Diesis pumps (was: Chain-of-major-thirds tunings)

"In search of the lost brain-cell" more likely.

That should have been:

12-tET allows
|----------------|
Ab:C :Eb to F: A: C to Db:F :Ab
|---------------|
and

|----------------|
G#:B#:D# to E: G#:B to C#:E#:G#
|---------------|

but only in 19-tET, and related chain-of-thirds tunings (incl. 22, 41-tET)
can one do:

|----------------|
Ab:C :Eb to Fb:Ab:Cb
=
E#:Gx:B# to C#:E#:G#
|----------------|

If we try to do the above in 12-tET we get

|----------------|
Ab:C :Eb to Fb:Ab:Cb
=
E :G#:B to C :E :G
|----------------|

i.e. We end up a chromatic semitone lower.

Recap: This is part of the "diesis-pump" chord progression
C, Ab, E, C which in 19-tET etc. becomes C, Ab, Fb/E#, C#.

JdL, is this a problem for your adaptive JI? Paul E's solution of putting
the roots in meantone won't help this one.

Regards,
-- Dave Keenan
http://dkeenan.com

Dave Keenan wrote,

>JdL, is this a problem for your adaptive JI? Paul E's solution of putting
>the roots in meantone won't help this one.

Clearly the 12-tET major third is the one that leads to a vanishing diesis,
so putting the roots in 12-tET is the right answer for
circle-of-major-thirds progressions (which you can find in Schubert and
Coltrane).

By the way, in your 10-out-of-22 scale, there's no reason to stop at 10, is
there? You can keep piling on major thirds in threes until you finally get a
proper scale (I think) at 19-out-of-22.

Paul H. Erlich wrote:
>
> Clearly the 12-tET major third is the one that leads to a vanishing diesis,
> so putting the roots in 12-tET is the right answer for
> circle-of-major-thirds progressions (which you can find in Schubert and
> Coltrane).

My favorite circle-of-major-thirds sequence is the second section of the
Brahms Alte Liebeslieder Walzer No. 8. Around the ring in 16 short
sweet bars.

Fred R.