[tuning] How to tune the piano to 12EDO by ear without counting beats.

I absolutely dislike 12edo, but happened to think of a method to tune the
piano to 12edo by ear without counting beats :)

Quite simple actually, though laboursome.
Start with for instance the C.
Tune the C# to 6 pure 3/1 fifths below C. (256/243)
Now tune A so that C# is 5/1 from A.
Now tune G so that G is 2 pure 3/1 fifths below A. (16/9)
Now you have an equal tempered fifth between C and G!
Or to be exact, a 3/1 fifth minus a Schisma, giving 16384/10935 of 700.0013
cents. More than precise enough.
Now store this C somwhere on the keyboard up or down by octaves where you
won't be tuning the C in order to get other keys tuned.
Now repeat the process above starting on G. And repeat untill all 12 keys
are tuned. Then spread them over the keyboard by 2/1 octaves.
Exactly what's most convenient procedure for transposing in 2/1 octaves etc
while tuning (as a total of 8 3/1 fifths and a 5/1 major third all going
down can't fit the keyboard) I'll leave for the tuner to decide should
anybody actually ever use this.
End result: 11 fifths of 700.0013 cents, and one fifth of 699.9857 cents per
octave. All have no audible difference at all from 700 cents "ideal".

Marcel

Well.. actually.
This is a rediculously crazy idea haha :)
It requires to tune 88 3/1 fifths, 11 5/1 major thirds, and many 2/1 octaves
to extreme precision as small errors could get amplified greatly.
If the small errors are completely random they don't matter much, but I bet
they won't be perfectly random enough in practice.
And well over 100 small errors can get pretty large pretty easily it seems
to me lol :)

Ah well.. in theory it could be done hehe.

Marcel

I absolutely dislike 12edo, but happened to think of a method to tune the
> piano to 12edo by ear without counting beats :)
>
> Quite simple actually, though laboursome.
> Start with for instance the C.
> Tune the C# to 6 pure 3/1 fifths below C. (256/243)
> Now tune A so that C# is 5/1 from A.
> Now tune G so that G is 2 pure 3/1 fifths below A. (16/9)
> Now you have an equal tempered fifth between C and G!
> Or to be exact, a 3/1 fifth minus a Schisma, giving 16384/10935 of 700.0013
> cents. More than precise enough.
> Now store this C somwhere on the keyboard up or down by octaves where you
> won't be tuning the C in order to get other keys tuned.
> Now repeat the process above starting on G. And repeat untill all 12 keys
> are tuned. Then spread them over the keyboard by 2/1 octaves.
> Exactly what's most convenient procedure for transposing in 2/1 octaves etc
> while tuning (as a total of 8 3/1 fifths and a 5/1 major third all going
> down can't fit the keyboard) I'll leave for the tuner to decide should
> anybody actually ever use this.
> End result: 11 fifths of 700.0013 cents, and one fifth of 699.9857 cents
> per octave. All have no audible difference at all from 700 cents "ideal".
>
> Marcel
>