Petrof Inharmonicity

[Mike Swendsen]

Del:
I really appreciate the quality and amount of information you supplied
regarding inharmonicity, harmonic structure, and soundboard.  I have never
heard or read such a succinct and to the point dicussion on the subject.
We are, indeed fortunate to have you as a resource on this list.
Thank You.
Mike Swendsen RPT
]Original Message-----
From: Delwin D Fandrich <pianobuilders@olynet.com>
To: pianotech@ptg.org <pianotech@ptg.org>
Date: Wednesday, March 04, 1998 10:02 AM
Subject: Re: Petrof Inharmonicity


>
>
>Mike Swendsen wrote:
>
>> I know there has been a lot of talk about inharmonicity, it being higher
or
>> lower than average, and quite frankly, I think that what is being listen
to
>> is not the in harmonicity of the instruments is question.
>>
>>
>> If you listen to the tone of a S&S for instance it is quite complex
 read
>> many harmonics, and most of them towards the high end) and with a Petrof
>> those very high harmonics are not so prominent,  on the other hand the
lower
>> harmonics are.  This gives the piano a very clean and clear sound, I have
>> heard some people say 'bright' but that isn't quite correct.  A Steinway
or
>> a Mason and Hamlin are bright, I.e. there is a strong sense of  higher
>> harmonics.
>>
>>
>> It would be interesting to have someone with a good frequency analyzer
test these
>> pianos, and show the results.
>> As far as the 'stretch' numbers on Petrofs go, they almost always fall
>> between 5.5 and 6.0
>>
>>
>> C. Mike Swendsen RPT
>
>------------------------------------
>
>Mike,
>
>No, you don't "hear" inharmonicity as such. As Bill points out, it will
have an effect on
>how the piano is tuned in that a piano with "high" inharmonicity will be
tuned somewhat
>sharper in the treble than will one with "low" inharmonicity. However,
inharmonicity by
>itself has no effect on what you hear in terms of tone quality.
>
>Inharmonicity is a calculated function of a stretched string. For example,
look at just
>one string, in this case C-40:
>    Length = 610 mm    Dia. = 0.042"    Tension = 160 lbs.    In = 0.42
>    Length = 640 mm    Dia. = 0.040"    Tension = 160 lbs.    In = 0.31
>    Length = 674 mm    Dia. = 0.038"    Tension = 160 lbs.    In = 0.23
>All three strings have a tension of 160 lbs. But each of the other
parameters varies. The
>harmonic structure of each of these strings will be different when struck,
but not
>"because" of inharmonicity. It will be different because each string has a
different
>speaking length and a different tension. In the examples given above -- if
everything else
>remains the same -- when struck, the longer string will have a bit more
energy in the
>fundamental and lower partials and the shorter string will have a bit more
energy in the
>higher partials. Inharmonicity is simply a by-product and it tells you how
the piano
>should be tuned.
>
>The harmonic structure excited in each of these strings will also be
affected by the
>elasticity of the hammer, and the by the exact point of excitation, i.e.,
the hammer
>strike point.
>
>None of which really tells you how the piano is going to sound.
>
>Regardless of the harmonic structure that is excited within the string when
struck, what
>you actually hear is determined mostly by the relationship of that string
to the
>bridge/soundboard/rib structure. That is, the relative amounts of each
excited harmonic
>within the string that are actually allowed into the soundboard, and the
rate at which
>they are allowed in. This energy transfer rate is determined by the mass
and stiffness
>characteristics of the soundboard. The mass and stiffness characteristic
make up what is
>referred to as a soundboard's characteristic impedance. Impedance is simply
a measure of
>the soundboard's reluctance or willingness to be moved when some external
source of energy
>attempts to move it. The problem is complicated a bit by the fact that the
soundboard is
>more or less reluctant or willing to be moved depending on the frequency of
the energy
>that is trying to move it.
>
>So, if a string's motion is made up of more than one frequency -- And it
is. The string's
>motion is highly complex. -- then we find that the soundboard is only
willing to respond
>easily to some of those frequencies. Because of the complex nature of
soundboard
>impedance, energy at some of the frequencies within the string will not be
readily
>accepted into the soundboard, while at others it will be welcomed with open
arms. Those
>that are readily accepted by the soundboard will make up the tone character
of the initial
>attack and for the first few milliseconds of the sustaining tone, those are
not so readily
>accepted will make up the tone character of the sustained sound. The rate
at which the
>overall energy package within the string is accepted into the soundboard
determines the
>overall sustain of the tone.
>
>It is this complex relationship between the energy spectrum within the
string and
>characteristic impedance of the soundboard assembly (including the design
of the bridges,
>the soundboard panel itself, the ribs, the crown characteristic of the
assembly, the
>mounting system of the assembly, etc.) that determine the tone
characteristic of any given
>piano.
>
>So, is everything now as clear as mud?
>
>Regards,
>
>Del
>