Was OnlyPure not P12ths Tunings

[Ric Brekne]

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 ?

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.

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...

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.