19/31 eqs

Oops...Paolo said something about me or Starrett commenting on the
stretch tuning concept as applied to these tunings...unfortunately, I
have not been actively following the thread, but can make a few comments
about these tunings. The major 3rd in 19 is about 379 cents, putting it
about 7cents lower than the 5/4 (and closer then the 12eq 3rd)...the
minor 3rd is almost perfect at 316 cents (rounded off). The 5th is 695
cents, and it definitely sound a bit flatter than I like it in chords.
The good thing about notes flatter than the pure harmonic is that you
can bend into them if you want (on a guitar, anyway) . In 31, I believe
the 3rd is at 387 cents, making it, for all practical purposes, perfect
with the 5/4...the minor 3rd is about 310 cents, making it 10 cents
closer to the 5/6 than 12 eq...the 5th is about 396 cents, again making
for a somewhat off sounding 5th. I have found, as my ear has gotten
better over the years, that the flat 5th of 19 and 31 (more in 19) does
bug me...the trade off is the better 3rds/6ths, which overall is worth
it. Of course, all eqs are "out of tune" somewhere, so it's part of the
deal...the increased number of keys for modulation, and the fascinating
new chordal/melodic possibilities are what I like about these tunings.
Just for the heck of it, 34 eq is a marvelous eq...both 3rds are only
2 cents sharp to pure, and the 5th is 4 cents sharp. There's also a
bunch of other interesting features, such as 2 cycles of 5ths, a cycle
of 34 major or minor 3rds, and the dreaded comma, which can be put to
very good use with a bit of patience. I have a composition which uses
the comma as a basic structural feature...it'll be on my 4th CD (which
is in the works). I don't know if this helps the stretch thread, but
there it is...Hstick

Neil wrote,

>Just for the heck of it, 34 eq is a marvelous eq...both 3rds are only
>2 cents sharp to pure, and the 5th is 4 cents sharp. There's also a
>bunch of other interesting features, such as 2 cycles of 5ths, a cycle
>of 34 major or minor 3rds, and the dreaded comma, which can be put to
>very good use with a bit of patience. I have a composition which uses
>the comma as a basic structural feature...it'll be on my 4th CD

Neil, I can't wait. I really liked the 34-tET pieces on your last CD, and
have always thought that triadic music would not work in 34 (or 22) unless
you used the comma as a structural feature . . . glad you've come to agree!
Before the CD comes out, care to elaborate on ways you used the comma as a
structural feature? I've used it in 22-tET (implying 7-limit harmony) within
a form of micro-chromaticism, where a line moving by the 54.5-cents
intervals of 22-tET can be harmonized in such a way that when analyzed in
JI, it's moving by various intervals like 48:49, 64:63, 256:243, and of
course 80:81 -- but unlike JI, you get a smoother line, since all the steps
are in JI . . . have you used a similar approach in 34, something different,
all of the above . . . ? Or shall it remain a secret until the CD comes out?

I wrote,

>but unlike JI, you get a smoother line, since all the steps
>are in JI

Whoops, I meant, "since all the steps are equal" . . . it's kind of like
that Mathieu quote about the chromatic scale in 12-tET, but of course this
time it's 22-tET . . .

>Just for the heck of it, 34 eq is a marvelous eq...both 3rds are only
>2 cents sharp to pure, and the 5th is 4 cents sharp. There's also a
>bunch of other interesting features, such as 2 cycles of 5ths, a cycle
>of 34 major or minor 3rds, and the dreaded comma, which can be put to
>very good use with a bit of patience. I have a composition which uses

There is also the 17-tet neutral third scale.Stack 7 neutral thirds and you get one kind of scale,10 and you get another kind of scale.There�s also the"altered"modes of LssLssL,LsLssssL and LsssLsL.

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Mats �ljare
Eskilstuna,Sweden
http://www.angelfire.com/mo/oljare
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--- In tuning@egroups.com, Neil Haverstick <STICK@U...> wrote:
> Oops...Paolo said something about me or Starrett commenting on
the
> stretch tuning concept as applied to these tunings...unfortunately,
I
> have not been actively following the thread, but can make a few
comments
> about these tunings. The major 3rd in 19 is about 379 cents,
putting it
> about 7cents lower than the 5/4 (and closer then the 12eq 3rd)...the
> minor 3rd is almost perfect at 316 cents (rounded off). The 5th is
695
> cents, and it definitely sound a bit flatter than I like it in
chords.
> The good thing about notes flatter than the pure harmonic is that
you
> can bend into them if you want (on a guitar, anyway) . In 31, I
believe
> the 3rd is at 387 cents, making it, for all practical purposes,
perfect
> with the 5/4...the minor 3rd is about 310 cents, making it 10 cents
> closer to the 5/6 than 12 eq...the 5th is about 396 cents, again
making
> for a somewhat off sounding 5th. I have found, as my ear has gotten
> better over the years, that the flat 5th of 19 and 31 (more in 19)
does
> bug me...the trade off is the better 3rds/6ths, which overall is
worth
> it. Of course, all eqs are "out of tune" somewhere, so it's part of
the
> deal...the increased number of keys for modulation, and the
fascinating
> new chordal/melodic possibilities are what I like about these
tunings.

Thanks for the response, Neil. It helps to get your perspective on
these alternate ETs, especially since you're coming from more of a
jazz background. So I take it that on your 31t-ET guitar you tune
your open strings to straight 31t-ET, rather than tuning your highest
strings slightly sharp and your lowest slightly flat?

> Just for the heck of it, 34 eq is a marvelous eq...both 3rds are
only
> 2 cents sharp to pure, and the 5th is 4 cents sharp. There's also a
> bunch of other interesting features, such as 2 cycles of 5ths, a
cycle
> of 34 major or minor 3rds, and the dreaded comma, which can be put
to
> very good use with a bit of patience. I have a composition which
uses
> the comma as a basic structural feature...it'll be on my 4th CD
(which
> is in the works). I don't know if this helps the stretch thread, but
> there it is...Hstick

I too am looking forward to hearing your upcoming CD.

Thanks,
Paolo