The last 22-kbd design is up : - /

Okay folks, that about does it. I have uploaded the last of my ideas
for a semi-traditional 22-equal keyboard. They are all there, in the
22-equal Keyboard Designs folder of the Photos section. I can think
of no other ways to apply this scale to a traditional keyboard
concept. This last one was suggested by Paul Erlich, though I'm not
sure if I got it right. It's based on the C Standard Pentachordal
Major.

If anyone sees a clear winner among these designs, or can think of
something that I haven't thought of, please let me know.

Gracias, amigos.

-Igliashon Jones

P.S. anyone got any suggestions on how to build an electric harp on
the cheap? I figure all I need is wood for the frame, a simple
bridge, a pickup, and tuning pegs. Any thoughts?

Anyone know the story on what's happened with Graham Breed's web site
which used to be at <www.microtonal.co.uk>? That domain seems no
longer to exist.

- Rich Holmes

--- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
<igliashon@s...> wrote:
>
> Okay, George. I think I understand you much better now.
Interesting
> idea about differently textured keys...I shall have to ask Stevie
> about his opinion on that.
>
> I think 22 is a little more of a challenge to make a lattice for
than
> 22, though. In 22, I desire to use 3 systems as different bases
for
> tonality: Paul's Pajara-based Decatonics, Super-pythagorean
> Diatonics, and Porcupine-8 Octatonics. In the first system, one
> constructs 10-note scales using 8 2-degree steps and 2 3-degree
> steps. In Diatonics, the scales are 2 1-degree steps and 5 4-
degree
> steps. And in Porcupine, it is 1 1-degree step and 7 3-degree
> steps. This makes designing a keyboard INSANELY difficult. I
> examined a suggested lattice for 22-based Diatonics, but that one
> makes playing in the other two systems (Porcupine especially!) very
> difficult. I haven't attempted one based on a decatonic scale yet,
> but one based on the Porcupine seems to work quite well. If it was
> mapped to a hex lattice, going "up" would ascend one degree,
> going "right" would ascend 3, and going "diagonal" would be 4.
It's
> almost exactly the same as the Wilson idea, now that I think about
> it, except that the axes are switched around. It is precisely that
> design I applied to my keyboard (though the last design I posted
did
> not feature the 4th row of duplicate white keys at the top that I
> later added), but modified to fit in one dimension. This removes
> some of the uniformity a lattice provides, since at one point the
> horizontal ascends by 1 degree instead of 3 (though I may yet find
a
> way around this), but this seems like the best compromise between
> traditional and general.

Almost makes you want to build 3 different keyboards for 22, eh? ;-)

> Would it be possible, do you think, to use rectangular (or even
> square) keys that would feel fairly traditional to make a lattice
> that could ascend uniformly without needing to stretch too far in
the
> vertical dimension?

More about square keys below.

From my experience with 22 on my Scalatron, I think you're being
overly concerned about y-axis issues. The keys on my Scalatron could
have been made smaller, in my opinion, by foreshortening the aspect
ratio along the y-axis, but even so, I haven't found 22 to present
any problem with vertical stretching, as long as I have duplicate
keys, which allow me to choose in which *direction* I will be
reaching. I've found that the y-dimension can even be used to
advantage by playing the closer keys with the thumb, e.g., the second-
lowest note of a chord may be played by crossing the right-hand thumb
under the fingers. This is a new technique, but that's to be
expected with new music and new tunings.

This statement from a later message of yours brings up another
concern with the y-axis:

> On Wilson's design, the Y-axis = 3 increments,
> so a porcupine scale would be totally vertical. Decatonics go in a
> series of staggered "W" shapes, and diatonics go on that nice
> staggered horizontal pattern.

I infer that you think it's undesirable to play a scale in which many
of the intervals are along a vertical. On the Bosanquet keyboard
tones separated by a single degree of 31-ET are not only directly one
above the other, but are two rows distant, but playing a panchromatic
scale (one involving all of the tones) in 31-ET is, unexpectedly, a
piece of cake. Even though the fingering pattern is very different
from anything I had ever done before (at least with the right hand),
it took me about 30 seconds to figure it out, and only about 2
minutes of practice to be able to play it quickly (i.e., as sixteenth
notes).

With Porcupine you're in a similar situation with the Bosanquet
geometry. When you're playing a two-dimensional keyboard, you have
to expect that *some* things are going to occur along the y-axis. On
the left-hand button system of my accordion (which I learned ~14
years before working on a Scalatron keyboard design) *all* scales (in
12-ET) are played with intervals frequently taken along the
equivalent of the y-axis (i.e., the axis parallel to the fingers),
while octaves are located along the x-axis (with all buttons being in
a single plane), so I already had quite a bit of 2-dimensional
experience behind me and therefore wasn't afraid to think outside the
x-axis.

The huge advantage offered by a homogeneous key layout is that even
seemingly weird fingering patterns aren't very difficult to learn,
because you're simultaneously learning them in every key.

> Indeed it seems that a uniform design might help
> in allowing multiple systems to be played on the same keyboard.

I'm not sure exactly how you're using the word "systems", but yes,
that's true regardless of whether you're referring to multiple scales
(diatonic, porcupine, and decatonic) within a single tuning (22-ET),
or multiple tunings (and multiple scales within those tunings) on a
single (generalized) keyboard. Transpositional invariance in a
keyboard has a lot to be said for it, and if you're seriously
considering a non-uniform arrangement of keys, then I think that
statement is worth repeating again, and again, and again -- if only
to drive home the point that you'll be doing a lot of practicing
again, and again, and again to achieve the same facility on a
heterogeneous layout. ;-)

> I
> must admit that I have lost a little enthusiasm for the traditional
> design since considering that three systems need to be accomodated
by
> one design.
>
> Rest assured, too, that I am not dead-set on anything yet; I'm
trying
> to avoid making a mistake as well, since it will be tremendous
effort
> to build this thing ourselves. If I seem stubborn, it's because I
> don't want Stevie to be stuck with something that he doesn't want
to
> play. Also, one thing I think we ought to keep in mind is that
this
> will be a MIDI controller; as such, the potential difficulty of
> transposing to some keys may feasibly be avoided simply be retuning
> the synthesizer.

That's also a way of reducing the number of duplicate keys you might
need. The GK Scalatron that Paul Rapoport got for McMaster U.
(Hamilton, Ontario) has 56 keys/octave, but he can play 41 and 53-ET
on it by toggling the entire keyboard up and down by 2 commas on the
fly by means of a foot switch. (But I don't think that you really
need anything like that for 22.)

> Apologies should be made for my earlier attitude; the internet
makes
> misunderstanding easy, and I'm all too accustomed to the "flame
wars"
> that occur on other forums.

Oh, they occur around here too, from time to time (more often than
any of us would like). :-(

> Your input is greatly appreciated, since
> you have a perspective that both Stevie and I are lacking. Please
> remember too that we are young, and we sort of have to learn at our
> own pace. Before we give in and go general, we first must make
sure
> that there are no alternatives that would be more favorable, and
this
> could take awhile (if it is indeed the case).

The best advice I could give is to take your time and think
everything through so you do it right the first time. Here are a few
things to think about:

1) For whatever reason, there may not be a second time.
2) One of the most difficult things about learning a new keyboard is
*unlearning* habits acquired on an existing one, so try to make your
*first* new one the *only one* you'll ever need. While it may be
economical to build your own keyboard, it will be very "expensive" in
terms of effort (i.e., inconvenient, frustrating, or daunting) later
on to do it all over again.
3) A transpositionally invariant keyboard will accommodate more
tunings than a non-uniform keyboard.
4) A Bosanquet generalized keyboard will accommodate more tunings
than a porcupine-generalized keyboard.
5) For whatever reason, there may not be a second time, so choose
wisely.

--- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
<igliashon@s...> wrote:
>
> Okay folks, that about does it. I have uploaded the last of my
ideas
> for a semi-traditional 22-equal keyboard. They are all there, in
the
> 22-equal Keyboard Designs folder of the Photos section. I can
think
> of no other ways to apply this scale to a traditional keyboard
> concept. This last one was suggested by Paul Erlich, though I'm
not
> sure if I got it right. It's based on the C Standard Pentachordal
> Major.
>
> If anyone sees a clear winner among these designs, or can think of
> something that I haven't thought of, please let me know.

Of these, I think that your "generalized trad porc-colored" would be,
in the long run, the easiest to learn, because it's the only one
having transpositional invariancy.

I notice that there are larger gaps between the top two rows of keys
(which, as far as I can tell, serves no real purpose and detracts
from the appearance). Eliminate the gaps and you have almost square
keys.

Regardless of which keyboard layout you choose, I would suggest
coloring the keys more traditionally: flats red, naturals white,
sharps black, and the remaining 5 light blue or cyan (with textured
surfaces on the sharp and flat keys). (What's traditional about the
coloring is that it's already been used on the Scalatron -- if you
care about maintaining any links to the past.) You don't need
coloring to emphasize a Porcupine pattern, because the layout already
does that for you, but when you' want to play C, D, E, etc., it's
very helpful to know they're white keys.

IMO the greatest downside to the trad-porc design is that the octaves
are not in the same rows, which means that some things will have to
be fingered differently in different octaves. This could be greatly
remedied by another row of duplicate keys, but that's more work
and/or expense. With laterally placed octaves the number of
duplicate keys drops, but in order to have that (and at the same time
a reasonable octave distance) you would need to have slanting rows.

Your insistence on using rectangular keys has severely limited your
options for an arrangement with transpositional invariancy.
Evidently this is a result of your desire to have key-levers that
operate switches, rather than having the key surfaces directly atop
the switches (which is what I suspect to be the reason for your
wanting a specialized keyboard). Are there any key switches
available with square tops that might be acceptable as key surfaces?
That would greatly simplify the construction, for you could then have
all of the keys in a single plane (which works just fine on the GK
Scalatron).

