Was OnlyPure not P12ths Tunings

[Bernhard Stopper]

HI Ric,
please forget my previous answer on this post.
I read it on the fly, and my answer may be interpreted false, feel free to 
use any of my suggestions i have made relating the Pure twelfth not 
concerning my patent filing.

Please see my following comments in this text.

----- Original Message ----- 
From: "Ric Brekne" <ricbrek@broadpark.no>
To: "pianotech" <pianotech@ptg.org>
Sent: Friday, April 15, 2005 8:11 PM
Subject: Was OnlyPure not P12ths Tunings


> Hi Ron K and Bernie :)
>
> Consider this and see if this makes sense to you.
>
> Take the 4 notes D3,A3,D4,and A4.
>
> You have a a 12th in D3 and A4.  Tune that so the lowest order partial 
> sets is pure to begin with.
> Then there are 4 three note combinations here.  D3,A3,D4 / D3,A3,A4 / 
> D3,D4,A4 / and A3, D4, A4.
>
> The trick is simply to get all 4 of these into as beatless a condition as 
> possible from within a pure 12th D3-A4 framework. Yes ?

Yes.

>
> Essentially, this is what I've been doing for the past 4-5 years. After 
> setting the 12th I tune A3 to A4 as a slightly  narrow 6:3 octave type so 
> that the D3-A3 5th  3:2 fifth type is acceptable. Usually turns out to 
> about a 3rd of a beat per second. Bernhards <<quasi pure sound>>  Then I 
> tune D4 tune to D3 as a pure 6:3 octave type, as much pure as the D4-A3 
> 4th and the D4 D4 5th allows for.  Compromising D4 for all three 
> relationships yeilds a slower then (ET) normal 4th, and a very quite 5th 
> and an octave that balances 4:2 and 6:3 so that a sense of pureness is 
> there.

No. this method does not ensure at all, that those four combinations sound
the purest possible (i.e. to get the smallest amplitude modulation).
You must do a nonlinear beat summation (numerically or by measurement or by 
ear)
of the whole spectra of the three notes invovlved.

and with all that, with a usual frequency measuring ETDs is not possible to 
measure beats correctly.
Tuning the three notes for pure state is like tuning with unison tuning 
precision.

Try doing this with an ETD on one note with three strings one after the 
other.
The difference you hear, is what the ETD lies. And this lie is in every ETD 
temperament.
You can measure up as many partials you want (like the Verituner does), that 
doesn´t change the result.
Piano sounds are nonlinear in frequency AND time.

>
> When I construct a curve using Tunelab 97 with these 4 anchours.. I simply 
> enter the 3rd partial frequencies for all four notes into the numerical 
> editor, and use the quadratic interpolator to construct a curve for first 
> D3,A3,D4, and then A3,D4, A4.  I then have a <<12ths temperament>> for the 
> entire range. This is easily extended to the treble just by tuning E6 to 
> the 3rd partial value for A4 and F5 to the 3rd partial value for D4 and 
> then redoing the process with the numerical editor for this extended 
> range.
> I find for the bass its best to balance octave types instead of extending 
> the 12th downwards.  I /think /this is because the inharmonicity and para 
> inharmonicity down there is better handled that way.
>
> Now.. this is a method if you will... that just about anyone could stumble 
> upon... and I fail to see how in itself this kind of methodology is 
> patentable... let alone enforceable once a patent is somehow managed.  If 
> applied in a particular ETD algorithm in a particular fashion I can see 
> it... but in itself ... ?? nah...

yes this is a method.
but it is no more patentable, since it is not new.

kind regards,

Bernhard

>
> Cheers
> RicB
>
>
>
>
> Bernhard writes:
>
> No, it should be pure for all of this 4 three-note combinations, the pure 
> state is only limited by inharmonicity.
> On a concert grand, you can easily reach a "quasi" pure sound of every 
> octave with a inner and or outer fifth.
>
>
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