melodic properties of Blackjack

Blackjack is the only microtonal scale I'm using at the present
time, so I'm getting more and more "accustomed."

Paul Erlich asserts that the scale was created for it's *harmonic*
rather than *melodic* properties.

However, maybe it's important to keep in mind that virtually *any*
invented scale *will* be used for melodic perposes, just out of the
musical nature of things.

As far as Blackjack is concerned, I think it's "kinky" kind of
melodies, with the very small "inflected" intervals creates an
interesting kind of microtonal melody.

I'm less fascinated with two other possibilities: the "every other
note" melodies of Blackjack which tend to sound a bit like 12-equal,
or the Mohajira, every *three* notes, which sounds a bit like the
diatonic collection.

Those two sound a bit too "familiar" so far to be appealing, but I
might find places for them...

In any case, Blackjack melodies *are* interesting and distinctive,
even though the scale wasn't designed so much with them in mind...

J. Pehrson

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

> Blackjack is the only microtonal scale I'm using at the present
> time, so I'm getting more and more "accustomed."
>
> Paul Erlich asserts that the scale was created for it's *harmonic*
> rather than *melodic* properties.

well, not entirely . . . as a periodicity block, the scale mimics the
entire just pitch continuum in a sense, which makes it melodically
quite well-distributed around the octave. compare with a truly purely
*harmonic* scale like the partch tonality diamond, which is far less
regularly distributed around the octave . . . it's hard to draw a
sharp line between "melodic" and "harmonic" properties, but certainly
the choice of 21 notes to create an MOS looks more like a "melodic"
than a "harmonic" decision in this light . . .

> However, maybe it's important to keep in mind that virtually *any*
> invented scale *will* be used for melodic perposes, just out of the
> musical nature of things.
>
> As far as Blackjack is concerned, I think it's "kinky" kind of
> melodies, with the very small "inflected" intervals creates an
> interesting kind of microtonal melody.
>
> I'm less fascinated with two other possibilities: the "every other
> note" melodies of Blackjack which tend to sound a bit like 12-
equal,
> or the Mohajira, every *three* notes, which sounds a bit like the
> diatonic collection.
>
> Those two sound a bit too "familiar" so far to be appealing, but I
> might find places for them...
>
> In any case, Blackjack melodies *are* interesting and distinctive,
> even though the scale wasn't designed so much with them in mind...

well, that's all true enough, and i guess i see your point better
now. i think i'd just go for a "freer" use of the blackjack pitches
to create beautiful melodies, rather than just running them up and
down (83 cents, 33 cents, 83 cents, 33 cents . . .) but that may be
just me.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44706.html#44727

> > Paul Erlich asserts that the scale was created for it's
*harmonic* rather than *melodic* properties.
>
> well, not entirely . . . as a periodicity block, the scale mimics
the entire just pitch continuum in a sense, which makes it
melodically quite well-distributed around the octave. compare with a
truly purely *harmonic* scale like the partch tonality diamond, which
is far less regularly distributed around the octave . . .

***Hi Paul,

Well, naturally, this is *EXTREMELY* interesting to me. Can you fill
this out a little bit for me? I take it what you mean is that the
inclusion, possibly of the *utonalities* in the diamond creates a
harmonic scale that is not, strictly speaking, a periodicity block...
or am I off base here? I remember when you were working on all the
just scales that had different visual lattices, almost like balloon
animals! Blackjack is, of course, even *more* symmetrical than most
of those I believe.

So, I guess we need to mitigate our perceptions that Blackjack is
first and formost a *harmonic* scale. I *thought* that was partially
what you were saying at one point. Maybe you're rethinking it? Or
maybe I didn't fully understand you the first time (more probable :)

it's hard to draw a
> sharp line between "melodic" and "harmonic" properties, but
certainly the choice of 21 notes to create an MOS looks more like
a "melodic" than a "harmonic" decision in this light . . .

