Yahoo Tuning Groups Ultimate Backup tuning 17 limit scale

Dear Tunesters
i have prepared a 17 ish scale for experimentation for my next exploration.
i would like to share it with the list to get some critiques, criticisms and
suggestions.
i think it is a sound(ha) scale for exploration and might lead to some
interesting territory
David Beardsley and I have already copyrighted this scale so no monkey biz
:-)

1/1 17/16 425/384 153/128 51/40 1377/1024 17/12 119/80 51/32
17/10 85/48 119/64 2/1

please let me know what you think
cheers to all

Pat Pagano, Director

South East Just Intonation Society
http://indians.australians.com/meherbaba/
http://www.screwmusicforever.com/SHREESWIFT/

🔗jpehrson@rcn.com

--- In tuning@y..., "shreeswifty" <ppagano@b...> wrote:

/tuning/topicId_19513.html#19513

>
> David Beardsley and I have already copyrighted this scale so no
monkey biz
> :-)
>
> 1/1 17/16 425/384 153/128 51/40 1377/1024 17/12 119/80
51/32 17/10 85/48 119/64 2/1
>

Well... since my "buddy in wackiness" Shree (just joking Shree)
didn't say much about how this was created, I was wondering if it was
immediately obvious to somebody... anybody. Paul... all...?? Looks
like all the numerators are divisible by 3, that's what I see...
Ratios are gettin' a little large there... good for the RI set
folks... Hmmm?

________ _______ ______ _
Joseph Pehrson

The immediately above is only theory and more that possibly could be
very wrong...

🔗jpehrson@rcn.com

🔗MONZ@JUNO.COM

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_19513.html#19514

> --- In tuning@y..., "shreeswifty" <ppagano@b...> wrote:
>
> /tuning/topicId_19513.html#19513
>
> >
> > David Beardsley and I have already copyrighted this scale so
> > no monkey biz
> > :-)
> >
> > 1/1 17/16 425/384 153/128 51/40 1377/1024 17/12 119/80
> > 51/32 17/10 85/48 119/64 2/1
> >
>
> Well... since my "buddy in wackiness" Shree (just joking Shree)
> didn't say much about how this was created, I was wondering if
> it was immediately obvious to somebody... anybody. Paul...
> all...?? Looks like all the numerators are divisible by 3, that's
> what I see...
> Ratios are gettin' a little large there... good for the RI set
> folks... Hmmm?
>
> ________ _______ ______ _
> Joseph Pehrson
>
> The immediately above is only theory and more that possibly
> could be very wrong...

Sorry Joe, it *is* very wrong. :(

Only four of the numerators, and three of the denominators,
are divisible by 3.

(How did you overlook 17? Surely when you divided 17 by 3
you got a remainder....?)

Actually, the tie that binds this scale together is that
17 is a factor in all the numerators.

Here's the prime-factor matrix of the scale:

2 3 5 7 17

2/1 1 0 0 0 0
119/64 - 6 0 0 1 1
85/48 - 4 -1 1 0 1
17/10 - 1 0 -1 0 1
51/32 - 5 1 0 0 1
119/80 - 4 0 -1 1 1
17/12 - 2 -1 0 0 1
1377/1024 -10 4 0 0 1
51/40 - 3 1 -1 0 1
153/128 - 7 2 0 0 1
425/384 - 7 -1 2 0 1
17/16 - 4 0 0 0 1
1/1 0 0 0 0 0

I wanted to make a "triangular" lattice of this here, but don't
have the brain-power right now to figure out how to represent
the 17-axis.

If I have time (which is not likely), I'll create a "Monzo"
lattice of it and put it in the "files" section.

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

🔗ligonj@northstate.net

🔗jpehrson@rcn.com

--- In tuning@y..., ligonj@n... wrote:

/tuning/topicId_19513.html#19518

> --- In tuning@y..., "shreeswifty" <ppagano@b...> wrote:
> > David Beardsley and I have already copyrighted this scale so no
> monkey biz
>
> Shreeswifty,
>
> Hello!
>
> I didn't even know this was possible! Are you serious? Did you
(were
> you able to) actually copyright this scale?
>
>
> Thanks,
>
> Jacky Ligon

I think the Shree is "pulling your leg" a little bit... If one can't
copyright a TITLE, certainly one can't copyright a SCALE.

If so... somebody could, theoretically, copyright the C-major scale!
Talk about Bill Gates' hegemony!

_________ ______ ______ _
Joseph Pehrson

🔗ligonj@northstate.net

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., ligonj@n... wrote:
>
> /tuning/topicId_19513.html#19518
>
> > --- In tuning@y..., "shreeswifty" <ppagano@b...> wrote:
> > > David Beardsley and I have already copyrighted this scale so no
> > monkey biz
> >
> > Shreeswifty,
> >
> > Hello!
> >
> > I didn't even know this was possible! Are you serious? Did you
> (were
> > you able to) actually copyright this scale?
> >
> >
> > Thanks,
> >
> > Jacky Ligon
>
> I think the Shree is "pulling your leg" a little bit... If one
can't
> copyright a TITLE, certainly one can't copyright a SCALE.
>
> If so... somebody could, theoretically, copyright the C-major
scale!
> Talk about Bill Gates' hegemony!
>

He he! Had me going there for a minute!

: )

Thanks Joseph.

Jacky

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗Pat Pagano <ppagano@bellsouth.net>

>
>
> Here's the prime-factor matrix of the scale:
>
> 2 3 5 7 17
>
> 2/1 1 0 0 0 0
> 119/64 - 6 0 0 1 1
> 85/48 - 4 -1 1 0 1
> 17/10 - 1 0 -1 0 1
> 51/32 - 5 1 0 0 1
> 119/80 - 4 0 -1 1 1
> 17/12 - 2 -1 0 0 1
> 1377/1024 -10 4 0 0 1
> 51/40 - 3 1 -1 0 1
> 153/128 - 7 2 0 0 1
> 425/384 - 7 -1 2 0 1
> 17/16 - 4 0 0 0 1
> 1/1 0 0 0 0 0
>
>
>
> If I have time (which is not likely), I'll create a "Monzo"
> lattice of it and put it in the "files" section.

that would be nice Joe, thanks.

