Optimum key for Blackjack in 6x12-tET notation?

was: I won't be the "white elephant..." [Blackjack]
/tuning/topicId_30143.html#30145

was: Apocalypse of the two (blackjack) elephants
/tuning/topicId_30143.html#30143

--- In tuning@y..., jpehrson@r... wrote:
> A "white elephant" is an American expression, maybe English, of
> something out of date. Perhaps you have that expression in
Australia
> too.

Don't worry Joseph. The entire English speaking world has been so colonised by US television that we know all your idiomatic expressions, even though you don't know ours.

> It appears you are saying that your original D-centered scale was
not
> the optimal one. I'm inferring that Graham Breed figured out the
> optimal one.

Yes and yes (either that or he's very close, just my humble opinion).

> I'm all for getting this eventually pinned down. However, as you
> know, and as Margo Schulter has mentioned on this list, the
> gravitational pull of "C" [even moreso, "big daddy" MIDDLE C] has a
> profound influence on our Western musical culture.

I'm not sure what this implies for our standard Blackjack key?

> I particularly like the fact that the "middle C" on my keyboard
> matches that of my traditional piano in 12-tET.

If that's all, then there's no problem. Any Blackjack note that is _notated_ the same as a 12-tET note will be _tuned_ the same as that 12-tET note. There's never been any argument about that.

> Well, I can see what you're saying, and C hasn't become "tonicized"
> in my Blackjack writing so far,

Has any note? Even temporarily? What notes occur most often in your Blackjack writing so far?

> but I think, quite frankly, I am more
> concerned about "middle C" being "middle C" on the standard piano
> than that the two small scale steps have to surround it... if that's
> any help...

That's a _huge_ help. So we'll make sure it has a C natural in it.

I understand that Allison wants the standard of "A" for
> the same reason...

Yes. The requirement to have both C and A naturals reduces the field to only 3 possibilities, and means that we must have naturals CGDA and can have no others.

> I believe there is a tiny error here, since I don't have an E. I
> believe it should be Ev.

Well spotted. I was just testing you. ;-)

> In "my" system, there are three naturals, and in Graham's there
> appear to be only FOUR.... so that's only an addition of *one* more
> natural. (Better check my math on that, Dave...)

Correct. :-) But FOUR naturals is the _most_ we can have (in a 12-tET based notation for Blackjack), and I haven't (yet) found or heard any reason not to have as many naturals as we can.

Me:
> > Notice something about Graham's key? Wherever there's a # there's
a
> v next to it and wherever there's a b there's a ^ next to it. So the
> ^ and v could be omitted if the player was told that # means 5/12
> tone sharp and b means 5/12 tone flat. Then we'd never need more
than
> one accidental per note.

Joseph:
> Well, quite frankly, I see a tiny problem with this. I think one of
> the great "virtues" of Blackjack is that it's a subset of 72-tET,
and
> one of the great virtues of 72-tET is that it *contains* 12-tET in
> all it's glory... So, I would prefer leaving the "original" sharps
> and flats of 12 and 72-tET intact and just "add on" from there. In
> that sense, I find the "double accidentals" actually *simpler!*

Sure. Forget I mentioned it. But the consistency should still help prevent mistakes and make sight reading easier.

> 1) A converted "color sticker" keyboard... I'll do that

Now that you're understanding how seeing patterns on the chain of secors helps avoid wolves, maybe you're ready for a different colouring method. One that has a colour for each chain of secors. The different chains are an octave apart. But we can worry about that later.

> 2) A converted visual Blackjack lattice of Paul's design, that I use
> all the time.

Sure. I will convert this if Paul wants me to. I can even provide #s where needed. ;-)

> 3) The 10 pages or so of Blackjack chords that Paul made all
> converted (parallel chords) since I use those all the time, too.

Hmm. I already converted (some of?) these once (more fool me). I'd rather not do it again.

> 4) The conversion of about 20 to 30 Tuning List posts related to
> my "former" key in Blackjack that I frequently use...

Maybe some tuning-list software genius can provide a perl script or something to do this, and therefore the chord charts too, assuming they are plain text files.

> Whew!... This had better be worth it, Dave.

I don't know. Wait and see what others think.

> So far, Paul Erlich has "weighed in" on the fact that the conversion
> isn't really worth the effort, at least that's been my impression.
> (I could be mistaken).

Well I agree that the conversion from C-centered to D-centered wouldn't have been worth it. It would still have only had three naturals. Good onya Paul.

But I think Graham's proposal, centered on B[, or equivalently centered on the G:D fifth, has significant advantages. I'm dying to hear what Paul thinks. I hope he has some good arguments against it. It wouldn't be any fun otherwise. ;-)

Graham, you apparently thought it was so obviously useful that it must have _already_ been the standard. Is that correct?

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

In-Reply-To: <3.0.6.32.20011113232821.00afbd70@uq.net.au>
Dave Keenan wrote:

> Graham, you apparently thought it was so obviously useful that it must
> have _already_ been the standard. Is that correct?

Half right -- I thought it was already the standard. I write Blackjack
with the decimal 0 at the point between the two quommas. All I did was
convert that to the 12*6 notation using your 4==D standard.

That gives the lattice at
<http://x31eq.com/miracle/blackjack.txt> which I used to
convert those chords. I notice I used Bv on the lattice but Bb in the
e-mail and you corrected that in the conversion chart.

The Python script at
<http://x31eq.com/miracle/decimal_conversion.py> can print out
the charts for whatever standard we settle on. Searching and replacing in
existing documents will be more difficult. I had to do the lattices by
hand, because names in different systems don't have the same number of
characters.

One thing about the < and >. If you have < followed by > on the same line
in an HTML file, it's interpreted as a tag and so vanishes. That's why
the 6*12 lattices I put up have to be text files. I see SciTE does
"replace in selection" which makes converting < to < in <PRE> blocks
easier, but using ^ and v in the first place is even easier still.

Graham

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:

/tuning/topicId_30148.html#30148

> was: I won't be the "white elephant..." [Blackjack]
> /tuning/topicId_30143.html#30145
>
> was: Apocalypse of the two (blackjack) elephants
> /tuning/topicId_30143.html#30143
>
> --- In tuning@y..., jpehrson@r... wrote:
> > A "white elephant" is an American expression, maybe English, of
> > something out of date. Perhaps you have that expression in
> Australia
> > too.
>
> Don't worry Joseph. The entire English speaking world has been so
colonised by US television that we know all your idiomatic
expressions, even though you don't know ours.
>

[JP:]
Hmmm. What it is that makes me think this is somehow related to some
of the problems America has recently been having...

