[CAUT] The Origins of P12ths tuning.

[Richard Brekne]

Hi Ron, Fred

Thanks for pointing out the typo :)  Gary's article btw is indeed very 
interesting in light of the discussion we've been carrying on. Very many 
of Fred's points are addressed and really... good ol' Fred raised some 
pretty poignant points along the way.  Gary's article goes along ways 
down the road with agreeing with much of what I understood Fred to be 
getting at.  That said... he does allude to the idea that the 3:1 and 
the 6:1 resolve much of our struggles to find the right balance in 
finding a fine stretch that balances very octave - double -- triple 
octave relationships and others.

I do have one bit to add to all this.  The last few days I've been 
tinkering a bit more with my own Tune lab based approach and have, I 
think, stumbled onto another interesting coincident. The 6:3:1.  
Immediately upon looking at that ratio one sees implied a 6:3 octave 
that matches both a perfect 19th and a perfect 12th.  Theres more...  
But just try a P-12ths temperament using D3-A4 as your temperament area. 
Then instead of your usual bass routine... tune D2(3) and D1(6) to 
A3(1).  That is to say use your ETD to zero on A3's fundamental then 
just tune D2 and D1 to it.  Tune downwards through the bass that way.  
Then take a look at all resulting 6:3 octave types. 

I agree with your comment Fred, that Gary and Bernhard seem to have 
approached the thing from different angles. My own was much along the 
lines of Gary's along with the strong influence of a very nice and very 
hands on ETD.... namely Tune Lab 97.  I still like that original tuning 
editor better then the present approach. Gave you more control.

Cheers
RicB

    I've been following the threads having to do with OnlyPure tuning
    software.  Very interesting.
     
    RicB writes: Gary Shulze, RTT Lansing, MI Chapter, PTG Journal May 1982
     
    I couldn't find it there - I found it in the March 1982 Journal.
     
     
    Ron Koval
    Concordia U.