>
> -monz
> http://www.monz/org
> "All roads lead to n^0"
>
>
>
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🔗Pat Pagano <ppagano@bellsouth.net>

🔗jpehrson@rcn.com

🔗Pat Pagano <ppagano@bellsouth.net>

Damn your'e good Keenan
you've found the significator...
cheers

Dave Keenan wrote:

> --- In tuning@y..., "shreeswifty" <ppagano@b...> wrote:
> > 1/1 17/16 425/384 153/128 51/40 1377/1024 17/12 119/80
> 51/32
> > 17/10 85/48 119/64 2/1
> >
> > please let me know what you think
> > cheers to all
>
> Hee hee! Very clever. But don't you want 85/64 instead of 1377/1024,
> or was that just to throw us off the scent? I won't give it away
> "just" yet. Let others think about it for a bit, or listen to it. :-)
>
> Regards,
> -- Dave Keenan
>
> The above is wrong and might well be theory.
>
> You do not need web access to participate. You may subscribe through
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🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗D.Stearns <STEARNS@CAPECOD.NET>

Joe Monzo wrote,

<<I wanted to make a "triangular" lattice of this here, but don't have
the brain-power right now to figure out how to represent the
17-axis.>>

I use an n/d*360 method to plot (or fudge, as the case may often be)
^2 prime axis's on an ASCII triangular lattice. The idea being that
you always assume periodicity at 360 degrees, and you rotate a diamond
so as to be a tetrahedron.

As you can also double plot odd factors using this method, you could
then give Pat and Dave's scale in the usual -- albeit a bit cramped
here -- ASCII triangular way:

425/384
/
/
/
85/48
/ \
/ \ 119/64 1377/1024
/ \ ./ `. /
17/12---17/16----51/32-------153/128
\ 1/1X
\ 119/80
\ /.' `.\
17/10---51/40

--Dan Stearns

🔗D.Stearns <STEARNS@CAPECOD.NET>

🔗shreeswifty <ppagano@bellsouth.net>

Very cool
how about 31

Pat Pagano, Director
South East Just Intonation Society
http://indians.australians.com/meherbaba/
http://www.screwmusicforever.com/SHREESWIFT/
----- Original Message -----
From: D.Stearns <STEARNS@CAPECOD.NET>
To: <tuning@yahoogroups.com>
Sent: Wednesday, February 28, 2001 4:11 AM
Subject: Re: [tuning] Re: 17 limit scale

> BTW, noticing that the lattice I gave for Pat and David's scale makes
> 323/320 = 1/1, you could change the denominators to factors of 19
> thereby morphing the scale from 17 up to 19...
>
> Here's the same lattice/scale morphed into 19:
>
> 125/114
> /
> /
> /
> 100/57
> / \
> / \ 35/19 405/304
> / \ ./ `. /
> 80/57---20/19---30/19---45/19
> \ 1/1X
> \ 28/19
> \ /.' `.\
> 32/19---24/19
>
>
> --Dan Stearns
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
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emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>
>

🔗D.Stearns <STEARNS@CAPECOD.NET>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

Thanks for the puzzle Pat and Dave,

Here's my take on it. It repeats some things that others have found,
but with a different conclusion.

Take this quite sensible 7-limit scale containing the standard or
Ptolemaic JI major scale.

25/3
/ \
/ \
5/3---5/4--15/8
/ \ / \ / \
/ \ /7/4\ / \
4/3---1/1---3/2---9/8
\ / \ /
\ /7/5\ /
8/5---6/5

C#
/ \
/ \
A --- E --- B
/ \ / \ / \
/ \ / A#\ / \
F --- C --- G --- D
\ / \ /
\ / F#\ /
Ab----Eb

and for no apparent reason tune the 5/4 a comma sharp.

25/3
/
/
5/3 15/8
/ \ / \
/ \ 7/4 / \
4/3---1/1---3/2---9/8--- --81/64
\ / \ /
\ /7/5\ /
8/5---6/5

Then mistune the 15/8 by about 7 cents sharp. Call that mistuning a
255:256 (a 17-limit comma) so that 15/8 becomes 32/17 and transpose
the whole scale so that 32/17 becomes the new 1/1. Thus cleverly
disguising its 7-limit origins.

So, (here I go again :) it isn't really a 17-limit JI scale in any
meaningful sense because there is only the one poor lonely 17-limit
interval, the 16:17 from 32/17 up to 2/1 (or 17:32 from 1/1 up to
32/17). With no larger harmonic series context to make its 17-ness
apparent, the 32/17 is doomed to always sound like a mistuned 15/8.
Similarly the 81/64 is doomed to sound like a mistuned 5/4 except in
that bare 8:9 or 4:9.

Now I duck for cover.

But I'd love to hear what anyone thinks about that 19-limit scale I
posted earlier:

1/1 18/17 64/57 384/323 323/256 171/128 17/12 3/2 1216/765 323/192
57/32 17/9 2/1

Regards,
-- Dave Keenan

In theory, theory and practice are the same, but in practice they are
not.

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗jpehrson@rcn.com

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_19513.html#19568

> Thanks for the puzzle Pat and Dave,
>
> Here's my take on it. It repeats some things that others have
found,
> but with a different conclusion.
>
> Take this quite sensible 7-limit scale containing the standard or
> Ptolemaic JI major scale.
>
> 25/3
> / \
> / \
> 5/3---5/4--15/8
> / \ / \ / \
> / \ /7/4\ / \
> 4/3---1/1---3/2---9/8
> \ / \ /
> \ /7/5\ /
> 8/5---6/5
>
> C#
> / \
> / \
> A --- E --- B
> / \ / \ / \
> / \ / A#\ / \
> F --- C --- G --- D
> \ / \ /
> \ / F#\ /
> Ab----Eb
>
>
> and for no apparent reason tune the 5/4 a comma sharp.
>
> 25/3
> /
> /
> 5/3 15/8
> / \ / \
> / \ 7/4 / \
> 4/3---1/1---3/2---9/8--- --81/64
> \ / \ /
> \ /7/5\ /
> 8/5---6/5
>
> Then mistune the 15/8 by about 7 cents sharp. Call that mistuning a
> 255:256 (a 17-limit comma) so that 15/8 becomes 32/17 and transpose
> the whole scale so that 32/17 becomes the new 1/1. Thus cleverly
> disguising its 7-limit origins.
>
> So, (here I go again :) it isn't really a 17-limit JI scale in any
> meaningful sense because there is only the one poor lonely 17-limit
> interval, the 16:17 from 32/17 up to 2/1 (or 17:32 from 1/1 up to
> 32/17). With no larger harmonic series context to make its 17-ness
> apparent, the 32/17 is doomed to always sound like a mistuned 15/8.
> Similarly the 81/64 is doomed to sound like a mistuned 5/4 except
in
> that bare 8:9 or 4:9.
>

Swift Shree, and Dave the Beardsley, what say ye to Dave Keenan's
comments about your tuning triumph??