If you use square keys and can eliminate the constraint against
slanting rows (but keep the vertical columns) you could have
something like this (for best viewing zoom to 100%):

/makemicromusic/files/secor/GKbd22Sq.gif

I realize that movement along the y-axis is quite a bit more than you
desired, but I think that the shortened octave distance more than
makes up for that. Why don't you and Stevie work out some patterns
on it and see what you think. Some things may seem a bit unorthodox
at first, but that's what alternate tunings are all about. I'm
confident that, with a few minutes of practice, Stevie could easily
play a porcupine scale with a thumb and 2 fingers on this keyboard.

Should you locate switches with square tops, there would also be a
possibility of orienting the edges along diagonals, which I suspect
would allow a better arrangement of keys (less spread out in the y-
direction, with keys staggered in adjacent rows).

Lastly, this is a true Bosanquet arrangement, so in addition to
transpositional invariance you also have the ability to use it for a
lot of other divisions (including 17, 19, 29, and 31). And its
NUMBER ONE ADVANTAGE is that whatever the time spent building and
learning can be applied toward those other divisions -- in other
words, you're not starting from scratch when (notice that I didn't
say "if") you want another tuning. And if you're ever called upon to
play someone else's generalized keyboard or decide to purchase one,
the previous time invested will pay *big* dividends.

Igliashon, Stevie: May you choose carefully and wisely, my friends.

--George

George:

looking at that design picture of yours, I am SOLD. It took me 10
seconds placing my fingers on the screen to figure out patterns for
each of the scale types we'd want to use, and not a single one seemed
the least bit difficult to me. And with transpositional
invariance...crikey! *I* could play the bloody thing! I'll show
this to Stevie and see if I can't convince him. Ay dios mio, I
totally underestimated this design. Not only is this one 10x easier
to play, it also would be 10x easier to build since we'd only need to
make 1 key shape: a square. Heck, we could probably find somewhere
to BUY the keys.
I mean, if we get around to building an acoustic piano we'll probably
have to go with one of our more traditional-looking designs, but for
a MIDI controller I think this is it.

Heck, with a good 6 or 7 octaves of that design laid out, it wouldn't
even look too un-keyboard like.

George, many thanks for your patience.

-Igliashon

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
> <igliashon@s...> wrote:
> >
> > Okay, George. I think I understand you much better now.
> Interesting
> > idea about differently textured keys...I shall have to ask Stevie
> > about his opinion on that.
> >
> > I think 22 is a little more of a challenge to make a lattice for
> than
> > 22, though. In 22, I desire to use 3 systems as different bases
> for
> > tonality: Paul's Pajara-based Decatonics, Super-pythagorean
> > Diatonics, and Porcupine-8 Octatonics. In the first system, one
> > constructs 10-note scales using 8 2-degree steps and 2 3-degree
> > steps. In Diatonics, the scales are 2 1-degree steps and 5 4-
> degree
> > steps. And in Porcupine, it is 1 1-degree step and 7 3-degree
> > steps. This makes designing a keyboard INSANELY difficult. I
> > examined a suggested lattice for 22-based Diatonics, but that one
> > makes playing in the other two systems (Porcupine especially!)
very
> > difficult. I haven't attempted one based on a decatonic scale
yet,
> > but one based on the Porcupine seems to work quite well. If it
was
> > mapped to a hex lattice, going "up" would ascend one degree,
> > going "right" would ascend 3, and going "diagonal" would be 4.
> It's
> > almost exactly the same as the Wilson idea, now that I think
about
> > it, except that the axes are switched around. It is precisely
that
> > design I applied to my keyboard (though the last design I posted
> did
> > not feature the 4th row of duplicate white keys at the top that I
> > later added), but modified to fit in one dimension. This removes
> > some of the uniformity a lattice provides, since at one point the
> > horizontal ascends by 1 degree instead of 3 (though I may yet
find
> a
> > way around this), but this seems like the best compromise between
> > traditional and general.
>
> Almost makes you want to build 3 different keyboards for 22, eh? ;-
)
>
> > Would it be possible, do you think, to use rectangular (or even
> > square) keys that would feel fairly traditional to make a lattice
> > that could ascend uniformly without needing to stretch too far in
> the
> > vertical dimension?
>
> More about square keys below.
>
> From my experience with 22 on my Scalatron, I think you're being
> overly concerned about y-axis issues. The keys on my Scalatron
could
> have been made smaller, in my opinion, by foreshortening the aspect
> ratio along the y-axis, but even so, I haven't found 22 to present
> any problem with vertical stretching, as long as I have duplicate
> keys, which allow me to choose in which *direction* I will be
> reaching. I've found that the y-dimension can even be used to
> advantage by playing the closer keys with the thumb, e.g., the
second-
> lowest note of a chord may be played by crossing the right-hand
thumb
> under the fingers. This is a new technique, but that's to be
> expected with new music and new tunings.
>
> This statement from a later message of yours brings up another
> concern with the y-axis:
>
> > On Wilson's design, the Y-axis = 3 increments,
> > so a porcupine scale would be totally vertical. Decatonics go in
a
> > series of staggered "W" shapes, and diatonics go on that nice
> > staggered horizontal pattern.
>
> I infer that you think it's undesirable to play a scale in which
many
> of the intervals are along a vertical. On the Bosanquet keyboard
> tones separated by a single degree of 31-ET are not only directly
one
> above the other, but are two rows distant, but playing a
panchromatic
> scale (one involving all of the tones) in 31-ET is, unexpectedly, a
> piece of cake. Even though the fingering pattern is very different
> from anything I had ever done before (at least with the right
hand),
> it took me about 30 seconds to figure it out, and only about 2
> minutes of practice to be able to play it quickly (i.e., as
sixteenth
> notes).
>
> With Porcupine you're in a similar situation with the Bosanquet
> geometry. When you're playing a two-dimensional keyboard, you have
> to expect that *some* things are going to occur along the y-axis.
On
> the left-hand button system of my accordion (which I learned ~14
> years before working on a Scalatron keyboard design) *all* scales
(in
> 12-ET) are played with intervals frequently taken along the
> equivalent of the y-axis (i.e., the axis parallel to the fingers),
> while octaves are located along the x-axis (with all buttons being
in
> a single plane), so I already had quite a bit of 2-dimensional
> experience behind me and therefore wasn't afraid to think outside
the
> x-axis.
>
> The huge advantage offered by a homogeneous key layout is that even
> seemingly weird fingering patterns aren't very difficult to learn,
> because you're simultaneously learning them in every key.
>
> > Indeed it seems that a uniform design might help
> > in allowing multiple systems to be played on the same keyboard.
>
> I'm not sure exactly how you're using the word "systems", but yes,
> that's true regardless of whether you're referring to multiple
scales
> (diatonic, porcupine, and decatonic) within a single tuning (22-
ET),
> or multiple tunings (and multiple scales within those tunings) on a
> single (generalized) keyboard. Transpositional invariance in a
> keyboard has a lot to be said for it, and if you're seriously
> considering a non-uniform arrangement of keys, then I think that
> statement is worth repeating again, and again, and again -- if only
> to drive home the point that you'll be doing a lot of practicing
> again, and again, and again to achieve the same facility on a
> heterogeneous layout. ;-)
>
> > I
> > must admit that I have lost a little enthusiasm for the
traditional
> > design since considering that three systems need to be
accomodated
> by
> > one design.
> >
> > Rest assured, too, that I am not dead-set on anything yet; I'm
> trying
> > to avoid making a mistake as well, since it will be tremendous
> effort
> > to build this thing ourselves. If I seem stubborn, it's because
I
> > don't want Stevie to be stuck with something that he doesn't want
> to
> > play. Also, one thing I think we ought to keep in mind is that
> this
> > will be a MIDI controller; as such, the potential difficulty of
> > transposing to some keys may feasibly be avoided simply be
retuning
> > the synthesizer.
>
> That's also a way of reducing the number of duplicate keys you
might
> need. The GK Scalatron that Paul Rapoport got for McMaster U.
> (Hamilton, Ontario) has 56 keys/octave, but he can play 41 and 53-
ET
> on it by toggling the entire keyboard up and down by 2 commas on
the
> fly by means of a foot switch. (But I don't think that you really
> need anything like that for 22.)
>
> > Apologies should be made for my earlier attitude; the internet
> makes
> > misunderstanding easy, and I'm all too accustomed to the "flame
> wars"
> > that occur on other forums.
>
> Oh, they occur around here too, from time to time (more often than
> any of us would like). :-(
>
> > Your input is greatly appreciated, since
> > you have a perspective that both Stevie and I are lacking.
Please
> > remember too that we are young, and we sort of have to learn at
our
> > own pace. Before we give in and go general, we first must make
> sure
> > that there are no alternatives that would be more favorable, and
> this
> > could take awhile (if it is indeed the case).
>
> The best advice I could give is to take your time and think
> everything through so you do it right the first time. Here are a
few
> things to think about:
>
> 1) For whatever reason, there may not be a second time.
> 2) One of the most difficult things about learning a new keyboard
is
> *unlearning* habits acquired on an existing one, so try to make
your
> *first* new one the *only one* you'll ever need. While it may be
> economical to build your own keyboard, it will be very "expensive"
in
> terms of effort (i.e., inconvenient, frustrating, or daunting)
later
> on to do it all over again.
> 3) A transpositionally invariant keyboard will accommodate more
> tunings than a non-uniform keyboard.
> 4) A Bosanquet generalized keyboard will accommodate more tunings
> than a porcupine-generalized keyboard.
> 5) For whatever reason, there may not be a second time, so choose
> wisely.
>
> --- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
> <igliashon@s...> wrote:
> >
> > Okay folks, that about does it. I have uploaded the last of my
> ideas
> > for a semi-traditional 22-equal keyboard. They are all there, in
> the
> > 22-equal Keyboard Designs folder of the Photos section. I can
> think
> > of no other ways to apply this scale to a traditional keyboard
> > concept. This last one was suggested by Paul Erlich, though I'm
> not
> > sure if I got it right. It's based on the C Standard
Pentachordal
> > Major.
> >
> > If anyone sees a clear winner among these designs, or can think
of
> > something that I haven't thought of, please let me know.
>
> Of these, I think that your "generalized trad porc-colored" would
be,
> in the long run, the easiest to learn, because it's the only one
> having transpositional invariancy.
>
> I notice that there are larger gaps between the top two rows of
keys
> (which, as far as I can tell, serves no real purpose and detracts
> from the appearance). Eliminate the gaps and you have almost
square
> keys.
>
> Regardless of which keyboard layout you choose, I would suggest
> coloring the keys more traditionally: flats red, naturals white,
> sharps black, and the remaining 5 light blue or cyan (with textured
> surfaces on the sharp and flat keys). (What's traditional about
the
> coloring is that it's already been used on the Scalatron -- if you
> care about maintaining any links to the past.) You don't need
> coloring to emphasize a Porcupine pattern, because the layout
already
> does that for you, but when you' want to play C, D, E, etc., it's
> very helpful to know they're white keys.
>
> IMO the greatest downside to the trad-porc design is that the
octaves
> are not in the same rows, which means that some things will have to
> be fingered differently in different octaves. This could be
greatly
> remedied by another row of duplicate keys, but that's more work
> and/or expense. With laterally placed octaves the number of
> duplicate keys drops, but in order to have that (and at the same
time
> a reasonable octave distance) you would need to have slanting rows.
>
> Your insistence on using rectangular keys has severely limited your
> options for an arrangement with transpositional invariancy.
> Evidently this is a result of your desire to have key-levers that
> operate switches, rather than having the key surfaces directly atop
> the switches (which is what I suspect to be the reason for your
> wanting a specialized keyboard). Are there any key switches
> available with square tops that might be acceptable as key
surfaces?
> That would greatly simplify the construction, for you could then
have
> all of the keys in a single plane (which works just fine on the GK
> Scalatron).
>
> If you use square keys and can eliminate the constraint against
> slanting rows (but keep the vertical columns) you could have
> something like this (for best viewing zoom to 100%):
>
>
/makemicromusic/files/secor/GKbd22Sq.gif
>
> I realize that movement along the y-axis is quite a bit more than
you
> desired, but I think that the shortened octave distance more than
> makes up for that. Why don't you and Stevie work out some patterns
> on it and see what you think. Some things may seem a bit
unorthodox
> at first, but that's what alternate tunings are all about. I'm
> confident that, with a few minutes of practice, Stevie could easily
> play a porcupine scale with a thumb and 2 fingers on this keyboard.
>
> Should you locate switches with square tops, there would also be a
> possibility of orienting the edges along diagonals, which I suspect
> would allow a better arrangement of keys (less spread out in the y-
> direction, with keys staggered in adjacent rows).
>
> Lastly, this is a true Bosanquet arrangement, so in addition to
> transpositional invariance you also have the ability to use it for
a
> lot of other divisions (including 17, 19, 29, and 31). And its
> NUMBER ONE ADVANTAGE is that whatever the time spent building and
> learning can be applied toward those other divisions -- in other
> words, you're not starting from scratch when (notice that I didn't
> say "if") you want another tuning. And if you're ever called upon
to
> play someone else's generalized keyboard or decide to purchase one,
> the previous time invested will pay *big* dividends.
>
> Igliashon, Stevie: May you choose carefully and wisely, my friends.
>
> --George