***Could you run by me again how the MOS works with Blackjack? I
know this kind of scale can only have *two* different sized steps, I
believe, and this, of course, would pertain to Blackjack.

> > In any case, Blackjack melodies *are* interesting and
distinctive, even though the scale wasn't designed so much with them
in mind...
>
> well, that's all true enough, and i guess i see your point better
> now. i think i'd just go for a "freer" use of the blackjack pitches
> to create beautiful melodies, rather than just running them up and
> down (83 cents, 33 cents, 83 cents, 33 cents . . .) but that may be
> just me.

***No, not really. I'm already not doing that anymore in my very
most recent piece (being composed right now... well not right this
*very* now, I'm on this damn list...) I'm basically doing *exactly*
what you suggest in the paragraph immediately above...

J. Pehrosn

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
>
> /tuning/topicId_44706.html#44727
>
> > > Paul Erlich asserts that the scale was created for it's
> *harmonic* rather than *melodic* properties.
> >
> > well, not entirely . . . as a periodicity block, the scale mimics
> the entire just pitch continuum in a sense, which makes it
> melodically quite well-distributed around the octave. compare with
a
> truly purely *harmonic* scale like the partch tonality diamond,
which
> is far less regularly distributed around the octave . . .
>
> ***Hi Paul,
>
> Well, naturally, this is *EXTREMELY* interesting to me. Can you
fill
> this out a little bit for me? I take it what you mean is that the
> inclusion, possibly of the *utonalities* in the diamond creates a
> harmonic scale that is not, strictly speaking, a periodicity
block...
> or am I off base here?

the utonalities are unavoidable; one you've set up the otonalities,
they're there. but the diamond is not a periodicity block because it's
not constructed that way; it's simply the set of pitches adjacent to a
central 1/1 in the higher-dimensional lattice.

> So, I guess we need to mitigate our perceptions that Blackjack is
> first and formost a *harmonic* scale. I *thought* that was
partially
> what you were saying at one point. Maybe you're rethinking it? Or
> maybe I didn't fully understand you the first time (more probable :)

well, let's put it this way. it's created with the goal of a certain
"homogeneity" (not too many sizes of each generic interval type) and
"uniformity" (covering the whole octave span somewhat evenly) in
pitch, and these are not harmonic series considerations, but good
voice-leading would be hard without them. but i don't see the
blackjack scale as a melodic entity in itself, the way the diatonic
scale or the 5-to-9 tone scales used in world musics are. so maybe we
should say "voice-leading properties" instead of "melodic" properties?
i don't know, the music you're creating kind of makes these old
terminologies difficult to apply . . .

> it's hard to draw a
> > sharp line between "melodic" and "harmonic" properties, but
> certainly the choice of 21 notes to create an MOS looks more like
> a "melodic" than a "harmonic" decision in this light . . .
>
> ***Could you run by me again how the MOS works with Blackjack? I
> know this kind of scale can only have *two* different sized steps, I
> believe, and this, of course, would pertain to Blackjack.

you got it! the secor generates MOSs at 10, 11, 21, 31, 41, . . .
notes.

> > > In any case, Blackjack melodies *are* interesting and
> distinctive, even though the scale wasn't designed so much with them
> in mind...
> >
> > well, that's all true enough, and i guess i see your point better
> > now. i think i'd just go for a "freer" use of the blackjack
pitches
> > to create beautiful melodies, rather than just running them up and
> > down (83 cents, 33 cents, 83 cents, 33 cents . . .) but that may
be
> > just me.
>
>
> ***No, not really. I'm already not doing that anymore in my very
> most recent piece (being composed right now... well not right this
> *very* now, I'm on this damn list...) I'm basically doing *exactly*
> what you suggest in the paragraph immediately above...

awesome! then your next piece will probably be my favorite of all your
blackjack pieces! especially if you *harmonize* such melodies with as
interesting progressions as you've shown you're capable of creating!