[DK:]
> > It appears you are saying that your original D-centered scale was
> not the optimal one. I'm inferring that Graham Breed figured out
the optimal one.
>
> Yes and yes (either that or he's very close, just my humble
opinion).

[JP:]
Well, Dave, I'm certainly glad, then, that I didn't change everything
around to the *first* Blackjack scale! :)

Maybe it's best to wait until more thinking (hopefully) has been
done...

> > I particularly like the fact that the "middle C" on my keyboard
> > matches that of my traditional piano in 12-tET.
>
> If that's all, then there's no problem. Any Blackjack note that is
_notated_ the same as a 12-tET note will be _tuned_ the same as that
12-tET note. There's never been any argument about that.
>
> > Well, I can see what you're saying, and C hasn't
become "tonicized" in my Blackjack writing so far,
>
> Has any note? Even temporarily? What notes occur most often in your
Blackjack writing so far?
>

[JP]
I haven't done a statistical analysis or anything of the kind, as
yet. I *do* know that certain "common tone" progressions that I have
been working on with the lattice seem to tonicize things, at least
temporarily. Maybe I'll know more about this as I work with it all
more..

> > but I think, quite frankly, I am more
> > concerned about "middle C" being "middle C" on the standard piano
> > than that the two small scale steps have to surround it... if
that's any help...
>
> That's a _huge_ help. So we'll make sure it has a C natural in it.
>

I guess that's really all that is necessary. I guess it's nice to
have the two little intervals on either side of the "C" but, if there
are significant advantages to doing something else, I can lose that
with few problems.

> I understand that Allison wants the standard of "A" for
> > the same reason...
>
> Yes. The requirement to have both C and A naturals reduces the
field to only 3 possibilities, and means that we must have naturals
CGDA and can have no others.
>
> > I believe there is a tiny error here, since I don't have an E. I
> > believe it should be Ev.
>
> Well spotted. I was just testing you. ;-)
>
> > In "my" system, there are three naturals, and in Graham's there
> > appear to be only FOUR.... so that's only an addition of *one*
more natural. (Better check my math on that, Dave...)
>
> Correct. :-) But FOUR naturals is the _most_ we can have (in a 12-
tET based notation for Blackjack), and I haven't (yet) found or heard
any reason not to have as many naturals as we can.
>
> Me:
> > > Notice something about Graham's key? Wherever there's a #
there's a v next to it and wherever there's a b there's a ^ next to
it. So the ^ and v could be omitted if the player was told that #
means 5/12 tone sharp and b means 5/12 tone flat. Then we'd never
need more than one accidental per note.
>
> Joseph:
> > Well, quite frankly, I see a tiny problem with this. I think one
of the great "virtues" of Blackjack is that it's a subset of 72-tET,
> and one of the great virtues of 72-tET is that it *contains* 12-tET
in all it's glory... So, I would prefer leaving the "original"
sharps and flats of 12 and 72-tET intact and just "add on" from
there. In that sense, I find the "double accidentals" actually
*simpler!*
>

> Sure. Forget I mentioned it. But the consistency should still help
prevent mistakes and make sight reading easier.
>

> > 1) A converted "color sticker" keyboard... I'll do that
>
> Now that you're understanding how seeing patterns on the chain of
secors helps avoid wolves, maybe you're ready for a different
colouring method. One that has a colour for each chain of secors. The
different chains are an octave apart. But we can worry about that
later.

[JP]
Yes, I remember you were trying to do that on your *previous* D-based
system. This could be an interesting refinement when things get
sorted out.

>
> > 2) A converted visual Blackjack lattice of Paul's design, that I
use all the time.
>
> Sure. I will convert this if Paul wants me to. I can even provide
#s where needed. ;-)
>
> > 3) The 10 pages or so of Blackjack chords that Paul made all
> > converted (parallel chords) since I use those all the time, too.
>
> Hmm. I already converted (some of?) these once (more fool me). I'd
rather not do it again.
>

[JP]
It's true, there may be some conversions as I recall. I'll have to
hunt around for those..

> > 4) The conversion of about 20 to 30 Tuning List posts related to
> > my "former" key in Blackjack that I frequently use...
>
> Maybe some tuning-list software genius can provide a perl script or
something to do this, and therefore the chord charts too, assuming
they are plain text files.
>
> > Whew!... This had better be worth it, Dave.
>
> I don't know. Wait and see what others think.
>
> > So far, Paul Erlich has "weighed in" on the fact that the
conversion isn't really worth the effort, at least that's been my
impression. (I could be mistaken).
>
> Well I agree that the conversion from C-centered to D-centered
wouldn't have been worth it. It would still have only had three
naturals. Good onya Paul.
>
> But I think Graham's proposal, centered on B[, or equivalently
centered on the G:D fifth, has significant advantages. I'm dying to
hear what Paul thinks. I hope he has some good arguments against it.
It wouldn't be any fun otherwise. ;-)
>
> Graham, you apparently thought it was so obviously useful that it
must have _already_ been the standard. Is that correct?
>

[JP]
It was the standard in Graham's brain, so he probably figured it
seeped into everybody else's by osmosis. But the inventor of the
GRAHAM BREED MIDI RELAY can do no wrong!!!

JP

--- In tuning@y..., graham@m... wrote:

/tuning/topicId_30148.html#30154

> One thing about the < and >. If you have < followed by > on the
same line in an HTML file, it's interpreted as a tag and so
vanishes. That's why the 6*12 lattices I put up have to be text
files. I see SciTE does "replace in selection" which makes
converting < to < in <PRE> blocks easier, but using ^ and v in the
first place is even easier still.
>
>
> Graham

Hmmm. Well, that HTML thing is not great, but, still, it's no reason
to necessarily default to a different ascii system...

Can you add an apostrophe or some such?? '<, etc?

JP

In-Reply-To: <9svb82+roph@eGroups.com>
Joseph Pehrson wrote:

> It was the standard in Graham's brain, so he probably figured it
> seeped into everybody else's by osmosis. But the inventor of the
> GRAHAM BREED MIDI RELAY can do no wrong!!!

Thanks for the vote of confidence, but I think I've changed my mind, and
now agree with Dave Keenan who thought he was agreeing with me. So I must
have gone wrong somewhere.