Heya George,

Just wondering... what is your no-holds-barred favorite
22-tET layout?

-Carl

--- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
<igliashon@s...> wrote:
>
> George:
>
> looking at that design picture of yours, I am SOLD.

Yikes! I'm completely stunned! :-}

> It took me 10
> seconds placing my fingers on the screen to figure out patterns for
> each of the scale types we'd want to use, and not a single one
seemed
> the least bit difficult to me. And with transpositional
> invariance...crikey! *I* could play the bloody thing!

Yes, that's exactly the reaction we got when we let others try out
the GK Scalatron at music conventions in the 1970's. The 7-white-5-
black diatonic pattern is immediately obvious, and the only habit you
have to break is that you no longer play flats the same as sharps --
you now go *below* the white keys to get them on the red keys.

BTW, the squares in the figure are 7/8-inch -- same as the width of a
piano key.

> I'll show
> this to Stevie and see if I can't convince him. Ay dios mio, I
> totally underestimated this design. Not only is this one 10x
easier
> to play, it also would be 10x easier to build since we'd only need
to
> make 1 key shape: a square. Heck, we could probably find somewhere
> to BUY the keys.

When we checked out momentary switches in the 1970's we found that
many of them were not very good for a synthesizer keyboard. It took
a bit of looking to find one having both an appropriate amount of
resistance (most were too "heavy") and key travel. Also, find out
what colors are available for key-tops. And get samples to try
before you buy anything.

> I mean, if we get around to building an acoustic piano we'll
probably
> have to go with one of our more traditional-looking designs, but
for
> a MIDI controller I think this is it.
>
> Heck, with a good 6 or 7 octaves of that design laid out, it
wouldn't
> even look too un-keyboard like.

One minor concern I have with this design is that there's no "white"
space separating the groups of 2 and 3 sharp and flat keys, so the
visual 2-and-3 pattern is not as obvious -- on the GK Scalatron it
almost jumps out at you. I'd like to see if I can remedy this by
slanting the vertical columns counter-clockwise a bit (and also
allowing the columns to "slide" past one another so as to keep the
octaves perfectly lateral), while increasing the octave distance to
about 140 mm (as on the GK Scalatron, which is still one key less
than on a piano). Another significant benefit that I would expect
from this is a shorter reach in the y-direction, which I know will be
important to you.

The keys would still be square, but the sides would all slant. You
can decide whether that's aesthetically acceptable after I've made a
diagram (which will take at least a few days, so more patience,
please). Previously I didn't think that square keys would be very
suitable for the Bosanquet geometry, but this latest go-round is
beginning to change my mind.

> George, many thanks for your patience.

And you, likewise.

Best,

--George

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Heya George,
>
> Just wondering... what is your no-holds-barred favorite
> 22-tET layout?
>
> -Carl

Hey Carl,

I thought I already answered that question:

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
> ... if you were to make the
> necessary improvements, one by one, to arrive at the
> best "specialized" 22-ET design, you would in fact end up with a
> *generalized* design!

For any division of the octave, up to about 31 tones, in which the
tones can be generated by a single chain of fifths, the Bosanquet
layout is my no-holds-barred favorite. As to what's the best key
shape and dimensions, I'm not completely certain, but it would have
to be something close to what we already did on the Scalatron, with
perhaps a compression of distance along the y-axis.

The two reasons I'm opposed to specialized keyboards for specific
tunings are that they lack the greatest advantages of Bosanquet's
generalized keyboard:

1) No need to commit to a particular tuning before you acquire one,
or to bother with the expense and inconvenience of separate keyboards
for different tunings;

2) The overall "feel" of playing (key travel, key distances, etc.)
does not change when you change tunings. Some intervals will be
mapped differently, but that's a relatively easy (mental) adjustment
to make.

Hey, I'd better quit -- I'm beginning to feel like I'm writing ad
copy. I need to get back to composing.

--George

>> Heya George,
>>
>> Just wondering... what is your no-holds-barred favorite
>> 22-tET layout?
>>
>> -Carl
>
>Hey Carl,
>
>I thought I already answered that question:

What is the "Bosanquet layout" for 22?

-Carl

> Yikes! I'm completely stunned! :-}

Actually, so was I. I've been mapping scales to the various layouts
Stevie, Paul and I came up with, and each one involves a hefty
compromise for at least one of the 3 systems. (To see what I'm
talking about, take a look at:

http://photobucket.com/albums/v170/igliashon_jones/

On 3 of our designs, I placed different colored dots to denote
members of various types of C major scales (the 3 3 1 3 3 3 3 3
porcupine-8 major, the 4 4 1 4 4 4 1 diatonic major, and the 2 2 3 2
2 2 3 2 2 2 Std. Pentachordal major). For my traditionally-shaped
general-esque design, I did seperate versions for each scale.

Looking at those designs, I couldn't imagine anyone trying to learn
to play all 3 systems on one keyboard. Just one of them would be
hard enough.

Then, compare them with the same scales mapped to your version.
Really, there's just no contest.

What really sold me though was the actual act of putting my fingers
to the screen and trying to finger chords and scales. Now, I have
scarcely any experience on the keyboard, but I found that I could run
my fingers up and down any scale pattern at a good 16th-note clip on
your design, and that was without even being able to feel keys under
my fingers! I tried to do that with other designs and found them way
too awkward. It just goes to show that you can't tell how playable
an instrument is just by looking at it.

Plus, I've been thinking about the sheer plethora of scales and modes
available in 22. The variety is exponentially greater than 12-equal,
so without transposable invariance, that could add up to hundreds of
patterns to memorize. Think about it: 7 diatonic modes + 10
pentachordal modes + 10 symmetric modes + 8 porcupine modes = 35
modal patterns x 22 possible key centers = *770* patterns, and that's
only with the BASIC patterns of 3 systems...when you add altered or
semi-chromatic scales...I don't even want to imagine! And what about
chord voicings? It hurts my head to think about it all. With a
system as rich as 22, I've come to realize that transpositional
invariance is really necessary to get the most out of an instrument.

> When we checked out momentary switches in the 1970's we found that
> many of them were not very good for a synthesizer keyboard. It
took
> a bit of looking to find one having both an appropriate amount of
> resistance (most were too "heavy") and key travel. Also, find out
> what colors are available for key-tops. And get samples to try
> before you buy anything.

Yeah, the actual construction is going to be the hard part. I'm sure
once we get to that phase we'll have more questions for you.

> One minor concern I have with this design is that there's
no "white"
> space separating the groups of 2 and 3 sharp and flat keys, so the
> visual 2-and-3 pattern is not as obvious -- on the GK Scalatron it
> almost jumps out at you.

