Pianotech

  • 1.  String scale question- Impedance?

    Posted 12-29-2020 14:36
    A friend of mine and myself ordered a string scale from Del Fandrich. We were perplexed by one of the parameters that was called String Impedance. There was no units of measure to go by so we were wondering what the numbers were telling us and how it was derived. Maybe Del or someone else could explain. Thanks in advance.

    -chris


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    Chernobieff Piano Restorations
    "Where Tone is Key"
    chernobieffpiano.com
    grandpianoman@protonmail.com
    Lenoir City, TN
    865-986-7720
    ------------------------------


  • 2.  RE: String scale question- Impedance?

    Posted 12-29-2020 15:16
    An interesting question
    are possibly helpful places to start.

    Best wishes

    David P

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    David Pinnegar, B.Sc., A.R.C.S.
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    +44 1342 850594



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  • 3.  RE: String scale question- Impedance?

    Posted 01-01-2021 12:12
    I was reading this article:

    https://www.quora.com/What-is-the-velocity-of-sound-through-steel-if-Young-s-modulus-and-density-are-given?share=1

    and it appears that the velocity of a sound wave through a material does not depend on its mass. If the numbers change just because the lengths change. I don't understand the value of the Z numbers on the stringing list. And that is regards to speed. As to stiffness of the wire, isn't that what inharmonicity shows?
    -chris

    ------------------------------
    Chernobieff Piano Restorations
    "Where Tone is Key"
    chernobieffpiano.com
    grandpianoman@protonmail.com
    Lenoir City, TN
    865-986-7720
    ------------------------------

    Original Message


  • 4.  RE: String scale question- Impedance?

    Registered Piano Technician
    Posted 01-02-2021 12:30
    The article that David P linked was helpful if you follow the math.

    Let me try to put it in more simple terms. Impedance is, roughly speaking, resistance to motion. If you're pushing a dead car across a level parking lot, impedance is a measure of how hard you need to push it (basically related to friction and mass of the car). Vibrating systems like a piano string are a bit more complicated.

    Imagine yourself holding one end of a garden hose that is stretched tight between you and the faucet. In this case, impedance is the answer to the question, "How hard to I have to waggle this end to get the whole hose to wave up and down?" The answer depends on the tension and linear mass density of the hose.
    Tension: if the hose is stretched really tight, you have to waggle it really hard to get the same height of waves that you would get on a loose hose.
    Linear mass density: It requires more force to waggle a fire hose instead of a garden hose.

    The impedance is the square root of (Tension x Linear mass density). If you increase the tension or the weight of a string, the impedance goes up. In the article that David linked, the impedance is "Z", the tension is "T", and the linear mass density is "ρ" (Greek letter rho). So

    The reason impedance is important is that it is a factor in how quickly energy is passed between vibrating systems. Note that the soundboard has its own impedance. (Think how hard the string has to waggle the bridge in order to get the soundboard to vibrate.) If the impedance of the strings are close to the impedance of the soundboard, energy transfers very quickly from the string to the soundboard and you get a loud "Whomp" with no sustain. We want the energy to transfer slowly from the string, but not too slowly, otherwise the piano sounds weak.

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    Anthony Willey, RPT
    http://willeypianotuning.com
    http://pianometer.com
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  • 5.  RE: String scale question- Impedance?

    Registered Piano Technician
    Posted 01-02-2021 16:49

    Anthony,

    I highly respect your educational level but one who has studied impedance in electrical systems, which are translatable to a certain level to mechanical systems, you have erred in your explanation of impedance. Your statement that impedance is the "resistance to motion" is somewhat misleading. Your analogy of pushing a dead car across a parking lot leads one down the wrong path of understanding impedance and resistance – which are two difference physical properties. As many of us know growing up in the early half of the 20-century, push-starting a car takes considerably more force to get the vehicle up to speed than it does to maintain a given speed. Impedance is the counteracting resistance during the time the vehicle is accelerating to a given speed. Once the vehicle is up to speed the only counteracting force is pure resistance.

    Therefore, this is why impedance is such a dominant factor in the vibrating string and its role in setting the soundboard in motion –the string is always changing speed as it vibrates from zero to maximum deflection and back again.
    Roger



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    Roger Gable
    Gable Piano
    Everett WA
    425-252-5000
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  • 6.  RE: String scale question- Impedance?