Here's a table:

D> F#v A> C#v E> G#v B>
Db^ F< Ab^ C< Eb^ G< Bb^
C E[ G B[ D F] A
Bv D> F#v A> C#v E> G#v
Bb< Db^ F< Ab^ C< Eb^ G<

Each row should be a neutral third MOS in 6*12 notation. The rows should
be separated by secors. That means each three adjacent rows are a
Blackjack scale.

If we want C and A in the scale, as we seem to be agreed, that leaves us
with one of these three scales. The question is, which one? I think I
used the bottom three rows before. But I think Dave thought I was using
the middle three rows because he said "centered on B[ or G-D" didn't he?
The only difference is Bb< instead of Bb^ and as this wasn't in the chords
I gave, who was to know? I wrote it A#< on the lattice anyway.

Well, there's not much to choose between these three, but I think the
middle one's best, because:

It's easiest to remember. Start with the Mohajira with A and C, and add a
secor either side of each note.

The secors between the Mohajiras all involve a change of note letter,
which must count for something.

The reason I wrote A#< instead of Bb< is that this note is nearer to A
than B. Whereas Bb^ is nearer to B, so I think that notation Just
Works(TM).

You can re-write it as

C#^ E#< G#^ B#< D#^ F#]^ A#^
C E[ G B[ D F] A
Cbv Db[v Gbv Ab[v Dbv Fb> Abv

which is a bit contrived, but does mean that you can ignore the
hieroglyphics and uniquely identify each note in a familiar way

C# E# G# B# D# F# A#
C E G B D F A
Cb Db Gb Ab Db Fb Ab

I can't think why you'd want to do that, because it's likely to confuse
more than it helps. Perhaps to make it easier to enter the notes into a
score editor. But being able to do so seems like as good a reason as any
to choose this option over the other two.

Graham

--- In tuning@y..., graham@m... wrote:
>
> Here's a table:
>
> D> F#v A> C#v E> G#v B>
> Db^ F< Ab^ C< Eb^ G< Bb^
> C E[ G B[ D F] A
> Bv D> F#v A> C#v E> G#v
> Bb< Db^ F< Ab^ C< Eb^ G<
>
> It's easiest to remember. Start with the Mohajira with A and C,
and add a
> secor either side of each note.
>
> The secors between the Mohajiras all involve a change of note
letter,
> which must count for something.

Is it true that in this key, all 7:9s, 5:4s, 11:9s, 6:5s, and 7:6s
are always spelled as thirds? If there's only way to acheive that, I
vote for the key that does.

With Paul Erlich's permission I have modified his beautiful colour perspective 7-limit Blackjack lattice diagrams to show the key centered on G:D that we are considering as a standard.

First the fully coloured lattice.
http://dkeenan.com/Music/Miracle/Blackjack7LatticeGD.gif

Then the one with periodicity blocks delimited by greyed edges. Note this is a different periodicity block to the one Paul used with the key centered on C.
http://dkeenan.com/Music/Miracle/Blackjack7LatticePBGD.gif

My current feeling is that the only other key with as much claim to becoming the standard might be the one transposed up a fifth from this, centered on D:A, having naturals GDAE. It doesn't have any C natural but it does have 4 notes that are open strings on guitar and violin etc.

Anyone want to suggest another key, or say what they think is good or bad about either of these two?

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:

> Then the one with periodicity blocks delimited by greyed edges.
Note this is a different periodicity block to the one Paul used

There was more than one.

> with the key centered on C.
> http://dkeenan.com/Music/Miracle/Blackjack7LatticePBGD.gif

Your colored blocks are poor in tetrads, however you assign B]. By
the way, I like notations that avoid "[" -- look again at the Sims-
Maneri notation:

https://www.mindeartheart.org/micro.html

But one of my block assignments had five otonal and five utonal
tetrads fully colored:

/tuning/files/perlich/scales/blackjack6.g
if

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:
>
> > Then the one with periodicity blocks delimited by greyed edges.
> Note this is a different periodicity block to the one Paul used
>
> There was more than one.

Oh. Sorry.

> > with the key centered on C.
> > http://dkeenan.com/Music/Miracle/Blackjack7LatticePBGD.gif
>
> Your colored blocks are poor in tetrads, however you assign B]. By
> the way, I like notations that avoid "[" -- look again at the Sims-
> Maneri notation:
>
> https://www.mindeartheart.org/micro.html

I looked. I don't get your point. Please explain.

> But one of my block assignments had five otonal and five utonal
> tetrads fully colored:
>
>
/tuning/files/perlich/scales/blackjack6.g
if

Very good. But 7-limit tetrads aren't everything. The PB I gave was
based on the two "delicious" chords a secor apart. That implies it
should be a 9-limit optimum, which doesn't show up on the 7-limit
lattice.

Anyway the PB doesn't matter, we're not trying to standardise that.

I had the idea that if we went thru every subset scale we've found and
looked at how many naturals they end up with in all their possible
positions (or maybe just the best position for each scale) then total
them all up, that might be a useful measure to compare keys.

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > I like notations that avoid "[" -- look again at the Sims-
> > Maneri notation:
> >
> > https://www.mindeartheart.org/micro.html
>
> I looked. I don't get your point. Please explain.

Well, ] looks right, but [ doesn't.

> 7-limit tetrads aren't everything. The PB I gave was
> based on the two "delicious" chords a secor apart. That implies it
> should be a 9-limit optimum,

Not necessarily, as far as I can see . . . does it have the most
possible 9-limit pentads and asses?

> Anyway the PB doesn't matter, we're not trying to standardise that.

True -- so why indicate it at all?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> >
> > > I like notations that avoid "[" -- look again at the Sims-
> > > Maneri notation:
> > >
> > > https://www.mindeartheart.org/micro.html
> >
> > I looked. I don't get your point. Please explain.
>
> Well, ] looks right, but [ doesn't.

Oh. Well I really don't think we should let our choice of ASCII
notation affect our choice of Blackjack key. It's only a product of
the limitations of our technology and could become irrelevant next
year.

> > 7-limit tetrads aren't everything. The PB I gave was
> > based on the two "delicious" chords a secor apart. That implies it
> > should be a 9-limit optimum,
>
> Not necessarily, as far as I can see . . . does it have the most
> possible 9-limit pentads and asses?

Apparently not. But it seems pretty good on a 9-limit dyadic basis so
it's probably got lots of "magic" chords, which are not obvious
from the lattice.

> > Anyway the PB doesn't matter, we're not trying to standardise
that.
>
> True -- so why indicate it at all?

If I'd shown this key with your PB (the one I was aware of) it would
have looked silly. One is centered on a note, the other on an
interval. I needed to show one that it made sense with.