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44706.html#44759

> the utonalities are unavoidable; one you've set up the otonalities,
> they're there. but the diamond is not a periodicity block because
it's not constructed that way; it's simply the set of pitches
adjacent to a central 1/1 in the higher-dimensional lattice.

***Hey Paul!

You know, I really think it's important for me to understand this a
bit more fully. Could you please spell out, if you have the time,
how these "adjacencies" work and how they differ from a periodicity
block...?? I've gotta know this, or at least get a glimmer.
Probably once I see it, I'll understand it, since I've been over some
of this before...

>
> > So, I guess we need to mitigate our perceptions that Blackjack is
> > first and formost a *harmonic* scale.

> well, let's put it this way. it's created with the goal of a
certain "homogeneity" (not too many sizes of each generic interval
type) and "uniformity" (covering the whole octave span somewhat
evenly) in
> pitch, and these are not harmonic series considerations, but good
> voice-leading would be hard without them. but i don't see the
> blackjack scale as a melodic entity in itself, the way the diatonic
> scale or the 5-to-9 tone scales used in world musics are. so maybe
we should say "voice-leading properties" instead of "melodic"
properties?
> i don't know, the music you're creating kind of makes these old
> terminologies difficult to apply . . .
>

***I'm not even fully "getting" how you think of the diatonic scale
as a melodic entity... You mean the half-steps pulling toward
certain notes?? That generally leads to more *harmonic*
considerations, though, yes?? I do realize that the creation of
Blackjack "minimized the number of notes required" as stated by Dave
Keenan in my prefaces... That certainly is a "melodic" property as
you allude to above...

> >
> > ***No, not really. I'm already not doing that anymore in my very
> > most recent piece (being composed right now... well not right
this *very* now, I'm on this damn list...) I'm basically doing
*exactly* what you suggest in the paragraph immediately above...
>
> awesome! then your next piece will probably be my favorite of all
your blackjack pieces! especially if you *harmonize* such melodies
with as interesting progressions as you've shown you're capable of
creating!

***Thanks, Paul. I have to admit I've been a bit sided or "fixated"
toward the *harmonic* side of Blackjack, but I guess that's only
natural, since it was what first fascinated me and also something I
had to become more comfortable with. As you know, my first pieces
*plotted* the lattices (that's why I made so many xerox copies of the
lattices) but now I've internalized some of this. In other words, I
can now recognize a *typical* Blackjack progression... or at least
one *I* hear as "typical" without alway having to plot anything, and
the lattices are more now just a *guide...*

So, I'm a bit freer to concentrate on purely esthetic matters and
matters of localized, linear form, which is more how I tend to see
melodies...

J. Pehrson

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
>
> /tuning/topicId_44706.html#44759
>
> > the utonalities are unavoidable; one you've set up the
otonalities,
> > they're there. but the diamond is not a periodicity block because
> it's not constructed that way; it's simply the set of pitches
> adjacent to a central 1/1 in the higher-dimensional lattice.
>
> ***Hey Paul!
>
> You know, I really think it's important for me to understand this a
> bit more fully. Could you please spell out, if you have the time,
> how these "adjacencies" work and how they differ from a periodicity
> block...?? I've gotta know this, or at least get a glimmer.
> Probably once I see it, I'll understand it, since I've been over
some
> of this before...

open up _the forms of tonality_, which is probably right next to you
right now. it illustrates the answers to these very questions, in a
form that most of its reviewers found very clear and accessible. read
the mentions of tonality diamonds and periodicity blocks with
particular attention.

