reason
stringed keyboard instruments are so well-adapted to musical
performance, despite the problems with fixed pitch that at first
seemed insurmountable.

As a practical matter it proves to be exceedingly difficult to tune a
set of unison strings to a true zero-beat condition (one even meets
cases where it is literally impossible to do so). The question arises
then whether or not people's preference for a slight detuning of the
unisons is simply a favorable response to the most familiar type of
sound, or whether something more fundamental is involved. Kirk finds
that piano tuners and musicians are unanimous in their verdict that
too-close tuning gives a tone that not only sounds dead but dies away
too rapidly. Laboratory measurement confirms the auditory impression
we gained in our initial experiments that slightly detuned (normal)
strings die away in about the same total length of time as a single
one of these strings when the other ones are prevented from vibrating.
However, when three strings are tuned exactly together they will
actually die away much more rapidly. The presence of other precisely
in­tune strings encourages each string to transfer its vibration more
rapidly to the soundboard and thence to the room! Let us first make
use of our knowledge of wave impedance to verify its consistency with
these observations and then go on to an example of the same kind of
physics displayed in an everyday experience far removed from acoustics.

In section 17.1 we learned that the wave impedance of a string is
equal to the square root of the product of tension T and mass per unit
length (Or2d). How do we find the corresponding impedance for a
triplet of identical strings acting together? The top part of figure
17.3 indicates the appearance of our three strings as they are
normally seen in a piano. The middle part of the diagram shows them
moved so close together that they are on the verge of touching. If
they were identical- tuned strings, they would stay precisely in step
with one another, and there would be no frictional or other force
acting between them to change things in case they did touch. In other
words, the three closely spaced strings will behave exactly like their
more separate cousins. In particular, the aggregate impedances are the
same in both cases. The bottom part of figure 17.3 shows the last step
in our imaginary set of transformations: here the strings are fused
together into a ribbon like whole, with no change of total mass or
tension. An extension of our former reasoning shows that this new sort
of string also retains the acoustical properties of its ancestor at
the top-as long as we confine ourselves to vibrations of the normal
type (up and down, as shown in the diagram).

Having done a little thinking about three strings acting precisely
together, we are now ready to calculate. Clearly, the total tension
acting on our composite string is three times the tension acting on
each of the original strings, so we must write 3T under the square
root sign where formerly there was a T. Similarly, any short length of
the composite has precisely three times the mass of a corresponding
length of ordinary wire, so we must also write 3(Or2d) in place of
Or2d in the formula. Putting all this together, we get:

(wave impedance of a tricord )= 3 x (Or2d) x 3T=

= 3 x ( wave impedance of a single wire )

This shows us that three strings acting precisely together produce a
threefold increase in the wave impedance, and thus a threefold
increase in the amplitude of the bridge motion, which ultimately leads
to a threefold reduction in the decay time of the vibration. You might
find it worthwhile to deduce this last assertion on the basis of the
principles outlined in section 6.1.

The expected difference in sound between a struck single string and a
perfectly tuned triplet of strings is not hard to figure out on the
basis of what we have just learned. First of all, the tone of the
precisely tuned triple strings will die away much more quickly, which
matches actual experience. Second, we would expect on the basis of
curve A in figure 13.5 that the perceived loudness of the fundamentals
of the tone (as expressed in sones) would be very nearly doubled
because of the threefold increase in source (soundboard) amplitude.
The cone would not actually appear this much louder, however, because
a short or decaying sound always sounds less loud that a steady one.
In the three­ string case the increased rapidity of the decay
partially offsets the perceived effect of the larger amplitude.

We seem by now to have left the slightly detuned strings of a real
piano in a sort of unexplained limbo between the single string and a
perfectly tuned triplet. The true behavior of detuned triplets will be
easy to understand once we have looked ac the everyday example I
promised a few paragraphs ago. Suppose you have undertaken to push
your friend's small car along a fairly level road. If the rolling
friction of the car is large, you may find is barely possible to keep
the vehicle rolling, and yet you will be able to move the car quire a
distance under these conditions without much strain and without
becoming winded. Suppose on the other hand that you have acquired a
helper in the pushing, so that the two of you together can get the
speed up to a fast walk. Pushing at this faster pace will soon leave
you winded and panting for breath, even if you are not pushing any
harder as an individual than you were during the solo performance. The
point is this: the energy you expend in pushing with a certain force
over a given distance will be spent in a much shorter rime if your
friend helps you make the trip more quickly. The rare at which you
work is increased because of the cooperative presence of your friend."

bye
A.S.

--- In tuning@yahoogroups.com, Ozan Yarman <ozanyarman@...> wrote:

>
> I understand you are searching for my published article here:
>
> http://www.musicstudies.org/Abjad_JIMS_071203.pdf
>
> Happy reading and season's greetings!
> Oz.
Thanx much! I look forward to a good read.

Ciao,

p

--- In tuning@yahoogroups.com, "threesixesinarow" <CACCOLA@...> wrote:
>
>
> http://i30.photobucket.com/albums/c348/mireut/sandersonB.png
>
> For the old "international pitch" with B calculated with the
> formula used by http://www.goptools.com/ps_screen.htm,
> http://www.accu-tuner.com/
>

If you don't mind my saying, that's a rather curious graph. It shows
the Erard 1840 having notes well below AAA (an error in plotting?) and
the Walter going down to about halfway between AAA and AA (it should
end at FF) with no increase of inharmonicity at all or even a
flattening out.

Also, all the values of B are insanely large. Around middle C it gives
B of order 1!! I suspect there is some problem of units involved in
the formula - perhaps the correct calculated value for steel piano
wire is 1000 times smaller, for instance. (I assume that the values
are calculated not measured.)

And I'm suspicious of the Bluethner curve: how does it manage to be so
close to the Walter at the beginning?

However, the overall format looks OK, and in particular the log-scale
for B is much more sensible than the linear one used by the RCM guys.

Anyway, I'm just about to show that what causes Paul et al. problems
in tuning is *not* the level of inharmonicity by itself, but its
profile from the bottom to the top of the instrument. And perhaps
surprisingly: problems occur at points where inharmonicity doesn't
grow fast *enough* with rising pitch.

Or, if one rephrases less surprisingly: if it doesn't fall fast enough
with falling pitch!
~~~T~~~

Thanks, Carl!

Oz.

On Dec 8, 2008, at 8:57 PM, Carl Lumma wrote:

>> I understand you are searching for my published article here:
>>
>> http://www.musicstudies.org/Abjad_JIMS_071203.pdf
>
> Ozan! Did I miss the original announcement of this article
> here? Anyway, congratulations!!
>
> -Carl

--- In tuning@yahoogroups.com, "Graham Breed" <gbreed@...> wrote:
> This has been on the list before. The basic theory (which I
> confirmed) is that stopping a string stretches it by about the same
> amount wherever you stretch it. So there will be a difference between
> stopped and open strings. The answer, then, is to adjust the length
> of open strings without affecting the fret placements. Hence you need
> nut adjustments. But bridge adjustments are still good enough for
> most people.

Hi Graham,

I totally agree. The required nut adjustments are very small compared
to the bridge adjustments and tend not to vary much between strings,
according to the classical guitar paper referred to here.
http://www.byersguitars.com/research/intonation.html

The bridge adjustments are set-backs of the order of 1 to 5 mm (steel
string guitar). The nut adjustments are set-forths. I use a fixed 0.5
mm nut setforth. I can only do fret placement within +- 0.25 mm
anyway. That's about +- 0.7 c at the nut and +- 1.4 c at the octave fret.

-- Dave Keenan