optimal diatonic not 5-limit JI

Of course, as soon as I wrote a posting discussing how
in certain contexts (namely, jazz) mistuning of the 3/2
can be largely ignored, I found another example exactly
to the contrary:

[Paul Erlich, TD 141.9, re: chain-of-'5th' chords]
> Observing 5-limit ratios for the thirds would mean one of the
> fifths would be off by a comma, which is often unacceptable even
> in passing.

I agree completely, and have found a very good example of how
unacceptable this is.

I sent an email to David Beardsley recently discussing
some 11-limit chords, and some of it relates strikingly
to this. We were discussing the 11-limit 'neutral' intervals,
but the point here is about the '5th' that is 'off by a comma'.
I've underlined the beginning of the releveant section
(altho we've also been talking about 11:9 here recently too):

[me, monz:]
> I've been playing around a lot with the 11/6 '7th'
> for about a year now. When I use it, it functions
> to me like a 'major 7th', but it really is neutral.
>
> And then, since my posting to TD 132 about that
> Etta James MIDI file, I've realized that there are
> some really interesting 11-limit '3rds' and '6ths',
> and that they quite typical of intervals in blues vocals.
> A prominent example from that 'article' is 99/80.
>
> Obviously this is pretty close to a 5/4 [= 100/80].
> ~17.4 cents flatter, to be (almost) exact.
> Also, not quite as 'neutral' as the typical 11-limit
> intervals which are very close to 1/4-tones, like
> 11/8 and 11/6, and your 'neutral 3rd' of 11/9.
> It leans a tiny bit toward the 'major' side of '3rd'.
>
> So the other day, I combined the two into a 'major 7th'
> chord to hear what it would sound like.
>
> Not very good.
> Reminded me of a car horn more than anything.
> I'm talking old-fashioned gas-guzzling American
> car horn, not the little Jap honk.
>
> Here's the chord:
>
> 1/1 : 99/80 : 3/2 : 11/6
>
> Now, imagine my suprise when I investigated the
> individual dyad subsets to find exactly where the
> unpleasantness was coming from. I expected it
> to be manifested somewhere in those 11-limit
> connections, but that wasn't it at all!
>
> The strong dissonance came from the 40/27 (a 5-limit
> interval) between the two 11-limit notes.
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
> I made two other versions of the chord that changed
> that 40/27 into a nice smooth 3/2:
>
> 1/1 : 99/80 : 3/2 : 297/160, and
> 1/1 : 11/9 : 3/2 : 11/6
>
> They both sound lovely.
> The top one definitely has a 'major' flavor,
> even tho it's very different from 8:10:12:15.
>
> The bottom one, which uses the 11/9 you mentioned,
> definitely has a 'neutral' flavor, neither major nor
> minor, although it can function as either, depending
> on context.

Joseph L. Monzo....................monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

___________________________________________________________________
You don't need to buy Internet access to use free Internet e-mail.
Get completely free e-mail from Juno at http://www.juno.com/getjuno.html
or call Juno at (800) 654-JUNO [654-5866]