_________ _____ ______ ___
Joseph Pehrson

🔗jpehrson@rcn.com

🔗D.Stearns <STEARNS@CAPECOD.NET>

Joseph Pehrson wrote,

<<Swift Shree, and Dave the Beardsley, what say ye to Dave Keenan's
comments about your tuning triumph??>>

While not my tuning = not my "fight", what the heek, I'll hazard an
comment of my own anyway.

What Dave K. says is true, or rather I agree with his points. However,
the two tunings are not the same... and this seemingly simple and
innocuous point (given the "evidence" of their nearness to each other)
can be very relevant in an actual musical context. I myself have had
experiences where subcommatic differences that I thought were an
utterly moot distinction were intolerable once introduced into a given
piece of music in a theoretically "problematic" tuning that I was
already very familiar with.

This is a symbiotic type distinction that's hard, if not impossible,
to quantify or adequately predict... however, Pat asked for a critique
of the tuning as a *tuning* and not as an integral and highly
sensitive to change component of a piece of music... and it is in that
context that Dave K. spoke his bit.

But, things aren't always as cut and dried as they appear, and all the
more so once music (gasp) is actually introduced into the fray.

--Dan Stearns

🔗shreeswifty <ppagano@bellsouth.net>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗MONZ@JUNO.COM

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗D.Stearns <STEARNS@CAPECOD.NET>

Dave Keenan wrote,

<<Basically, calling it a 17-limit scale is a joke. It's a (mode of a)
7 limit scale with one note (the 1/1) mistuned by 7 cents.>>

I doubt Pat or Dave B. thought it was or had "a joke" in mind when
they used or posted it.

How about this: Perhaps you could better show some of why you think it
is not the best thing to call "a 17-limit scale" by giving a counter
example of what you think "a 17-limit scale" should in some sense
ideally be?

Perhaps you don't even think seventeeness <sic> is valid, or
palpable... ?

Whatever the case may be, I'm just trying to steer this thread into a
potentially better or more productive place... because simply nay
saying somebody's scale accomplishes, well, what?

My guess would be that that "what" is -- and I'm assuming something as
you might see it here, which is usually a pretty bad idea, so feel
free to blast me big if I'm wrong or misrepresenting your views --
dispelling shaky and potentially misleading connotations. But I think
a positive 17 counterexample from you, rather than just the 'it's a
joke because __________' example, would enrich the whole deal a bit
more. Or at least make the theorists v. musician divide not quite as
curt and counterproductive as it can often seem to be here at the
tuning list.

I know it is probably too tough to say what you feel is right and pull
the punch too, but a lot of times musicians just ain't too concerned
with the minutia of the lingo and its precise meanings. But it usually
isn't just a bunch of bullshit either... it's usually some honest
coming together of interests and (importantly) actual doing... in this
case musical doing.

I think 'the theorists and 'the musicians' simply don't even need each
other! In fact, each steps all over the other's toes and basically
only makes a nuisance of itself for the other add infinitum!

But I guess I also happen to think that they *can* indeed learn from
each other as well given the proper alignment of the stars and the
pull of the tide and, well, whatever else occasionally leads to this
odd truce and almost neighborly cohabitation.

--Dan Stearns

🔗jpehrson@rcn.com

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

/tuning/topicId_19513.html#19888

> Dave Keenan wrote,
>
> <<Basically, calling it a 17-limit scale is a joke. It's a (mode of
a)7 limit scale with one note (the 1/1) mistuned by 7 cents.>>
>
> I doubt Pat or Dave B. thought it was or had "a joke" in mind when
> they used or posted it.
>
> How about this: Perhaps you could better show some of why you think
it is not the best thing to call "a 17-limit scale" by giving a
counter example of what you think "a 17-limit scale" should in some
sense ideally be?
>
> Perhaps you don't even think seventeeness <sic> is valid, or
> palpable... ?
>
> Whatever the case may be, I'm just trying to steer this thread into
a potentially better or more productive place... because simply nay
> saying somebody's scale accomplishes, well, what?
>

One would think that I would be smart enough to stay out of the
"fray" on this one, but I'm not, so here goes:

Even more importantly is the fact that Dave Keenan stated that
certain pitches in Pat Pagano's and David Beardsley's scale were
"out of tune." He stated that basically they would be perceived as
DIFFERENT pitches than Pat and David intended, only "mistuned."

That would be a more important point to "refute" than the "17-ness"
business...

In fact, it would be quite interesting to hear/learn more about it...

By the way, I think it is quite reasonable that some of the
theoretically minded here "trash and thrash" certain tuning efforts...

I had what I thought was a great 19-note just scale until Paul Erlich
showed me that it looked like "Beepy the Robot..." I trashed it
since...

>
> I think 'the theorists and 'the musicians' simply don't even need
each other! In fact, each steps all over the other's toes and
basically only makes a nuisance of itself for the other add infinitum!
>

I don't know, Dan... You must be in a strange mood today... I know
SO many musicians who have profited from studying theory and reading
theoreticians. Most of the time one goes into such studies "kicking
and screaming" but many times to good result...

Think "counterpoint" for instance...

_______ _____ ______ ____
Joseph Pehrson

🔗D.Stearns <STEARNS@CAPECOD.NET>

Joseph Pehrson wrote,

<<Even more importantly is the fact that Dave Keenan stated that
certain pitches in Pat Pagano's and David Beardsley's scale were "out
of tune." He stated that basically they would be perceived as
DIFFERENT pitches than Pat and David intended, only "mistuned." That
would be a more important point to "refute" than the "17-ness"
business...>>

As I said before, I've had actual pieces (fast, busy, dense pieces)
where the tuning was sensitive (in a negative way) to tiny subcommatic
changes that would've made the tuning more theoretically sound... this
would only be apparent in the context of that piece of music...
careful A B type comparative listening outside of the context of that
music would've led to completely different answers... and as far as
*that* tuning in *that* piece goes, they would be useless answers as
well.

At what point so-and-so is an "out of tune" so-and-so is not an easily
and so cavalierly addressed problem if one takes (gasp) music into
consideration.

I'm very much interested in theoretical efforts to make these types of
distinctions. But I'm interested in them theoretically, and not so
much musically.

<<I had what I thought was a great 19-note just scale until Paul
Erlich showed me that it looked like "Beepy the Robot..." I trashed
it since...>>

Suppose it had been a scale that you found by ear, and this scale
looked even worse than Beepy... would you have so quickly trashed it
'cause so-and-so showed you that it is a really 'bad' scale? (Please,
oh please say no!)

