Yahoo Tuning Groups Ultimate Backup tuning 2, 3, 17 and 19

Hello everyone!

I have discovered an ingenious system of ratios representing a tuning
that perfectly meets the same intention as a temperament usually has.
I wonder how far this is known, because I suppose someone somewhere
must have thinked this out before me, although I know it's a somewhat
unconventional approach. Have any of you heard about it? The ratios
are:

1/1, 18/17, 9/8, 19/16, 24/19, 4/3, 17/12*, 3/2, 19/12,
32/19, 16/9, 17/9, 2/1.

*The tritone ratio 17/12 is replaceable by a 24/17 ratio.

There is a lot of logical patterns inherent in this line, which may
be more obvious if the fractions are notated with bigger numbers:

18/18, 18/17, 18/16, 19/16, 24/19, 16/12, 17/12, 18/12, 19/12, 32/19,
32/18, 17/9, 18/9

and with the 24/17 tritone ratio:

18/18, 18/17, 18/16, 19/16, 24/19, 24/18, 24/17, 24/16, 19/12, 32/19,
16/9, 17/9, 18/9.

Regarding the phytagorean intervals as a kind of framework, comments
should be superfluous, but make particular attention to the 16-17-18-
19 series for the numerators in the mid-section in the upper line
moving one step to left, becoming denominators and changing direction
in the line down under. It's also fascinating how the ratios can be
considered in pairs, if the rightmost part of the upper row is mixed
together with the leftmost downunder. The tritone ratio has to be
ignored at first. In every second pair the denominator decreases by
one from left to right, in the others, the numerator increases by
one. The other part of every fraction in each pair is constant. The
tritone ratio becomes a third "member" to one of the two pairs on
each side, left or right, depending on which is chosen. These
patterns are quite elegant, aren't they?

There is also a kind of 3-part symmetry in this tuning which it has
in common with the tuning of the traditional just intonated scale:
from 1/1 to 3/2 with the square-root of 3/2 as an axis, from 4/3 to
2/1 using the other kind of tritone, with the square-root of 8/3 as
an axis, and for the whole scale with the square-root of 2 as an axis.

The tuning is highly versatile. No ratio deviates more than 5 cents
from its equivalent 12EDO tone. ...Any comments about it?

🔗D.Stearns <STEARNS@CAPECOD.NET>

Hi there,

Yes, the 12-tone, 2,3,17,19 prime set is one I've looked at
before--here's what I got:

1/1, 17/16, 9/8, 19/16, 24/19, 4/3, (24/17-17/12), 3/2, 19/12, 32/19,
16/9, 32/17, 2/1

Here's how it would lattice out from a 16:17:18:19 harmonic series
segment:

19/12------9/16
3/2-`.----9/8 `.
17/12---`.17/16 `.
4/3-------1/1-------3/2
`. 32/17`.---24/17
`.16/9----`.-4/3
32/19-----24/19

BTW, I didn't recognize your name, are you a new poster? If so,
welcome aboard!

take care,

--Dan Stearns

----- Original Message -----
From: "xmacmixmax" <knurgen@hotmail.com>
To: <tuning@yahoogroups.com>
Sent: Saturday, May 18, 2002 6:05 AM
Subject: [tuning] 2, 3, 17 and 19

