> Richard Dobson wrote:
> (snip)
>
>> It is also a practical matter - the core of a wound string is
>> relatively narrow-gauge, making it as easy to wrap around tuning pegs
>> and pins as the higher-pitch ones. And for instruments where the hand
>> is in direct contact with the string, clearly thickness has to be kept
>> to a minimum while obtaining the necessary pitch range.
>
> I only recently got to try an electric guitar. I was
> somewhat surprised on the thickness of the low strings.
> (I didn't have a pick so was doing it by hand.)
The frequency of a limp string's fundamental is equal to v/(2*L). where
v is the velocity of a transverse wave on the string. and L is the
distance between the bridges. (The factor 2 arises because L is a half
wavelength.) In turn, v = sqrt(T/(m/l), where T is the tension and m/l
is mass per unit length, rho. Since m goes as dia^2 and T/dia^2 is
proportional to unit stress, a string of any given material and length
tunes to the same frequency if the unit stress is the same. To say that
better, as long as the material and unit stress is unchanged, the
frequency will also be unchanged.
Higher tensions produce louder sounds because the string has more energy
for the same displacement. A thicker string doesn't in itself produce a
lower tone. To lower the pitch without making the string too slack, it
is wound in a way that adds little stiffness and bears little of the
tension. The wound string has greater tension and is therefore louder
than an unwound string of the same tension-bearing material and pitch.
jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Richard Dobson●February 23, 20092009-02-23
Jerry Avins wrote:
> Richard Dobson wrote:
>
>> ... Stiffness is significantly
>> limited, for obvious reasons, on wood-based instruments,
> ...
>
> I assume you mean tension here. Am I wrong?
>
>
Nope, I was writing severely quickly. As a rule of thumb, the target
tension for each string on a modern grand piano is around 150 pounds.
There is a formula somewhere for calculating the required thickness of
string, for a given pitch and tension. The tension over the whole
instrument is measured in tens of tons. I opted for an easy life and
built a harpsichord from a kit instead. The wires can actually all be
wrapped into small coils just like guitar strings. Still have some lying
around, to do something with some day.
Richard Dobson
Reply by Glen Herrmannsfeldt●February 23, 20092009-02-23
Richard Dobson wrote:
(snip)
> It is also a practical matter - the core of a wound string
> is relatively narrow-gauge, making it as easy to wrap around tuning pegs
> and pins as the higher-pitch ones. And for instruments where the hand
> is in direct contact with the string, clearly thickness has to be kept
> to a minimum while obtaining the necessary pitch range.
I only recently got to try an electric guitar. I was
somewhat surprised on the thickness of the low strings.
(I didn't have a pick so was doing it by hand.)
-- glen
Reply by Jerry Avins●February 23, 20092009-02-23
Richard Dobson wrote:
> ... Stiffness is
> significantly limited, for obvious reasons, on wood-based instruments,
...
I assume you mean tension here. Am I wrong?
Increasing the diameter of a solid string makes it heavier and stiffer.
Winding a smaller-diameter to the weight of the larger solid one
increases its weight with little effect on its stiffness. Exactly where
the winding stops before the bridge subtly affects the inharmonicity.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Richard Dobson●February 22, 20092009-02-22
Jerry Avins wrote:
> Richard Dobson wrote:
>> Jerry Avins wrote:
>> ..
>>> The beats occur only if the strings are tuned differently enough.
>>> With normal tuning, the common bridge ensures that they vibrate in
>>> synchrony.
>>>
>>> Jerry
>>
>> Piano strings are extremely stiff relative to thickness etc,
>> especially the large ones at the low end, and the harmonics are sharp
>> with respect to the fundamental (i.e. it is half-way towards metal-bar
>> behaviour, and why one needs an iron frame to manage the huge tension
>> forces). Indeed an objective listening of the typical bass piano
>> string would have to conclude it was more bell-like than a vibrating
>> string, especially when played forcefully. Tuning such things is
>> definitely more an art than a science, and electronic tuning aids are
>> not much use. All in all it is very complex behaviour!
>
> Winding strings to weight them without adding significant stiffness is a
> technique older than pianos. (Silver alloy is often used on violin
> strings; silver for its durability and weight. Gold would be better yet,
+ chrome, titanium, tungsten, aluminium; all sorts of metals are used.