For 22, I think a slightly different color scheme would be
appropriate. Since flats and sharps are always a single step from
the nearest white key, I think they should BOTH be "colored"--red for
flat, cyan for sharp (or possibly vice-versa)--so that the semi-
sharps/semi-flats create a row of blacks between the colors. This
would help when using decatonic scales, I think. One thing I've been
thinking about too is that it might be useful to use semi-transparent
uncolored keys with colored LEDs underneath them. That way, you
could program different colorschemes to correspond with different key
mappings and tunings that you could activate with the flick of a
switch. Of course this would be more difficult and expensive and we
probably won't bother to do it ourselves (since this will be a
primarily 22-based instrument), but for future generalized keyboards
it could be an option.

>I'd like to see if I can remedy this by
> slanting the vertical columns counter-clockwise a bit (and also
> allowing the columns to "slide" past one another so as to keep the
> octaves perfectly lateral), while increasing the octave distance to
> about 140 mm (as on the GK Scalatron, which is still one key less
> than on a piano). Another significant benefit that I would expect
> from this is a shorter reach in the y-direction, which I know will
be
> important to you.

I look forward to seeing how this iteration turns out. As it stands
I think the design is perfectly fine, but who knows? This may be
even better. I certainly don't think slanted keys should pose a
problem for us, though i've yet to speak with Stevie on the matter.
I'm fairly confident that he will be easily persuaded with a quick
demonstration, though.

Regards,
-Igliashon

>> Yikes! I'm completely stunned! :-}
>
>Actually, so was I. I've been mapping scales to the various layouts
>Stevie, Paul and I came up with, and each one involves a hefty
>compromise for at least one of the 3 systems. (To see what I'm
>talking about, take a look at:
>
>http://photobucket.com/albums/v170/igliashon_jones/
>
>On 3 of our designs, I placed different colored dots to denote
>members of various types of C major scales (the 3 3 1 3 3 3 3 3
>porcupine-8 major, the 4 4 1 4 4 4 1 diatonic major, and the 2 2 3 2
>2 2 3 2 2 2 Std. Pentachordal major). For my traditionally-shaped
>general-esque design, I did seperate versions for each scale.

Hey, great work! Have you considered putting numbers (scale
degrees) instead of just dots? That lets viewer see the fingering
sequence at a glance.

-Carl

Bueno idea! I'll get 'em up asap (since I have nothing better to do).

-Igs

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Yikes! I'm completely stunned! :-}
> >
> >Actually, so was I. I've been mapping scales to the various
layouts
> >Stevie, Paul and I came up with, and each one involves a hefty
> >compromise for at least one of the 3 systems. (To see what I'm
> >talking about, take a look at:
> >
> >http://photobucket.com/albums/v170/igliashon_jones/
> >
> >On 3 of our designs, I placed different colored dots to denote
> >members of various types of C major scales (the 3 3 1 3 3 3 3 3
> >porcupine-8 major, the 4 4 1 4 4 4 1 diatonic major, and the 2 2 3
2
> >2 2 3 2 2 2 Std. Pentachordal major). For my traditionally-shaped
> >general-esque design, I did seperate versions for each scale.
>
> Hey, great work! Have you considered putting numbers (scale
> degrees) instead of just dots? That lets viewer see the fingering
> sequence at a glance.
>
> -Carl

> > Hey, great work! Have you considered putting numbers (scale
> > degrees) instead of just dots? That lets viewer see the fingering
> > sequence at a glance.
> >
> > -Carl

Done and done. They are now available for viewing at the same site.

-igs

>> > Hey, great work! Have you considered putting numbers (scale
>> > degrees) instead of just dots? That lets viewer see the fingering
>> > sequence at a glance.
>> >
>> > -Carl
>
>Done and done. They are now available for viewing at the same site.

Great work, but only the first few seem to be done. Some of the
designs between 10 and 16 look interesting.

-Carl

Check it now, should be in order. I didn't add numbers to two of my
my trad-shaped semi generals because the patterns I think are self-
explanatory. Note that there are alternate fingerings for a few of
the scales on the Secor designs; which hand is playing the scale will
determine the optimal fingering.

-Igs

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> > Hey, great work! Have you considered putting numbers (scale
> >> > degrees) instead of just dots? That lets viewer see the
fingering
> >> > sequence at a glance.
> >> >
> >> > -Carl
> >
> >Done and done. They are now available for viewing at the same
site.
>
> Great work, but only the first few seem to be done. Some of the
> designs between 10 and 16 look interesting.
>
> -Carl

--- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
<igliashon@s...> wrote:
>
> > Yikes! I'm completely stunned! :-}
>
> Actually, so was I. ...
>
> What really sold me though was the actual act of putting my fingers
> to the screen and trying to finger chords and scales.

Ah, you've brought back memories of what I did back in 1974 (playing
19, 22, and 31 on a paper diagram), prior to approaching the Motorola
Scalatron Company with my idea -- and then finding shortly thereafter
that Bosanquet beat me to it by almost exactly 100 years! :-) While
this was momentarily a little deflating to my ego, the up-side was
that I had confirmation that I was on the right track. When Erv
Wilson and John Chalmers heard about what we doing, they each made a
trip from California to the Chicago area to see the keyboard while
the instrument was still under construction. Erv's input regarding
key shape and dimensions proved to be indispensable.

Of course, no one knew about a Porcupine or Decatonic subset of 22 at
the time, so your testing of this latest (square-key) proposed
incarnation has gone a step farther.

> ...
> > One minor concern I have with this design is that there's
no "white"
> > space separating the groups of 2 and 3 sharp and flat keys, so
the
> > visual 2-and-3 pattern is not as obvious -- on the GK Scalatron
it
> > almost jumps out at you.
>
> For 22, I think a slightly different color scheme would be
> appropriate. Since flats and sharps are always a single step from
> the nearest white key, I think they should BOTH be "colored"--red
for
> flat, cyan for sharp (or possibly vice-versa)--so that the semi-
> sharps/semi-flats create a row of blacks between the colors. This
> would help when using decatonic scales, I think.

The long-standing tradition established by Bosanquet is alternating 7-
white and 5-black, as one proceeds along a chain of fifths (the
generating interval). Even though we employed additional key colors
on the Scalatron (5 on two of the GK instruments, and 9 colors on the
third one), we still retained an alternating 7-light-5-dark pattern
that would be meaningful for multiple tunings (e.g., red is "dark"
and pink is "light"). I would encourage you to abide by that
tradition, for two reasons:

1) While I do see some logic in choosing complementary colors for
sharps and flats (opposites), the strong contrast between alternating
light and dark rows of keys are very effective in helping one to
perceive the coloring pattern. I have observed that cyan (or light
blue) and white are less easily distinguished in subdued lighting, so
I would want to avoid having them on adjacent keys.

> One thing I've been
> thinking about too is that it might be useful to use semi-
transparent
> uncolored keys with colored LEDs underneath them. That way, you
> could program different colorschemes to correspond with different
key
> mappings and tunings that you could activate with the flick of a
> switch. Of course this would be more difficult and expensive and
we
> probably won't bother to do it ourselves (since this will be a
> primarily 22-based instrument), but for future generalized
keyboards
> it could be an option.

The key switches that we used on the GK Scalatron were also capable
of being lighted. We briefly discussed the possibility of having
patterns of lights that could change along with the tuning, but we
didn't pursue it.

> >I'd like to see if I can remedy this by
> > slanting the vertical columns counter-clockwise a bit ...
>
> I look forward to seeing how this iteration turns out. As it
stands
> I think the design is perfectly fine, but who knows? This may be
> even better.

I expect that it would definitely be better if you ever decided to
use the keyboard for other tunings, 19 or meantone, for example. The
current diagram is very definitely biased toward 22 in that adjacent
keys in each column differ in pitch by 1deg22 (~55 cents), but for
most other tunings this interval will be larger.

I colored the extreme keys in the diagram as duplicates specific to
22, but I don't think that would be a serious drawback if you used
the keyboard for other tunings, because I've found that, most of the
time, playing is done by interval-patterns (as you enthusiastically
observed in your test report). My Scalatron keyboard has 31-specific
coloring, but I can find the 22-ET duplicate keys without any trouble.

Anyway, we'll see what I can come up with. This is going to take a
bit more time to do than the current diagram, because figuring out
the dimensions and angles will be a little more complicated.

--George

"George D. Secor" <gdsecor@...> writes:

> Ah, you've brought back memories of what I did back in 1974 (playing
> 19, 22, and 31 on a paper diagram), prior to approaching the Motorola
> Scalatron Company with my idea -- and then finding shortly thereafter
> that Bosanquet beat me to it by almost exactly 100 years! :-)

That's nothing... in my youth I 'discovered' 53-equal, only about 20
centuries too late to claim precedence...

- Rich Holmes

--- In MakeMicroMusic@yahoogroups.com, Rich Holmes<rsholmes@m...>
wrote:
> "George D. Secor" <gdsecor@y...> writes:
>
> > Ah, you've brought back memories of what I did back in 1974
(playing
> > 19, 22, and 31 on a paper diagram), prior to approaching the
Motorola
> > Scalatron Company with my idea -- and then finding shortly
thereafter
> > that Bosanquet beat me to it by almost exactly 100 years! :-)
>
> That's nothing... in my youth I 'discovered' 53-equal, only about 20
> centuries too late to claim precedence...
>
> - Rich Holmes

Aw, shucks! That's nothing... in *my* youth I 'discovered' 19, 22,
31, 41, 53 and 72-equal, and a bunch of others (but not 46, now one
of my favorites; drat!!!), etc., etc., as have many others before me,
and since.

And there have also been at least a couple others who
have 'discovered' the Bosanquet keyboard geometry in one form or
another, most notably Adriaan Fokker and Erv Wilson.

