para-harmonicity

[Kent Swafford]

Richard Brekne wrote:

>Hi list
>
>Not so long ago there was some talk about the phenomenon refered to by 
>some as
>para inharmonicity. The reasons, descriptions, what-to-dos about it, etc 
>seemed
>pretty vague, as if folks are just starting to get a grip on this. Jim 
>Coleman
>contributed with an interesting bit on ploting measured harmonicity against
>squared partial numbers, describing para-inharmonicity as any deviation 
>from the
>straight line in the resulting graph.
>
>My query is simply is there any more specific information about
>para-inharmonicity. Do we really know what causes it, or how predictable 
>it is.
>Has there been any serious research done, if so where can one read about 
>this.
>
>Richard Brekne
>Sydneskleiven 1
>5010 Bergen, Norway
>
>E-mail Richard Brekne
>Richard Brekne Website

Para-harmonicity is the termed coined by Marty Reyburn, Dean Reyburn's 
wife, to explain a phenomenon that Dean became aware of while developing 
CyberTuner. Here is his definition:

"Para-harmonicity is inharmonicity which is not explained by the usual 
formulae (it can be negative or positive)."

The phenomenon that Dean became aware of is a simple one -- the 
inharmonicity constant isn't constant.

Chameleon, the tuning calculator that is a part or RCT, measures multiple 
partials of multiple notes in order to have plenty of data with which to 
calculate an accurate tuning. After Dean started having these 
measurements of all these partials at hand he became aware that it made a 
difference what partials were used to calculate the inharmonic "constant".

If you understand the concept of the inharmonic constant you know that 
according to the theory, if you know the placement of any two partials of 
a given note, you should be able to predict where any of the other 
partials will be. This turns out to be quite untrue in practice.

(This is one of the reasons that Chameleon is a superior tuning 
calculator. It measures the actual placement of multiple partials rather 
than simply measuring the deviation between single pairs of partials and 
then calculating the tuning based on an inharmonic constant that has 
proven to be inaccurate.)

There is a demonstration in RCT of para-harmonicity that I would love to 
show you. There is a page in RCT called Pianalyzer which will listen to a 
single piano note and automatically measure most of the partials (1-8 
plus 10 and 12). It then automatically calculates the inharmonic constant 
for each partial. All of the numbers are generally different from every 
other one, the lower partials being more inconsistent than higher 
partials.

So, to answer your question about how predictable para-harmonicity is, it 
is inherently unpredictable.

As to what to do about para-harmonicity, I have found the best approach 
to these vagaries is to tune every day with RCT. I have developed a 
number of RCT-specific techniques that I believe let me tune well despite 
para-harmonicity.

Kent Swafford