blackjack scales

So, really, blackjack seems to "have it all" once one learns how to
work with it.

As far as scales are concerned, the use of "every other" note creates
a scale not too dissimilar from our 12-tET chromatic (well it's a
full Secors at 116 cents, so it's a little wider per "semitone...")

And, the use of every *other* note is fascinating because
the "Mohajira" scale is somewhat remotely comparable to a diatonic
collection with 8 notes! Maybe a little "out of tune" or different
from our 12-tET diatonic, but still somewhat related.

Could someone please run down the background of this Mohajira and how
it is related to the diatonic collection, if there is any
relationship, and the history of this scale. I'd really like to know
more about this!!!!

Thanks!

Joseph Pehrson

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

> Could someone please run down the background of this Mohajira and how
> it is related to the diatonic collection, if there is any
> relationship, and the history of this scale. I'd really like to know
> more about this!!!!
>
> Thanks!
>
> Joseph Pehrson

Mohajira is the mode that goes 3 4 3 4 3 4 3 in 24-tET. It's supposedly a rare Arabic mode, but
I've never heard it used. Graham Breed has studied it extensively -- go to

http://x31eq.com/7plus3.htm

and study especially the section called "The 7-Note Scales". Also note the section that refers to
Mohajira as "anti-Dorian", which comes from Carey and Clampitt's paper on "duals" to familiar
scales (Graham provides a clickable link to that paper).

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_29682.html#29692

>
> Mohajira is the mode that goes 3 4 3 4 3 4 3 in 24-tET. It's
supposedly a rare Arabic mode, but
> I've never heard it used. Graham Breed has studied it extensively --
go to
>
> http://x31eq.com/7plus3.htm
>
> and study especially the section called "The 7-Note Scales". Also
note the section that refers to
> Mohajira as "anti-Dorian", which comes from Carey and Clampitt's
paper on "duals" to familiar scales (Graham provides a clickable link
to that paper).

Well... this is very cool, particularly in light of the other scalar
possibilities of blackjack. Paul, you've really been expanding my
palette with these scale subsets and, before long, there will be some
music showing this...it's already begun.

Like anything else, blackjack takes a certain practical "learning
curve" with hands-on experience and different things to try with it.

Unfortunately, I couldn't get the Carey and Clampitt paper link to
work... I just get a "page not found" message... so if you have any
other ideas of how to find that on the Web, I would be very
interested.

The idea of alterations or "duals" to familiar scales is a
fascinating one... I believe I recall an instance where we got
a "warped" kind of octatonic, Bartok-sounding scale out of
misperception of the Bohlen-Pierce scale... if I remember correctly.
Was that right??

_______ _______ ______
Joseph Pehrson

In-Reply-To: <9ri5vq+4i3o@eGroups.com>
Joseph Pehrson wrote:

> Unfortunately, I couldn't get the Carey and Clampitt paper link to
> work... I just get a "page not found" message... so if you have any
> other ideas of how to find that on the Web, I would be very
> interested.

The link is to the Perspectives of New Music site. Looks like they've
removed the file. Here's the relevant table of contents:

<http://depts.washington.edu/pnm/v34n2.htm>

Graham

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

> Unfortunately, I couldn't get the Carey and Clampitt paper link to
> work... I just get a "page not found" message... so if you have any
> other ideas of how to find that on the Web, I would be very
> interested.

It seems to be off-line, but luckily I printed out a copy before it
went off-line . . . an abstract is still available:

http://theory.esm.rochester.edu/sessions/abstracts/carey.html

So it seems the "anti-diatonic" scales simply reverse the role of
step-interval multiplicities and generator spans relative to the
diatonic collection. I'm sure any of our more mathematically astute
readers can explain this more fully. Note, though, that as an
abstract set-theoretic operation, this doesn't hold as much weight
for me as do the consonance-type considerations, which are on the
feeble side for the "anti-diatonic" scales but quite strong for
Blackjack as a whole . . .

