Petrof Inharmonicity

[Billbrpt]

Dear List:

I received this question from an outside reader about inharmonicity in his
Petrof piano.  I think it would be best responded to by the List, especially
those who are in the manufacturing and rebuilding end.  I'll explain my
limitations in my response following the question.

<<Subj:	 Petrof Inharmonicity
Date:	98-03-02 10:38:49 EST
From:	cvandenhandel@aviall.com (Cornelius Van Den Handel)
To:	Billbrpt@aol.com

Dear Mr. Bremmer,

I read your technical notes in the PIANOTECH archives with interest.  As an
engineer, I'm intrigued by your description of pianos in terms of their
inharmonicity, with the Steinway's and the Kawai's on the higher and lower
ends of the inharmonicity scale.  I own a Petrof 7'9" grand which I purchased
new three years ago.  If you have any experience with the Petrof designs, I
would be very interested in whether you consider them to be low or high
inharmonicity.

Also, I spent some time in the local showrooms this weekend, and had the
opportunity to play new 7' Mason & Hamlin -- how would you describe its tone?

To see if I'm at all close, I'd say that the M&H is on the higher end of the
scale, probably less than the S&S B I played yesterday.  The tone of my Petrof
seems less complex than the S&S, too, so I'd guess its inharmonicity is
moderate to high.

Cork Van Den Handel>>

    I have to admit that I really do not know what role inharmonicity plays in
tone.  I have come to understand quite a bit in recent years what effect it
has on tuning as far as temperament and octaves go.  The fact that there is
inharmonicity means that an octave must be greater in width than is
theoretical (1200¢).  This also means that all 3rds are wider and all 5ths
which are tempered must be tempered less than theoretical.

    The SAT and Reyburn programs used with ETD's effectively stretch an ET out
to meet the calculated inharmonicity a piano has.  Sometimes these programs do
not produce results which are entirely accurate because the pianos scale
design is not uniform.  Sometimes a combination of two programs solves that
problem.

    While I choose not to tune in ET, I still take a sampling of the
Inharmonicity a piano has the way Dr. Al Sanderson originally invented.  I
take a reading of the difference between the way the note F4 reads when read
on octave 5 and then on octave 6 (this is the difference between the 2nd & 4th
partials).  This was called the "stretch factor" with Sanderson's first
program which was known as a "stretch tuning".  Later, he developed a more
complex program that takes 3 samples.  It is the FAC program you will often
see mentioned on the List.

     I don't need any more than the sampling from F4 for my purposes because I
only need to have a sampling from the temperament octave to know what sizes of
intervals I will construct.  I construct all of my programed tunings by a
combination of calculated interval sizes, direct interval construction and a
method known as "equal-beating".

     The "stretch factor" number of most pianos comes out to be between 3 & 7
with a number somewhere in the range of 5 being average.  When I figured out a
way to program an SAT to produce any of the Syntonic Meantone Temperaments, I
found that I was limited to only 3 choices.  Therefore, I had to decide
whether the piano's scale was "low", "medium" or "high" inharmonicity.  These
descriptions are mine and not any manufacturer's nor do they come from any
other source other than what I just described.   A number of 3 (or below) to
4.5, I consider to be low, from 4.6 to 5.8, I consider to be medium or
moderate, 5.9 or above I consider to be high.

    I have consistently found Steinways to be in the high range, usually right
about 6 but I have seen them as high as 7.5.  Yamahas, Young Changs and
Samicks are always in the moderate range.  I have always found Kawais to be
low but once I found a 7 foot model to be on the low end of medium.   Baldwin
concert grands are low but the parlor grands are medium.  Acrosonics are high
but their wound string section doesn't seem to match the tenor.  This is one
of the pianos where two FAC programs need to be used.    Mason & Hamlin and
Sohmers are always low.  These two are well known as parlor pianos and usually
have a deep, rich but mellow tone.   Kimballs & Kohler & Campbells are always
high (very high).  

    I seldom tune a Petrof.  I did one grand just before Christmas but I
honestly don't remember what its value was.  I would guess it was on the high
end of moderate and possibly high.

    Again, I don't really know what role inharmonicity plays in tone or its
complexities but if you ask me, I would always want a high inharmonicity piano
like the Steinway for a piano concerto.  The high inharmonicity allows greater
stretching of the octaves without introducing any distortion in them.  This
allows the piano to compete with the string sections who have a tendency to
push the pitch upwards and make the piano sound flat in comparison.  When
tuning a 1/7 comma meantone temperament, which has only a slight wolf (a wide
5th between Ab & Eb), a high inharmonicity piano will naturally produce a less
dissonant wolf than a low one will.

   On the other hand, a low inharmonicity piano makes a seemingly more
appropriate choice as a chamber or parlor piano.  Of course, Baldwin and Kawai
concert grands sound great as concerto instruments too and Steinways sound
great in living rooms.  It still helps to know what general range a piano's
inharmonicity falls in in order to manipulate a tuning for a given situation.

   If there is anyone on the List who tunes a Petrof regularly and uses an FAC
program, he/she may be able to tell you whether the figures seem low, moderate
or high in comparison to most other pianos.

    Thank you for your interest,

     Bill Bremmer RPT
     Madison, Wisconsin