Yahoo Tuning Groups Ultimate Backup tuning Dave Keenan's scales

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > And the fact that they are all subsets of 72-tET is the
> > real "clincher..." There's a good chance I'll be trying to use
these
> > at some point.
>
> Here's the scale I was discussing, smithgw18, in 72-et. See what you
> think. Is this a good scale?
>
> ! smithgw18_72
> smithgw18 in 72-et
> 18
> !
> 66.666667
> 116.666667
> 150.000000
> 200.000000
> 266.666667
> 383.333333
> 466.666667
> 500.000000
> 583.333333
> 650.000000
> 700.000000
> 766.666667
> 816.666667
> 883.333333
> 966.666667
> 1000.000000
> 1083.333333
> 1200.000000

***Playing around a bit with this in Scala... there is indeed
something intriguing about it. A couple of the small steps here and
there, but a larger chromatic feel. Very curious.

I'd really have to do some composing in it to see how it would work
out. Maybe I'll do that...

Thanks!

P.S... I didn't realize, Gene, how many scales you already had in
the Scala archives a this point...

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Playing around a bit with this in Scala... there is indeed
> something intriguing about it. A couple of the small steps here and
> there, but a larger chromatic feel. Very curious.

Thanks for the feedback. It is awfully quirky compared to Blackjack,
but it packs a lot of septimal harmony into 18 notes. Kraig doesn't
like the idea of measuring the worth of such scales by chord counts,
but if you abandon the theory that scales should be highly regular and
not quirky, what else do you have as a way of assessing them? I'd like
feedback on that, especially from people who think like Kraig. Saying
with Jon that there is no such thing as a bad scale is not of any use
as input either; use another word than "bad" if you prefer, but I
still would like ideas on what makes a scale worthy of consideration.
The sheer number of possibilities is boggling.

> P.S... I didn't realize, Gene, how many scales you already had in
> the Scala archives a this point...

I was a little surprised by that also; a few years back and there were
none.

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > ***Playing around a bit with this in Scala... there is indeed
> > something intriguing about it. A couple of the small steps here
and
> > there, but a larger chromatic feel. Very curious.
>
> Thanks for the feedback. It is awfully quirky compared to Blackjack,
> but it packs a lot of septimal harmony into 18 notes. Kraig doesn't
> like the idea of measuring the worth of such scales by chord counts,
> but if you abandon the theory that scales should be highly regular
and
> not quirky, what else do you have as a way of assessing them? I'd
like
> feedback on that, especially from people who think like Kraig.
Saying
> with Jon that there is no such thing as a bad scale is not of any
use
> as input either; use another word than "bad" if you prefer, but I
> still would like ideas on what makes a scale worthy of
consideration.
> The sheer number of possibilities is boggling.
>
> > P.S... I didn't realize, Gene, how many scales you already had
in
> > the Scala archives a this point...
>
> I was a little surprised by that also; a few years back and there
were
> none.

***Looka like Manuel's been following your work, as he should...

Hmmm... I agree that scales need not necessarily be "regular" and
not "quirky..." That's the way an engineer might think, but I don't
believe, necessarily, a composer... A lot of this has to do with
personal taste and how it actually feels and sounds to work with the
scale, which is why it is hard to appraise them immediately.

I'm *still* getting a grip on Blackjack after 5 or 6
fairly "substantial" pieces.

It came up again the other night. I had a obvious triadic harmony
that was made complex by other stuff going on. It was hard to hear
if I had the right note to make it "just" or "near just..."

I'm just now learning, with regard to Blackjack, to just forget about
it. If it doesn't bother me when I hear it composing, it shouldn't
be "corrected" theoretically later... Personally, I should be
listening to things not "correcting" them...

All a fascinating process. I hope to have more comments to offer
after I work with some of these other scales...