> Hello everyone!
>
> I have discovered an ingenious system of ratios representing a
tuning
> that perfectly meets the same intention as a temperament usually
has.
> I wonder how far this is known, because I suppose someone somewhere
> must have thinked this out before me, although I know it's a
somewhat
> unconventional approach. Have any of you heard about it? The ratios
> are:
>
> 1/1, 18/17, 9/8, 19/16, 24/19, 4/3, 17/12*, 3/2, 19/12,
> 32/19, 16/9, 17/9, 2/1.
>
> *The tritone ratio 17/12 is replaceable by a 24/17 ratio.
>
> There is a lot of logical patterns inherent in this line, which may
> be more obvious if the fractions are notated with bigger numbers:
>
> 18/18, 18/17, 18/16, 19/16, 24/19, 16/12, 17/12, 18/12, 19/12,
32/19,
> 32/18, 17/9, 18/9
>
> and with the 24/17 tritone ratio:
>
> 18/18, 18/17, 18/16, 19/16, 24/19, 24/18, 24/17, 24/16, 19/12,
32/19,
> 16/9, 17/9, 18/9.
>
> Regarding the phytagorean intervals as a kind of framework, comments
> should be superfluous, but make particular attention to the
16-17-18-
> 19 series for the numerators in the mid-section in the upper line
> moving one step to left, becoming denominators and changing
direction
> in the line down under. It's also fascinating how the ratios can be
> considered in pairs, if the rightmost part of the upper row is mixed
> together with the leftmost downunder. The tritone ratio has to be
> ignored at first. In every second pair the denominator decreases by
> one from left to right, in the others, the numerator increases by
> one. The other part of every fraction in each pair is constant. The
> tritone ratio becomes a third "member" to one of the two pairs on
> each side, left or right, depending on which is chosen. These
> patterns are quite elegant, aren't they?
>
> There is also a kind of 3-part symmetry in this tuning which it has
> in common with the tuning of the traditional just intonated scale:
> from 1/1 to 3/2 with the square-root of 3/2 as an axis, from 4/3 to
> 2/1 using the other kind of tritone, with the square-root of 8/3 as
> an axis, and for the whole scale with the square-root of 2 as an
axis.
>
> The tuning is highly versatile. No ratio deviates more than 5 cents
> from its equivalent 12EDO tone. ...Any comments about it?
>
>
> ------------------------ Yahoo! Groups
Sponsor ---------------------~-->
> Take the Yahoo! Groups survey for a chance to win $1,000.
> Your opinion is very important to us!
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> --------------------------------------------------------------------
-~->
>
> You do not need web access to participate. You may subscribe
through
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>
>
> Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
>
>

🔗D.Stearns <STEARNS@CAPECOD.NET>

Though it should be obvious, I notice that I left the 1 out of the 19
in the 19/16. So here's what the lattice should've looked like:

19/12-----19/16
3/2-`.----9/8 `.
17/12---`.17/16 `.
4/3-------1/1-------3/2
`. 32/17`.---24/17
`.16/9----`.-4/3
32/19-----24/19

----- Original Message -----
From: "D.Stearns" <stearns@capecod.net>
To: <tuning@yahoogroups.com>
Sent: Saturday, May 18, 2002 3:12 PM
Subject: Re: [tuning] 2, 3, 17 and 19

