the Blackjack keyboard "problem"

I'm beginning to think that just running Blackjack or 72-tET up a
regular Halberstadt linearly is problematic.

I've spent too much time thinking of a "C" as a "C" and a "G" as
a "G" -- to take ridiculously simple examples.

It's really annoying, on the overall, to have them now different
pitches, although it is, seemingly, the easiest solution of the
moment.

I really don't know what the answer is. Footpedals to make 72-tET
alterations?? But then would all the notes in chords have to be
altered at the same kind?? More than one pedal??

Some kind of Bosanquet or other bouquet? Dunno. That's a whole new
learning experience, but I suppose if the keyboard has a close enough
resemblance to the familiar Halberstadt one might learn it. But I
would rather somehow have some kind of "convertible" keyboard that
could play *both* earlier "regular" 12-tET music *and* 72...

Dunno. I'll "suffer through it" but I'm rebelling a little bit.
Looking at Blackjack notation, for instance, makes me want to play
the notes as alterations from 12-tET on the keyboard! And now they
are all in different places, which makes nonsense of my "accustomed"
sense of keyboard pitch and intervals.

I love microtonality, but I want my 72 [12-tET] keyboard notes
back! :)

J. Pehrson

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> I'm beginning to think that just running Blackjack or 72-tET up a
> regular Halberstadt linearly is problematic.
>
> I've spent too much time thinking of a "C" as a "C" and a "G" as
> a "G" -- to take ridiculously simple examples.
>
> It's really annoying, on the overall, to have them now different
> pitches, although it is, seemingly, the easiest solution of the
> moment.
>
> I really don't know what the answer is. Footpedals to make 72-tET
> alterations?? But then would all the notes in chords have to be
> altered at the same kind?? More than one pedal??
>
> Some kind of Bosanquet or other bouquet? Dunno. That's a whole
new
> learning experience, but I suppose if the keyboard has a close
enough
> resemblance to the familiar Halberstadt one might learn it. But I
> would rather somehow have some kind of "convertible" keyboard that
> could play *both* earlier "regular" 12-tET music *and* 72...
>
> Dunno. I'll "suffer through it" but I'm rebelling a little bit.
> Looking at Blackjack notation, for instance, makes me want to play
> the notes as alterations from 12-tET on the keyboard! And now they
> are all in different places, which makes nonsense of
my "accustomed"
> sense of keyboard pitch and intervals.
>
> I love microtonality, but I want my 72 [12-tET] keyboard notes
> back! :)
>
> J. Pehrson

Joseph,

I have been hard at work on the sagittal notation project with Dave
Keenan on tuning-math, and I didn't read your posting until today. I
thought I should respond immediately.

I empathize with you -- the lack of a proper keyboard is just plain
frustrating!!! But I have already been doing something about it.

The article that I wrote in Xenharmonikon 3 in 1975 that (almost
correctly) defined what has since come to be known as the Miracle
tuning also gave a keyboard layout that can be used for this, as well
as for 31-ET, 41-ET, 72-ET, and Partch's 11-limit JI.

Last year I took that design and fleshed it out -- key shape and
dimensions and a color-coding scheme.

You can see it at:

/tuning-math/files/secor/kbds/KbDec72.bmp

and if you wish to download the file, there is a zipped version:

/tuning-math/files/secor/kbds/KbDec72.zip

I also made what I am sure will turn out to be a controversial
modification -- flipping it over so that the rows are right-rising
rather than left-rising. I have a good justification for this -- a
result of the experience that I since gained using the Bosanquet
generalized keyboard Scalatron. (Details will be provided if anyone
wishes to take issue with this.)

