Son of the Return of Scale =

[Ron Nossaman]

>Ron,
>
>I remember the previous post, but is it the adjusted lengths by section
>that's troubling you? I mean, shouldn't the lengths between sections be
>adjusted accordingly and if so, why not by guage as well.

Not troubling me, exactly, it's just interesting that anyone would go to
the trouble unless there was some compelling - read "obvious", or even
"detectable" reason for doing so. It seems odd to adjust the speaking
length progression by gauge change to try to standardize wire tension when
there's no clear benefit derived. With the Cable Nelson, they were shooting
in the dark, pretty much, with only a partial picture of the effects of the
process on tension and inharmonicity. Realistically, I can commiserate with
their attempts to hang their scaling philosophy on something they could
anticipate - like tension, in an attempt to at least appear to have a plan.
One has to start with something, after all, and when you don't have all the
rules, you play the cards you have in the most logical manner you know how.
 At the time the Young Chang was built, this information was available in
some form, but they went for the equal tension anyway. Lacking any
explanation of the reasoning behind the design from the designer(s), I can
only wonder what the anticipated benefits were, and how the reality held up
against the theory. In this light, I find the Young Chang far more
disturbing than the Cable Nelson. Don't you? Incidentally, the lengths
between sections shouldn't be "adjusted", per se. It's the added space
taken up by the plate strut between unisons across section breaks that
necessitates the bridge dogleg at those points. The speaking length
progressions should ideally be continuous across section breaks. The unison
spacing along the bridge is discontinuous, not the speaking length
progression. Logarithmic scale progression rates are often changed at
section breaks to accommodate different length pianos, but that's just
because it's a handy spot to make the change, since it's tough to pick out
visually. You could build a 5' piano with the same scale as a 9' piano in
the last two octaves or so with no problems, but you would have to change
the progression from there on down to accommodate the overall length of the
piano. But this doesn't have anything to do with equal tension scaling.
It's just one of those annoying concessions to reality that have to be
dealt with somehow in piano design. 

As far as I know, this is accurate. If I'm out to lunch on any of this, I
trust that some passing piano designer will pause momentarily and
straighten me out. If corrections or enlightening details are forthcoming,
at least two of us stand ready to learn something. 


>For you and me, at least, the influence of soundboards to inharmonicity
>seems to remain an undefined variable, while Del Fandrich's posts offer
>only hints at solutions. 

I don't have any data, nor have I heard of any that I recall, that
soundboard impedance and/or configuration affects inharmonicity. There
could very well be a connection but it's at least a couple of layers back
in the mystery stack for me at this point, and I predict that the effect
will be negligible as far as real world tuning goes, when/if it's finally
quantified. In other words, It's on the list for consideration, but hasn't
shown any potential for a high priority.


>Our own in-house calculations of Mehlin and
>Wolfendon scales, which do adjust for guage changes, seem quite
>satisfactory according to the out-dated formulas at hand. 

Yea, but that's one of the points. I used to make a very convincing
arrowhead, using authentic methods of the period, but there doesn't seem to
be much consumer demand 6,000 years after the technology was established.
Was the Young Chang an attempted technological time machine?



>Still, as far
>as I know, the only true equal tension scale is Robert Wornum's, per his
>patent which involves a single guage for all of the un-wound strings,
>determined by doubling lengths per octave.

At what number of decimal points does something become a "true" something?
I don't seem to have gotten the memo. Purity at the expense of performance
is a concept that has been proven through history to be a somewhat less
then optimal approach in real world application. Pragmatists seem to
outnumber purists by a considerable margin, and are themselves outnumbered
by a nearly infinite factor by subjective impressionists. So even with the
best of all possible graphs, if it doesn't sound "good" (whatever that is)
to Joe or Jane Consumer, it ain't gonna fly, regardless of categorical
equality.  


>Wornum's quadrupled inharmonicity per octave may be foiled by his
>soundboards 'loose' at one end, attached only to a slight beech liner. I
>wish there was a grand in this country from which to take measurements -
>I have no idea how his bass looks, and can only assume that its tension
>was measured by placing weights on the strings in the manner suggested
>to violinists. Perhaps someone on the list services one of his Equal
>Tension uprights and could assist with core, winding and end-length
>measurements.

I'm interested. Operator with spreadsheet is standing by.



>Anyhow, hearkening back to Bill Bremmer's "reverse well-tempered"
>readings from a Yamaha electronic piano, it occurred to me today that
>samples are spread across sections, so that inharmonicity remains
>constant for a number of notes, then jumps to the next sample group. Not
>so curious considering how cheaply these things are made - I'd agree
>with him, how frequently I encounter RWT, guaged in part by roughness
>rather than beats.

Does inharmonicity really remain constant? I remember Bill's post, but I
don't remember any such details. Confirmation?



>Has anyone made readings for inharmonicity on soft wire? I'm prepared to
>do this, but I'd appreciate data if anyone already has done so: I'm
>interested both in installed wire and wire independent of soundboards.

This comparison would be interesting for modern piano wire too with enough
samplings under defined conditions. 


>I'm looking forward to taking Del's course in scaling small pianos at
>the national in Arlington,
>Clark

I'll be there, guess I'll see you there too.

Ron N