Since you've seduced me into playing "can you top this", how about
this one. In April 2001 the Miracle temperament was discovered
jointly by Paul Erlich and Dave Keenan and quickly became the hottest
topic of the year on the main tuning list. Two months later, Paul
/tuning/topicId_25489.html#25536
and Dave
/tuning/topicId_25575.html#25575
realized that they had only 'discovered' it. My original discovery
(consisting of both the Miracle generator and keyboard geometry,
which I did not consider especially significant at the time) took
place in the very same year that I 'discovered' the Bosanquet
keyboard geometry, and it was documented the following year in
Xenharmonikon #3 (February 1975; a minor correction appeared in XH5):
http://www.anaphoria.com/secor.PDF

If you were to ask me to compare my initial feelings about
my 'discovery' vs. the 'discovery' of my other discovery, I would
have to say that the former was more exciting and productive (in that
it led to the building of a new microtonal instrument), but the
latter was both more fun and gratifying (leading to the establishment
and cementing of new and enduring friendships).

Pardon me for overly reminiscing, but the past eight months (and
particularly the first two weeks of this year) have been very trying
for both me and my family. Sometimes it helps to look back at a
couple of bright spots in one's past to keep a balanced perspective
and to share one's thoughts and insights with the hope that it may
encourage others to keep on making their own discoveries
(or 'discoveries', as the case me be).

--George

i think we have all recreated ideas of others in the past. It seems though that it shows how good they are, to be the solution to widely separated people both in time and place is quite an accomplishment!

Rich Holmes wrote:

>"George D. Secor" <gdsecor@...> writes:
>
> >
>>Ah, you've brought back memories of what I did back in 1974 (playing >>19, 22, and 31 on a paper diagram), prior to approaching the Motorola >>Scalatron Company with my idea -- and then finding shortly thereafter >>that Bosanquet beat me to it by almost exactly 100 years! :-)
>> >>
>
>That's nothing... in my youth I 'discovered' 53-equal, only about 20
>centuries too late to claim precedence...
>
>- Rich Holmes
>
>
>
> >Yahoo! Groups Links
>
>
>
> >
>
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

Hello George!
I just want to say how much i have enjoyed your presence , on and off in these forums. and how much i appreciate the good and important work you do!

George D. Secor wrote:

>
>
>Pardon me for overly reminiscing, but the past eight months (and >particularly the first two weeks of this year) have been very trying >for both me and my family. Sometimes it helps to look back at a >couple of bright spots in one's past to keep a balanced perspective >and to share one's thoughts and insights with the hope that it may >encourage others to keep on making their own discoveries >(or 'discoveries', as the case me be).
>
>--George
>
>
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

George,

{Kraig wrote...}
> I just want to say how much i have enjoyed your presence , on and off in > these forums. and how much i appreciate the good and important work you do!

Seconded and thirded. I sometimes wonder if this disparate group really can be termed a community; when I think about you and all you've done (and the wise and gentle way you've done it), I can't think of it as anything _but_ a community.

Cheers,
Jon

--- In MakeMicroMusic@yahoogroups.com, "Jonathan M. Szanto"
<JSZANTO@A...> wrote:
> George,
>
> {Kraig wrote...}
> > I just want to say how much i have enjoyed your presence , on
and off in
> > these forums. and how much i appreciate the good and important
work you do!
>
> Seconded and thirded. I sometimes wonder if this disparate group
really can
> be termed a community; when I think about you and all you've done
(and the
> wise and gentle way you've done it), I can't think of it as
anything _but_
> a community.
>
> Cheers,
> Jon

Thanks, guys! I was starting to feel uneasy about straying a little
too far from the MMM topic, but I guess keyboards, discoveries,
inspiration, appreciation, encouragement, and a sense of community
are all ingredients that make the process of creating meaningful
music a whole lot easier and more enjoyable. And some of these
incidental things that we share may be helpful in ways we never
expected and/or of which we are completely unaware.

Okay, now that we've had our thought for the day, let's get on with
it by taking Prent's advice to set aside at least ten minutes today
to work on something significant!

--George

--- In MakeMicroMusic@yahoogroups.com, "Jonathan M. Szanto"
<JSZANTO@A...> wrote:
> George,
>
> {Kraig wrote...}
> > I just want to say how much i have enjoyed your presence , on and
off in
> > these forums. and how much i appreciate the good and important
work you do!
>
> Seconded and thirded. I sometimes wonder if this disparate group

Fourthed.

Thank you for sharing some of the thought processes behind your music
and your instrument design(s).

Paolo

George,

Seriously, what did you mean by the "Bosanquet layout"
for 22?

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> What is the "Bosanquet layout" for 22?

[silence]

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> George,
>
> Seriously, what did you mean by the "Bosanquet layout"
> for 22?
>
> -Carl

Sorry, Carl, but I got stuck trying to figure what you meant by the
question, which requires either a brief and simple answer or a long
and complicated one.

The brief answer: Simply take the Bosanquet keyboard geometry and
map 22 to it (there's only one way to do it) -- size and shape of
keys, angles of rows and columns open to interpretation. Rows of
keys are right-rising, according to the precedent set by the inventor
(and followed by Erv Wilson and myself in the Microzone and
Scalatron, respectively).

The complicated answer would involve an explanation of the Bosanquet
keyboard geometry, which I think you can find somewhere in
Helmholtz/Ellis _Sensations of Tone_.

--George

>> George,
>>
>> Seriously, what did you mean by the "Bosanquet layout"
>> for 22?
>
>Sorry, Carl, but I got stuck trying to figure what you meant by the
>question, which requires either a brief and simple answer or a long
>and complicated one.

No prob.

>The brief answer: Simply take the Bosanquet keyboard geometry and
>map 22 to it (there's only one way to do it)

I never know what the term 'Bosanquet geometry' meant. Is it
just that fifths should.... do what?

>-- size and shape of
>keys, angles of rows and columns open to interpretation.

And your choice is ovals on a plane, inclined slightly up
and away from the player, right?

>Rows of keys are right-rising, according to the precedent set by
>the inventor (and followed by Erv Wilson and myself in the Microzone
>and Scalatron, respectively).

Right-rising, so that the octaves come out parallel to the body
of the player? Or...

>The complicated answer would involve an explanation of the Bosanquet
>keyboard geometry, which I think you can find somewhere in
>Helmholtz/Ellis _Sensations of Tone_.

Really? I have a 1950's hardcover of that, but it's in storage.
But I have Bosanquet's book. But I don't remember this term.

He doesn't discuss 22, but in the forward, Rasch includes a diagram
from one of Bosaquet's later papers, in which the scheme had to
be changed to accommodate 22.

-Carl

There are actually a few ways to lay out the 22 on a generalized keyboard , depending on what you consider the generator of you scale. the one i put forth fall into this category and choose them to show how close IJ had come to such a thing. Interesting the last is the one i used on my 22 tone Eikosany, at least in theroy as when one lays out the tuning using a template for the intervals you end up with a quite irregular shape. this can be seen on this page . As my musical interest where away from the major scale as opposed to towards it.
http://anaphoria.com/musinst.html
the bottom diagram which i am sorry is so small. the gaps toward the bottom make it easy to stand in such place to play although a keyboard like this would work.

Having laid out thiese vibes in 3 different ways, it was interesting how it effected the music that came out of it. Much more than one might guess at once and even if i have people occasionally come over and pound on all these things, i am aware how just how things are laid out , influences what people play.

George D. Secor wrote:

>--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >
>>What is the "Bosanquet layout" for 22?
>> >>
>
>[silence]
>
>--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >
>>George,
>>
>>Seriously, what did you mean by the "Bosanquet layout"
>>for 22?
>>
>>-Carl
>> >>
>
>Sorry, Carl, but I got stuck trying to figure what you meant by the >question, which requires either a brief and simple answer or a long >and complicated one.
>
>The brief answer: Simply take the Bosanquet keyboard geometry and >map 22 to it (there's only one way to do it) -- size and shape of >keys, angles of rows and columns open to interpretation. Rows of >keys are right-rising, according to the precedent set by the inventor >(and followed by Erv Wilson and myself in the Microzone and >Scalatron, respectively).
>
>The complicated answer would involve an explanation of the Bosanquet >keyboard geometry, which I think you can find somewhere in >Helmholtz/Ellis _Sensations of Tone_.
>
>--George
>
>
>
>
>
>
>
> >Yahoo! Groups Links
>
>
>
> >
>
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> George,
> >>
> >> Seriously, what did you mean by the "Bosanquet layout"
> >> for 22?
> >
> >Sorry, Carl, but I got stuck trying to figure what you meant by
the
> >question, which requires either a brief and simple answer or a
long
> >and complicated one.
>
> No prob.
>
> >The brief answer: Simply take the Bosanquet keyboard geometry and
> >map 22 to it (there's only one way to do it)
>
> I never know what the term 'Bosanquet geometry' meant. Is it
> just that fifths should.... do what?

A Bosanquet keyboard geometry or layout is simply a generalized
keyboard that uses the fifth as the generating interval. The
location of a particular key along the y-dimension is a direct
function of the location of its pitch in the chain of fifths.

> >-- size and shape of
> >keys, angles of rows and columns open to interpretation.
>
> And your choice is ovals on a plane,

On the GK Scalatron we used ellipses. Erv Wilson's hexagons were my
first choice (because the key surfaces make more efficient use of
available area), but it was anticipated that there might be a problem
getting the key switches aligned sufficiently parallel with one
another, so for aesthetic reasons a shape having no straight edges
was chosen.

Erv judged the shape of Bosanquet's keys as relatively inefficient,
because the back half of each key surface can be played only by
putting the finger or thumb between two adjacent keys that are higher
in elevation (which can get a bit tricky). Otherwise, the shape of
the keys isn't too critical, and the "best" choice then probably
comes down to whatever is most practical to manufacture. I'm still
working on a slanting-square design for Igs (which is turning out
better than I expected) that has almost exactly the same key-axis
dimensions as the GK Scalatron, the biggest difference (apart from
the key shape) being that the octave distance is 3 mm shorter. Once
I finish this, I'll have to send Erv a copy.