> Hi there,
>
> Yes, the 12-tone, 2,3,17,19 prime set is one I've looked at
> before--here's what I got:
>
> 1/1, 17/16, 9/8, 19/16, 24/19, 4/3, (24/17-17/12), 3/2, 19/12,
32/19,
> 16/9, 32/17, 2/1
>
> Here's how it would lattice out from a 16:17:18:19 harmonic series
> segment:
>
>
> 19/12------9/16
> 3/2-`.----9/8 `.
> 17/12---`.17/16 `.
> 4/3-------1/1-------3/2
> `. 32/17`.---24/17
> `.16/9----`.-4/3
> 32/19-----24/19
>
>
> BTW, I didn't recognize your name, are you a new poster? If so,
> welcome aboard!
>
>
> take care,
>
> --Dan Stearns
>
>
>
> ----- Original Message -----
> From: "xmacmixmax" <knurgen@hotmail.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, May 18, 2002 6:05 AM
> Subject: [tuning] 2, 3, 17 and 19
>
>
> > Hello everyone!
> >
> > I have discovered an ingenious system of ratios representing a
> tuning
> > that perfectly meets the same intention as a temperament usually
> has.
> > I wonder how far this is known, because I suppose someone
somewhere
> > must have thinked this out before me, although I know it's a
> somewhat
> > unconventional approach. Have any of you heard about it? The
ratios
> > are:
> >
> > 1/1, 18/17, 9/8, 19/16, 24/19, 4/3, 17/12*, 3/2, 19/12,
> > 32/19, 16/9, 17/9, 2/1.
> >
> > *The tritone ratio 17/12 is replaceable by a 24/17 ratio.
> >
> > There is a lot of logical patterns inherent in this line, which
may
> > be more obvious if the fractions are notated with bigger numbers:
> >
> > 18/18, 18/17, 18/16, 19/16, 24/19, 16/12, 17/12, 18/12, 19/12,
> 32/19,
> > 32/18, 17/9, 18/9
> >
> > and with the 24/17 tritone ratio:
> >
> > 18/18, 18/17, 18/16, 19/16, 24/19, 24/18, 24/17, 24/16, 19/12,
> 32/19,
> > 16/9, 17/9, 18/9.
> >
> > Regarding the phytagorean intervals as a kind of framework,
comments
> > should be superfluous, but make particular attention to the
> 16-17-18-
> > 19 series for the numerators in the mid-section in the upper line
> > moving one step to left, becoming denominators and changing
> direction
> > in the line down under. It's also fascinating how the ratios can
be
> > considered in pairs, if the rightmost part of the upper row is
mixed
> > together with the leftmost downunder. The tritone ratio has to be
> > ignored at first. In every second pair the denominator decreases
by
> > one from left to right, in the others, the numerator increases by
> > one. The other part of every fraction in each pair is constant.
The
> > tritone ratio becomes a third "member" to one of the two pairs on
> > each side, left or right, depending on which is chosen. These
> > patterns are quite elegant, aren't they?
> >
> > There is also a kind of 3-part symmetry in this tuning which it
has
> > in common with the tuning of the traditional just intonated scale:
> > from 1/1 to 3/2 with the square-root of 3/2 as an axis, from 4/3
to
> > 2/1 using the other kind of tritone, with the square-root of 8/3
as
> > an axis, and for the whole scale with the square-root of 2 as an
> axis.
> >
> > The tuning is highly versatile. No ratio deviates more than 5
cents
> > from its equivalent 12EDO tone. ...Any comments about it?
> >
> >
> > ------------------------ Yahoo! Groups
> Sponsor ---------------------~-->
> > Take the Yahoo! Groups survey for a chance to win $1,000.
> > Your opinion is very important to us!
> > http://us.click.yahoo.com/NOFBfD/uAJEAA/Ey.GAA/RrLolB/TM
>
> --------------------------------------------------------------------
> -~->
> >
> > You do not need web access to participate. You may subscribe
> through
> > email. Send an empty email to one of these addresses:
> > tuning-subscribe@yahoogroups.com - join the tuning group.
> > tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning
> group.
> > tuning-nomail@yahoogroups.com - put your email message delivery
on
> hold for the tuning group.
> > tuning-digest@yahoogroups.com - change your subscription to
daily
> digest mode.
> > tuning-normal@yahoogroups.com - change your subscription to
> individual emails.
> > tuning-help@yahoogroups.com - receive general help information.
> >
> >
> > Your use of Yahoo! Groups is subject to
> http://docs.yahoo.com/info/terms/
> >
> >
>

🔗xmacmixmax <knurgen@hotmail.com>

Thanks for the replies I've got so far!

Yes, it's logical with two eligible ratios for the minor second and
the major seventh. They correspond to the two eligible tritone ratios
in respect of the 3-part symmetry that I mentioned. Using the 17/16
and 32/17 ratios may be regarded as more logically correct in one
way, in that it provides an even more coherent pattern. Well, you may
already have realized this, Dan.

It's probably wrong to put my variant in a similar lattice as your
one, so I think this is an appropriate one: (with some luck, it will
appear as intended)

19/12---19/16
3/2 /
17/9---17/12 /
16/9-----4/3-----1/1-----3/2-----9/8
/ 24/17---18/17
/ 4/3
32/19---24/19

BTW, Yes, I am a new poster. Thank you for your welcome!

