[pianotech] Tunic Onlypure Tuner

[Jeff Deutschle]

Thanks John:

Let me try to explain what I mean better. My practical definition for
ET is where the M3's and the M6s beat progressively faster. I prefer
this definition because it allows any type of stretch, but still
requires that all notes be tuned within a few tenths of a cent of the
stretch's ideal.  When a twelfth is tuned, to it's sweet spot or
otherwise, this also defines the width of all the intervals within the
twelfth.

I don't see how any equal beating or even integer beating, such as 3
beats for every 2 beats, (which are supposed to cause a beat
cancelling effect) between fourths, fifths, and octaves that are tuned
to the notes of the twelfth can guarantee that when the circle of
fourths, fifths or twelfths (depending on how you look at it) is
completed that the M3s and M6s will all beat progressively faster.

On one piano the results might be fifths that are too narrow for the
twelfth, producing one wider-than-just fifth when the circle is
completed and causing unevenly progressive M3s and M6s. On another
piano the final fifth may be too narrow.

Now if the answer is that then the twelfth was not tuned to its "sweet
spot", then we are talking in circles....


On Mon, Mar 9, 2009 at 9:09 AM, John Formsma <formsma at gmail.com> wrote:
>
>
> On Mon, Mar 9, 2009 at 7:51 AM, Jeff Deutschle <oaronshoulder at gmail.com>
> wrote:
>>
>>
>> When I tried it, I ended up with nearly pure fourths and fifths...
>
> You can't have both. They are mutually exclusive.
>
>
>>
>> When I really think about it, how could equal
>> beating intervals guarantee ET?
>
> I guess it depends on one's definition of ET. I think ET is loosely defined
> as all the 4ths in the temperament beating roughly the same as other 4ths,
> and all the 5ths beating the same as other 5ths, with evenly progressing
> chromatic m3s, M3s, m6s, and M6s.
> You can have a pure 5ths ET, a pure 4ths ET, or many combinations of a
> mixture of varying widths of 4ths and 5ths.  As long as 4ths are roughly the
> same, and 5ths roughly the same, you can call it ET (at least in my world).
> Now, my opinion is that the best sounding ET is one with 5ths nearly pure.
> Otherwise, there is too much activity in 5ths (and then 12ths and 19ths as
> you progress out of the temperament -- they become far too narrow).
> --
> JF
>



-- 
Regards,
Jeff Deutschle

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