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> >
> > > ***Playing around a bit with this in Scala... there is indeed
> > > something intriguing about it. A couple of the small steps here
> and
> > > there, but a larger chromatic feel. Very curious.
> >
> > Thanks for the feedback. It is awfully quirky compared to Blackjack,
> > but it packs a lot of septimal harmony into 18 notes. Kraig doesn't
> > like the idea of measuring the worth of such scales by chord counts,
> > but if you abandon the theory that scales should be highly regular
> and
> > not quirky, what else do you have as a way of assessing them? I'd
> like
> > feedback on that, especially from people who think like Kraig.
> Saying
> > with Jon that there is no such thing as a bad scale is not of any
> use
> > as input either; use another word than "bad" if you prefer, but I
> > still would like ideas on what makes a scale worthy of
> consideration.
> > The sheer number of possibilities is boggling.
> >
> > > P.S... I didn't realize, Gene, how many scales you already had
> in
> > > the Scala archives a this point...
> >
> > I was a little surprised by that also; a few years back and there
> were
> > none.
>
>
> ***Looka like Manuel's been following your work, as he should...
>
>
> Hmmm... I agree that scales need not necessarily be "regular" and
> not "quirky..." That's the way an engineer might think, but I don't
> believe, necessarily, a composer... A lot of this has to do with
> personal taste and how it actually feels and sounds to work with the
> scale, which is why it is hard to appraise them immediately.
>
> I'm *still* getting a grip on Blackjack after 5 or 6
> fairly "substantial" pieces.
>
> It came up again the other night. I had a obvious triadic harmony
> that was made complex by other stuff going on. It was hard to hear
> if I had the right note to make it "just" or "near just..."
>
> I'm just now learning, with regard to Blackjack, to just forget about
> it. If it doesn't bother me when I hear it composing, it shouldn't
> be "corrected" theoretically later... Personally, I should be
> listening to things not "correcting" them...
>
> All a fascinating process. I hope to have more comments to offer
> after I work with some of these other scales...

To the list of which, you might add this:

/tuning-math/message/12374

This is also pretty twisted, but it does have a certain regularity of
structure, even so--in Scala speak, the 7-limit JI version is
"JI-epimorphic in non-monotonic order", and the 72-et version (the
third one listed) inherits the regularity. The noteworthy feature is
another one noted by Scala: "Scale contains a complete diamond 1 3 5
7". So it's both permutation epimorphic, giving it a certain kind of
regularity, and it contains a 7-limit tonality diamond, all in a
compass of 18 notes. But one of its steps is a comma, which of course
is even smaller in 72-et, so it's not exactly smooth city.

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Hi all,

Gene wrote:

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
>
> > ***Playing around a bit with this in Scala... there is indeed
> > something intriguing about it. A couple of the small steps here and
> > there, but a larger chromatic feel. Very curious.
>
> Thanks for the feedback. It is awfully quirky compared to Blackjack,
> but it packs a lot of septimal harmony into 18 notes. Kraig doesn't
> like the idea of measuring the worth of such scales by chord counts,
> but if you abandon the theory that scales should be highly regular and
> not quirky, what else do you have as a way of assessing them? I'd like
> feedback on that, especially from people who think like Kraig. Saying
> with Jon that there is no such thing as a bad scale is not of any use
> as input either; use another word than "bad" if you prefer, but I
> still would like ideas on what makes a scale worthy of consideration.
> The sheer number of possibilities is boggling.
>
> > P.S... I didn't realize, Gene, how many scales you already had in
> > the Scala archives a this point...
>
> I was a little surprised by that also; a few years back and there were
> none.
>

Gene,

> ... if you abandon the theory that scales should be highly regular and
> not quirky ...

I did so long ago. One doesn't always need that regularity, and it can
be stifling.

I certainly "think like Kraig", at least in respect of the primacy of
melody over harmony in the music I make. If Kraig "doesn't like the idea
of measuring the worth" [_utility_?] "of such scales by chord counts",
that's not surprising given his preference for melodic values. In fact,
it might be said that in a multilinear, contrapuntal style, where Melody is
King, while passing and accidental harmonies are but graces in its court,
necessarily, the number of _discords_ is a good measure of the richness,
variety and colour brought to that court by a well-chosen scale ...

As you wrote -
> The sheer number of possibilities is boggling.

And this is how it struck me, with every new digest from the lists
bringing yet more varieties of scales from the fertile inventions of
yourself and others, Ossa piled on Pelion. I thought: "But of what use
are they all? And how could I ever hope to mine their riches, in the few
short years of a human lifetime?" I dwelt on this at length, with some
perplexity, and finally, a faint glimmer of an answer arrived, carried as
an unseen passenger, a tiny mite on the feather of the email pigeon. At
last, I seized on it, and bent the microscope upon it, and all was clear:
its name was Purpose. "If you want to do this", you wrote, "then such-
and-such will suit you better than so-and-so." And I saw that it was so.
The saga was at an end, and I had passed from the Val[e] of Perplexity
into the Sunny Plains of Clear Intent!