> > > So, I guess we need to mitigate our perceptions that Blackjack
is
> > > first and formost a *harmonic* scale.
>
>
> > well, let's put it this way. it's created with the goal of a
> certain "homogeneity" (not too many sizes of each generic interval
> type) and "uniformity" (covering the whole octave span somewhat
> evenly) in
> > pitch, and these are not harmonic series considerations, but good
> > voice-leading would be hard without them. but i don't see the
> > blackjack scale as a melodic entity in itself, the way the
diatonic
> > scale or the 5-to-9 tone scales used in world musics are. so
maybe
> we should say "voice-leading properties" instead of "melodic"
> properties?
> > i don't know, the music you're creating kind of makes these old
> > terminologies difficult to apply . . .
> >
>
> ***I'm not even fully "getting" how you think of the diatonic scale
> as a melodic entity... You mean the half-steps pulling toward
> certain notes?? That generally leads to more *harmonic*
> considerations, though, yes??

i call those *tonal* considerations. so if you're simply trying to
write *modal* or *atonal* music, such things don't matter much.

> I do realize that the creation of
> Blackjack "minimized the number of notes required" as stated by
Dave
> Keenan in my prefaces... That certainly is a "melodic" property as
> you allude to above...

hmm . . . i think that's neither. and it's the *generator* that
minimizes the notes required for this-and-that, not the particular
choice of scale. for example, in order to have a full 11-limit hexad,
you need 23 notes (not 21) if you're generating the scale through
consecutive secors. but that's less than would be required by any
other generator, given such a high degree of harmonic accuracy. it's
pretty cool that george secor discovered this generator back in '75.

the fact that you *are* generating the scale by consecutively
applying a single generator, particularly if you extend just far
enough to get an MOS, may seem like a very melodic thing to do. but,
perhaps more esoterically for now, we know that a great majority of
the interesting and important MOSs, as well as multiply-repeating
analogues such as the familiar octatonic (diminished) scale, the
hexatonic (augmented) scale, the blackwood 10-out-of-15 scale, and my
10-out-of-22 scales, and even nMOSs like helmholtz-24 and groven-36
if you allow torsion, but fundamentally no other kinds of scales, are
what you get when you take a fokker periodicity block and temper out
all but one of the unison vectors. this seems like more of a harmonic
thing to do, since you're taking a chunk of the harmonic lattice and
then connecting the edges with tempering, doesn't it?

(dear reader: if the last paragraph didn't make much sense to you,
but you're curious, you might want to join the tuning-math list, scan
the archives, and ask lots of questions)

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_44706.html#44805

<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> >
> > /tuning/topicId_44706.html#44759
> >
> > > the utonalities are unavoidable; one you've set up the
> otonalities,
> > > they're there. but the diamond is not a periodicity block
because
> > it's not constructed that way; it's simply the set of pitches
> > adjacent to a central 1/1 in the higher-dimensional lattice.
> >
> > ***Hey Paul!
> >
> > You know, I really think it's important for me to understand this
a
> > bit more fully. Could you please spell out, if you have the
time,
> > how these "adjacencies" work and how they differ from a
periodicity
> > block...?? I've gotta know this, or at least get a glimmer.
> > Probably once I see it, I'll understand it, since I've been over
> some
> > of this before...
>
> open up _the forms of tonality_, which is probably right next to
you
> right now. it illustrates the answers to these very questions, in a
> form that most of its reviewers found very clear and accessible.
read
> the mentions of tonality diamonds and periodicity blocks with
> particular attention.
>

***Thanks so much, Paul, for your response, which I mostly
understood. I'll reread _The Forms of Tonality_ which is, indeed,
practically in front of me, and I'll be back with a few more
questions...

best,

Joseph

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> >
> > /tuning/topicId_44706.html#44727

> > So, I guess we need to mitigate our perceptions that Blackjack is
> > first and formost a *harmonic* scale. I *thought* that was
> partially
> > what you were saying at one point. Maybe you're rethinking it? Or
> > maybe I didn't fully understand you the first time (more probable :)
>
> well, let's put it this way. it's created with the goal of a certain
> "homogeneity" (not too many sizes of each generic interval type) and
> "uniformity" (covering the whole octave span somewhat evenly) in
> pitch, and these are not harmonic series considerations, but good
> voice-leading would be hard without them. but i don't see the
> blackjack scale as a melodic entity in itself, the way the diatonic
> scale or the 5-to-9 tone scales used in world musics are. so maybe we
> should say "voice-leading properties" instead of "melodic" properties?
> i don't know, the music you're creating kind of makes these old
> terminologies difficult to apply . . .