> inclined slightly up
> and away from the player, right?

Right. An angle of about 17 degrees allows a natural arm motion as
one moves along the y-direction.

> >Rows of keys are right-rising, according to the precedent set by
> >the inventor (and followed by Erv Wilson and myself in the
Microzone
> >and Scalatron, respectively).
>
> Right-rising, so that the octaves come out parallel to the body
> of the player? ...

So that a line parallel to the x-axis passes through all octaves of
the same pitch. Left-rising with a fourth as generator would have
been possible, but that results in different scale fingerings. A
right-rising layout allows one to use the conventional sequence of
fingers for a right-hand C major scale for the meantone family of
tunings.

> >The complicated answer would involve an explanation of the
Bosanquet
> >keyboard geometry, which I think you can find somewhere in
> >Helmholtz/Ellis _Sensations of Tone_.
>
> Really? I have a 1950's hardcover of that, but it's in storage.
> But I have Bosanquet's book.

That's even better!

> But I don't remember this term.

It's not in his book. He simply named his keyboard a generalized
keyboard because it possesses these very desirable characteristics:

1) It accommodates multiple tunings (as opposed to being a
specialized keyboard for a single tuning);
2) It does not require special fingering patterns for different keys.

Since that time, others, such as Erv Wilson, have observed that
various other generating intervals may be used to define a keyboard
layouts having the above characteristics. Some of these will
accommodate divisions not possible on the Bosanquet layout; e.g.,
using a hemi-fifth as generator will accommodate 10, 14, and 24 (in
addition to 17, 31, and 41), but not 19, 22, 29 or 46, while using a
hemi-fourth as generator will accommodate 10, 14, 24 (in addition to
19 and 29), but not 17, 22, 31, 41, or 46.

Since many different kinds of generalized keyboard layouts (or
geometries) are possible, I employed the term "Bosanquet layout" to
specify the one that Bosanquet originated -- the one using a fifth as
the generating interval. The Bosanquet geometry is the closest thing
to a "universal" layout, because it accommodates more of the "best"
divisions than any other, and it's the easiest to learn, because it
allows one to retain many fingering patterns used on the conventional
keyboard.

> He doesn't discuss 22, but in the forward, Rasch includes a diagram
> from one of Bosaquet's later papers, in which the scheme had to
> be changed to accommodate 22.

Yes, I was rather surprised that Bosanquet overlooked 22 when I read
his book, but I understand that he realized this shortly thereafter.

--George

--- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
<igliashon@s...> wrote:
> [GS wrote:]
> > One minor concern I have with this design is that there's
no "white"
> > space separating the groups of 2 and 3 sharp and flat keys, so
the
> > visual 2-and-3 pattern is not as obvious -- on the GK Scalatron
it
> > almost jumps out at you.

This has been fixed in the latest design, which incorporates the
following changes:

> >I'd like to see if I can remedy this by
> > slanting the vertical columns counter-clockwise a bit (and also
> > allowing the columns to "slide" past one another so as to keep
the
> > octaves perfectly lateral), while increasing the octave distance
to
> > about 140 mm (as on the GK Scalatron, which is still one key less
> > than on a piano). Another significant benefit that I would
expect
> > from this is a shorter reach in the y-direction, which I know
will be
> > important to you.
>
> I look forward to seeing how this iteration turns out. As it
stands
> I think the design is perfectly fine, but who knows? This may be
> even better. I certainly don't think slanted keys should pose a
> problem for us, though i've yet to speak with Stevie on the
matter.
> I'm fairly confident that he will be easily persuaded with a quick
> demonstration, though.

Here is the file with the square slanted keys:

/makemicromusic/files/secor/GKbd22s1.gif

Compared with the non-slanted version, I think you'll find that the
Porcupine scale will be even easier, because the sharp keys have been
shifted to the left, making the reach in the y-direction shorter.
Even though I've added 3 more keys/octave to this diagram (which I
think will be very useful), the overall vertical spread is still
less, even though the keys are 1 mm larger!

The angles and dimensions are almost exactly the same as on the GK
Scalatron (the octave distance on this new design being 3 mm less),
so I already know that tunings with narrower fifths than 22 will also
work better. If Stevie were to learn this keyboard, he would have no
trouble playing the GK Scalatron or Microzone keyboard, because the
kinesthetic "feel" would be very similar (a claim that I can't make
for the previous design) -- in spite of the very different key shape.

Let me know what you think.

--George

Hello george!
I was using the term Bosanquet in a broader sense , so under your use of the term, they are not 'Bosanquet' but just 'generalized". It is probably best to use it as you have which is also how Erv does. It is in this context that Hanson keyboard which is another generalized design of importance. It accommodates 72 better than the Bosanquet.
In regard to the 22 tone keyboard. it is my understanding that his original book was twice as long and this keyboard may have been omitted from the published version. it is a shame that there is no copy of his original plan for his book as it would also be interesting if he included

George D. Secor wrote:

> Since many different kinds of generalized keyboard layouts (or
>
>geometries) are possible, I employed the term "Bosanquet layout" to >specify the one that Bosanquet originated -- the one using a fifth as >the generating interval. The Bosanquet geometry is the closest thing >to a "universal" layout, because it accommodates more of the "best" >divisions than any other, and it's the easiest to learn, because it >allows one to retain many fingering patterns used on the conventional >keyboard.
>
> >
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

[Kraig wrote...]
> In regard to the 22 tone keyboard. it is my understanding that his
>original book was twice as long and this keyboard may have been omitted
>from the published version. it is a shame that there is no copy of his
>original plan for his book as it would also be interesting if he included

Hi Kraig. Where did you hear this?

-Carl

Erv had gotten this info from somewhere

Carl Lumma wrote:

>[Kraig wrote...]
> >
>>In regard to the 22 tone keyboard. it is my understanding that his >>original book was twice as long and this keyboard may have been omitted >> >>
>>from the published version. it is a shame that there is no copy of his > >
>>original plan for his book as it would also be interesting if he included
>> >>
>
>Hi Kraig. Where did you hear this?
>
>-Carl
>
>
>
>
> >Yahoo! Groups Links
>
>
>
> >
>
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In MakeMicroMusic@yahoogroups.com, Kraig Grady <kraiggrady@a...>
wrote:
> Hello george!
> I was using the term Bosanquet in a broader sense , so under your
use
> of the term, they are not 'Bosanquet' but just 'generalized". It is
> probably best to use it as you have which is also how Erv does. It
is in
> this context that Hanson keyboard which is another generalized
design of
> importance. It accommodates 72 better than the Bosanquet.

A bit of an understatement -- the Bosanquet geometry won't
accommodate 72 at all.

> In regard to the 22 tone keyboard. it is my understanding that his
> original book was twice as long and this keyboard may have been
omitted
> from the published version.

From what *was* published, I didn't get that impression at all. I
thought that Bosanquet came across as intending to be pretty
systematic and thorough about what he was discussing, and I concluded
that (as incredible as it may seem) he must not have noticed 22 until
later.

--George

>>[Kraig wrote...]
>>>In regard to the 22 tone keyboard. it is my understanding that his
>>>original book was twice as long and this keyboard may have been omitted
>>>from the published version. it is a shame that there is no copy of his
>>>original plan for his book as it would also be interesting if he
>>>included
>>
>>Hi Kraig. Where did you hear this?
>
>Erv had gotten this info from somewhere

Huh. Have you read Rasch's preface to the Treatise? He traces
Bosanquet's output mentioning 22, and doesn't mention this. . .

-Carl

possibly the 22 is later then. still over a century to any of us

Carl Lumma wrote:

>>>[Kraig wrote...]
>>> >>>
>>>>In regard to the 22 tone keyboard. it is my understanding that his
>>>>original book was twice as long and this keyboard may have been omitted
>>>> >>>>
>>>>from the published version. it is a shame that there is no copy of his
>>> >>>
>>>>original plan for his book as it would also be interesting if he
>>>>included
>>>> >>>>
>>>Hi Kraig. Where did you hear this?
>>> >>>
>>Erv had gotten this info from somewhere
>> >>
>
>Huh. Have you read Rasch's preface to the Treatise? He traces
>Bosanquet's output mentioning 22, and doesn't mention this. . .
>
>-Carl
>
>
>
>
> >Yahoo! Groups Links
>
>
>
> >
>
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

> Let me know what you think.
>
> --George

Well, scales are definitely a bit easier, but one thing Mr. Erlich
pointed out to me is that on this design (and the previous one) it is
quite difficult to play his decatonic tetrachords. Normal triads are
alright, but extending the chords by adding those extra 7-limit notes
requires a pretty awkward fingering, one that would be very difficult
to reach in the context of performance.

Can you think of any ways to improve this? Bear in mind that we have
no problem sacrificing the appearance of a diatonic layout, since we
will be more heavily relying upon the 8- and 10-note scales based on
the porcupine and pajara generators, respectively. We will be mostly
relying on 22-equal and 15-equal (though we can probably use a
standard keyboard for 15), and someday might possibly expand to 29 or
26; regardless, the goal is to move away from diatonic tonality into
more unusual territory. It seems that your current design, while not
prohibitive of different scales, is fairly biased toward diatonic
scales, favoring meantone temperaments and scales with 7-note LLsLLLs
scales. Do you have any different types of mapping up your sleeve
that might be more suited to a decatonic or "porcuponic" approach?

Many thanks,

-Igliashon

"Igliashon Jones" <igliashon@...> writes:

> Well, scales are definitely a bit easier, but one thing Mr. Erlich
> pointed out to me is that on this design (and the previous one) it is
> quite difficult to play his decatonic tetrachords.

I assume you mean tetrads here.

> Normal triads are
> alright, but extending the chords by adding those extra 7-limit notes
> requires a pretty awkward fingering, one that would be very difficult
> to reach in the context of performance.

