[CAUT] P-12ths was: Tuning a Steinway D and aBosendorfer Imperial together

[Richard Brekne]

Hi all again.

A few comments about the origins of the P12th.  Kent asked me to hunt 
down the specific column I have refered to several times from the early 
eighties / late seventies that specifically talks about the P-12th (and 
If I remember correctly mentions the 19th root of 3). I spent an hour 
yesterday looking through quickly about 30 issues from that time period 
and the <<journyey>> was really quite cool.

I have not found the column I remember, but will.  But I have dug up 
quite a bit on the way. So far, the first time I see a direct reference 
to using the P-12th as a tuning priority was in 1982.  Much earlier tho 
there are many articles that clearly dance, and in progressive fashion, 
around the idea of using this priority. There was a whole slew of posts 
that went along the lines of the discussions we have here... 
time-delayed and individually selected as required by the medium at the 
time (the Journal itself) In these discussions many tuning priorities 
for temperaments and octave stretching were thrown back and forth.  
Curiously with  some degree of tension amoung some of the 
participants... but I digress.  In many of these, and an increasing 
degree as the years passed, the idea of the major 3rd, 10th, 17th were 
sentral. On occasion reference to the 4th above the 3rd... or the major 
6th are thrown in... and gradually one sees more a picture of using 
these in slightly compromised form to essentially achieve what is in 
fact a P-12th interval that governs octave stretch. It is not 
specifically identified until the article in 1982 (of the articles I 
have dug up so far).  When I find the specific article I have in my 
memory I will post it, along with a bunch of others in chronological 
order for anyone who is interested.

Now one can re-read these articles and interpret them in any way one 
wants mind you... but the likely hood that some would indeed read these 
and move in the direction of P-12ths is rather impossible to argue 
against.... Especially since it starts getting directly mentioned at 
some point.

All this pre-dates Stoppers work. That said... it takes nothing away 
from Stopper.  His math treatise on the matter are to my knowledge the 
first and the comma he arrives out can be called whatever he wants it to 
be called... that is the usual rights of someone who discovers such 
things.  That said... it is clear as I have said many times that several 
folks, completely independent of each other and without knowledge of 
each others work and the time periods in which such work was done have 
been moving in so similar a fashion that any claim to originating the 
basic concept of using the P-12th as a tuning priority will not stand.  
It falls into the category of
prior knowledge and can not be patented.  Stoppers exact implementation 
CAN be legally patented, and his math treatises copyrighted... and that 
should be respected.  But anyone wanting to do an Aural P-12th tuning 
can freely do so, and anyone wanting to use another ETD with a self 
constructed template can also do so freely.

Cheers
RicB