Not really. Melodic properties are those that relate to pitches
occurring one after the other in time, or to the approximate
magnitudes of the intervals, in particular the step intervals, whereas
Harmonic properties relate to notes sounding simultaneously and often
depend more precisely on intervals' deviations from small whole number
ratios.

To talk of the Melodic properties of a tuning does not (to me) imply
that the tuning is itself a melodic entity or is capable of being
perceived as a melodic gestalt.

> > it's hard to draw a
> > > sharp line between "melodic" and "harmonic" properties, but
> > certainly the choice of 21 notes to create an MOS looks more like
> > a "melodic" than a "harmonic" decision in this light . . .

It _is_ a melodic decision. The fact that, as Paul has discovered,
MOSs or well formed scales correspond to periodicity blocks, does not
make it a harmonic property, because the reason for carving out a
periodicity block from a JI lattice is itself, at least partly, a
melodic one. Namely to have a scale with few comma-sized step intervals.

> > > > In any case, Blackjack melodies *are* interesting and
> > distinctive, even though the scale wasn't designed so much with them
> > in mind...
> > >
> > > well, that's all true enough, and i guess i see your point better
> > > now. i think i'd just go for a "freer" use of the blackjack
> pitches
> > > to create beautiful melodies, rather than just running them up and
> > > down (83 cents, 33 cents, 83 cents, 33 cents . . .) but that may
> be
> > > just me.
> >
> >
> > ***No, not really. I'm already not doing that anymore in my very
> > most recent piece (being composed right now... well not right this
> > *very* now, I'm on this damn list...) I'm basically doing *exactly*
> > what you suggest in the paragraph immediately above...
>
> awesome! then your next piece will probably be my favorite of all your
> blackjack pieces! especially if you *harmonize* such melodies with as
> interesting progressions as you've shown you're capable of creating!

I totally agree.

I'd love to hear what happens when you choose a Blackjack subset scale
having 5 to 9 notes and containing no 33 cent steps and no steps wider
than 233 cents, possibly even tetrachordal, and stick to it for a
while for melody, while only allowing notes in that scale, or their 33
cent inflections (but still in Blackjack) to be used in harmonising it.

An early criticism of Blackjack was that it had no such melodic
scales. I think rather that there are so many, it is hard to choose
one for a given piece.

Of course once such a melodic scale is established in the piece, it
might be allowed to modulate. Of course you can't modulate very far by
fifths in Blackjack, but more likely by secors or 7:8s (or 4:7s) or
neutral thirds.

-- Dave Keenan

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

/tuning/topicId_44706.html#45026
>
> I'd love to hear what happens when you choose a Blackjack subset
scale having 5 to 9 notes and containing no 33 cent steps and no
steps wider than 233 cents, possibly even tetrachordal, and stick to
it for a while for melody, while only allowing notes in that scale,
or their 33 cent inflections (but still in Blackjack) to be used in
harmonising it.
>

***Well, I don't know, Dave, if it would be as interesting. Although
from a *theoretical* angle this may seem sophisticated, there is much
charm in using the consecutive 33 cent step. I consider it an
*integral* part of the Blackjack melodic sound, and probably would be
pretty loath not to use it much...

