JI Key Distance Function Temperaments

JI Key Distance Function Temperaments:

I'm working on developing a set of temperaments which are based on JI.
The deviation from the JI pitch for any particular interval is
targeted to
have an algebraic function that is dependent on the distance of the
key from the JI central key.

Some Mean Tone temperaments exhibit a linear deviation for the 3rd,
4th, 5th and major 6th intervals according to the distance from the
central key.

Are there any other precedents to this kind of approach?

Steve

--- In tuning@y..., steve.sycamore@s... wrote:
> JI Key Distance Function Temperaments:
>
> I'm working on developing a set of temperaments which are based on
JI.
> The deviation from the JI pitch for any particular interval is
> targeted to
> have an algebraic function that is dependent on the distance of the
> key from the JI central key.
>
> Some Mean Tone temperaments exhibit a linear deviation for the 3rd,
> 4th, 5th and major 6th intervals according to the distance from the
> central key.

That is not true of any meantone temperaments -- you are probably
thinking of well-temperaments.
>
> Are there any other precedents to this kind of approach?

Yes, many well-temperaments have been constructed on this principle.
I was referring to this principle also when discussing the 22-
tone "shrutar" tunings a few months ago. Please e-mail me off list if
you'd like to explore the mathematics of this further.