That's it from me for the night,

Regards,
-- Dave Keenan

In-Reply-To: <9t28bu+uujk@eGroups.com>
Paul Erlich asked:

> Is it true that in this key, all 7:9s, 5:4s, 11:9s, 6:5s, and 7:6s
> are always spelled as thirds? If there's only way to acheive that, I
> vote for the key that does.

No. That's impossible for any scale with consecutive 5:4 approximations
that tempers out the septimal kleisma.

225 5 5 9 1
--- = - x - x - x -
224 4 4 7 2

So two major thirds plus a diminished fourth add up to an octave. They
can't all be spelled as thirds. If you've ever tried notating an
augmented triad, you'll know that circle can't be squared.

I think even the simpler and more relevant goal of all 5-limit intervals
being "correct" can't be done.

3:2 approximates to 6 secors
8:5 approximates to 7 secors

That means 7 fifths plus 6 major thirds add up to 6 octaves. Or 7 6:5
minor thirds and 13 5:4 major thirds. For them all to be spelled
consistently, a circle of 20 thirds would have to end up when it started.
That won't work with 7-based notation, because 20 isn't a multiple of 7.
As Blackjack is 5-limit connected and has 21 notes it won't work for that
either. I'm not so sure about that proof, but it does seem to apply.

We have to settle for fifths and neutral thirds being consistent.

Graham

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:

/tuning/topicId_30148.html#30251

> With Paul Erlich's permission I have modified his beautiful colour
perspective 7-limit Blackjack lattice diagrams to show the key
centered on G:D that we are considering as a standard.
>
> First the fully coloured lattice.
> http://dkeenan.com/Music/Miracle/Blackjack7LatticeGD.gif
>
> Then the one with periodicity blocks delimited by greyed edges.
Note this is a different periodicity block to the one Paul used with
the key centered on C.
> http://dkeenan.com/Music/Miracle/Blackjack7LatticePBGD.gif
>
> My current feeling is that the only other key with as much claim to
becoming the standard might be the one transposed up a fifth from
this, centered on D:A, having naturals GDAE. It doesn't have any C
natural but it does have 4 notes that are open strings on guitar and
violin etc.
>
> Anyone want to suggest another key, or say what they think is good
or bad about either of these two?
>

Hi Dave!

Well, this is all very cool, but my guess is I should wait a bit
longer and follow the discussion before I "change everything
around..." Of course, my *current* and *former* Blackjack pieces
will have a slightly different notation...

Oh well, the good news is that even if I change the standard, with
the compositional procedures I use, for the most part everything will
*SOUND* pretty much the same, anyway!

JP

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

/tuning/topicId_30148.html#30253

> --- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:
>
> > Then the one with periodicity blocks delimited by greyed edges.
> Note this is a different periodicity block to the one Paul used
>
> There was more than one.
>
> > with the key centered on C.
> > http://dkeenan.com/Music/Miracle/Blackjack7LatticePBGD.gif
>
> Your colored blocks are poor in tetrads, however you assign B]. By
> the way, I like notations that avoid "[" -- look again at the Sims-
> Maneri notation:
>
> https://www.mindeartheart.org/micro.html
>

Well, the issue of the use of "[" seems somewhat a moot point, in
*my* opinion. Or should we call it a "Mook" point??

Close enough for jazz, I say...

JP

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

/tuning/topicId_30148.html#30256

>
> Very good. But 7-limit tetrads aren't everything.

OOOOh.... dunno! They seem *very* important in *my* Blackjack
composing so far, anyway...

JP

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

> > > 7-limit tetrads aren't everything. The PB I gave was
> > > based on the two "delicious" chords a secor apart. That implies
it
> > > should be a 9-limit optimum,
> >
> > Not necessarily, as far as I can see . . . does it have the most
> > possible 9-limit pentads and asses?
>
> Apparently not. But it seems pretty good on a 9-limit dyadic basis
so
> it's probably got lots of "magic" chords, which are not obvious
> from the lattice.

Wait a minute, Dave. Once you divvy up the lattice like this, you're
not allowing any "magic" to take place at all, since none of
the "double meanings" can show up within a single block!

--- In tuning@y..., graham@m... wrote:
> In-Reply-To: <9t28bu+uujk@e...>
> Paul Erlich asked:
>
> > Is it true that in this key, all 7:9s, 5:4s, 11:9s, 6:5s, and
7:6s
> > are always spelled as thirds? If there's only way to acheive
that, I
> > vote for the key that does.
>
> No. That's impossible

George Secor didn't think so -- see principle (1) in:

http://www.anaphoria.com/secor.PDF

Of course there must be some mitigating factor?

Paul:
> > > Is it true that in this key, all 7:9s, 5:4s, 11:9s, 6:5s, and
> 7:6s
> > > are always spelled as thirds? If there's only way to acheive
> that, I
> > > vote for the key that does.

Me:
> > No. That's impossible

Paul:
> George Secor didn't think so -- see principle (1) in:
>
> http://www.anaphoria.com/secor.PDF
>
> Of course there must be some mitigating factor?

He's talking about the Partch 43 note JI scale. You can name the thirds you
get in that consistently, but not the extra ones from Miracle temperament.
The latter are jagged lines in the diagram on p. 2, and you can see that some
of them aren't spelled right.

Graham

--- In tuning@y..., jpehrson@r... wrote:
> Hi Dave!
>
> Well, this is all very cool, but my guess is I should wait a bit
> longer and follow the discussion before I "change everything
> around..."

Absolutely! In fact I intend no pressure on you to change _ever_. You
may remember I suggested that if the standard ends up being different
from what you're using, you just need a table (or find-and-replace
script) to translate, when communicating about it on the tuning list.

> Of course, my *current* and *former* Blackjack pieces
> will have a slightly different notation...

Sure. No problem.

> Oh well, the good news is that even if I change the standard, with
> the compositional procedures I use, for the most part everything
will
> *SOUND* pretty much the same, anyway!

Yes, if we go for the G:D centered one it would only mean transposing
down by 150 cents from your current key. But we shouldn't let that
influence us in trying to determine what might be the best standard
key for an indefinite future.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> Wait a minute, Dave. Once you divvy up the lattice like this, you're
> not allowing any "magic" to take place at all, since none of
> the "double meanings" can show up within a single block!

Yes. You're absolutely right. So what do I really mean?
What I actually did was to take it as given that the G:D fifth was in
the centre of the PB and then to add the other notes of the "delicious
chords in their closest positions to that, then add the remaining
notes so as to keep the PB as compact and convex as possible.

