G13#11 chord

Joe Monzo wrote,

>Recent psychoacoustical research has shown that people tend to hear
>the most consonant intervals as wider (= upper note sharper) than
>the small-integer ratios. The ubiquitousness of 12-tET for several
>generations now may be what accounts for this (if it is indeed
>caused by cultural conditioning, which it may not be).

Well, just about as many small-integer ratios are flat in 12-tET as
small-integer ratios that are sharp!

By the way, when I plug various 12-tET voicings of the G13#11 chord into my
total diadic harmonic entropy minimizer, it usually either moves the F# all
the way up to G, or moves the A up to Bb, or moves the Bb up to B. But one
voicing, G B c# d e f a, comes out OK as:

0 389 581 700 892 1016 1400

What I see here is that the G6/9 chord contained within this chord is being
pretty much meantone-ized (though the fourths here take a lot more tempering
than the fifths), as you agree it should. Meanwhile, the c# makes a nice
major triad with the a and e while also making a ~7:5 with g and a ~7:9 with
f, while the f makes a ~6:5 with d.

> Paul H. Erlich
> http://www.egroups.com/message/tuning/11750
>
> Joe Monzo wrote,
>
> >Recent psychoacoustical research has shown that people tend to hear
> >the most consonant intervals as wider (= upper note sharper) than
> >the small-integer ratios. The ubiquitousness of 12-tET for several
> >generations now may be what accounts for this (if it is indeed
> >caused by cultural conditioning, which it may not be).
>
> Well, just about as many small-integer ratios are flat in 12-tET as
> small-integer ratios that are sharp!

Of course I realize that from a catholic perspective which
takes account of all consonant ratios, this is true, Paul.

But since I was demonstrating a rationalization of the G13#11
chord which was based on a 'best harmonic fit', I noticed that
*from a harmonic perspective* (please note my emphasis!), what
I say above is true.

PS -
I'm in the process of preparing a webpage to go with my
MIDI-file of your rationalization of the G13#11, as outputted
by your 'total diadic harmonic entropy minimizer'.
(Where can I get one of those?... ;-)

-monz
http://www.ixpres.com/interval/monzo/homepage.html