P.S. Joseph -- can you locate the three pitches in Blackjack which
can serve as the "tonic" of a Mohajira scale?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_29682.html#29722

> P.S. Joseph -- can you locate the three pitches in Blackjack which
> can serve as the "tonic" of a Mohajira scale?

Hmmm, Paul, I was thinking I was getting some pretty good ones with
tonics just using the first three white notes on the keyboard, which
would mean C, Db^, D<.

I would have thought there would be even more, by continuning to
transpose up by a keyboard wholetone... unless those are
somehow "repeats..."

Unless I'm "off base" here...

Thanks!

_________ ___________ ______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29682.html#29722
>
> > P.S. Joseph -- can you locate the three pitches in Blackjack
which
> > can serve as the "tonic" of a Mohajira scale?
>
> Hmmm, Paul, I was thinking I was getting some pretty good ones with
> tonics just using the first three white notes on the keyboard,
which
> would mean C, Db^, D<.

Well, those are _modes_ of Mohajira, but by "tonic" I meant "first
note in the original mode". Mohajira, again, is 3 4 3 4 3 4 3, with a
conventional perfect fifth and conventional perfect fourth above the
tonic.
>
> I would have thought there would be even more, by continuning to
> transpose up by a keyboard wholetone... unless those are
> somehow "repeats..."

Yes, there are only three Mohajira scales in Blackjack, much as there
are only two whole-tone scales in 12-tET . . .

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_29682.html#29757

>
> Well, those are _modes_ of Mohajira, but by "tonic" I meant "first
> note in the original mode". Mohajira, again, is 3 4 3 4 3 4 3, with
a conventional perfect fifth and conventional perfect fourth above
the tonic.
> >

Hmmm. There must be really something I'm not "getting..." I thought
that the Mohajira was every *third* pitch of blackjack, which would
make it 3 3 3 3 3 3 3... ??

_______ _______ _______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29682.html#29757
>
> >
> > Well, those are _modes_ of Mohajira, but by "tonic" I
meant "first
> > note in the original mode". Mohajira, again, is 3 4 3 4 3 4 3,
with
> a conventional perfect fifth and conventional perfect fourth above
> the tonic.
> > >
>
> Hmmm. There must be really something I'm not "getting..." I
thought
> that the Mohajira was every *third* pitch of blackjack, which would
> make it 3 3 3 3 3 3 3... ??

Joseph, I meant that in steps of 24-tET, it's 3 4 3 4 3 4 3. In steps
of 72-tET, then, it's 9 12 9 12 9 12 9.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_29682.html#29778

> > Hmmm. There must be really something I'm not "getting..." I
> thought that the Mohajira was every *third* pitch of blackjack,
which would make it 3 3 3 3 3 3 3... ??
>
> Joseph, I meant that in steps of 24-tET, it's 3 4 3 4 3 4 3. In
steps of 72-tET, then, it's 9 12 9 12 9 12 9.

Oh... but, still I'm not quite getting how I can distinguish a "root"
of a Mohajira scale from one of the "modes..." (??)

If it's anything like the whole-tone scale in 12-tET there really
*isn't* a root... it's all the same... (??)

Do I get a "hint??"

JP

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29682.html#29778
>
> > > Hmmm. There must be really something I'm not "getting..." I
> > thought that the Mohajira was every *third* pitch of blackjack,
> which would make it 3 3 3 3 3 3 3... ??
> >
> > Joseph, I meant that in steps of 24-tET, it's 3 4 3 4 3 4 3. In
> steps of 72-tET, then, it's 9 12 9 12 9 12 9.
>
> Oh... but, still I'm not quite getting how I can distinguish
a "root"
> of a Mohajira scale from one of the "modes..." (??)

Why not?

2nd mode: 12 9 12 9 12 9 9
3rd mode: 9 12 9 12 9 9 12
4th mode: 12 9 12 9 9 12 9
5th mode: 9 12 9 9 12 9 12
6th mode: 12 9 9 12 9 12 9

Or just look at Graham's page again -- "anti-Phrygian", "anti-
Lydian", etc. . . .
>
> If it's anything like the whole-tone scale in 12-tET there really
> *isn't* a root... it's all the same... (??)

