termination and inharmonicity (Long)

[Richard Brekne]

Ron Nossaman wrote:

>

    Richard Brekne wrote:

> >you can get into this buisness of longitudinal modes.. and termination
> profiles DO havean >effect.. and the effect does not have to be soooo very
> large to make an impact.
>
> So what are the effects of longitudinal modes on inharmonicity? Also, how
> does termination shape (generally) correlate to inharmonicity? I don't have
> access to the article and I'm curious.

I didnt really say that longitudinal modes affect inharmonicity... at least not
perhaps in the way you may be thinking. Yet longitudinal modes do play into the
harmonic picture (in the bass and lower tenor quite a bit) and manipulation of
them can affect the total harmonic (inharmonic) picture. For example, and I
think you already know all this Ron but for others who may not.. If the first
logitudinal mode (LM1) has very close to the same frequency as one of the
transverse mode partials, then this partial is going to come through very loud
indeed... if it is a bit flat (as in say 1 Hz  or bps) of that transverse
partial then you have a bit of a problem... if it matches nearly perfectly the
result is often a kind of "wolf tone".. or a loud objectionable emphasis of the
coincident Transverse Mode (TRn) for that string (how objectionable or not
depends on the actual coincident involved). A little sharp will present
similiar problems to a little flat.. but perhaps be less annoying maybe even
desirable as that situation matches the "normal" inharmonic condition of
running sharp of theoretical.  (On a side note we may be touching on negative
inharmoncity in the first case above)

"Longitudinal mode 1 (LM1) is nearly independent of string tension but somewhat
dependant on string termination conditions....."   "Generally LM1 should be
tuned by design in 100 cent increments, and the resulting frequencies should be
the same as actual TR1 frequencies higher up on the keyboard" (Conklin1990)
Conklin suggests that the LM1 / TR1 ratio should be around 4800 cents. Actually
just a bit sharp of this... "a little higher, to the fundemental transverse
frequency of the string four keyboard octaves above" (Also on the side this
would seem to point to the desirability of tuning to the concert pitch the
scale was calculated for.. as  LM1 is independant of string tension)

Conklin doesnt get into just how termination points play into all this in this
particular article.. but Weinreich touches on the subject of termination in
Askenfelts publication in 1990. "If the support is springy, that is one which
displaces sideways in the direction in which the string applies a force to it,
there will no longer be an exact node at the support. Instead, the extrapolated
node will be somewhat beyond the physical end of the string; or in other words,
the string will "think" that it is longer then it really is, causing it to
lower its frequency.... The opposite happens with a massy support.  Weinreich
is talking transvers modes here.. so I am not sure if this is the kind of
"dependency" Conklin refers to above or not in regards to Longitudinals. Yet
one determinant for Longitudinals is the speaking lenght of the string. And if
that, due to the bridge condition, is "apparently" longer or shorter then it is
physically, this may relate also to Longitudinals. (my thoughts there)
Weinreichs comments on termination points are primarilly in reference to the
bridge and not the front termination point. (Weinreichs article is no doubt
very interesting reading for you Ron... as it deals mainly on this issue of
string coupling)


Grin... now on to what I personally was refering to when it comes to the front
termination point. This is simply as I have stated before. A thin and sharp
aggraffe / capo / whathaveyou.. will allow the string to "flex" around the
termination point to some greater degree then a wide and round one. This in
itself lowers string stiffness (McMorrow 1989) which means a lowering of
inharmonicity. The article presented by Coltman way back in 1938 shows this,
tho his article is largely a presentation of a view of inharmonicity that is
the result of an intermediate termination condition. That is to say a
termination condition that is neither perfectly clamped nor perfectly hinged.
Included in this article are the formuliæ for the two "extreme" conditions and
his modification for the intermediate condition.

Also amplitude plays a role in all this, and it is my understanding that this
also if effected  in some way by these two different kinds of front termination
points. Tho I havent read though all the lines enough times to dicern in any
clear sense what that relationship is yet... so I wont comment further on that.

The point is that inharmonitiy...while primarilly a function of the basic
string characteristics,, length, diameter...etc etc.. is also dependant to some
"controllable" degree on other factors. To my knowledge the only one of these
factors that has been exploited in any sense of the word as a part of the
"scale" is this idea of tuning the longitudinals, Baldwin I believe was very
hip on this  for a while.

Hope that answers your query.. and that I havent dug toooooo deep a hole for
myself.. grin

regards



>
>
> BTW, from a scaling point of view, the inharmonicity formula just gives you
> a visual means of smoothing the plotted curve at scale discontinuities,
> like speaking length progression changes at plate struts, bass/tenor break,
> plain/single wound, and single/double wound. It isn't really necessary that
> it be all that accurate unless you are using it to compute tunings or
> arguing minutiae.

Didnt know that.. I thought it was much more a part of scale design then what I
think I read in your comment here. I want to get a hold of a copy of Fenners
book on scaleing. I simply got to know more about all this. .... grin

>

>
>
> Ron N

--
Richard Brekne
Associate PTG, N.P.T.F.
Bergen, Norway