Inharmonicity Judgments in aural tuning, starting with decent thirds.

[Richard Moody]

Since in theory the thirds smothly increase in beat rates and double every
octave, to me it made sense to simply set the first three thirds in the
temp octave. (a--a1)  Then f--a  is half of f1--a1,   I set the first
three thirds, a--c#1--f1--a1, then go for the first fifths,a1--d1 and
a--e1.  Now if the next logical fifth is bb--f1  then the check of that
would be bb..d1 then compared with a..c#1.   Now if these two sucessive
thirds don't sound successively a tiny bit faster, or worse, it helps to
get this straightened out before going on. If there is a mistake then
f--d1 sixth comes into play and now you hear four contiguous thirds from
f--a through f1--a1.  Adjust wich ever needs adjusting then go back to
bb--d1 third, and if that is OK than bb--eb1 fourth then eb1--b  third and
b compared (fourth)to e1 tuned earlier. 
	An advantavage to this system is for the tuners who like to start with C,
but have a conract obligation to come out with A440.  Simple set a1 (A4)
to source and tune middle C to the correct beat of that sixth.  
	By establishing the beats of contig. thirds first you will find you can
get fifths and fourth the way you like them without compounding errors. 

In piano tuner (88note) nomenclature, Source--A4   means tune A4 to
source.  A4--A3 means tune A3 to A4.  A3--C#4.  C#4--F4.   F4...A4. 
(F4...A4 means listen to the third F4...A4)  Get these contigious thirds
right.   Then tune A3--E4 then A4--D4  listen to A3..D4   and E4..A4. 
tune F4--Bb3 (tune Bb3 to F4) listen to Bb3...D4.  If that third is ok
with A3...C#4 then proceed.  If not tune F4--F3 and listen to F3...D4
sixth.  That sixth must be slower than any third you have tuned so far. If
you are still having trouble, don't worry, in two years you will be much
better, just like playing the piano.   

So what does this have to do with inharmonicity in aural tuning?  When you
tune the bass beatless in octaves down from the temp octave , but you
listen to fifths and esp 12ths and they start to sound ucky (sour) and you
find you can stretch the bass octave to a pleasant vibrato (beat)(out of
tune) and the fifths and 12ths suddenly sound pleasing musical,.... that
is dealing with inharmonicity in aural tuning.  One and only one example
of it.Spinets and consoles are good examples.  And its tough because all
pianos aren't inharmonic the same way. If you want to go nuts in the
treble,  I think the sns console would qualify as a  famous example. 

Richard Moody  

----------
> From: Carl Root <rootfamily@erols.com>
> To: pianotech@ptg.org
> Subject: Re: Inharmonicity Judgments
> Date: Friday, February 26, 1999 4:03 PM
> 
> Jim Coleman, Sr. wrote:
> > 
> > Hi Carl:
> > 
> > For many years I tuned using the Wm Braid White temperament. I finally
> > caught on to the fact that in the middle of his sequence he used the
> > contiguous M3rds to prove that he had not skewed the 4ths and 5ths in
one
> > direction or another. So, I decided that if this is the real test of a
> > temperament, why not start there and still use the 4ths and 5ths as
they
> > are interconnected with the 3rds.
> 
> I went through a similar progression, except that I discovered 'Both
> Ways from the Middle" - F, A, Bd, D . . . - before contiguous thirds. 
> As you know, it's a great intermediate step as you convert from a
> sequence based on fourths and fifths to one based on thirds.  It is also
> the best way to start the second contiguous thirds series a half step up
> from F, A, C# . . . ..    
>