Well, it's not like the whole-tone scale in _that_ respect! I just
meant that, just as the chromatic scale can be partitioned into two
whole-tone scales with no overlap and no missing notes, so the
Blackjack scale can be partitioned into three Mohajira scales with no
overlap and no missing notes.
>
> Do I get a "hint??"

Hopefully I've given you enough here to solve the puzzle: Where are
the roots of the three Mohajira scales in Blackjack?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_29682.html#29786

> Well, it's not like the whole-tone scale in _that_ respect! I just
> meant that, just as the chromatic scale can be partitioned into two
> whole-tone scales with no overlap and no missing notes, so the
> Blackjack scale can be partitioned into three Mohajira scales with
no overlap and no missing notes.
> >
> > Do I get a "hint??"
>
> Hopefully I've given you enough here to solve the puzzle: Where are
> the roots of the three Mohajira scales in Blackjack?

Paul... you're making me think... that's not good for me...

Ummm... Ok, I know now that the Mohajira *has* to be on one of the 24-
tET pitches of 72 equal... so that narrows it somewhat...

On the basis of *sound* I would say the three roots are:

A], D], E]

??

wrong?

JP

Joseph wrote:
>Ummm... Ok, I know now that the Mohajira *has* to be on one of the 24-
>tET pitches of 72 equal... so that narrows it somewhat...

No...

>On the basis of *sound* I would say the three roots are:
>A], D], E]
>wrong?

Alas. You already mentioned one: every third step from the beginning.
on C. Another hint, remove those notes, where can you start with you
have left?

Manuel

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29682.html#29786
>
> > Well, it's not like the whole-tone scale in _that_ respect! I
just
> > meant that, just as the chromatic scale can be partitioned into
two
> > whole-tone scales with no overlap and no missing notes, so the
> > Blackjack scale can be partitioned into three Mohajira scales
with
> no overlap and no missing notes.
> > >
> > > Do I get a "hint??"
> >
> > Hopefully I've given you enough here to solve the puzzle: Where
are
> > the roots of the three Mohajira scales in Blackjack?
>
>
> Paul... you're making me think... that's not good for me...
>
> Ummm... Ok, I know now that the Mohajira *has* to be on one of the
24-
> tET pitches of 72 equal... so that narrows it somewhat...
>
> On the basis of *sound* I would say the three roots are:
>
> A], D], E]
>
> ??
>
> wrong?

I'm afraid so. Those notes are all part of a _single_ Mohajira
scale . . . you haven't touched the other two.

The mistake you're making is in thinking that certain pitches in 72-
tET are "in" 24-tET, while others are "out of" 24-tET.

In this context, that's not correct. Instead, you should be thinking
of 72-tET as _three interlaced_ 24-tET systems.

24 + 24 + 24 = 72.

Blackjack, too, has 1/3 of its pitches in one 24-tET system, 1/3 of
its pitches in a second 24-tET system, and 1/3 of its pitches in the
remaining one -- this should be evident from looking at the
accidentals.

Now, since Mohajira is a subset of 24-tET, and contains 1/3 as many
notes as Blackjack, the above step immediately shows you the three
Mohajira scales.

Now simply look at the step structure of each of these and find the
roots: since the scale goes 3 4 3 4 3 4 3 in quartertones, the root
can be easily located in between the two consecutive 3/4-tone steps.

Capish?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_29682.html#29797

> The mistake you're making is in thinking that certain pitches in 72-
> tET are "in" 24-tET, while others are "out of" 24-tET.
>
> In this context, that's not correct. Instead, you should be
thinking of 72-tET as _three interlaced_ 24-tET systems.
>
> 24 + 24 + 24 = 72.
>

Hi Paul...

Actually, I was thinking about this last night after I made that
post... It didn't make any sense to have that particular 24-tET
subset as "special" since we're dealing with an ET...

Ok... so it's very clear that we're dealing with three chains...