<<I don't know, Dan... You must be in a strange mood today... I know
SO many musicians who have profited from studying theory and reading
theoreticians. Most of the time one goes into such studies "kicking
and screaming" but many times to good result...>>

Sure, of course. It was a (mostly) tongue in cheek lead into my little
"neighborly" end point.

<<Think "counterpoint" for instance...>>

Ah, counterpoint schmounterpoint! Only kidding (sort of).

--Dan Stearns

🔗jpehrson@rcn.com

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

/tuning/topicId_19513.html#19893

> Joseph Pehrson wrote,
>
> <<Even more importantly is the fact that Dave Keenan stated that
> certain pitches in Pat Pagano's and David Beardsley's scale were
"out of tune." He stated that basically they would be perceived as
> DIFFERENT pitches than Pat and David intended, only "mistuned." That
> would be a more important point to "refute" than the "17-ness"
> business...>>
>
> As I said before, I've had actual pieces (fast, busy, dense pieces)
> where the tuning was sensitive (in a negative way) to tiny
subcommatic changes that would've made the tuning more theoretically
sound... this would only be apparent in the context of that piece of
music... careful A B type comparative listening outside of the
context of that music would've led to completely different answers...
and as far as *that* tuning in *that* piece goes, they would be
useless answers as well.
>
> At what point so-and-so is an "out of tune" so-and-so is not an
easily and so cavalierly addressed problem if one takes (gasp) music
into consideration.

Hi Dan!

So then, what's the point of studying "well constructed" scales, like
the MOS patterns that Erv Wilson and Margo Schulter have outlined for
us??

If "everything's the same" then there would be no point in such
studies at all, would there... (??)

> I'm very much interested in theoretical efforts to make these types
of distinctions. But I'm interested in them theoretically, and not so
> much musically.
>

The fact that some of the more symmetrical scales, like the Schulter
example explained, were some of the favorites and most frequently used
in history, can't be mere accident...

Are you certain you're not just advocating an "anything goes"
philosophy??

>
> <<Think "counterpoint" for instance...>>
>
> Ah, counterpoint schmounterpoint! Only kidding (sort of).
>
> --Dan Stearns

To each his own...

________ _____ _____ ____
Joseph Pehrson

🔗D.Stearns <STEARNS@CAPECOD.NET>

🔗MONZ@JUNO.COM

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_19513.html#19828

> --- In tuning@y..., MONZ@J... wrote:
> Hi Monz,
>
> Welcome back.

Thanks. I'm not really totally "back"... just had a little more
time than usual to peek at the Tuning List postings. I expect
to be popping in only occasionally at least until after my
lecture at Microfest next month.

>
> You seem to have missed one of my posts on the topic.
>
> /tuning/topicId_19513.html#19568
> and its errata
> /tuning/topicId_19513.html#19568

Nope - I saw them. I made the webpage in a hurry, and I'm
sorry that I forgot to include your posts. I'll update the
page as soon as I can.

>
> Basically, calling it a 17-limit scale is a joke. It's a
> mode of a) 7 limit scale with one note (the 1/1) mistuned
> by 7 cents.

Well... as evidenced by Dan Stearns's subsequent comments,
I'm not so sure I'd call that a "joke". But I do understand
your point that a measly little 7-cent mistuning may not
be enough to qualify this scale as exhibiting "17-ness" in
any substantial way.

But then again, that measly little 7-cent mistuning *may*
indeed be enough to differentiate this tuning from the regular
7-limit one. It (as always) depends on musical context.
Unfortunately I have not yet found the time to hear the pieces
based on this tuning.

The point that my lattice diagram emphasizes so strongly is
the same one you made: that this tuning must be considered to
be a modal shift of the one portrayed in my "simplified" lattice
(the third one on my webpage).

http://www.ixpres.com/interval/monzo/pagano-beardsley/7-17-limit.htm

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

🔗shreeswifty <ppagano@bellsouth.net>

Ummm
i don't know what you guys are arguing about really.
Dan's appraisal of the scale is succinct and honest but a bit off base.IMHO
i have used the scale for pieces for about a week or so and it sounds very
nice.
Some of the things you may say about the scale may be true if you look at it
from certain perspectives
but i did in fact post the scale for people to critique and comment and
maybe even make some music
with it.
For Dan it seems a scale he would not use--that's fine.
Joe may try it --who knows
All the ratios are multiples of 17/16 ---that was the brain teaser
none of you geniuses got it.
smoochies

Pat Pagano, Director
South East Just Intonation Society
http://indians.australians.com/meherbaba/
http://www.screwmusicforever.com/SHREESWIFT/

🔗David Beardsley <xouoxno@virtulink.com>

Dan wrote:

> Dave Keenan wrote,
>
> <<Basically, calling it a 17-limit scale is a joke. It's a (mode of a)
> 7 limit scale with one note (the 1/1) mistuned by 7 cents.>>

There's no misstuning. The only misstuning is where Dave changed
the tuning into something else, at which point it isn't Pat's
tuning anymore - it's now Dave's tuning..

> I doubt Pat or Dave B. thought it was or had "a joke" in mind when
> they used or posted it.

No joke.

> How about this: Perhaps you could better show some of why you think it
> is not the best thing to call "a 17-limit scale" by giving a counter
> example of what you think "a 17-limit scale" should in some sense
> ideally be?

I'd like to see that too. Thanks Dan.

--
* D a v i d B e a r d s l e y
* 49/32 R a d i o "all microtonal, all the time"
* http://www.virtulink.com/immp/lookhere.htm
* http://mp3.com/davidbeardsley

🔗David Beardsley <xouoxno@virtulink.com>

"D.Stearns" wrote:

> At what point so-and-so is an "out of tune" so-and-so is not an easily
> and so cavalierly addressed problem if one takes (gasp) music into
> consideration.

Good point. One of the things I like about microtonality is how,
as a composer, I have a broader pallet of colors (pitches) available
to me for my music. Having someone (DK) on the Tuning List (OF
ALL PLACES!!!) that a 17-limit interval is out of tune is just
the silliest SH*T I've heard in ages.

--
* D a v i d B e a r d s l e y
* 49/32 R a d i o "all microtonal, all the time"
* http://www.virtulink.com/immp/lookhere.htm
* http://mp3.com/davidbeardsley

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Dave Keenan wrote,
>
> <<Basically, calling it a 17-limit scale is a joke. It's a (mode of
a)
> 7 limit scale with one note (the 1/1) mistuned by 7 cents.>>
>
> I doubt Pat or Dave B. thought it was or had "a joke" in mind when
> they used or posted it.