Given these values:
1. The ability to produce melodies of varied character, strong and supple,
light and nuanced, agonised or tender, brutal, pleading, martial, joyous,
coquettish, robust, serene, peaceful, transcendent ... you name it!
2. The ability to have those melodies interact freely, as characters in a
story, through passing harmonies and discords;

- any scale system that supports those values is "good" to exactly the
degree that it supports those values, and "bad" to exactly the degree
that it fails to support those values.

But the values come first. Choose a different set of values (these are
mine) and you will require different scale materials - different musical
resources. Thus, it seems to me that the answer to your question is simply
and necessarily a relative one; each individual may give an individual
answer, which is, for all that, objective rather than subjective. To be
objective, one merely needs to know one's objectives! ... as one can then
measure against them. But there are NO universal musical objectives; it
follows that there can be no universal measure of value. Instead, every
measure is _based_ on a set of values, which may be personal preferences
engendered by chance circumstances.

I prefer the melodic virtues to the harmonic. While I do not decry the
latter, I'm more likely to pursue the former. Therefore I want scales
which give me good (easy and accurate) melodic leaps and steps, and
enough of them to give sufficient variety that I can use them expressively.
As a byproduct, I'm likely to find that a scale with these melodic virtues
will also possess some harmonic ones, providing a pleasing variety of both
concords and discords. Rather than counting the triads, of any type,
I'd count the intervals within the scale. How many fifths does it give me?
and how good are they? Thirds? Seconds? What kinds are they? These
are the questions by which I, personally, rate the utility of a scale. But
I won't pretend that I do so very systematically; often, in fact, a scale
results from the cumulative melodic choices I make. So much so, that in
the light of a finished composition, I'm left wondering what kind of fourth,
or seventh, or some other "omitted" degree, the scale might have.

HT(rambling)H! :-)

Yahya

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🔗Jon Szanto <jszanto@cox.net>

Hi Yahya,

Just wanted to thank you for that elaborate and eloquent post -
certainly phrased with more finesse and grace than I can usually
muster! This, I fear, will always be one of the rough spots in the
microtonal world, where one side has a difficult side seeing the
other. I value what Gene has done, in his endless search for new
tunings (I have an obsession with sound/patch design, and have
hundreds more than I'll probably ever use); I simply don't approach
music in the same way as he, and many others don't. One can take a
very global (literally) look at this issue, and see that there are
entire musical cultures of each side of this duality (harmony/melody),
as well as those that successfully bridge the two.

Heck, babbling again. Thanks for your thoughts...