> Blackjack, too, has 1/3 of its pitches in one 24-tET system, 1/3 of
> its pitches in a second 24-tET system, and 1/3 of its pitches in
the remaining one -- this should be evident from looking at the
> accidentals.
>
> Now, since Mohajira is a subset of 24-tET, and contains 1/3 as many
> notes as Blackjack, the above step immediately shows you the three
> Mohajira scales.
>
> Now simply look at the step structure of each of these and find the
> roots: since the scale goes 3 4 3 4 3 4 3 in quartertones, the root
> can be easily located in between the two consecutive 3/4-tone steps.
>
> Capish?

Well... I am *definitely* certain now of E[ being the root, since it
is the only way from the blackjack pitches we get the quartertone
pattern 3 4 3 4 3 4 3....

However, I'm not figuring out yet how to find the other roots...

I just ran out of time... so I'll try that part of it tomorrow...

JP

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

/tuning/topicId_29682.html#29817

> >
> > Capish?
>
>
> Well... I am *definitely* certain now of E[ being the root, since
it is the only way from the blackjack pitches we get the quartertone
> pattern 3 4 3 4 3 4 3....
>
> However, I'm not figuring out yet how to find the other roots...
>
> I just ran out of time... so I'll try that part of it tomorrow...
>
> JP

Well, it's "tomorrow" and I think I *might* have the solution to this
puzzle... The candidates that look like they would fit the correct
Mohajira pattern in Blackjack to be the "tonic" appear to be:

E[ (which I had guessed before), Db^ and D>

Is that correct??

JP

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., jpehrson@r... wrote:
>
> /tuning/topicId_29682.html#29817
>
> > >
> > > Capish?
> >
> >
> > Well... I am *definitely* certain now of E[ being the root, since
> it is the only way from the blackjack pitches we get the
quartertone
> > pattern 3 4 3 4 3 4 3....
> >
> > However, I'm not figuring out yet how to find the other roots...
> >
> > I just ran out of time... so I'll try that part of it tomorrow...
> >
> > JP
>
>
> Well, it's "tomorrow" and I think I *might* have the solution to
this
> puzzle... The candidates that look like they would fit the correct
> Mohajira pattern in Blackjack to be the "tonic" appear to be:
>
> E[ (which I had guessed before), Db^ and D>
>
> Is that correct??

Let's check E[.

Taking every third note from there, we get the scale

E[ F G A[ B[ C D[ E[

the intervals in 24-tET being

3 4 3 4 3 3 4

. . . which is not quite the same as

3 4 3 4 3 4 3

So, sorry Joseph, E[ is not correct.

I'll give you a chance to submit another answer for where the three
Mohajira roots are.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_29682.html#29831

>
> Let's check E[.
>
> Taking every third note from there, we get the scale
>
> E[ F G A[ B[ C D[ E[
>
> the intervals in 24-tET being
>
> 3 4 3 4 3 3 4
>
> . . . which is not quite the same as
>
> 3 4 3 4 3 4 3
>
> So, sorry Joseph, E[ is not correct.
>
> I'll give you a chance to submit another answer for where the three
> Mohajira roots are.

Well... we'll try this puzzle again!

It looks as though you have actually given the first one away in the
above. If I'm understanding this, I am to look for the pitch that is
between the two 3's....

In that case, it *has* to be "C." I thought at one point you said
the Mohajira starting on "C" was one of the "modes" but maybe I was
just getting confused.

So, I'll say "C.." [Did I get the buzzer yet??]

Now...

As to the other two.... using the same procedures of trying to find
the patterns of threes and fours I get:

Db^

which is actually one of the ones I had before....

However, now I have a *new* candidate for the THIRD one:

Bv

So, in total, the three roots are (maybe):

C, Db^ and Bv

How was *that* try???

:)

________ ________ _______
Joseph Pehrson

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

> So, in total, the three roots are (maybe):
>
> C, Db^ and Bv
>
> How was *that* try???
>
> :)

You got it! The roots are C (the center), one secor above C, and one
secor below C.

In general, if you find any structure in Blackjack (or Canasta, or
Miracle-41, etc.), you're most likely to find it one secor away, a
little less likely to find it two secors away, a little less likely
still to find it three secors away, and so on . . . this should be
obvious from Dave Keenan's "slide rules" . . .