Aw, C'mon Dan. You know what a kidder Pat is. Don't you remember the
stuff about having copyrighted the scale. And Pat's response to my
"Hee hee, very clever" post (although maybe someone can tell me what a
"significator" is). He's probably laughing his head off that we are
having this argument.

But hey, if I've got it wrong, and this wasn't intended as a joke or
hoax, then I offer my sincere apologies. I have been extremely rude.

> How about this: Perhaps you could better show some of why you think
it
> is not the best thing to call "a 17-limit scale" by giving a counter
> example of what you think "a 17-limit scale" should in some sense
> ideally be?

Ok. See below.

> Perhaps you don't even think seventeeness <sic> is valid, or
> palpable... ?

Oh dear. Whether anyone can recognise 17-ness _as_such_, I don't know.
But you should know that I am quite convinced that ratios of 17 can be
just, in a large enough otonal context. I've stated before my
understanding that barbershop quartets can lock in on a 10:12:14:17
diminished seventh chord.

The easiest-to-generate examples of true 17-limit just scales are
probably harmonic series segments. Here's a 12-tone octave-based
17-prime-limit one: 14:15:16:17:18:20:21:22:24:25:26:27:28. If we mean
17-odd-limit, we can only do 10 tones 9:10:11:12:13:14:15:16:17:18.

We could do a dekany or higher CPS with 17 as a factor.

But what you really want to know is what I would consider a
_borderline_ 17-limit just scale. I like Monzo's idea of calling
something a 7-17-limit scale, but still don't think that applies to
Pat and Dave's scale. So what would be a borderline 7-17-limit just
scale?

Any scale that contained a single barbershop diminished seventh with
all other notes connected to it directly or indirectly by 7-limit
intervals, would do. Can anyone tell me if there are any triads in
which a 17 can be tuned by ear. Maybe some with equal difference tones
as per Kraig Grady's criteria e.g. 9:13:17, 11:14:17, 13:15:17. If so,
we could hang a scale off one or more of these and call it 17-limit
just.

Does anyone claim to be able to tune a 17-limit dyad by listening to
beats? Because that's what Pat and Dave's scale has; a single bare
17-limit dyad. Invertible and octave extendible of course, but never
any more otonal than a dyad.

-- Dave Keenan

In case I forget to write it, you can just assume that all of my posts
end with: The above is only theory and might well be wrong.

🔗shreeswifty <ppagano@bellsouth.net>

🔗David Beardsley <xouoxno@virtulink.com>

David Beardsley wrote:

> One of the things I like about microtonality is how,
> as a composer, I have a broader pallet of colors (pitches) available
> to me for my music. Having someone (DK) on the Tuning List (OF
> ALL PLACES!!!) that a 17-limit interval is out of tune is just

This should have read:

suggest that a 17-limit interval is out of tune is just

now I'm getting to be like Paul...

--
* D a v i d B e a r d s l e y
* 49/32 R a d i o "all microtonal, all the time"
* http://www.virtulink.com/immp/lookhere.htm
* http://mp3.com/davidbeardsley

🔗jpehrson@rcn.com

--- In tuning@y..., "shreeswifty" <ppagano@b...> wrote:

/tuning/topicId_19513.html#19903

> but i did in fact post the scale for people to critique and comment
and maybe even make some music
> with it.
> For Dan it seems a scale he would not use--that's fine.
> Joe may try it --who knows

Yes, indeed, I have been trying it. Actually, since it is "somewhat
in the ballpark" of quasi 12-equal it turns out to be quite
interesting for Medieval and Renaissance music... I think it is all
the various sized thirds... which makes it particularly "active..."

Currently I have been using it to play items from the "Fitzwilliam
Virginal Book" with a harpsichord patch.

William Byrd's "Jhon come kisse me now" works rather well..

And, from another codex, best of all was "Like a Virgin." Superb!

________ ______ _____
Joseph Pehrson

🔗shreeswifty <ppagano@bellsouth.net>

I must admit i tend to use 12 just ...12 just relationships to the duple @
first
then proceed to pollenate passing tones in as Beardsley may as well in his
power dive swoops on the lapsteel
cheers

Pat Pagano, Director
South East Just Intonation Society
http://indians.australians.com/meherbaba/
http://www.screwmusicforever.com/SHREESWIFT/
----- Original Message -----
From: <jpehrson@rcn.com>
To: <tuning@yahoogroups.com>
Sent: Wednesday, March 07, 2001 9:18 PM
Subject: [tuning] Re: 17 limit scale

> --- In tuning@y..., "shreeswifty" <ppagano@b...> wrote:
>
> /tuning/topicId_19513.html#19903
>
>
> > but i did in fact post the scale for people to critique and comment
> and maybe even make some music
> > with it.
> > For Dan it seems a scale he would not use--that's fine.
> > Joe may try it --who knows
>
> Yes, indeed, I have been trying it. Actually, since it is "somewhat
> in the ballpark" of quasi 12-equal it turns out to be quite
> interesting for Medieval and Renaissance music... I think it is all
> the various sized thirds... which makes it particularly "active..."
>
> Currently I have been using it to play items from the "Fitzwilliam
> Virginal Book" with a harpsichord patch.
>
> William Byrd's "Jhon come kisse me now" works rather well..
>
> And, from another codex, best of all was "Like a Virgin." Superb!
>
> ________ ______ _____
> Joseph Pehrson
>
>
>
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
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>
>
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>
>
>

🔗D.Stearns <STEARNS@CAPECOD.NET>

Dave Keenan wrote,

<<But hey, if I've got it wrong, and this wasn't intended as a joke or
hoax, then I offer my sincere apologies. I have been extremely rude.>>

No, unless I've lost all sense of what's what, always a possibility,
it was definitely not a joke or a hoax! Just a scale Pat posted as
something that he and Dave B. had used. But I thought you knew this,
so "joke" here had an entirely different slant... perhaps a bit of a
misunderstanding all the way around then?

Anyway, glad to see your examples, thanks... and I'll see if I can't
dig up some of the 17 based 9-tone scales I tried when I was looking
at Enrique Ubieta's bimodal chord. I also remember trying some
polychords where the 17 was a flat nine. I'll see if I can't find some
of these as well.

--Dan Stearns

🔗Graham Breed <graham@microtonal.co.uk>

🔗D.Stearns <STEARNS@CAPECOD.NET>

Pat Pagano wrote,

<<Dan's appraisal of the scale is succinct and honest but a bit off
base. [SNIP] For Dan it seems a scale he would not use-->>

Hmm, I think you might be confusing me and Dave Keenan? All I really
did was make an ASCII lattice for it:

425/384
/
/
/
85/48
/ \
/ \ 119/64 1377/1024
/ \ ./ `. /
17/12---17/16---51/32--153/128
\ 1/1X /
\ 119/80 /
\ /.' `.\ /
17/10---51/40

And 'defend' it and its kind a bit.