Another aim, which I hoped to achieve indirectly by this means, was to
have as few lines greyed out as possible (particularly if ratios of 9
were included as well). One could count the number of coloured lines
in each of our PBs and compare them (grey out another arbitrary two
attached to B[ on mine).

So I'm taking a 9-limit dyadic optimisation approach and you're taking
a 7-limit tetradic one. Neither are likely to have any impact on the
choice of a standard key, but are interesting in their own right.

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

/tuning/topicId_30148.html#30256

> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:
> >
> > > Then the one with periodicity blocks delimited by greyed edges.
> > Note this is a different periodicity block to the one Paul used
> >
> > There was more than one.
>
> Oh. Sorry.
>
> > > with the key centered on C.
> > >
http://dkeenan.com/Music/Miracle/Blackjack7LatticePBGD.gif
> >
> > Your colored blocks are poor in tetrads, however you assign B].

You know... I looked at this lattice again, and I really think it's
going to be a problem.

I can't even find my "beloved" C:G:Ev:Bb< tetrad which has become
like a "C-major chord" in my new Blackjack composing!

JP

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

/tuning/topicId_30148.html#30289

> --- In tuning@y..., jpehrson@r... wrote:
>
> > Oh well, the good news is that even if I change the standard,
with the compositional procedures I use, for the most part everything
> will *SOUND* pretty much the same, anyway!
>
> Yes, if we go for the G:D centered one it would only mean
transposing
> down by 150 cents from your current key. But we shouldn't let that
> influence us in trying to determine what might be the best standard
> key for an indefinite future.

Of course... I agree! However, if the "new" Blackjack scale messes
up the visual lattices so they don't show the *basic* "everyday*
tetrads of Blackjack, that could be a problem.

That *is* a problem with the "new" version, yes??

JP

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

/tuning/topicId_30148.html#30290

> So I'm taking a 9-limit dyadic optimisation approach and you're
taking a 7-limit tetradic one. Neither are likely to have any impact
on the choice of a standard key, but are interesting in their own
right.

But, we can't use the two different lattices and retain the same
pitch names for Blackjack, is that correct??

JP

Joseph Pehrson wrote:
> You know... I looked at this lattice again, and I really think it's
> going to be a problem.
>
> I can't even find my "beloved" C:G:Ev:Bb< tetrad which has become
> like a "C-major chord" in my new Blackjack composing!

> ... if the "new" Blackjack scale messes
> up the visual lattices so they don't show the *basic* "everyday*
> tetrads of Blackjack, that could be a problem.
>
> That *is* a problem with the "new" version, yes??

Dave Keenan to Paul Erlich:
>> So I'm taking a 9-limit dyadic optimisation approach and you're
>> taking a 7-limit tetradic one. Neither are likely to have any impact
>> on the choice of a standard key, but are interesting in their own
>> right.

Joseph Pehrson:
> But, we can't use the two different lattices and retain the same
> pitch names for Blackjack, is that correct??

Joseph,

What do you mean "two different lattices"? There's only one (7-limit) Blackjack lattice. It's only the pitch names that _can_ change.

You seem to be confusing one particular periodicity block, in the endlessly repeating lattice, with Blackjack itself. Blackjack is so much more than any particular periodicity block. The PB I gave was simply a single example of a harmonically meaningful one centered on a fifth, rather than on a note.

Since this PB doesn't suit you, you should ignore
http://dkeenan.com/Music/Miracle/Blackjack7LatticePBGD.gif
(It has no necessary relationship to the proposed standard key.)
and only consider
http://dkeenan.com/Music/Miracle/Blackjack7LatticeGD.gif

Also, I expect you have naturally tended to compose around chords that had simple spellings in the key you are using. I'm afraid the fact that a different key _then_ treats these specific works badly, doesn't seem too relevant to our attempt to find an all-round most-convenient key.

What is a "beloved", "basic" or "everyday" tetrad to you, may not be so to another composer, or even to you in a week's time!

Lets look at _all_eight_ of the available tetrads, on the slide rule below. The top line gives the notation for the Blackjack key that is centered on C. The second line shows the only Blackjack key that contains both C and A natural and has the chain of natural fifths centered within the chain of secors. The patterns for otonal and utonal 7-limit tetrads are shown below those.

By sliding the patterns along we find that the C-centered key has only one otonal and one utonal tetrad whose root (and consequently fifth) is natural (Csm7, FmSM6). The G:D-centered key has two of each (Gsm7, Dsm7, CmSM6, GmSM6).

C> D[Eb< Ev F Gb^ G> A[Bb< Bv C Db^ D> E[ F<F#v G Ab^ A> B[ C<
Bv C Db^ D> E[ F<F#v G Ab^ A> B[ C<C#v D Eb^ E> F] G<G#v A Bb^
5--------------7-----1-----------------3
1/3---------------1/1---1/7------------1/5

But of course to limit our comparison of possible standard keys to considering only these tetrads, or even to the entire 7-limit, would be to limit it to a tiny part of the resources of this tuning.

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

It seems that the first thing we might agree on, is whether it is better to have 3 naturals or 4, in our standard Blackjack key.

The problem with finding the best standard, is that we need to predict the future. It seems to me that the best bet we have for doing that, is to look at the past. We have in the Scala archive, a repository of scales (but unfortunately not chords) that people have found to be interesting. Unfortunately there is no indication of just _how_ interesting, but it's a start, and some of us can add that information.

We know that some 70 or so of these are approximate subsets of Blackjack. See
/tuning/topicId_28857.html#28857

Maybe Manuel can suggest how we might easily examine each of these to determine the maximum number of naturals it has when in its optimum position within a given Blackjack key. We could then use these numbers to compare Blackjack keys.

Note there are two kinds of key being considered here. The Blackjack key within 72-tET and the key of a subset scale within that Blackjack key.

Some facts about Blackjack in 6x12-tET notation:

Blackjack has 6 chains of fifths. In 6x12-tET notation these are of course subsets of the 6 cycles of fifths in 72-tET.

Each chain of fifths will have the same Sims accidental (or none) against all its notes, except for the chain which may have either quarter-tone sharp or quarter tone flat accidentals (or both). So there is the "<" chain, the "v" chain, the 12-tET chain, the "^" chain, the ">" chain and the "[]" chain.

Blackjack has 3 chains of fifths which are 4 notes long and 3 chains which are 3 notes long. 3*4 + 3*3 = 21

Naturals can only occur in _one_ chain of fifths (the 12-tET chain). This can either be a chain of 3 notes or a chain of 4 notes. There is no known reason to include anything _but_ naturals in this (12-tET) chain.