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_29682.html#29889

> --- In tuning@y..., jpehrson@r... wrote:
>
> > So, in total, the three roots are (maybe):
> >
> > C, Db^ and Bv
> >
> > How was *that* try???
> >
> > :)
>
> You got it! The roots are C (the center), one secor above C, and
one
> secor below C.
>
> In general, if you find any structure in Blackjack (or Canasta, or
> Miracle-41, etc.), you're most likely to find it one secor away, a
> little less likely to find it two secors away, a little less likely
> still to find it three secors away, and so on . . . this should be
> obvious from Dave Keenan's "slide rules" . . .

Great, Paul...

I hate to say it, though, but I never quite got the hang of how to
use the Keenan "slide rules..." Maybe if you can get some time, you
could do a little "tutorial" on that... I'm sure it would be very
valuable for me...

I think I lost the archive number for the "slide rules" too....

Joseph

jpehrson@rcn.com wrote:

> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29682.html#29889
>
> > --- In tuning@y..., jpehrson@r... wrote:
> >
> > > So, in total, the three roots are (maybe):
> > >
> > > C, Db^ and Bv
> > >
> > > How was *that* try???
> > >
> > > :)
> >
> > You got it! The roots are C (the center), one secor above C, and
> one
> > secor below C.
> >
> > In general, if you find any structure in Blackjack (or Canasta, or
> > Miracle-41, etc.), you're most likely to find it one secor away, a
> > little less likely to find it two secors away, a little less likely
> > still to find it three secors away, and so on . . . this should be
> > obvious from Dave Keenan's "slide rules" . . .
>
> Great, Paul...
>
> I hate to say it, though, but I never quite got the hang of how to
> use the Keenan "slide rules..." Maybe if you can get some time, you
> could do a little "tutorial" on that... I'm sure it would be very
> valuable for me...
>
> I think I lost the archive number for the "slide rules" too....
>
> Joseph

If I might humbly interject here, the slide rules are excellent but I'd recommend viewing them in
Courier in order for everything to line up properly. Two of Dave Keenan's posts with slide rules are as
follows : -

Fri 11 May - 'Blackjack - Pentads,tetrads, triads, hexanies'

Sat 12 May - '12 tone scales and 9-limit asses'

Hope this helps

Best Wishes

jpehrson@rcn.com wrote:

> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29682.html#29889
>
> > --- In tuning@y..., jpehrson@r... wrote:
> >
> > > So, in total, the three roots are (maybe):
> > >
> > > C, Db^ and Bv
> > >
> > > How was *that* try???
> > >
> > > :)
> >
> > You got it! The roots are C (the center), one secor above C, and
> one
> > secor below C.
> >
> > In general, if you find any structure in Blackjack (or Canasta, or
> > Miracle-41, etc.), you're most likely to find it one secor away, a
> > little less likely to find it two secors away, a little less likely
> > still to find it three secors away, and so on . . . this should be
> > obvious from Dave Keenan's "slide rules" . . .
>
> Great, Paul...
>
> I hate to say it, though, but I never quite got the hang of how to
> use the Keenan "slide rules..." Maybe if you can get some time, you
> could do a little "tutorial" on that... I'm sure it would be very
> valuable for me...
>
> I think I lost the archive number for the "slide rules" too....
>
> Joseph

If I might humbly interject here, the slide rules are excellent but I'd recommend viewing them in
Courier in order for everything to line up properly. Two of Dave Keenan's posts with slide rules are as
follows : -

Fri 11 May - 'Blackjack - Pentads,tetrads, triads, hexanies'

Sat 12 May - '12 tone scales and 9-limit asses'

Hope this helps

Best Wishes

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> Fri 11 May - 'Blackjack - Pentads,tetrads, triads, hexanies'

These should help you find the 4:5:6:9:11 and 4:6:7:9:11 pentads.

Sat 12 May - '12 tone scales and 9-limit asses'

Ah yes -- those 9-limit asses could also be used to base some
harmonically nice 6- or 8-tone subsets of Blackjack upon.