<<All the ratios are multiples of 17/16 ---that was the brain teaser>>

How so? (How are they "multiples of 17/16" that is.)

--Dan Stearns

🔗shreeswifty <ppagano@bellsouth.net>

Whooops
sorry Dan
yes i meant Dave Keenan ,,,
the lattices were/are very cool

all the scale memebers are some traditional ratio muliplied by the 17/16
example 17/16*9/8 ==153/128 etc.....

remember folks that the scale
and yes even the term "seventeeness" is intellectual property of Pat Pagano
& David Bearsdley and violators will be dealt with quickly.

cheers

Pat Pagano, Director
South East Just Intonation Society
http://indians.australians.com/meherbaba/
http://www.screwmusicforever.com/SHREESWIFT/
----- Original Message -----
From: D.Stearns <STEARNS@CAPECOD.NET>
To: <tuning@yahoogroups.com>
Sent: Thursday, March 08, 2001 12:27 AM
Subject: [tuning] Re: 17 limit scale

> Pat Pagano wrote,
>
> <<Dan's appraisal of the scale is succinct and honest but a bit off
> base. [SNIP] For Dan it seems a scale he would not use-->>
>
> Hmm, I think you might be confusing me and Dave Keenan? All I really
> did was make an ASCII lattice for it:
>
> 425/384
> /
> /
> /
> 85/48
> / \
> / \ 119/64 1377/1024
> / \ ./ `. /
> 17/12---17/16---51/32--153/128
> \ 1/1X /
> \ 119/80 /
> \ /.' `.\ /
> 17/10---51/40
>
> And 'defend' it and its kind a bit.
>
>
> <<All the ratios are multiples of 17/16 ---that was the brain teaser>>
>
> How so? (How are they "multiples of 17/16" that is.)
>
> --Dan Stearns
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
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>
>
>

🔗ligonj@northstate.net

🔗jpehrson@rcn.com

--- In tuning@y..., "Graham Breed" <graham@m...> wrote:

> I must have missed that one. When did anybody say a 17-limit
interval was out of tune?

Hello, Graham... I believe the following is the correct post...

/tuning/topicId_19513.html#19568

I was actually hoping for a bit more "controversy" and "in-depth"
discussion of this scale and opinions...

But, it was rather tame... (read "lame")

With Paul gone, we can't even seem to get into good arguments any
more... :) :(

(I'm sure you'll "help out" again sometime... :) )

best,
_________ ______ ______ _____
Joseph Pehrson

🔗shreeswifty <ppagano@bellsouth.net>

Your'e a gem Jacky

Pat Pagano, Director
South East Just Intonation Society
http://indians.australians.com/meherbaba/
http://www.screwmusicforever.com/SHREESWIFT/
----- Original Message -----
From: <ligonj@northstate.net>
To: <tuning@yahoogroups.com>
Sent: Thursday, March 08, 2001 9:16 AM
Subject: [tuning] Re: 17 limit scale

> --- In tuning@y..., "shreeswifty" <ppagano@b...> wrote:
> > remember folks that the scale
> > and yes even the term "seventeeness" is intellectual property of
> Pat Pagano
> > & David Bearsdley and violators will be dealt with quickly.
> >
> > cheers
>
>
> Dear Pat and David,
>
> I thought I better get busy at the Library of Congress, since you
> guys are laying claim to allot of prime territory, so I have got a
> copyright on all prime ratios up to 1,213.
>
> Since I wish to keep my knee-caps in tact, I will avoid using ratios
> of 7 and 17.
>
> JL
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
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>
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>
>
>

🔗jpehrson@rcn.com

🔗ligonj@northstate.net

--- In tuning@y..., jpehrson@r... wrote:
> With Paul gone, we can't even seem to get into good arguments any
> more... :) :(

Is there anything left that we haven't argued to death?

Looks like a good time for a revival of Prime Series Theory!

Didn't you think that was a good spin on the Primes issue? Man, I got
third degree burns from that exchange - plum tanned my old hide.

Yes! This *IS* the answer! We needn't go another day without flames!

Let me see - hmmm, well I stopped at 6 digit primes....

}: )

🔗shreeswifty <ppagano@bellsouth.net>

Um we have a licensing agreement with Tiger Beat, Joe.
Pat Pagano, Director
South East Just Intonation Society
http://indians.australians.com/meherbaba/
http://www.screwmusicforever.com/SHREESWIFT/
----- Original Message -----
From: <jpehrson@rcn.com>
To: <tuning@yahoogroups.com>
Sent: Thursday, March 08, 2001 9:42 AM
Subject: [tuning] Re: 17 limit scale

> --- In tuning@y..., "shreeswifty" <ppagano@b...> wrote:
>
> /tuning/topicId_19513.html#19928
>
> >
> > and yes even the term "seventeeness" is intellectual property of
> Pat
> Pagano & David Bearsdley and violators will be dealt with quickly.
> >
> > cheers
> >
>
> We must IMMEDIATELY appraise the "teen magazine" people of this
> important fact!
>
> _________ _____ ______ ____
> Joseph Pehrson
>
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
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>
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>
>
>

🔗Afmmjr@aol.com

🔗jpehrson@rcn.com

--- In tuning@y..., Afmmjr@a... wrote:

/tuning/topicId_19513.html#19937

> Pat, since I used the term "seventeenness" before you have on this
list, I am considering bringing charges against you for falsely
claiming originality on this term.
>
> Joseph, am I being tough enough?
>

Yeah, man! Go to it New Yaaaaakaaaa!

Oh... buy the way, it is true that I heard Johnny's TRESPASS in the
original 17-limit scale about, I think 5 years ago...

Surely, Johnny isn't "Trespassing" by performing his "Trespass??"

> As for Paul Erlich, I got my angst released in a telephone call.
Sometimes, the telephone is the only way to go for better
communication.
>
> Johnny Reinhard

True, but we didn't all get to participate in the "fun!"

Best,

Joseph

P.S. People on this list know I'm half-kidding. I *DO* like
"vigorous" debate, though... That's the term Paul used... (I think
people know by now that I was a "Paul student" despite our
differences
in ages...!)

_________ ______ _____ ____
Joseph Pehrson

🔗Afmmjr@aol.com

🔗jpehrson@rcn.com

--- In tuning@y..., Afmmjr@a... wrote:

/tuning/topicId_19513.html#19939

> In a message dated 3/8/01 10:50:17 AM Eastern Standard Time,
jpehrson@r... writes:
>
> > Oh... buy the way, it is true that I heard Johnny's TRESPASS in
the original 17-limit scale about, I think 5 years ago...