Cheers,
Jon

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
> Hi all,
>
> Gene wrote:
>
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> >
> > > ***Playing around a bit with this in Scala... there is indeed
> > > something intriguing about it. A couple of the small steps here and
> > > there, but a larger chromatic feel. Very curious.
> >
> > Thanks for the feedback. It is awfully quirky compared to Blackjack,
> > but it packs a lot of septimal harmony into 18 notes. Kraig doesn't
> > like the idea of measuring the worth of such scales by chord counts,
> > but if you abandon the theory that scales should be highly regular and
> > not quirky, what else do you have as a way of assessing them? I'd like
> > feedback on that, especially from people who think like Kraig. Saying
> > with Jon that there is no such thing as a bad scale is not of any use
> > as input either; use another word than "bad" if you prefer, but I
> > still would like ideas on what makes a scale worthy of consideration.
> > The sheer number of possibilities is boggling.
> >
> > > P.S... I didn't realize, Gene, how many scales you already had in
> > > the Scala archives a this point...
> >
> > I was a little surprised by that also; a few years back and there were
> > none.
> >
>
> Gene,
>
> > ... if you abandon the theory that scales should be highly regular and
> > not quirky ...
>
> I did so long ago. One doesn't always need that regularity, and it can
> be stifling.
>
> I certainly "think like Kraig", at least in respect of the primacy of
> melody over harmony in the music I make. If Kraig "doesn't like the
idea
> of measuring the worth" [_utility_?] "of such scales by chord counts",
> that's not surprising given his preference for melodic values. In fact,
> it might be said that in a multilinear, contrapuntal style, where
Melody is
> King, while passing and accidental harmonies are but graces in its
court,
> necessarily, the number of _discords_ is a good measure of the richness,
> variety and colour brought to that court by a well-chosen scale ...
>
> As you wrote -
> > The sheer number of possibilities is boggling.
>
> And this is how it struck me, with every new digest from the lists
> bringing yet more varieties of scales from the fertile inventions of
> yourself and others, Ossa piled on Pelion. I thought: "But of what use
> are they all? And how could I ever hope to mine their riches, in
the few
> short years of a human lifetime?" I dwelt on this at length, with some
> perplexity, and finally, a faint glimmer of an answer arrived,
carried as
> an unseen passenger, a tiny mite on the feather of the email pigeon. At
> last, I seized on it, and bent the microscope upon it, and all was
clear:
> its name was Purpose. "If you want to do this", you wrote, "then such-
> and-such will suit you better than so-and-so." And I saw that it
was so.
> The saga was at an end, and I had passed from the Val[e] of Perplexity
> into the Sunny Plains of Clear Intent!
>
> Given these values:
> 1. The ability to produce melodies of varied character, strong and
supple,
> light and nuanced, agonised or tender, brutal, pleading, martial,
joyous,
> coquettish, robust, serene, peaceful, transcendent ... you name it!
> 2. The ability to have those melodies interact freely, as
characters in a
> story, through passing harmonies and discords;
>
> - any scale system that supports those values is "good" to exactly the
> degree that it supports those values, and "bad" to exactly the degree
> that it fails to support those values.
>
> But the values come first. Choose a different set of values (these are
> mine) and you will require different scale materials - different musical
> resources. Thus, it seems to me that the answer to your question is
simply
> and necessarily a relative one; each individual may give an individual
> answer, which is, for all that, objective rather than subjective. To be
> objective, one merely needs to know one's objectives! ... as one
can then
> measure against them. But there are NO universal musical objectives; it
> follows that there can be no universal measure of value. Instead, every
> measure is _based_ on a set of values, which may be personal preferences
> engendered by chance circumstances.
>
> I prefer the melodic virtues to the harmonic. While I do not decry the
> latter, I'm more likely to pursue the former. Therefore I want scales
> which give me good (easy and accurate) melodic leaps and steps, and
> enough of them to give sufficient variety that I can use them
expressively.
> As a byproduct, I'm likely to find that a scale with these melodic
virtues
> will also possess some harmonic ones, providing a pleasing variety
of both
> concords and discords. Rather than counting the triads, of any type,
> I'd count the intervals within the scale. How many fifths does it
give me?
> and how good are they? Thirds? Seconds? What kinds are they? These
> are the questions by which I, personally, rate the utility of a
scale. But
> I won't pretend that I do so very systematically; often, in fact, a
scale
> results from the cumulative melodic choices I make. So much so, that in
> the light of a finished composition, I'm left wondering what kind of
fourth,
> or seventh, or some other "omitted" degree, the scale might have.
>
> HT(rambling)H! :-)
>
> Yahya
>
> --
> No virus found in this outgoing message.
> Checked by AVG Anti-Virus.
> Version: 7.0.323 / Virus Database: 267.8.9/41 - Release Date: 5/7/05

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> I certainly "think like Kraig", at least in respect of the primacy of
> melody over harmony in the music I make. If Kraig "doesn't like the
idea
> of measuring the worth" [_utility_?] "of such scales by chord counts",
> that's not surprising given his preference for melodic values. In fact,
> it might be said that in a multilinear, contrapuntal style, where
Melody is
> King, while passing and accidental harmonies are but graces in its
court,
> necessarily, the number of _discords_ is a good measure of the richness,
> variety and colour brought to that court by a well-chosen scale ...

But then how do you evaluate a scale for potential usefulness? There
are far to many to simply try them out.
Rather than counting the triads, of any type,
> I'd count the intervals within the scale.

That can certainly be done; in fact, if you just want intervals and
the associated triads from some predetermined set, then graph theory
and the characteristic polynomial are useful. If you like to use MOS,
then the proportions of the various kind of intervals depends strongly
on what temperament you use. For instance in meantone you will always
have lots of fifths and fourths, since these are generators. In
miracle, lots of 8/7 and 7/4 intervals, since these are two
generators. And so forth. That, in fact, can be a very useful way of
rating a temperament according to individual purposes. However you may
not want a rank two temperament, and if you do, you may not want a
MOS. MOS are very special and there are far fewer of them than
reasonable sorts of scales in general.

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Jon Szanto wrote:

> Hi Yahya,
>
> Just wanted to thank you for that elaborate and eloquent post -
> certainly phrased with more finesse and grace than I can usually
> muster! This, I fear, will always be one of the rough spots in the
> microtonal world, where one side has a difficult side seeing the
> other. I value what Gene has done, in his endless search for new
> tunings (I have an obsession with sound/patch design, and have
> hundreds more than I'll probably ever use); I simply don't approach
> music in the same way as he, and many others don't. One can take a
> very global (literally) look at this issue, and see that there are
> entire musical cultures of each side of this duality (harmony/melody),
> as well as those that successfully bridge the two.
>
> Heck, babbling again. Thanks for your thoughts...
>
> Cheers,
> Jon

Jon, it was my pleasure.

