Call for scaling spreadsheets

[Frank Emerson]

Joe and Ron,

I have been following this thread for some time.  As a designer of scales
for new pianos, I could offer a VERY lengthy discourse on this subject.  I
do not have time to get into this, and on that scale.  Ron, your
contribution seems to me to be the most practical and applicable to the
immediate situation.  When one is designing a new piano, with a full palate
of variables at his disposal, many things must be taken into consideration.
On the other hand, when you have the bass strings, and every other variable
is "nailed down," all that you have to determine is the number of strings
to replace with each wire gage.  Without control of any other variable,
such as speaking length, hitch pin placement, bridge configuration, bridge
pin configuration, bridge design, soundboard design, rib placement and
design, etc., all you have to determine is the wire gage to use for each
note.

Forget about inharmonicity, loudness factor, stiffness, characteristic
impedance, longitudinal mode partials, etc, etc.  All of these are valid
considerations if you are designing a new scale, but all are irrelevant,
and beyond your control, if all you need to know is what gages of wire to
use for each note in the plain wire sections.  I have a multi-page
spreadsheet for such calculations, but it is an ever evolving thing.  Each
time I use it, I add new calculations.  It would be useless to anyone who
is not familiar with its evolutionary development.

Count the hitch pins in each plain wire section.  This will tell you a lot
about the original design intent. If there are three hitch pins for every
two unisons, this simplifies things.  If there are more hitch pins than
this ratio, you have to determine how many strings have to be tied off and
how the side bearing would be influenced.  

All you need, in terms of a spreadsheet, is a simple calculation of the
tension for each note and a graph to display the tension from note to note.
A reasonable target tension is 160psi.  Ideally you want to minimize the
range of fluctuation either side of this target.  Each time you increase
the diameter of the wire, you will see a peak in the graph.  This will
guide you in determining when and where to change the wire gage.  You must
always have an even number of notes per wire gage, unless you have enough
hitch pins to allow tied-off strings to account for this.  The goal is to
keep the fluctuation in tension within as narrow a range as possible.  In
smaller pianos, it is expected and acceptable to allow a slight upward
curve in the tension in the highest few notes of the treble.Get the tension
right in this range, and trust that the original design takes all of the
other considerations into account 

Frank Emerson
pianoguru at earthlink.net


> [Original Message]
> From: Ron Nossaman <rnossaman at cox.net>
> To: Pianotech List <pianotech at ptg.org>
> Date: 9/29/2006 3:37:59 PM
> Subject: Re: Call for scaling spreadsheets
>
>
> > I guess my question that started this great discussion was really can
one
> > start with a given ( the bass strings ) and produce a scale that will
> > compliment them.
> > Joe Goss RPT
>
> Sure one can, but it won't be all that complimentary because 
> that's backward. Without moving bridges and changing speaking 
> lengths, about all you can do with plain wire is determine 
> tension ranges with wire gage. Inharmonicity will be what you 
> get. By far the most control and improvement in rescaling 
> happens in the bass, which in this case is already nailed down 
> to whatever the existing bass strings give you.
> Ron N
>