Canute Greenson

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Though it should be obvious, I notice that I left the 1 out of the
19
> in the 19/16. So here's what the lattice should've looked like:
>
>
> 19/12-----19/16
> 3/2-`.----9/8 `.
> 17/12---`.17/16 `.
> 4/3-------1/1-------3/2
> `. 32/17`.---24/17
> `.16/9----`.-4/3
> 32/19-----24/19
>
>
>
> ----- Original Message -----
> From: "D.Stearns" <stearns@c...>
> To: <tuning@y...>
> Sent: Saturday, May 18, 2002 3:12 PM
> Subject: Re: [tuning] 2, 3, 17 and 19
>
>
> > Hi there,
> >
> > Yes, the 12-tone, 2,3,17,19 prime set is one I've looked at
> > before--here's what I got:
> >
> > 1/1, 17/16, 9/8, 19/16, 24/19, 4/3, (24/17-17/12), 3/2, 19/12,
> 32/19,
> > 16/9, 32/17, 2/1
> >
> > Here's how it would lattice out from a 16:17:18:19 harmonic series
> > segment:
> >
> >
> > 19/12------9/16
> > 3/2-`.----9/8 `.
> > 17/12---`.17/16 `.
> > 4/3-------1/1-------3/2
> > `. 32/17`.---24/17
> > `.16/9----`.-4/3
> > 32/19-----24/19
> >
> >
> > BTW, I didn't recognize your name, are you a new poster? If so,
> > welcome aboard!
> >
> >
> > take care,
> >
> > --Dan Stearns
> >
> >
> >
> > ----- Original Message -----
> > From: "xmacmixmax" <knurgen@h...>
> > To: <tuning@y...>
> > Sent: Saturday, May 18, 2002 6:05 AM
> > Subject: [tuning] 2, 3, 17 and 19
> >
> >
> > > Hello everyone!
> > >
> > > I have discovered an ingenious system of ratios representing a
> > tuning
> > > that perfectly meets the same intention as a temperament usually
> > has.
> > > I wonder how far this is known, because I suppose someone
> somewhere
> > > must have thinked this out before me, although I know it's a
> > somewhat
> > > unconventional approach. Have any of you heard about it? The
> ratios
> > > are:
> > >
> > > 1/1, 18/17, 9/8, 19/16, 24/19, 4/3, 17/12*, 3/2, 19/12,
> > > 32/19, 16/9, 17/9, 2/1.
> > >
> > > *The tritone ratio 17/12 is replaceable by a 24/17 ratio.
> > >
> > > There is a lot of logical patterns inherent in this line, which
> may
> > > be more obvious if the fractions are notated with bigger
numbers:
> > >
> > > 18/18, 18/17, 18/16, 19/16, 24/19, 16/12, 17/12, 18/12, 19/12,
> > 32/19,
> > > 32/18, 17/9, 18/9
> > >
> > > and with the 24/17 tritone ratio:
> > >
> > > 18/18, 18/17, 18/16, 19/16, 24/19, 24/18, 24/17, 24/16, 19/12,
> > 32/19,
> > > 16/9, 17/9, 18/9.
> > >
> > > Regarding the phytagorean intervals as a kind of framework,
> comments
> > > should be superfluous, but make particular attention to the
> > 16-17-18-
> > > 19 series for the numerators in the mid-section in the upper
line
> > > moving one step to left, becoming denominators and changing
> > direction
> > > in the line down under. It's also fascinating how the ratios
can
> be
> > > considered in pairs, if the rightmost part of the upper row is
> mixed
> > > together with the leftmost downunder. The tritone ratio has to
be
> > > ignored at first. In every second pair the denominator decreases
> by
> > > one from left to right, in the others, the numerator increases
by
> > > one. The other part of every fraction in each pair is constant.
> The
> > > tritone ratio becomes a third "member" to one of the two pairs
on
> > > each side, left or right, depending on which is chosen. These
> > > patterns are quite elegant, aren't they?
> > >
> > > There is also a kind of 3-part symmetry in this tuning which it
> has
> > > in common with the tuning of the traditional just intonated
scale:
> > > from 1/1 to 3/2 with the square-root of 3/2 as an axis, from 4/3
> to
> > > 2/1 using the other kind of tritone, with the square-root of 8/3
> as
> > > an axis, and for the whole scale with the square-root of 2 as an
> > axis.
> > >
> > > The tuning is highly versatile. No ratio deviates more than 5
> cents
> > > from its equivalent 12EDO tone. ...Any comments about it?
> > >
> > >
> > > ------------------------ Yahoo! Groups
> > Sponsor ---------------------~-->
> > > Take the Yahoo! Groups survey for a chance to win $1,000.
> > > Your opinion is very important to us!
> > > http://us.click.yahoo.com/NOFBfD/uAJEAA/Ey.GAA/RrLolB/TM
> >
> >
--------------------------------------------------------------------
> > -~->
> > >
> > > You do not need web access to participate. You may subscribe
> > through
> > > email. Send an empty email to one of these addresses:
> > > tuning-subscribe@y... - join the tuning group.
> > > tuning-unsubscribe@y... - unsubscribe from the tuning
> > group.
> > > tuning-nomail@y... - put your email message delivery
> on
> > hold for the tuning group.
> > > tuning-digest@y... - change your subscription to
> daily
> > digest mode.
> > > tuning-normal@y... - change your subscription to
> > individual emails.
> > > tuning-help@y... - receive general help information.
> > >
> > >
> > > Your use of Yahoo! Groups is subject to
> > http://docs.yahoo.com/info/terms/
> > >
> > >
> >