> An early criticism of Blackjack was that it had no such melodic
> scales. I think rather that there are so many, it is hard to choose
> one for a given piece.
>
> Of course once such a melodic scale is established in the piece, it
> might be allowed to modulate. Of course you can't modulate very far
by
> fifths in Blackjack, but more likely by secors or 7:8s (or 4:7s) or
> neutral thirds.
>

***Would you mind, Dave, spelling out some of these
melodic "kernels..." (Paul hates this word... :) in the standard
Blackjack scale and I can issue a few "opinions" on them?? (Always
the fun part... :)

Joseph

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <D.KEENAN@U...> wrote:
>
> /tuning/topicId_44706.html#45026
> >
> > I'd love to hear what happens when you choose a Blackjack subset
> scale having 5 to 9 notes and containing no 33 cent steps and no
> steps wider than 233 cents, possibly even tetrachordal, and stick to
> it for a while for melody, while only allowing notes in that scale,
> or their 33 cent inflections (but still in Blackjack) to be used in
> harmonising it.
> >
>
> ***Well, I don't know, Dave, if it would be as interesting. Although
> from a *theoretical* angle this may seem sophisticated, there is much
> charm in using the consecutive 33 cent step. I consider it an
> *integral* part of the Blackjack melodic sound, and probably would be
> pretty loath not to use it much...

Well OK. Don't stop using them. They would occur in the harmony in any
case. But for the purpose I'm considering, you would just think of
them as grace-notes or inflections, but essentially the same note.

> > An early criticism of Blackjack was that it had no such melodic
> > scales. I think rather that there are so many, it is hard to choose
> > one for a given piece.
> >
> > Of course once such a melodic scale is established in the piece, it
> > might be allowed to modulate. Of course you can't modulate very far
> by
> > fifths in Blackjack, but more likely by secors or 7:8s (or 4:7s) or
> > neutral thirds.
> >
>
> ***Would you mind, Dave, spelling out some of these
> melodic "kernels..." (Paul hates this word... :) in the standard
> Blackjack scale and I can issue a few "opinions" on them?? (Always
> the fun part... :)
>
> Joseph

I'm afraid I don't have time to get into this. Way back we did list
many subsets (or near-subsets) of Blackjack that Manuel found in the
Scala archive. You can use recent versions of Scala to do this
yourself. Just SET MAX DIFF to 5 cents before using the COMPARE
/SUBSETS function or something like that.

But you could also approach it in this way: Melodically we can
consider Blackjack to be 10-tET with inflections. There are 9 clusters
of 2 notes and 1 cluster of 3 notes, but treat all the clusters as
equals at first and consider each cluster as if it were a single note.

Treat 10-EDO in the Blackjack case as analogous to 12-EDO in the usual
case. Now start knocking out notes (corresponding to whole clusters in
Blackjack), but don't knock out two adjacent ones (at least for a
first pass). How many ways can you do this to 10-EDO and end up with a
unique scale of 5 to 9 notes (treating rotations as equivalent)? i.e.
There's only one with 5 notes, probably very boring, and only one with
9 notes, probably too many notes to really grok. I think there are 4
with 8 notes (but forget the symmetrical one), 5 with 7 notes and 2
with 6 notes. Drawing decimal clock-faces might help in finding these.
Now use Scala to find the Rothenberg-stability of each of these (as
actual subsets of 10-EDO not Blackjack), and pick the one with the
greatest stability to try first.

Now having chosen a subset of 10-EDO we have to choose how to
translate it back into Blackjack. The only real issue is which note to
map to the 3-cluster. Maximising JI harmonies might be used to help
in deciding this, or it might be based on finer-grained melodic
considerations. We might also want to decide which note in each
cluster is to be considered the "natural" or uninflected note. But
that might not be important, or could be decided later.

So we would be working from purely melodic considerations, trusting
that simply by limiting ourselves to notes within Blackjack we are
likely to have many harmonic possibilities.

You might get someone on tuning-math to help with the above
theoretical prioritising of choices, but since there are only about 10
worth trying, you might simply use trial and error. Just mark 2 or 3
or 4 per octave, of the 33 cent clusters, on your keyboard, in some
way meaning "do not use", and fool around.

Actually it would be a useful experiment to have you choose your
favourite without knowing anything about Rothenberg stability.

-- Dave Keenan