    Posted 01-02-2021 17:01
    What we're looking at in the car pushing analogy is momentum. This is a lag between the push and the movement and the analogue electrically is an electromagnetic coil. The other analogy is pushing against a spring, which electrically is a capacitor and on the next cycle of which becomes a push rather than a resisting force. It then becomes rather more complicated in terms of leading and lagging phase differences and the combination of the lead and the lag can result in a resonance which depending on the configuration either blocks energy draining from the system or empties it really fast.

    My tuning work enters that debate with the piano significantly as conventional wisdom wants the energy from  the string/soundboard system to be released for as long as possible to give sustain - but it's a mushy messy sustain which has led to pianists using the sustain pedal as a loud pedal, amplifying each individual chord operating the pedal as a kickdrum.

    By reason of the change in resonance that my tuning brings, the sustain is shorter, but the resonance of harmonicly according vibrations is louder and the resulting system allows the pedal to be engaged for extended periods, just as Beethoven and Chopin specified.

    Best wishes

    David P

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    David Pinnegar, B.Sc., A.R.C.S.
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    +44 1342 850594



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  • 7.  RE: String scale question- Impedance?

    Posted 01-02-2021 19:57
    Thank you Anthony, David and Roger,
    That all helps.

    -chris

    ------------------------------
    Chernobieff Piano Restorations
    "Where Tone is Key"
    chernobieffpiano.com
    grandpianoman@protonmail.com
    Lenoir City, TN
    865-986-7720
    ------------------------------

    Original Message


  • 8.  RE: String scale question- Impedance?

    Registered Piano Technician
    Posted 01-04-2021 00:13
    Roger,
    Maybe the car wasn't the best analogy. I was trying to find something relatable, and friction is something we can all appreciate.
    I don't think that "resistance" is that unrelated to impedance though. It is a type of impedance. In a DC circuit, the impedance is simply the resistance. (In an AC circuit it's only part of the impedance.) In the electrical to mechanical analogy, Inductance = Inertia (getting the car up to speed), Resistance = Friction (what it takes to keep the car moving), and Capacitance = Restoring force (if the car were attached to a large spring). So in that sense pushing the car is obviously a bad comparison to a piano string, since the dominant factor in the vibrating string is the restoring force (the tension pulling it back toward the middle) and that restoring force is not present in the car analogy.

    ------------------------------
    Anthony Willey, RPT
    http://willeypianotuning.com
    http://pianometer.com
    ------------------------------

    Original Message


  • 9.  RE: String scale question- Impedance?

    Posted 01-04-2021 06:10
    This is the point of the electrical circuit analogy with capacitor and coil, and the difference in time response to the application of a force and resulting movement, and phase in vibrational systems.

    The car represents a mass. That offers a sluggish response to the application of force. In terms of a cyclic system, the movement lags the push, 90 degrees back phase. The resistance of the rolling of the car should be minimal but the frictional resistance kicks in at the time of the force and the movement, zero phase. In a cyclic push-pull operation, a capacitor or spring stores the energy from the peak of the last movement and puts it back into the system pushing it forward, so 90 degrees forward phase.

    Old fashioned texts defined the point on a repeating vibrational system by cos theta vs sine theta, but modern annotation of the wave equation uses e to the power of -i or -j (square root of -1) multiplied by the phase angle theta (in radians) multiplied by x or t, distance or time. It sounds complicated but plugging the numbers in gives the right results.

    To be frank in my opinion the acoustical theory is interesting in terms of piano design, although just as with loudspeaker design it's what the ear hears that counts, and the tension analysis and graphs as set out in Malcolm Rose's book on Stringing Practice http://www.malcolm-rose.com/Stringing-Practice/stringing-practice.htm is all that's required to look at a stringing scheme visually and see what it's doing. From the technique that he sets out in that we can see what the progression looks like from bottom to top and tweak as appropriate.

    Whilst Malcolm Rose's book sets out instruments up to 1856 it would be very interesting indeed to see the graphs for representative different size instruments from different leading brands as at perhaps 1900, 1950 and the 21st century. Are any published anywhere?

    This would give a piano technician an idea of the ball-park tensions to aim for and specify string gauges appropriately.

    Best wishes

    David P

    --
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    David Pinnegar, B.Sc., A.R.C.S.
    - - - - - - - - - - - - - - - - - - - - - - - -
    +44 1342 850594



    Original Message