>
> Joseph, "harmonic 17" which has a 17 multiple in each of it's
ratios, is NOT "17 limit." Let us please be clear about it. There
is a different quality to it, a different character,

Gotcha... thanks!

>and there is no 12-tET "lookalike" syndrome to it (alluded to by
Kraig for 17-limit.)
>

It is true... I was actually even playing "William Byrd" on it!

_________ _____ ____ ___
Joseph Pehrson

🔗David Beardsley <xouoxno@virtulink.com>

🔗Afmmjr@aol.com

🔗jpehrson@rcn.com

--- In tuning@y..., Afmmjr@a... wrote:

/tuning/topicId_19513.html#19945

> Perhaps. David B., you could check the discussions on seventeeness
and "harmonic 17" in Message 339 on 10 Aug 1998. The limit in JI is
based on the powerful resonance of the first 5 harmonics. "Harmonic
17" has a different etching. Paul Hahn had discussed this on the
list.
>
> 1/1
> 18/17
> 17/16
> 34/31
> 19/17
> 17/15
> 20/17
> 17/14
> 22/17
> 17/13
> 24/17
> 26/17
> 17/11
> 28/17
> 34/20
> 62/34
> 34/17
>
>
> Johnny Reinhard

Hi Johnny!

Of course, this is not message 339 of THIS archive... This present
archive began with Message #1 on December 28, 1998!

You must mean the Mills College Archives. Many of us don't have
access to that... although we would like to. It got "lost" in the
transition to egroups...
_______ ______ _____ ____
Joseph Pehrson

🔗David Beardsley <xouoxno@virtulink.com>

🔗MONZ@JUNO.COM

--- In tuning@y..., "shreeswifty" <ppagano@b...> wrote:

/tuning/topicId_19513.html#19903

> All the ratios are multiples of 17/16 ---that was the brain teaser
> none of you geniuses got it.

When I wrote this:

/tuning/topicId_19513.html#19517

> Here's the prime-factor matrix of the scale:
>
>
> 2 3 5 7 17
>
> 2/1 1 0 0 0 0
> 119/64 - 6 0 0 1 1
> 85/48 - 4 -1 1 0 1
> 17/10 - 1 0 -1 0 1
> 51/32 - 5 1 0 0 1
> 119/80 - 4 0 -1 1 1
> 17/12 - 2 -1 0 0 1
> 1377/1024 -10 4 0 0 1
> 51/40 - 3 1 -1 0 1
> 153/128 - 7 2 0 0 1
> 425/384 - 7 -1 2 0 1
> 17/16 - 4 0 0 0 1
> 1/1 0 0 0 0 0
>

I was saying the same thing.

Dan Stearns and Dave Keenan both recognized this also.

(And yes, Pat, it does look like a cool scale. If I ever
have time to compose again, I just may try it out...)

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

🔗shreeswifty <ppagano@bellsouth.net>

Haha
got me there Mr. Reinhard.
i think you can file for a late registration of the copyright.
But since it has been more than 5 years you can forget about the punitive damages :-)
cheers to all

I am so glad you are all having fun with the Pagano-Beardsley scale

p.s.s i have this lawyer aquaintance downtown......

Pat Pagano, Director
South East Just Intonation Society
http://indians.australians.com/meherbaba/
http://www.screwmusicforever.com/SHREESWIFT/
----- Original Message -----
From: Afmmjr@aol.com
To: tuning@yahoogroups.com
Sent: Thursday, March 08, 2001 10:39 AM
Subject: Re: [tuning] Re: 17 limit scale

Pat, since I used the term "seventeenness" before you have on this list, I am
considering bringing charges against you for falsely claiming originality on
this term.

Joseph, am I being tough enough?

As for Paul Erlich, I got my angst released in a telephone call. Sometimes,
the telephone is the only way to go for better communication.

Johnny Reinhard
Yahoo! Groups Sponsor

You do not need web access to participate. You may subscribe through
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🔗D.Stearns <STEARNS@CAPECOD.NET>

I wrote,

<<glad to see your examples, thanks... and I'll see if I can't dig up
some of the 17 based 9-tone scales I tried when I was looking at
Enrique Ubieta's bimodal chord. I also remember trying some polychords
where the 17 was a flat nine. I'll see if I can't find some of these
as well.>>

Here's a couple of the types of seventeen examples that I was thinking
of.

The polychords I used were usually ones where you could space the
triads so that there was no shared tone, like an eleven flat nine
chord for instance if you consider it to be a combination of a major
and a minor triad rather than a dominant seventh and a minor triad. So
by using the 17th harmonic as flat nine in this chord you can exploit
both the 256/255 and the 85/84 to get an 11th close to an 8/3, and a
flat seventh close to a 7/4. Here's a C11b9:

85/48---85/64
\ 5/4
\ / \
\ / \
17/16 \
1/1-----3/2

I remember looking at a bunch of symmetrically designed 9-tone scales,
and one of those was based on a 1/(34:29:27) series segment
interpretation of Ubieta's bimodal chord.

1/1 29/27 34/29 34/27 783/578 1156/783 27/17 29/17 54/29 2/1

This RI scale was theoretically interesting because it turned out to
be a neat little pseudo "well-tempered" interpretation of 9-tET:

0 124 275 399 526 674 801 925 1076 1200
0 151 275 402 550 677 801 952 1076 1200
0 124 251 399 526 650 801 925 1049 1200
0 127 275 402 526 677 801 925 1076 1200
0 148 275 399 550 674 798 949 1073 1200
0 127 251 402 526 650 801 925 1052 1200
0 124 275 399 523 674 798 925 1073 1200
0 151 275 399 550 674 801 949 1076 1200
0 124 248 399 523 650 798 925 1049 1200
0 124 275 399 526 674 801 925 1076 1200

One of the other seventeen things I remember trying and being happy
with back then was this 1/(20:17:16) 9-tone scale:

1/1 17/16 20/17 5/4 34/25 25/17 8/5 17/10 32/17 2/1

--Dan Stearns

🔗MONZ@JUNO.COM

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_19513.html#19938

> P.S. People on this list know I'm half-kidding. I *DO* like
> "vigorous" debate, though... That's the term Paul used... (I think
> people know by now that I was a "Paul student" despite our
> differences in ages...!)

Wasn't practically everyone on this list a "Paul student"?

(I know I sure was!... and that was *after* I came to the
conclusion that I knew more about tuning theory than anyone else...)