🔗emotionaljourney22 <paul@stretch-music.com>

🔗xmacmixmax <knurgen@hotmail.com>

🔗emotionaljourney22 <paul@stretch-music.com>

--- In tuning@y..., "xmacmixmax" <knurgen@h...> wrote:

> Thank you, Paul!
>
> Then I know a little bit more. I hope Joe will read it. I have
> searched somewhat for it among sites associated with him, but it's
> like looking for a needle in a haystack, even when I restrict the
> search.
>
>
>
> Canute Greenson

hi canute.

for unrelated reasons, i just decided to take a peek over at the
Making Microtonal Music list (which i'm not a member of for the time
being), and amazingly the answer popped right out at me in the first
message i clicked on. the message linked to this page by joe:

http://www.ixpres.com/interval/monzo/ganassi/ganassi.htm

it appears that renaissance, not medieval, would have been a better
description of this thinker's timeframe. perhaps there's another one
like this monz knows of who *is* medieval -- but i probably just got
it wrong.

other stuff: i had the pleasure last night to participate in a
recording session with a number of excellent musicians, including an
oud player schooled in traditional Ottoman music. during breaks, he
and the doumbek player (who is also in my band, Stretch) launched
into some intense duets, featuring the kaleidoscopically shifting
maqams of Turkish music. though i've heard this music before, having
it performed in front of me by (supposedly) my peers was eye-opening.
unabashedly microtonal music of great cultural depth is not only out
there, it's alive and well even here in the heart of the Great
Satan :)

anyway, the oud player is well-versed in the 53-tone (koma) theory
taught in Turkey, and we're planning to get together to discuss this
stuff in detail (instruments in hand, of course). since these topics
have come up before, i'll report back here with my findings. of
course, the theory does not bring nearly as much joy as listening to,
let alone playing, the music . . . but intellectual curiosity about
tunings and scales and modes does appear to infect musicians from all
corners, which is why it's nice this list exists.

finally, and off-topic: Stretch has finally received a copy of our 3-
somg demo CD, back from mastering in NYC. i feel that the recording
is of high quality, and while my playing is not as spirited as on the
mp3.com material, my "compositional" structures, and the roster of
musicians, have both been expanded. the net result is a more
listenable set showing a good deal more maturity, yet still plenty of
fun. anyone who's read this far may e-mail me their snail-mail
address, and i will send them a copy of this CD (i'll try to include
some impromptu studio outtakes, featuring both very ugly and very
beautiful moments, for all those who request those as well -- that
may take some extra time to put together).