Hearing beats

[Richard Brekne]

Jenneetah wrote:

>> I typically do a 3:1  D3(3)--A4(1)  tested with a F2(5) and then set 
>> A3(2) to a position slightly narrow of D3(3) and slightly wide of A4(1).
>
>
> So you're essentially balancing A3(2) between D3(3) and A4(1). That 
> means that the single octave compass is based on that pure 3:1.

Yep... and the rest of the piano upwards of the D3--A4 12th is tuned to 
a P 12th.  as well. I was delighted to hear that Bernhard Stopper 
actually has documented a mathematical basis for this.  Far more formal 
then my own musings and construction of a P 12th tuning with tunelab 
based on the 19th root of 3. Still, my own little inventiveness worked 
out great by my own ears... and when he told of  his prior work on the 
matter I was pleased pink as it simply confirmed that what I had been 
fooling around with was indeed very supportable by applied tuning theory 
as well. Unfortunate that Stoppers work was not publised in the States 
when it first came out, and that tuners didnt start experiementing with 
it from the get go.  Smart guy our Bernnie :)

The bass tho, I tune with the best comprimise between 6:3 and 4:2 that I 
can get.  I like a tight bass.

>
> Thus far you've been describing aural tuning steps, does this continue 
> for the temperament? If so, would that be a 4ths/5ths or a 3ds/6ths 
> temperament? I'd be much more interested in the latter, but I can 
> already see how it would be executed.
>
You can do it either way really.... all dependent on whether or not you 
prioritize 3rds and 6ths progression over 4ths and 5ths.  I prefer the 
latter as the 5th is so near to the heart of the 12th. 
 

>> I find it very easy to set D3(3) to an A440 fork using the 6th below 
>> test as an aid. Then setting A4(1) to that same is a snap. Which 
>> yeilds me an A4(1) at 440.
>
>
> Not much different from directly comparing the A4(1) to the F2(5). The 
> latter would take care of the oboist looking for A440 in A4(1). The 
> former would also keep a bassoonist happy who might look for his A440 
> at D3(3).


Yes... the same thing really... but doing both and comparing insures 
more accuracy... for me anyways.


Cheers
RicB