I suspect that no-one may have expected _quite_ such an answer
as I gave, but did my best to answer honestly what matters to me
about a scale, and to try to share the feelings (if not necessarily
the reasons) behind those values. I'm sorry it was SO elaborate,
baroque maybe, but sometimes I've found, even mathematics can
be very finely nuanced and subtle.

Gene has certainly uncovered many more scale types and structures
than I would have thought existed; moreover, he continues to point
out aspects of their structures that have proven musically useful
in other, historic scales, such as regularity and epimorphism. These
structural insights are valuable. I can envisage an expert system that
can tell you, given your requirements for, say, chains of pure major
thirds and minor sevenths, with no more than four step sizes in all,
what scales fulfil those requirements and how well different
temperaments of those scales trade off accuracy in intonation
against number of scale steps. This expert system might be called
"a composer", or it might be a computer program; but either way, it
would want to have the kind of knowledge that Gene has been mining
for us all.

For which, let me here say, simply, "Thank you, Gene!"

Regards,
Yahya

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🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Gene,

You wrote:
> ...
> But then how do you evaluate a scale for potential usefulness? There
> are far to many to simply try them out.
> > Rather than counting the triads, of any type,
> > I'd count the intervals within the scale.
>
> That can certainly be done; in fact, if you just want intervals and
> the associated triads from some predetermined set, then graph theory
> and the characteristic polynomial are useful.

At this point, I'll take your word for it. Perhaps you could point me
to some earlier messages showing how to use graph theory and the
characteristic polynomial for selecting intervals and triads? And can
you invert the techniques, to find useful supersets of sets of intervals
or triads / tetrads / etc?

> If you like to use MOS,
> then the proportions of the various kind of intervals depends strongly
> on what temperament you use. For instance in meantone you will always
> have lots of fifths and fourths, since these are generators. In
> miracle, lots of 8/7 and 7/4 intervals, since these are two
> generators. And so forth. That, in fact, can be a very useful way of
> rating a temperament according to individual purposes. However you may
> not want a rank two temperament, and if you do, you may not want a
> MOS. MOS are very special and there are far fewer of them than
> reasonable sorts of scales in general.

Gene, please remind me, what is special about a MOS?

Regards,
Yahya

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🔗Ozan Yarman <ozanyarman@superonline.com>

Brother Yahya, I'm wondering if you ever received my lenghty response on Maqam Music tuning prior to my Moscow journey from which I returned recently.

Cordially,
Ozan

----- Original Message -----
From: Yahya Abdal-Aziz
To: tuning@yahoogroups.com
Sent: 11 Temmuz 2005 Pazartesi 17:20
Subject: [tuning] Re: Dave Keenan's scales

Gene,

Gene, please remind me, what is special about a MOS?

Regards,
Yahya

🔗Aaron Krister Johnson <aaron@akjmusic.com>

On Monday 11 July 2005 9:20 am, Yahya Abdal-Aziz wrote:

> Gene has certainly uncovered many more scale types and structures
> than I would have thought existed; moreover, he continues to point
> out aspects of their structures that have proven musically useful
> in other, historic scales, such as regularity and epimorphism. These
> structural insights are valuable. I can envisage an expert system that
> can tell you, given your requirements for, say, chains of pure major
> thirds and minor sevenths, with no more than four step sizes in all,
> what scales fulfil those requirements and how well different
> temperaments of those scales trade off accuracy in intonation
> against number of scale steps. This expert system might be called
> "a composer", or it might be a computer program; but either way, it
> would want to have the kind of knowledge that Gene has been mining
> for us all.
>
> For which, let me here say, simply, "Thank you, Gene!"

I second that, and I echoed that sentiment in my earlier post where I begged
for less formality and hardcore math in definitions. However, my praise for
Gene was buried underneath a few pragraphs of complaining about all the
math-speak, so I want to correct that by putting it front and center. Yes,
thanks Gene for all the creative math discovery you do. In my case, your
discoveries have born musical fruit many times over, esp. with the your 3 and
7 JI scales, which I notice Manuel hasn't put in the archives yet.

Best,
Aaron.