So the number of naturals possible in a subset scale depends entirely on how its chain(s) of fifths can be aligned with the 12-tET chain within the given Blackjack key. Consider the slide-rule pattern of some subset scale. If one can slide it alondg to a position where the subset's longest chain of fifths coincides completely with the 12-tET chain in the chosen Blackjack key, then it will have as many naturals as are possible.

If a subset scale has a chain of fifths with 4 notes, it certainly can't achieve the maximum number of naturals (4) in a Blackjack key whose chain of naturals is only 3 notes long.

So for every pitch in the subset, we'd like to calculate how many secors it is above or below the 1/1. Then we can find its longest chain(s) of fifths and see how they can be aligned.

I have a strong feeling that a large number of subsets have chains of four fifths, since it's probably the most popular interval on the planet, (after the unison and octave).

Do we really need to do the excercise? Is anyone still not totally convinced that it is better to have 4 naturals than 3 in the standard Blackjack key? If anyone has the slightest doubt, we should do it. So speak up.

Let me repeat what should be obvious: A standard Blackjack key will not suit every conceivable purpose. There will be times when a composer will have a good reason to use a different one. But we want a standard one as a "lingua franca" and it should be the best compromise we can come up with, such that composers would feel the need to use a different one as rarely as possible.

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

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

> Of course... I agree! However, if the "new" Blackjack scale messes
> up the visual lattices so they don't show the *basic* "everyday*
> tetrads of Blackjack, that could be a problem.
>
> That *is* a problem with the "new" version, yes??
>
> JP

Joseph, look at Dave's first lattice, not the second one.

Dave, why center on G-D when D-A was much more common historically?
Centering Canasta on D-A would give C, G, D, A, E, and B in Canasta,
encompassing the open strings of all the bowed string instruments,
plus the guitar.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
>
> /tuning/topicId_30148.html#30290
>
> > So I'm taking a 9-limit dyadic optimisation approach and you're
> taking a 7-limit tetradic one. Neither are likely to have any
impact
> on the choice of a standard key, but are interesting in their own
> right.
>
> But, we can't use the two different lattices and retain the same
> pitch names for Blackjack, is that correct??
>
> JP

Joseph, forget about these lattices where certain intervals
are "grayed" out. They're not relevant for you, though they might be
relevant for someone insisting on using strict JI (where the "grayed"
out intervals would be the wolves). You should focus instead on the
lattices where none of the intervals are "grayed" out.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> Dave, why center on G-D when D-A was much more common historically?
> Centering Canasta on D-A would give C, G, D, A, E, and B in Canasta,
> encompassing the open strings of all the bowed string instruments,
> plus the guitar.

Hey Paul! I already asked that exact question myself two days ago. See
/tuning/topicId_30148.html#30251

But of course we're talking about a standard key for Blackjack, not
Canasta. Whether Blackjack is CGDA or GDAE it can still be contained
in a CGDAEB Canasta.

The problem of course with a GDAE Blackjack is that it has no C
natural in it, and some folks seem rather attached to C natural. Not
me I hasten to add. I think that Joseph might be very glad to have a
GDAE-based Blackjack key were he ever to use live strings in a
composition.

Also, the GDAE one is the one I proposed a week or two ago, and you
converted to hertz, for Alison, and she has apparently started work
on. Then I thought, "Woah there! We're about to set in stone (well
steel actually) something which we haven't necessarily thought out as
well as we can. Let's get as many minds as possible onto it."

CGDA and GDAE are entirely equal in all purely number-theoretical and
notation-combinatorial properties. It is only real-world and
historical properties on which they differ.

Regards,
-- Dave Keenan

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

/tuning/topicId_30148.html#30332

>
> But of course we're talking about a standard key for Blackjack, not
> Canasta. Whether Blackjack is CGDA or GDAE it can still be
contained
> in a CGDAEB Canasta.
>
> The problem of course with a GDAE Blackjack is that it has no C
> natural in it, and some folks seem rather attached to C natural.
Not me I hasten to add. I think that Joseph might be very glad to
have a GDAE-based Blackjack key were he ever to use live strings in a
> composition.
>

Hi Dave!

Well, I *do* believe I'll miss my "C natural..." On the other hand,
my very next piece is going to be for cello and blackjack, so this is
something to think about!

Thanks!

Joseph

--- In tuning@y..., jpehrson@r... wrote:
> Well, I *do* believe I'll miss my "C natural..." On the other hand,
> my very next piece is going to be for cello and blackjack, so this
is
> something to think about!

Ah well, I just learnt (prompted by Paul's comment) that while the
violin and double bass have GDAE and the Guitar has GDAEB, the viola
and cello have CGDA. But the cello and viola will still be better off
with (GDA)E than with your current F(CG), and of course there are a
lot more violins, basses and guitars in the world than violas or
cellos.

FCG C-centered Blackjack naturals
CGDA cello, viola
GDAE violin, bass
GDAEB guitar
GDAE D:A-centered Blackjack naturals

So yeah. GDAE is still looking better than CGDA.

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:

/tuning/topicId_30148.html#30327
>
> Do we really need to do the excercise? Is anyone still not totally
convinced that it is better to have 4 naturals than 3 in the standard
Blackjack key? If anyone has the slightest doubt, we should do it. So
speak up.
>

Hi Dave...

Thanks for this interesting post, which really clarified for me what
you are doing... Well, you certainly have a point about 4 being
larger than 3, at least in *my* arithmetic book... but what happens
when one of the 3 is "C." Given the historical background of "C
natural" that has to "weigh in" a little bit in the calculation, yes??

> Let me repeat what should be obvious: A standard Blackjack key will
not suit every conceivable purpose. There will be times when a
composer will have a good reason to use a different one. But we want
a standard one as a "lingua franca" and it should be the best
compromise we can come up with, such that composers would feel the
need to use a different one as rarely as possible.
>

Of course, we also have to take into account that most composers
won't be "modulating" between Blackjack keys, at least not *yet.*
I've been using "common tone" harmonic progressions and that's about
as far as I've got with it.

But "modulation" between keys? That's quite a theoretical leap for
Blackjack, isn't it? And it rather sounds like one can't use two
different "keys" at the same time, correct?

Thanks!

Joseph

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

/tuning/topicId_30148.html#30328

>
> Joseph, look at Dave's first lattice, not the second one.
>

I can't seem to get the page to open at the moment. Is there
something "funky" about Dave's site at the moment??