I think weight and stiffness are almost independent parameters. It is
not so much a question of avoiding stiffness, as of lowering the
frequency for a given string length (and tension). Uprights and baby
grands have fatter bass strings than a full-length grand will have, and
sound correspondingly more metallic. The stiffness increases the
capacity for loudness (and clearly impacts on tone too). Stiffness is
significantly limited, for obvious reasons, on wood-based instruments,
not only violins but also harpsichords, early fortepianos, guitars,
harps, etc. It is also a practical matter - the core of a wound string
is relatively narrow-gauge, making it as easy to wrap around tuning pegs
and pins as the higher-pitch ones. And for instruments where the hand
is in direct contact with the string, clearly thickness has to be kept
to a minimum while obtaining the necessary pitch range.
Richard Dobson
Reply by noodle22●February 22, 20092009-02-22
Wow, very informative. Thanks.
I checked out this picture on wikipedia
http://en.wikipedia.org/wiki/Piano_tuning
Looks like a piano has multiple strings (which I did not realize since I
use a keyboard) which I guess helps explain beating. I've now read a bit
about inharmonics with piano's and must assume that is what the issue is.
Also, it looks like (I could be totally wrong because I don't really know)
to tune a piano, you want to first remove all the beats and then slightly
detune the strings. Very interesting and sounds like quite the task.
As for the 60 Hz hum, it is small relative to my signal (when I actually
play a note) so maybe it is not an issue. I remember when I did an FFT
initially, I could see it but it was easy to remove in the freq domain.
After experimenting some more, it seems like possibly less an issue in the
time domain since the main peaks stand out so much more strongly.
Reply by Glen Herrmannsfeldt●February 22, 20092009-02-22
Jerry Avins wrote:
> I just looked at the demo carefully. It only approximates the phenomenon
> I wrote of. An old test of good layout, shielding, and filtering was
> construction of two oscillators at about 1 MHz in the same chassis
> running off the same supply, with a frequency difference of only 10 Hz.
> In some communication receivers, it's impossible to get a beat with the
> BFO of less than 40 Hz or so. Its easy to ascribe that to the speaker or
> headphones, but usually it's lock-up.
On Feb 21, 3:24 pm, "noodle22" <jw970...@yahoo.com> wrote:
> >what's the green and what's the orange?
>
> green = my processed signal
> orange = peaks that the computer has identified
>
> >you mean "average magnitude difference function"? never heard of
> >"average mean distance function", at least in the context of pitch
> >detection.
>
> you are correct
>
> > what's a "center peak"
> > For your application do you need the negative
> > shift? Isn't that going to always produce a reflection about the zero
> > when used with real data? I guess you used a canned program and
> > didn't want to muck with it?
>
> I can answer both of these at the same time. I am doing my correlation by
> "sliding" an array of data across another array of data and each time I
> slide it, I sum the multiplication of all the cooresponding elements.
>
> Ie
>
> ...|1|3|4|
> |1|3|4|
>
> .|1|3|4|
> |1|3|4|
>
> |1|3|4|
> |1|3|4|
>
> |1|3|4|
> .|1|3|4|
>
> |1|3|4|
> ...|1|3|4|
>
> so the end result is |4|15|26|15|4
>
> The center peak I was referring to was the "26" point where the signals
> are perfectly correlated.
>
> I set up the library so that I could correlate any two signals (not a
> canned program but something I wrote myself) but I did not really think
> about it a whole lot and I see that I only need half to correlate half of
> it if I am doing an auto correlation. Thanks for the tip. I will update
> my program and I think it will significantly improve performance if I cut
> my data in half.
>
> >Yes, this is interesting. I think there is something to learn here.
> >Your image is a bit hard to see. You might try providing a higher
> >resolution image. It looks like each of the peaks is actually
> >multiple peaks. If you consider a central point of this group of
> >peaks, the spacing appears to be about 58 or so bins. The interesting
> >part is that the sequence of the peaks in a cluster reverses on each
> >harmonic. This is exactly the effect you see when a signal is
> >undersampled and you get aliasing in the spectrum. I'm not saying
> >that is what you are seeing, but it may have similar causes.
>
> To be honest, I don't know a whole lot about aliasing. After reading your
> comment, I increased the sampling frequency to 44100Hz and had the same
> problem. However, you are absolutely right about there being groups of
> peaks. This was even more evident at the 44100 sampling rate. Does this
> sound like it could still be aliasing?
>
> >To get a better understanding of what you should expect to see, what
> >is the sample rate?
>
> 12300Hz. I am trying to cover a frequency range of about 25 hz to 500hz
>
> >What is the frequency of the note you used?
