Re: 24tet stuff

Welcome Nikita,

I'm just a beginner in microtonality and only stumbled into
24EDO since it approximated a tuning I was interested in.

Some things I found was that to my ears,
250 ~= 7/6 (about as good an approximation as
400 to 5/4)
and
950 ~= 7/4 (about as good an approximation as
1000 to 9/5)

Of course, 350 and 550 also give 11/9 and 11/8
approximations as well. (And real JI folks will shoot
me for mentioning those as acceptable approximations
but my ears are pretty accomodating at this point).

All this is to say that you can investigate some
of the higher limit JI ideas (as badly out of tune)
as you can 5-(prime)-limit in 12.

Another thing is taking Margos style of thinking of
resolution and apply it to intervals across the two
embedded 12 systems. So for instance, a tritone in
one EDO resolves to a P5 by opposite quarter tones

650 -> 700
50 -> 0

or

1150 -> 1200
750 -> 700

(which I believe Margo showed). I am referring here
to dyads composed of specific note names (arranged
vertically) resolving (by "->") to a similar dyad.

This second is very much in the spirit of the
augmented second in a harmonic minor scale, but
stretched all the way out to a "major third".

Another...

950 -> 1200
150 -> 0

Hope this shows another approach or viewpoint that
you can find some inspiration with.

Bob Valentine

> ----- Original Message -----
> From: Robert C Valentine <BVAL@IIL.INTEL.COM>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, June 10, 2001 3:36 AM
> Subject: [tuning] Re: 24tet stuff
>

>
> Welcome Nikita,
>
> I'm just a beginner in microtonality and only stumbled into
> 24EDO since it approximated a tuning I was interested in.
>
> Some things I found was that to my ears,
> 250 ~= 7/6 (about as good an approximation as
> 400 to 5/4)
> and
> 950 ~= 7/4 (about as good an approximation as
> 1000 to 9/5)

Thank you, Bob... I've been saying this for years.
(But Paul Erlich is probably going to complain...)

I find both of these approximations to 7-limit intervals
to work fine in 24-EDO harmony. In many cases I like
the sound of them better than 7/6 and 7/4.

Yes, when viewing 24-EDO in a systemic sense, the errors
here will cause inconsistency. Perhaps the 24-EDO
intervals are approximating some other ratio more
closely and some of us like how it sounds.

>
> Of course, 350 and 550 also give 11/9 and 11/8
> approximations as well. (And real JI folks will shoot
> me for mentioning those as acceptable approximations
> but my ears are pretty accomodating at this point).

Bob, your ears don't have to do a whole lot of
accomodating to accept 2^(7/24) and 2^(11/24) as
11:9 and 11:8, respectively. They're approximated
quite well in 24-EDO:

ratio cents cents error of 24-EDO

11:9 ~347.4079406 +~2.592059366
11:8 ~551.3179424 -~1.317942365

And don't forget one of my favorite intervals,
approximated very well in 24-EDO, the "undecimal
major 7th":

11:6 ~1049.362941 +~0.637058501

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> I find both of these approximations to 7-limit intervals
> to work fine in 24-EDO harmony. In many cases I like
> the sound of them better than 7/6 and 7/4.

If so, then why do you call them "approximations to 7-limit intervals"? Seems like you
should re-examine your assumptions!
>
> Yes, when viewing 24-EDO in a systemic sense, the errors
> here will cause inconsistency. Perhaps the 24-EDO
> intervals are approximating some other ratio more
> closely and some of us like how it sounds.

Or maybe some of us like how it sounds _despite_ any ratio-considerations.
>
> And don't forget one of my favorite intervals,
> approximated very well in 24-EDO, the "undecimal
> major 7th":
>
> 11:6 ~1049.362941 +~0.637058501

This is the only ratio of 11 that appears as a local minimum in the first octave of my
"standard" harmonic entropy curves. So I'm not surprised that it's one of your favorite
intervals (though I am suprised by your first statement above about preferring 250 and
950 over 7/6 and 7/4).