Last year Erv Wilson sent me a diagram of a keyboard sketch he made
using this tuning geometry, and it was also right-rising. I
responded by sending him a color printout of an earlier version of
the above file, along with a letter (4 October 2001). A portion of
my reply follows:

<< The first thing I noticed is that your arrangement of keys also
reverses my original order for the rows, which puts us in complete
agreement on that one crucial issue, much to my relief. The only
points on which we seem to differ are the shape and dimensions of the
keys, which will determine for the most part the specific angles and
distances for the columns and rows. I tried a hexagon, but found
that a rectangle offered a couple of distinct advantages:

-- Hexagons are most natural for keys staggered in adjacent rows,
whereas the arrangement of pitches suggests that nearly vertical
columns of keys would be the most appropriate.

-- Having ten lateral keys per octave requires that the keys be as
close together as possible in order to keep intervals within easy
reach. Rectangles pack together most closely, given the preference
for vertical columns of keys.

I have enclosed several sheets illustrating my proposed keyboard. (I
was in the process of putting some ratios on one octave of keys, so
the key labeling is only partially complete.) The keys resemble
computer keys, but they are actually narrower and taller – narrower
for a better octave reach, and taller to make it easier to avoid the
thumb accidentally pressing two keys at once in adjacent rows. (I
did not judge that a short lateral distance would be a significant
problem, since the side of the thumb would generally be parallel to
the long dimension or, when stretching, the diagonal dimension of a
key.)

The "decimal keyboard" concept is linked to the generating interval
scale at the left, C being the origin. Notice that the keys
immediately above the C are identified as +10G, +20G, etc. In a
computer interface, this property could be used for easy integer
identification of each pitch (within an octave), with the tens digit
being the number of keys along the y-axis (including the sign of the
integer) and the units digit being the number of keys along the x-
axis, C (or 1/1) being the origin; units would thus range from 0 to
9. Such integers could be stored digitally in a single byte of
information in the range +/-127, with –128 serving to indicate a rest.

The color coding is based on the six circles of fifths in 72-ET. I
initially tried six colors (one for each circle of 12 keys), with
light (for 7 keys) and dark versions (for 5 keys) of each color
(e.g., white & black, pink & red, etc.), but the result, as viewed on
the computer screen, was almost impossible to comprehend.

By trying various modifications of this initial idea (using fewer
colors), I finally based it on the two sets of 36-ET in 72-ET,
retaining the 7 vs. 5 contrast within each circle of fifths. In 72-
ET neighboring keys in the same column differ by two degrees of 72-ET
(2deg72), so that 3 contiguous keys in a single column belong to the
same set of 36. If these are all colored using the same 7 plus 5
pattern in all three circles, the sets of 5 (dark) in each circle can
be readily identified on the layout in sub-groups of 2 and 3, just as
on the Bosanquet keyboard. These are the black and red keys on my
keyboard.

For the light colors corresponding to black and red, I chose
complementary colors: white and a light cyan. Inasmuch as this did
not result in easily distinguishable sub-groups of 3 and 4, I hit
upon the idea of making the outer keys in each column set of 3 a
grayish version of the central key, i.e., gray and grayish-cyan.
This then makes the 7 white and 7 light-cyan keys easy to identify in
sub-groups of 3 and 4. Since the white keys are the naturals C
through B and the light-cyan keys are the seven tones 1deg72 lower,
the tones in a Ptolemaic sequence (i.e., so-called "just" major
scale) on C are played entirely on white and light-cyan keys.

In 41-ET, these corresponding tones in the white and light-cyan
groups are a single degree (or comma) apart, whereas in 31-ET they
are duplicate keys for the same tones. (These properties also apply
to the black and red groups and the gray and grayish-cyan groups as
well.)

I have thus given my comments in the form of a counter-proposal and
would welcome your comments. >>

Erv's reply (13 Oct 2001) was brief, but enthusiastic:

<< Dear George,

Thanks for the very excellent material of Oct 4, 01. Do it! When
can I get delivery of a working keyboard? ... I apologize for being
brief but there are crops in the field. I will take your packet w.
me to the ranch and send you a response when I get back.

Adios!