Hmm, I am not a keyboardist of any more than minimal skill, on any
sort of musical keyboard, so maybe I need some further explanation...
but putting my fingers on the screen I get a different impression. A
major tetrad is e.g. degrees 0, 7, 13, 18, and where I think that
feels awkward is on the 7. Omit the 7 and the other three lie almost
in a line, seems natural enough to me; but the 7 lies way off that
line. A 0, 8, 13, 18 tetrad feels much easier but of course isn't
what's wanted.

The minor tetrad is 0, 6, 13, 17 and is worse; I have to stretch
further to pick up the 6, and the close proximity of 13 and 17 makes
it hard for me to hit both with my fourth and fifth fingers -- due to
the difference in the lengths of those fingers -- while also reaching
for the other two notes. (And I can't reach the 6 at all if I use the
third and fourth fingers for 13 and 17.)

I notice the tetrads on 2 (2, 9, 15, 20 and 2, 8, 15, 19) are easier
if I use 2 in the lower cyan row and the 15, 19, and 20 in the upper
cyan and black rows. The minor tetrad especially. But crossing that
many rows would make for difficult scales, I'd think.

> It seems that your current design, while not
> prohibitive of different scales, is fairly biased toward diatonic
> scales, favoring meantone temperaments and scales with 7-note LLsLLLs
> scales. Do you have any different types of mapping up your sleeve
> that might be more suited to a decatonic or "porcuponic" approach?

The Bosenquet-style design seems to me to be biased not so much toward
diatonic scales as toward scales composed mainly of "major seconds",
i.e. steps of about 200 cents. Scales with smaller intervals then
necessarily have notes fairly far out of line with one another. I
guess I could imagine a Bosenquet-like layout with adjacent notes
differing by something closer to 100 cents, with a 22-note layout
looking very roughly something like (view this in a monospaced font)

1 3 5 7 ...
13 14 16 18 20 0 2 4 6 ...
1 3 5 7 9 11 13 15 17 19 21 1 3 5 ...
0 2 4 6 8 10 12 14 16 18 20
21 1 3 5 7 9

(tilted to put octaves on a horizontal line and with notes added to or
subtracted from columns as needed); but this not only involves a lot
of duplicate notes, it also nearly doubles the octave stretch.

- Rich Holmes

--- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
<igliashon@s...> wrote:
>
> > Let me know what you think.
> >
> > --George
>
> Well, scales are definitely a bit easier, but one thing Mr. Erlich
> pointed out to me is that on this design (and the previous one) it
is
> quite difficult to play his decatonic tetrachords. Normal triads
are
> alright, but extending the chords by adding those extra 7-limit
notes
> requires a pretty awkward fingering, one that would be very
difficult
> to reach in the context of performance.

Yes, I admit that some chord positions are a bit more difficult that
what we're accustomed to. It takes some getting used to, but with a
little practice you can learn to grab these pretty quickly.

I do have a couple of suggestions about playing tetrads in 22 on the
Bosanquet layout. Sometimes the best fingerings are not immediately
obvious, e.g., the utonal in first inversion consisting of 0,6,13,17
degrees can probably be played by the right hand most easily by
taking 6 with the thumb crossed under.

Another possibility for making everything a little easier is
foreshortening the y-axis by making the key size smaller. The
squares in this latest design are longer on a side than piano keys
are wide, so it wouldn't really hurt to make them somewhat smaller.

> Can you think of any ways to improve this? Bear in mind that we
have
> no problem sacrificing the appearance of a diatonic layout, since
we
> will be more heavily relying upon the 8- and 10-note scales based
on
> the porcupine and pajara generators, respectively. We will be
mostly
> relying on 22-equal and 15-equal (though we can probably use a
> standard keyboard for 15), and someday might possibly expand to 29
or
> 26; regardless, the goal is to move away from diatonic tonality
into
> more unusual territory. It seems that your current design, while
not
> prohibitive of different scales, is fairly biased toward diatonic
> scales, favoring meantone temperaments and scales with 7-note
LLsLLLs
> scales. Do you have any different types of mapping up your sleeve
> that might be more suited to a decatonic or "porcuponic" approach?

Igliashon, I already replied to Paul off-list before I read your
message, and I'll forward a copy to you. It addresses some other
issues relating to non-Bosanquet generalized layouts.

I'll have more to say later after I give this some more thought.

Best,

--George

> I assume you mean tetrads here.

Doh! Yep. Tetrads, not tetrachords...big difference (the trials and
tribulations of posting when deliriously tired).

> A major tetrad is e.g. degrees 0, 7, 13, 18, and where I think that
> feels awkward is on the 7. Omit the 7 and the other three lie
almost
> in a line, seems natural enough to me; but the 7 lies way off that
> line. A 0, 8, 13, 18 tetrad feels much easier but of course isn't
> what's wanted.

Yeah, it is the 7 that makes it hard, but it's do-able if you don't
have to add the 18 since you can use your pinky for the 13 (or the 0
for the left hand)

> The minor tetrad is 0, 6, 13, 17 and is worse; I have to stretch
> further to pick up the 6, and the close proximity of 13 and 17 makes
> it hard for me to hit both with my fourth and fifth fingers -- due
to
> the difference in the lengths of those fingers -- while also
reaching
> for the other two notes. (And I can't reach the 6 at all if I use
the
> third and fourth fingers for 13 and 17.)

Exactly...those minors are what kill me.

> I notice the tetrads on 2 (2, 9, 15, 20 and 2, 8, 15, 19) are easier
> if I use 2 in the lower cyan row and the 15, 19, and 20 in the upper
> cyan and black rows. The minor tetrad especially. But crossing
that
> many rows would make for difficult scales, I'd think.

> The Bosenquet-style design seems to me to be biased not so much
toward
> diatonic scales as toward scales composed mainly of "major seconds",
> i.e. steps of about 200 cents.

Yeah, that's a better way to put it, though most popular scales that
consist primarily of major 2nds are reasonably diatonic (or
hexatonic, I suppose).

> (tilted to put octaves on a horizontal line and with notes added to
or
> subtracted from columns as needed); but this not only involves a lot
> of duplicate notes, it also nearly doubles the octave stretch.

I think the ideal layout isn't necessarily one that would put the
scale in a line, but would put the tetrads in lines (or nearly
lines). When you consider that a triad in 22 will be formed with a
root, fifth, and one of 4 thirds (or a root, fourth, and one of 4
sixths), and that the most consonant triads will be formed using
the "prime 5-limit" thirds (i.e. degrees 6 and 7), a layout that puts
the 9/7 supermajor (degree 8) nearly on a line from the root makes
little sense.

BTW, Paul Erlich just uploaded a bunch of tentative diagrams for
generalized 22-et keyboards based on several different generators,
but they seem to be too small to read on my screen. Can anyone else
read them?

-igs

"Igliashon Jones" <igliashon@...> writes:

> Exactly...those minors are what kill me.

Hmm, call me whacko but ... on paper it seems like it'd work to play 0
with finger 1 (thumb), 6 with finger 2, and 13 and 17 both with finger
5! Then I don't need to curl up finger 4 to reach 13, which makes the
stretch to 6 much easier. Whether that would work on a real keyboard
I don't know. (It's a bit like on a conventional keyboard if I ever
wanted to play a chord of C-Eb-C'-D', I could do it only by playing C'
and D' with finger 5 on the crack between them. Though in that case
it's because it's a long stretch along the keyboard rather than across
it.)

Also, I just noticed since note 3 is not duplicated, you have to use a
different key pattern for a minor tetrad on 3. Likewise for 12. So
duplicates for these probably should be added.

> BTW, Paul Erlich just uploaded a bunch of tentative diagrams for
> generalized 22-et keyboards based on several different generators,
> but they seem to be too small to read on my screen. Can anyone else
> read them?

It's not your screen. They're too low a resolution for the key labels
to be legible.

- Rich Holmes

--- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
<igliashon@s...> wrote:
>
> [Rich Holmes:]
> > A major tetrad is e.g. degrees 0, 7, 13, 18, and where I think
that
> > feels awkward is on the 7. Omit the 7 and the other three lie
almost
> > in a line, seems natural enough to me; but the 7 lies way off that
> > line. A 0, 8, 13, 18 tetrad feels much easier but of course isn't
> > what's wanted.
>
> Yeah, it is the 7 that makes it hard, but it's do-able if you don't
> have to add the 18 since you can use your pinky for the 13 (or the
0
> for the left hand)

Are you trying to play these on your computer screen, or on a paper
prinout? Whatever the case, try putting a ruler near the markings at
either the left or bottom of the diagram to see whether it^s the
correct size; on my screen the octave distance is more than 20 mm too
large. I tried some of these chords out on my Scalatron keyboard
last night (on which the dimensions are slightly greater than in the
figure) and had no problem playing this particular tetrad with
fingering 1-2-4-5.

> > The minor tetrad is 0, 6, 13, 17 and is worse; I have to stretch
> > further to pick up the 6, and the close proximity of 13 and 17
makes
> > it hard for me to hit both with my fourth and fifth fingers --
due to
> > the difference in the lengths of those fingers -- while also
reaching
> > for the other two notes. (And I can't reach the 6 at all if I
use the
> > third and fourth fingers for 13 and 17.)
>
> Exactly...those minors are what kill me.

As I said in message
/makemicromusic/topicId_8475.html#8611
the easiest fingering is to cross the thumb under: 2-1-4-5 (noting
that this can be used in all 22 keys with the 12 duplicates I have in
the diagram.) I also tried it with the 1-2-4-5 fingering and found
it was not as difficult as doing it on a computer screen.

As I said in the above message, the key dimensions would not have to
be as large as what I show, and slightly smaller keys would make a
big difference in your ability to reach these chords.

> ...
> I think the ideal layout isn't necessarily one that would put the
> scale in a line, but would put the tetrads in lines (or nearly
> lines).