JP

--- In tuning@y..., jpehrson@r... wrote:
> Thanks for this interesting post, which really clarified for me what
> you are doing... Well, you certainly have a point about 4 being
> larger than 3, at least in *my* arithmetic book... but what happens
> when one of the 3 is "C." Given the historical background of "C
> natural" that has to "weigh in" a little bit in the calculation,
yes??

Absolutely. But the C could be one of 4 naturals, instead of one of
only 3, as in the lattice I renamed recently. So do you agree that it
is better to have 4 naturals than 3, provided one of the naturals is a
C?

I personally think it is better to have 4 naturals than 3,
irrespective of whether there's a C in there or not. Having G, D and A
in there seems more important to me, notation-wise.

So for me the only question is, how much weight should the desire to
have a C (as in CGDA) carry against the desire to have GDAE for open
strings of violin, bass and guitar?

> But "modulation" between keys? That's quite a theoretical leap for
> Blackjack, isn't it?

Indeed! I wasn't suggesting modulation between Blackjack keys within
the one piece. I'm merely saying that, no matter what standard we come
up with, it will always be possible to write a piece that would have
fewer accidentals if transposed to a different Blackjack key.

> And it rather sounds like one can't use two
> different "keys" at the same time, correct?

Correct. Unless you have more than 21 notes per octave, which I
understand to be outside the scope of this standardisation effort.

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

> > Given the historical background of "C
> > natural" that has to "weigh in" a little bit in the calculation,
> > yes??
>
[...]
> So for me the only question is, how much weight should the desire
to
> have a C (as in CGDA) carry against the desire to have GDAE for
open
> strings of violin, bass and guitar?

I don't see any historical reason to weight C natural more highly.
Historically, before well-temperaments, most keyboards were tuned in
Pythaogorean or meantone Eb-G# -- that is, around a central D-A fifth.

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

/tuning/topicId_30148.html#30365

> --- In tuning@y..., jpehrson@r... wrote:
> > Thanks for this interesting post, which really clarified for me
what you are doing... Well, you certainly have a point about 4 being
> > larger than 3, at least in *my* arithmetic book... but what
happens when one of the 3 is "C." Given the historical background
of "C natural" that has to "weigh in" a little bit in the
calculation, yes??
>

[Dave Keenan]:
> Absolutely. But the C could be one of 4 naturals, instead of one of
> only 3, as in the lattice I renamed recently. So do you agree that
it is better to have 4 naturals than 3, provided one of the naturals
is a C?
>

He he... now *that* would be just a little difficult to disagree
with! :)

> I personally think it is better to have 4 naturals than 3,
> irrespective of whether there's a C in there or not. Having G, D
and A in there seems more important to me, notation-wise.
>
> So for me the only question is, how much weight should the desire
to have a C (as in CGDA) carry against the desire to have GDAE for
open strings of violin, bass and guitar?

Well, I don't know if it's because my background is that of a
*pianist* or not, but I would be quite upset if there were no C-
naturals in Blackjack.

For me, it really is a significant basis of music, in an historical
way... It would be rather disturbing, for *me* anyway, not to have
it.

I would't even be as upset if I had to omit an "A"...A-440, or
whatever the tuning standard would be. Although, it looks as though
we can get CGDA, which, in *my* book, is a suitable compromise, even
though some violinists might complain about the E!

JP

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

/tuning/topicId_30148.html#30366

> I don't see any historical reason to weight C natural more highly.
> Historically, before well-temperaments, most keyboards were tuned
in Pythaogorean or meantone Eb-G# -- that is, around a central D-A
fifth.

However, Paul, are you really saying that C-natural isn't all that
important as a "base note" on a contemporary keyboard??

I find it quite "comforting" and "orienting" myself... :) so I don't
know about that...!

JP

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

> Well, I don't know if it's because my background is that of a
> *pianist* or not, but I would be quite upset if there were no C-
> naturals in Blackjack.

I tend to think of everything in the key of C.
But none of what I usually think of in the key of C works in
Blackjack anyway! Diatonic scales, etc -- all gone!
So to prevent confusion, maybe it would be better if there _weren't_
a C! You could still think of everything in the key of C if you
wanted to -- even if you had a C in your particular Blackjack setup,
most things you'd find in it wouldn't be available in the key of C
anyway!
If you want C to be like a "root" or "tonal center" in your scale,
your best bet would be to use the Blackjack centered on the fifth C-
G, which would have naturals F-C-G-D. That's what I recommend for
you, if you think "C-centeredness" and "C-rootedness" is going to
dominate your composing style. But I don't think this should be
a "standard" for everyone!

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

/tuning/topicId_30148.html#30376

> --- In tuning@y..., jpehrson@r... wrote:
>
> > Well, I don't know if it's because my background is that of a
> > *pianist* or not, but I would be quite upset if there were no C-
> > naturals in Blackjack.
>
> I tend to think of everything in the key of C.
> But none of what I usually think of in the key of C works in
> Blackjack anyway! Diatonic scales, etc -- all gone!
> So to prevent confusion, maybe it would be better if there
_weren't_
> a C! You could still think of everything in the key of C if you
> wanted to -- even if you had a C in your particular Blackjack
setup,
> most things you'd find in it wouldn't be available in the key of C
> anyway!
> If you want C to be like a "root" or "tonal center" in your scale,
> your best bet would be to use the Blackjack centered on the fifth C-
> G, which would have naturals F-C-G-D. That's what I recommend for
> you, if you think "C-centeredness" and "C-rootedness" is going to
> dominate your composing style. But I don't think this should be
> a "standard" for everyone!

Well, I guess the only real relationship in my composing is the fact
that I tend to like to use the tetrad: C:Ev:G:Bb< as the starting
point for certain things... and I really like the "middle C"
coinciding with a traditional piano.

I could probably *adapt* to anything... but in my composing so far,
given the system I already have, I've gravitated to these things...

JP

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

> Well, I guess the only real relationship in my composing is the
fact
> that I tend to like to use the tetrad: C:Ev:G:Bb< as the starting
> point for certain things...

That would work best if you had C-G in the center, rather than just C
as you do now . . .

> and I really like the "middle C"
> coinciding with a traditional piano.

Well, how about a compromise -- everyone will adopt the key that Dave
proposed, with G-D in the center; you'll continue to have "middle C"
coinciding with that of a traditional piano (though you'll have to
shuffle all your stickers around); and you'll promise to try to use G-
D (as in the chords G:Bv:D:F< and G:Bb^:D:E>) rather than C-G as a
starting point . . .?