Erv W. >>

The files that I just put out (on tuning-math) have the note names
labeled in sagittal notation (old 72-ET version with all straight
flags). I also included ratios on the keys for 19-limit JI (which
can be done to a certain extent, should anyone wish to go that high).

I understand that Johnny Reinhard recently got some funding to
develop a new keyboard. Perhaps if you make enough noise, he might
be persuaded to consider this one.

--George

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

/tuning/topicId_36964.html#37151
>
> Joseph,
>
> I have been hard at work on the sagittal notation project with Dave
> Keenan on tuning-math, and I didn't read your posting until today.
I
> thought I should respond immediately.
>
> I empathize with you -- the lack of a proper keyboard is just plain
> frustrating!!! But I have already been doing something about it.
>

***Thanks so very much, George, for your report back on this. Well,
your design is certainly interesting, and I'm going to study it
through some more. Eventually, as you seem to indicate, we have to
come up with something that can bring our *past* keyboard experiences
into the present.

>
> I understand that Johnny Reinhard recently got some funding to
> develop a new keyboard. Perhaps if you make enough noise, he might
> be persuaded to consider this one.
>

***Yes, it is true that Johnny is working in these directions. I
believe the project is still in a somewhat "classified" stage, but
Johnny will report back on it later, most probably.

Joseph

Hi, George. Good to see you posting. I haven't been too active lately
on this list, so I'm wondering. How is your saggital 72-ET
progressing? I was quite intrigued by it and felt some of the
feedback on this list was a bit overly critical and sometimes even
rather extreme in its pickiness even though I used to work for a
human factors design firm, but I guess or hope that's how things get
optimized.

I've been meaning to ask this, hoping you hadn't been discouraged,
and was very glad to see you're still on it "with a little help from
your friends".

Gratefully,

Bob

--- In tuning@y..., "robert_wendell" <rwendell@c...> wrote:
> Hi, George. Good to see you posting. I haven't been too active
lately
> on this list, so I'm wondering.

Hi, Bob!

Great to hear from you.

> How is your saggital 72-ET
> progressing?

It's blossomed into much, much more than just a 72-ET notation since
the discussion was moved to tuning-math.

The current objective is to produce a unified notation that can be
used for both rational intervals (or JI), many different ET's, and
other systems. Just as having an alphabet common to many different
written languages makes it much easier to learn to read certain
foreign languages, so would having a single set of symbols that can
be used for many different tonal systems make it easier for musicians
to learn to read music written for various systems, both just and
tempered. This is possible if the *meanings* of the symbols do not
change from one tonal system to another; rather it is the *selection*
of the symbols that varies.

As a part of this objective, it was also desired that the notation
would be very powerful and versatile, capable of notating rational
intervals involving many different prime numbers. But in doing this,
it was also desired that this would not make it more complicated to
do the simpler things -- the more complicated features are there if
you need them, but they don't get in the way if you don't.

> I was quite intrigued by it and felt some of the
> feedback on this list was a bit overly critical and sometimes even
> rather extreme in its pickiness even though I used to work for a
> human factors design firm, but I guess or hope that's how things
get
> optimized.

Dave Keenan and I have been working intensively on this, trying out
many different solutions to various problems, just so we can be sure
that we do it right the first time and don't have to change it later
(which might upset a few people). This has taken a lot of patience,
and the process can be quite trying at times. But I believe that the
time that was spent trying things that were eventually discarded was
not wasted -- we wanted to try as many things as we could possibly
think of, because that enabled us to see why the approach that we
finally chose is the best one.

We've made a lot of progress since the end of February and have
reached agreement on all sorts of details for many different tonal
systems -- ET's up to (and even beyond) 217-ET, rational intervals to
at least the 19 or 23 limit (and considerably beyond), and adaptive
JI (using 217-ET as 7 times 31-ET) being the principal things.