>
> I think it was supposed to be around 40Hz
Is this supposed to be E1? The low frequency of your signal relative
to the high sample rate precludes aliasing problems unless there is
significant noise above half the sample rate. So I think we can
exclude that. 40 Hz is a *really* low note, but since you are
concerned with 60 Hz hum, I expect this really is the frequency you
are seeing.
But now I'm not sure what sample rate you are using. If you are still
using 12300 Hz, I would expect the peaks to be multiples of a little
over 300. If the sample rate is 44100, then a 40 Hz peak will be at
bin 1102. I would expect your 60 Hz component to show at bins 205 or
735 for the 12300 Hz and 44100 Hz sample rates respectively.
Also, if you provide larger images or at least the bin number for the
peaks, that might help to figure out what you are seeing.
If you want to measure 500 Hz with a 44100 sample rate, you can filter
out the harmonics above 500 Hz. That will help for the high end, but
not so much the low end.
Rick
Reply by Jerry Avins●February 22, 20092009-02-22
Jerry Avins wrote:
> Richard Dobson wrote:
>> Jerry Avins wrote:
>> ..
>>> The beats occur only if the strings are tuned differently enough.
>>> With normal tuning, the common bridge ensures that they vibrate in
>>> synchrony.
>>>
>>> Jerry
>>
>> Piano strings are extremely stiff relative to thickness etc,
>> especially the large ones at the low end, and the harmonics are sharp
>> with respect to the fundamental (i.e. it is half-way towards metal-bar
>> behaviour, and why one needs an iron frame to manage the huge tension
>> forces). Indeed an objective listening of the typical bass piano
>> string would have to conclude it was more bell-like than a vibrating
>> string, especially when played forcefully. Tuning such things is
>> definitely more an art than a science, and electronic tuning aids are
>> not much use. All in all it is very complex behaviour!
>
> Winding strings to weight them without adding significant stiffness is a
> technique older than pianos. (Silver alloy is often used on violin
> strings; silver for its durability and weight. Gold would be better yet,
> but hey ....
>
> When piano strings nearly identically tuned are struck simultaneously,
> they vibrate as one. When the strings are slightly detuned, the vibrate
> at the same frequency, but energy passes back and forth between them as
> well as into the bridge. That reduces the volume and prolongs the sound.
> Identical tuning produces a short, loud, klunky sound. Slight detuning
> produces produces a softer, more bell-like sound. Further detuning
> breaks the lock and produces the very audible beats that are that
> "piano-out-of-tune" sound with a single note. The lock-in frequency
> range depends on the tightness of the coupling and the Q of the
> resonators. See a demo at http://tinyurl.com/cv74lh
I just looked at the demo carefully. It only approximates the phenomenon
I wrote of. An old test of good layout, shielding, and filtering was
construction of two oscillators at about 1 MHz in the same chassis
running off the same supply, with a frequency difference of only 10 Hz.
In some communication receivers, it's impossible to get a beat with the
BFO of less than 40 Hz or so. Its easy to ascribe that to the speaker or
headphones, but usually it's lock-up.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Jerry Avins●February 22, 20092009-02-22
Richard Dobson wrote:
> Jerry Avins wrote:
> ..
>> The beats occur only if the strings are tuned differently enough. With
>> normal tuning, the common bridge ensures that they vibrate in synchrony.
>>
>> Jerry
>
> Piano strings are extremely stiff relative to thickness etc, especially
> the large ones at the low end, and the harmonics are sharp with respect
> to the fundamental (i.e. it is half-way towards metal-bar behaviour, and
> why one needs an iron frame to manage the huge tension forces). Indeed
> an objective listening of the typical bass piano string would have to
> conclude it was more bell-like than a vibrating string, especially when
> played forcefully. Tuning such things is definitely more an art than a
> science, and electronic tuning aids are not much use. All in all it is
> very complex behaviour!
Winding strings to weight them without adding significant stiffness is a
technique older than pianos. (Silver alloy is often used on violin
strings; silver for its durability and weight. Gold would be better yet,
but hey ....
When piano strings nearly identically tuned are struck simultaneously,
they vibrate as one. When the strings are slightly detuned, the vibrate
at the same frequency, but energy passes back and forth between them as
well as into the bridge. That reduces the volume and prolongs the sound.
Identical tuning produces a short, loud, klunky sound. Slight detuning
produces produces a softer, more bell-like sound. Further detuning
breaks the lock and produces the very audible beats that are that
"piano-out-of-tune" sound with a single note. The lock-in frequency
range depends on the tightness of the coupling and the Q of the
resonators. See a demo at http://tinyurl.com/cv74lh
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������