--- In tuning@y..., jpehrson@r... wrote:
> Well, I don't know if it's because my background is that of a
> *pianist* or not, but I would be quite upset if there were no C-
> naturals in Blackjack.

I want to understand what it is you would actually miss.
a. That particular pitch around 261 Hz, and its octaves?
b. The ocurrence of C natural in staff notation?
c. The correspondence between middle-C on your Halberstadt keyboard
with a. above.
d. The correspondence between middle-C on your Halberstadt keyboard
with b. above.
e. Something else.

As well as answering the above for yourself, you might try to answer
it for "the average keyboard player".

Of course any other real keyboard players should chime in with their
answers too. Please also say if you'd be just as happy with the
Blackjack naturals being GDAE as CGDA.

Regards,

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:

/tuning/topicId_30148.html#30324
>

> http://dkeenan.com/Music/Miracle/Blackjack7LatticeGD.gif
>

I printed out Dave Keenan's Blackjack lattice, in the key centered on
G, D and I really think I would have no trouble with it.

I actually like the string of fifths: C-G-D-A on the lattice. That
seems pretty direct.

Additionally, the tetrads are really not difficult at all to follow.
Sure, I don't have one based on C, but the Ab^:C:Eb^:F#v is almost as
intuitive. And, I still have such tetrads as: G:Bv:D:F< which are
very simple...

It seems the accidentals are a bit more logical than the older
lattice, too. We didn't use *any* sharps at all in that one, due to
space limitations. I'm assuming there's some *logical* reason for
the use of sharps and flats i *this* one.

Of course, this lattice *does* have a "C natural" in it. That helps
a lot, as far as I'm concerned. I would have no trouble accepting
this lattice as the "new standard..."

If it didn't have a "C-natural" in it, I believe I wouldn't be so
immediately inclined toward it.

Is this one the proposal for the "new standard...??"

Joseph Pehrson

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

/tuning/topicId_30148.html#30382

> --- In tuning@y..., jpehrson@r... wrote:
>
> > Well, I guess the only real relationship in my composing is the
> fact
> > that I tend to like to use the tetrad: C:Ev:G:Bb< as the
starting
> > point for certain things...
>
> That would work best if you had C-G in the center, rather than just
C
> as you do now . . .
>
> > and I really like the "middle C"
> > coinciding with a traditional piano.
>
> Well, how about a compromise -- everyone will adopt the key that
Dave
> proposed, with G-D in the center; you'll continue to have "middle
C"
> coinciding with that of a traditional piano (though you'll have to
> shuffle all your stickers around); and you'll promise to try to use
G-
> D (as in the chords G:Bv:D:F< and G:Bb^:D:E>) rather than C-G as a
> starting point . . .?

This is funny... because I just wrote a post on this very topic! :)

JP

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

/tuning/topicId_30148.html#30383

> --- In tuning@y..., jpehrson@r... wrote:
> > Well, I don't know if it's because my background is that of a
> > *pianist* or not, but I would be quite upset if there were no C-
> > naturals in Blackjack.
>
> I want to understand what it is you would actually miss.
> a. That particular pitch around 261 Hz, and its octaves?

Hi Dave...

Well, I guess I *would* miss that, since my "traditional" piano is
tuned to it, and I'm pretty much used to the sound of it, even though
I don't have "perfect pitch..."

> b. The ocurrence of C natural in staff notation?

Yes, I would also miss that...

> c. The correspondence between middle-C on your Halberstadt keyboard
> with a. above.

Yes, I'd miss that too...

> d. The correspondence between middle-C on your Halberstadt keyboard
> with b. above.

I'd also miss that!

> e. Something else.

Probably, too!

I don't know if that's being so helpful. I "missed" all a-e (!!) :)

>
> As well as answering the above for yourself, you might try to
answer it for "the average keyboard player".

Probably "middle C" is a "grounding point" for an "average keyboard
player" so probably other people would feel the same way I do!

>
> Of course any other real keyboard players should chime in with
their
> answers too. Please also say if you'd be just as happy with the
> Blackjack naturals being GDAE as CGDA.
>

No, definitely not. I looked at your lattice again, and I'm *very*
happy with CGDA, if that were to become the "new standard..." I'd be
*much* less inclined to go with GDAE...

JP

--- In tuning@y..., jpehrson@r... wrote:
> I looked at your lattice again, and I'm *very*
> happy with CGDA, if that were to become the "new standard..." I'd be
> *much* less inclined to go with GDAE...

Hmm. So probably keyboardists, cellists, and violists want CGDA, and
violinists, guitarists and bassists (both double-bass and fretless
electric) want GDAE.

If sheer weight of numbers would decide it, then we could probably
ignore the cellists and violists (sorry folks). And we should note
that, of the instruments mentioned, only the violin and bass can play
Blackjack without modification (provided we go for GDAE).

Any guitar would need a suitably modified fingerboard. However
existing 31-tET guitars could be used immediately (for 7-limit
Blackjack harmony only). They'd only need to retune the B string to B>
or B[ (provided we go for GDAE).

With 21 notes to the octave instead of 12, any keyboardist is going to
have a serious learning curve no matter what the notation. I find it
very hard to imagine that a keyboardist new to Blackjack would be
terribly upset to find that the middle-C key now plays a C< (33 cents
lower) when every other key on the keyboard produces a note that bears
no resemblance whatsoever to the pitch it used to be!

It seems to me that the opportunity to have at least violins and
basses able to play Blackjack without modification is an opportunity
not to be missed. I'd want to hear from a few more keyboard players or
anyone else with an argument for CGDA rather than GDAE, before blowing
that opportunity.

Both Margo Schulter and Paul Erlich have pointed out that the
traditional Eb to G# meantone keyboard tuning is centered on D:A, as
is the GDAE Blackjack tuning.

What other instruments have "open tunings" that we should be
considering. It doesn't seem like we should worry too much about wind
and brass that have only a single open note (with octaves).

Personally, I'm currently undecided between CGDA and GDAE and would
greatly appreciate any new arguments or opinions that might help us
decide one way or the other.

Regards,
-- Dave Keenan

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

/tuning/topicId_30148.html#30388

I find it
> very hard to imagine that a keyboardist new to Blackjack would be
> terribly upset to find that the middle-C key now plays a C< (33
cents lower) when every other key on the keyboard produces a note
that bears no resemblance whatsoever to the pitch it used to be!
>

Dunno, Dave... For me, anyway, it's quite comforting to have "Middle
C" "Middle C"... but you'll have to poll the others!

JP