One thing on which we never agreed is whether there should be only a
single symbol to modify a natural note (thereby replacing
conventional sharp and flat symbols with new ones), or whether the
new symbols should be used in conjunction with conventional sharp and
flat symbols. On this we have agreed to disagree; the notation will
be presented in such a way as to give the composer the option to use
it either way, thereby letting the marketplace decide which way is
best (assuming that the notation makes it into the marketplace).

> I've been meaning to ask this, hoping you hadn't been discouraged,
> and was very glad to see you're still on it "with a little help
from
> your friends".
>
> Gratefully,
>
> Bob

I appreciate your concern. I'm sorry if I seemed to drop out of
sight, but the rapid pace of the notation project was making it
difficult for me even to keep up with reading the postings on the
main list, much less respond to anything.

We hope to bring the specifics of this new notation out on the main
tuning list soon.

Please stay tuned!

--George

Thank you so very much for the thorough update, George! I never
expected so much. This is very exciting news! I believe microtonality
is the direction evolutionary pressure will take us with music as a
profound and beautiful art and not just superficial entertainment,
although I believe that will be affected also.

Some comprehensive, consistent notational system seems necessary to
me in paving the way, or perhaps better, uncorking the bottle so that
what I believe to be the natural pressure to evolve in this direction
can express itself more freely and easily.

Most gratefully,

Bob

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> --- In tuning@y..., "robert_wendell" <rwendell@c...> wrote:
> > Hi, George. Good to see you posting. I haven't been too active
> lately
> > on this list, so I'm wondering.
>
> Hi, Bob!
>
> Great to hear from you.
>
> > How is your saggital 72-ET
> > progressing?
>
> It's blossomed into much, much more than just a 72-ET notation
since
> the discussion was moved to tuning-math.
>
> The current objective is to produce a unified notation that can be
> used for both rational intervals (or JI), many different ET's, and
> other systems. Just as having an alphabet common to many different
> written languages makes it much easier to learn to read certain
> foreign languages, so would having a single set of symbols that can
> be used for many different tonal systems make it easier for
musicians
> to learn to read music written for various systems, both just and
> tempered. This is possible if the *meanings* of the symbols do not
> change from one tonal system to another; rather it is the
*selection*
> of the symbols that varies.
>
> As a part of this objective, it was also desired that the notation
> would be very powerful and versatile, capable of notating rational
> intervals involving many different prime numbers. But in doing
this,
> it was also desired that this would not make it more complicated to
> do the simpler things -- the more complicated features are there if
> you need them, but they don't get in the way if you don't.
>
> > I was quite intrigued by it and felt some of the
> > feedback on this list was a bit overly critical and sometimes
even
> > rather extreme in its pickiness even though I used to work for a
> > human factors design firm, but I guess or hope that's how things
> get
> > optimized.
>
> Dave Keenan and I have been working intensively on this, trying out
> many different solutions to various problems, just so we can be
sure
> that we do it right the first time and don't have to change it
later
> (which might upset a few people). This has taken a lot of
patience,
> and the process can be quite trying at times. But I believe that
the
> time that was spent trying things that were eventually discarded
was
> not wasted -- we wanted to try as many things as we could possibly
> think of, because that enabled us to see why the approach that we
> finally chose is the best one.
>
> We've made a lot of progress since the end of February and have
> reached agreement on all sorts of details for many different tonal
> systems -- ET's up to (and even beyond) 217-ET, rational intervals
to
> at least the 19 or 23 limit (and considerably beyond), and adaptive
> JI (using 217-ET as 7 times 31-ET) being the principal things.
>
> One thing on which we never agreed is whether there should be only
a
> single symbol to modify a natural note (thereby replacing
> conventional sharp and flat symbols with new ones), or whether the
> new symbols should be used in conjunction with conventional sharp
and
> flat symbols. On this we have agreed to disagree; the notation
will
> be presented in such a way as to give the composer the option to
use
> it either way, thereby letting the marketplace decide which way is
> best (assuming that the notation makes it into the marketplace).
>
> > I've been meaning to ask this, hoping you hadn't been
discouraged,
> > and was very glad to see you're still on it "with a little help
> from
> > your friends".
> >
> > Gratefully,
> >
> > Bob
>
> I appreciate your concern. I'm sorry if I seemed to drop out of
> sight, but the rapid pace of the notation project was making it
> difficult for me even to keep up with reading the postings on the
> main list, much less respond to anything.
>
> We hope to bring the specifics of this new notation out on the main
> tuning list soon.
>
> Please stay tuned!
>
> --George