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

🔗MONZ@JUNO.COM

--- In tuning@y..., David Beardsley <xouoxno@v...> wrote:

/tuning/topicId_19513.html#19947

> Afmmjr@a... wrote:
> >
> > Perhaps. David B., you could check the discussions on
> > seventeeness and "harmonic 17" in Message 339 on 10 Aug 1998.
> > The limit in JI is based on the powerful resonance of the
> > first 5 harmonics. "Harmonic 17" has a different
> > etching. Paul Hahn had discussed this on the list.
>
> Thanks, an actual example makes it a lot clearer.
>
> Whole lotta 17 goin' on there. Interesting tuning, I'll have to
> check it out.

I seem to recall from the time of this original discussion that
this "Trespass" scale was put into the Scala archive.

At any rate, it's easy enough to paste Johnny's recent listing
of it into Scala, and take a look at many of this scale's
interesting properties. How 'bout one of you Scala-heads
taking on that job?

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

🔗jpehrson@rcn.com

--- In tuning@y..., MONZ@J... wrote:

/tuning/topicId_19513.html#20024

> --- In tuning@y..., jpehrson@r... wrote:
>
> /tuning/topicId_19513.html#19938
>
> > P.S. People on this list know I'm half-kidding. I *DO* like
> > "vigorous" debate, though... That's the term Paul used... (I
think people know by now that I was a "Paul student" despite our
> > differences in ages...!)
>
>
> Wasn't practically everyone on this list a "Paul student"?
>
> (I know I sure was!... and that was *after* I came to the
> conclusion that I knew more about tuning theory than anyone else...)
>

Amen!

Or like the sequence from Berlioz' "The Damnation of Faust":

Amen amen amen amen amen amen amen amen amen...

__________ _______ ___
Joseph Pehrson

🔗jpehrson@rcn.com

--- In tuning@y..., MONZ@J... wrote:

/tuning/topicId_19513.html#20025

> I seem to recall from the time of this original discussion that
> this "Trespass" scale was put into the Scala archive.
>
> At any rate, it's easy enough to paste Johnny's recent listing
> of it into Scala, and take a look at many of this scale's
> interesting properties. How 'bout one of you Scala-heads
> taking on that job?
>

Hi Monz!

Yes, the "Trespass" scale is in the Scala archive... However, it
seems to be of a slightly different version (toward the end) than the
scale that Johnny recently posted.

Johnny, could you please help determine which is the REAL Trespass,
or whether these are varients??

The recent Reinhard post:

/tuning/topicId_19513.html#19945

1/1
18/17
17/16
34/31
19/17
17/15
20/17
17/14
22/17
17/13
24/17
26/17
17/11
28/17
34/20
62/34
34/17

And the SCALA file: reinhard17.scl

|
Reinhard's tuning for "Trespass", 1998
0: 1/1 0.000 unison, perfect prime
1: 18/17 98.955 Arabic lute index finger
2: 17/16 104.955 17th harmonic
3: 34/31 159.920
4: 19/17 192.558
5: 17/15 216.687
6: 20/17 281.358
7: 17/14 336.130 supraminor third
8: 22/17 446.363
9: 17/13 464.428
10: 24/17 597.000 1st septendecimal tritone
11: 26/17 735.572
12: 17/11 753.637
13: 28/17 863.870 submajor sixth
14: 17/10 918.642
15: 31/17 1040.080
16: 32/17 1095.045 17th subharmonic
17: 2/1 1200.000 octave

|
Number of notes : 17
Smallest interval : 289/288, 6.0008 cents
Average interval (divided octave) : 70.588 cents
Average / Smallest interval : 11.763104
Largest interval of one step : 13/12, 138.5727 cents
Largest / Average interval : 1.963113
Largest / Smallest interval : 23.092298
Least squares average interval : 64.5111 cents
Median interval of one step : 32/31, 54.9644 cents
Interval standard deviation : 42.3500 cents
Interval skew :-0.0058 cents
Scale is not proper
Number of different intervals : 192 = 12.00000 / class
Smallest interval difference : 8960/8959, 0.1932 cents
Most common intervals : 4/3, 498.0450 cents & inv.,
amount: 3
Number of recognisable fifths : 6, average 703.620 cents
Lumma stability : 0.010001
Impropriety factor : 0.905389
Prime limit : 31
Odd number limit : 961 (O: 961 U: 289)
Fundamental : 1/126606480,-26.916 octaves,
0.000 Hz.
Guide tone : too high to compute
Exponens Consonantiae : 1.827329E+18, 60.6644 octaves
Euler's gradus suavitatis : 190
Wille's k value : 67259692
Vogel's harmonic complexity : 90.82353
Wilson's harmonic complexity : 196
Rectangular lattice diameter : 16
Triangular lattice diameter : 4
Prime exponents' range and average:
2: -4 .. 5 0.64706
3: -1 .. 2 0.11765
5: -1 .. 1 -0.05882
7: -1 .. 1 0.00000
11: -1 .. 1 0.00000
13: -1 .. 1 0.00000
17: -1 .. 1 -0.11765
19: 0 .. 1 0.05882
31: -1 .. 1 0.00000
Average exponent except of 2 : 0.00000
Average absolute exponent except of 2: 32 / 17 = 1.88235
Average distance from equal tempered : 84.4709 cents, 1.196670 steps
Standard deviation from equal tempered : 24.3132 cents, 0.344436 steps
Maximum distance from equal tempered : 170.8664 cents, 2.420606
steps
Geometric average of pitches 0..n : 528.067 cents
Arithmetic average of pitches 0..n : 568.802 cents
Harmonic average of pitches 0..n : 487.331 cents
Geometric average of pitches 1..n-1: 519.075 cents
Arithmetic average of pitches 1..n-1: 551.414 cents
Harmonic average of pitches 1..n-1: 486.736 cents
Geometric average of pitches 1..n : 559.129 cents
Arithmetic average of pitches 1..n : 597.087 cents
Harmonic average of pitches 1..n : 521.171 cents

🔗Afmmjr@aol.com

🔗Kraig Grady <kraiggrady@anaphoria.com>

I glad you all gained from this individual , I am sorry in my case it was not universal

jpehrson@rcn.com wrote:

> > Wasn't practically everyone on this list a "Paul student"?
> >
> > (I know I sure was!... and that was *after* I came to the
> > conclusion that I knew more about tuning theory than anyone else...)
> >
>
> Amen!
>
> Or like the sequence from Berlioz' "The Damnation of Faust":
>
> Amen amen amen amen amen amen amen amen amen...
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

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