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

>...the notation will
> be presented in such a way as to give the composer the option to
use
> it either way, thereby letting the marketplace decide which way is
> best (assuming that the notation makes it into the marketplace).

Perhaps you should consider making the notation itself public domain
and then market a software tutorial to promote its use?

...One possibility, anyway, that occurred to me as potentially
optimal in terms of mutual synergy. I would think each would promote
the other for maximum growth rate toward a desirable de facto
standard. I'm concerned about a useless plethora of "de facto non-
standards" that this approach could potentially circumvent.

Cheers,

Bob

--- In tuning@y..., "robert_wendell" <rwendell@c...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> >...the notation will
> > be presented in such a way as to give the composer the option to
use
> > it either way, thereby letting the marketplace decide which way
is
> > best (assuming that the notation makes it into the marketplace).

The reason for this is threefold:

1) Dave Keenan and I have not been able to agree on this one major
point (i.e., single vs. double symbols), nor have we been able to
arrive at any sort of compromise;

2) Others may also have strong feelings about one or the other
option; to impose a decision might tend to exclude this notation from
consideration by those who would disagree with that decision;

3) The difference between the two options is purely cosmetic; the
theoretical basis for these is the same.

> Perhaps you should consider making the notation itself public
domain
> and then market a software tutorial to promote its use?

We have touched on the issue of copyright vs. public domain but have
not yet drawn any conclusions. A tutorial will be an absolute
necessity, but with such a limited market I would hesitate to make
any financial imposition on potential users. I imagine that any
tutorial that we produce within the foreseeable future will be
copyrighted, but downloadable for free for anyone who wants it.

> ...One possibility, anyway, that occurred to me as potentially
> optimal in terms of mutual synergy. I would think each would
promote
> the other for maximum growth rate toward a desirable de facto
> standard. I'm concerned about a useless plethora of "de facto non-
> standards" that this approach could potentially circumvent.

We have tried to make the notation flexible enough to prevent that
from happening.

For example, there are at least a couple of variations on how to
notate just intervals, and the most suitable choice will depend on
how complicated the selection of tones may be (which would favor
mapping them onto a large ET such as 217) vs. how important it may be
to distinguish intervals that differ by a very small amount (which
would favor the use of rational symbols). There would probably not
be any significant differences in the symbols unless one exceeded a
harmonic limit of 13.

Also, we are currently in the process of working out standard sets of
symbols for all of the ET's so that no one else will have to puzzle
over how to notate any of them.

--George

>1) Dave Keenan and I have not been able to agree on this one major
>point (i.e., single vs. double symbols), nor have we been able to
>arrive at any sort of compromise;

I vote for single.

-Carl

--- In tuning@y..., Carl Lumma <carl@l...> wrote:
> >1) Dave Keenan and I have not been able to agree on this one major
> >point (i.e., single vs. double symbols), nor have we been able to
> >arrive at any sort of compromise;
>
> I vote for single.
>
> -Carl

Sorry, you can't vote by e-mail. Votes can be cast only by actually
*using* the notation, once it is made available. (And I would hope
that there would not be too many who would vote "none of the above"
by *not* using it.)

--George

I wrote...

>>1) Dave Keenan and I have not been able to agree on this one major
>>point (i.e., single vs. double symbols), nor have we been able to
>>arrive at any sort of compromise;
>
>I vote for single.

On second thought, I guess this would depend on how badly it caused
a proliferation of symbols.

-Carl