Yes, but for 22 there isn't any that will also keep the octaves
within a reasonable distance without making the keys very narrow.
And you'll most likely prefer a generating interval that will allow
you multiple tunings.

Since the y-axis location of each key is a direct function of the
position of its corresponding tone in the chain of generators, I did
a quick survey of positions (expressed as the number of generators
distant from C) for otonal and utonal tetrads for the Bosanquet and
Porcupine layouts. For the utonal tetrads I give two different
fingerings:

G=13deg22 (Bosanquet)
Octaves 6 key-widths distant
Usable divisions of the octave: 12, 17, 19, 22, 26, 27, 29, 31, ...
Otonal tetrad (C-E\-G-Bb): 0G, +9G, +1G, -2G
Total spread: 11G
Utonal tetrad (C-Eb/-G-A): 0G, +14G, +1G, +3G or 0G, -8G, +1G, +3G
Total spread: 14G or 11G

G=3deg22 (Porcupine)
Octaves 7.5 key-widths distant
Usable divisions of the octave: 15, 22, 23, 29, 31, ...
Otonal tetrad (C-E\-G-Bb): 0G, -5G, -3G, +6G
Total spread: 11G
Utonal tetrad (C-Eb/-G-A): 0G, 2G, -3G, +9G or 0G, 2G, -3G, +9G, -13G
Total spread: 12G or 15G

Total spread for each tetrad is calculated as the difference between
the largest and smallest G-values. Considering that the total spread
for the Porcupine layout is not significantly better (or worse) than
the Bosanquet, the only real advantage it would seem to have is that
it gives you 15-ET with transpositional invariance. (And although I
also list 31 as a "usable" division in a "Porcupine" layout, it would
not be very suitable: an otonal tetrad comes up 0G, -13G, -11G, -17G.)

Getting back to 22, I looked at a 7deg22 (major-third) generator but
didn't even bother to finish tabulating that one, since 3/2 is +5G
and 7/4 is -10G, for a spread of 15G (which is awful).

> When you consider that a triad in 22 will be formed with a
> root, fifth, and one of 4 thirds (or a root, fourth, and one of 4
> sixths), and that the most consonant triads will be formed using
> the "prime 5-limit" thirds (i.e. degrees 6 and 7), a layout that
puts
> the 9/7 supermajor (degree 8) nearly on a line from the root makes
> little sense.

Hmmm, sounds like you're attaching little or no importance to the
subminor (6:7:9) triad, which is not only better approximated in 22
than the major triad, but also one of the most consonant chords
beyond the 5-limit. And if you ever get around to utilizing the full
harmonic potential of 22 by taking it to the 11-limit, you'll observe
that 8 degrees also represents 11:14.

> BTW, Paul Erlich just uploaded a bunch of tentative diagrams for
> generalized 22-et keyboards based on several different generators,
> but they seem to be too small to read on my screen. Can anyone
else
> read them?

Igs, have you started looking for any commercially available square-
top switches that could be used for keys? It would help a lot if we
knew what the key dimensions might be.

--George

"George D. Secor" <gdsecor@...> writes:

> Are you trying to play these on your computer screen, or on a paper
> prinout?

The former initially, but later I tried the latter.

> I tried some of these chords out on my Scalatron keyboard
> last night (on which the dimensions are slightly greater than in the
> figure) and had no problem playing this particular tetrad with
> fingering 1-2-4-5.

Maybe it's my hands.

- Rich Holmes

> As I said in message
> /makemicromusic/topicId_8475.html#8611
> the easiest fingering is to cross the thumb under: 2-1-4-5 (noting
> that this can be used in all 22 keys with the 12 duplicates I have
in
> the diagram.) I also tried it with the 1-2-4-5 fingering and found
> it was not as difficult as doing it on a computer screen.

Oh, I've tried it on paper alright, and I was actually referring to
your suggested fingering when assessing the difficulty. Now, I
didn't say it's not playable, but try playing a bunch of tetrads in a
sequence at a decent tempo; they're pretty tough to grab at speed.
It would be learnable in time, but the whole point of having a
generalized keyboard is that it's supposed to be EASY, and this is
definitely not.

>
> As I said in the above message, the key dimensions would not have
to
> be as large as what I show, and slightly smaller keys would make a
> big difference in your ability to reach these chords.

Actually, I think it is due to the fact that some notes are too close
together or at the wrong angle to each other that this design is
difficult. Seriously, the Bosanquet design wasn't meant to
accomodate scales based on the Pajara generator or the Porcupine.
Strangely, I think so far Paul's tentative "Doublewide"-based
keyboard works the best for 22; scales are only slightly more complex
than on the bosanquet but chords are MUCH easier. Of course I have
no idea which other temperaments are supported by Doublewide since
Stevie still has my copy of Paul's last paper.

To see the correct versions of Paul's designs, check out

http://photobucket.com/albums/v170/igliashon_jones/

As soon as I get Photoshop back up and running, I'll try to flesh
these out a bit.
> Hmmm, sounds like you're attaching little or no importance to the
> subminor (6:7:9) triad, which is not only better approximated in 22
> than the major triad, but also one of the most consonant chords
> beyond the 5-limit. And if you ever get around to utilizing the
full
> harmonic potential of 22 by taking it to the 11-limit, you'll
observe
> that 8 degrees also represents 11:14.

Well, I don't mean to ignore the 6:7:9 triad, it's just in 22 my two
favorite tonal systems (Porcupine and Decatonic) don't really make
use of it. It's still very important and we're certainly not going
to ignore 22's diatonic possibilities, but we'd rather make
decatonics and porcupine easier at the expense of diatonics than vice-
versa. Ideally all 4 types of triad should be playable with equal
and minimal difficulty.

> Igs, have you started looking for any commercially available square-
> top switches that could be used for keys? It would help a lot if
we
> knew what the key dimensions might be.

It would help if I knew where to look. Can you recommend me any
starting points?

Respectfully,
-igs

Igliashin!

These are not square top, but they sure look sharp. Old arcade
game style buttons at $3.75 apiece.

http://www.allelectronics.com/cgi-bin/category.cgi?category=700
325&type=store

The range of colors (white, black, blue, red, yellow, green) is
nice, they look very easy to mount, and they are reputed to hold
up to lots of abuse. No minimum order, so you could get one to
test.

With these buttons and a doepfer controller ($100, perhaps
slightly overpriced, but very easy to use), a 4 octave keyboard in a
wooden enclosure would clock in at around $500. Not bad!

Yours,
Aaron Hunt

--- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
<igliashon@s...> wrote:

> > Igs, have you started looking for any commercially available
square-
> > top switches that could be used for keys? It would help a lot
if
> we
> > knew what the key dimensions might be.
>
>
> It would help if I knew where to look. Can you recommend me
any
> starting points?
>
> Respectfully,
> -igs

Hmm, same switches, a lot cheaper! $2.59 each:

http://www.marvac.com/SearchResult.aspx?CategoryID=760

AH

--- In MakeMicroMusic@yahoogroups.com, "gooseplex"
<cfaah@e...> wrote:
>
> Igliashin!
>
> These are not square top, but they sure look sharp. Old arcade
> game style buttons at $3.75 apiece.
>
>
http://www.allelectronics.com/cgi-bin/category.cgi?category=700
> 325&type=store
>
> The range of colors (white, black, blue, red, yellow, green) is
> nice, they look very easy to mount, and they are reputed to hold
> up to lots of abuse. No minimum order, so you could get one to
> test.
>
> With these buttons and a doepfer controller ($100, perhaps
> slightly overpriced, but very easy to use), a 4 octave keyboard in
a
> wooden enclosure would clock in at around $500. Not bad!
>
> Yours,
> Aaron Hunt
>
>
> --- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
> <igliashon@s...> wrote:
>
> > > Igs, have you started looking for any commercially available
> square-
> > > top switches that could be used for keys? It would help a
lot
> if
> > we
> > > knew what the key dimensions might be.
> >
> >
> > It would help if I knew where to look. Can you recommend
me
> any
> > starting points?
> >
> > Respectfully,
> > -igs

Thanks, Aaron! I'll check one of 'em out, see how they feel. That'd
be really funny, using arcade-style buttons on a keyboard--it'd be
like playing a videogame!

-igs

--- In MakeMicroMusic@yahoogroups.com, "gooseplex" <cfaah@e...> wrote:
>
> Hmm, same switches, a lot cheaper! $2.59 each:
>
> http://www.marvac.com/SearchResult.aspx?CategoryID=760
>
> AH
>
> --- In MakeMicroMusic@yahoogroups.com, "gooseplex"
> <cfaah@e...> wrote:
> >
> > Igliashin!
> >
> > These are not square top, but they sure look sharp. Old arcade
> > game style buttons at $3.75 apiece.
> >
> >
> http://www.allelectronics.com/cgi-bin/category.cgi?category=700
> > 325&type=store
> >
> > The range of colors (white, black, blue, red, yellow, green) is
> > nice, they look very easy to mount, and they are reputed to hold
> > up to lots of abuse. No minimum order, so you could get one to
> > test.
> >
> > With these buttons and a doepfer controller ($100, perhaps
> > slightly overpriced, but very easy to use), a 4 octave keyboard
in
> a
> > wooden enclosure would clock in at around $500. Not bad!
> >
> > Yours,
> > Aaron Hunt
> >
> >
> > --- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
> > <igliashon@s...> wrote:
> >
> > > > Igs, have you started looking for any commercially available
> > square-
> > > > top switches that could be used for keys? It would help a
> lot
> > if
> > > we
> > > > knew what the key dimensions might be.
> > >
> > >
> > > It would help if I knew where to look. Can you recommend
> me
> > any
> > > starting points?
> > >
> > > Respectfully,
> > > -igs

Okay, after further consideration, we've found that Paul's design
based on the Magic generator seems to be optimal for 22. Tetrads
fall in a nice, neat, 4-finger row, and scales are pretty much a
cinch. To see what I mean, go to:

http://img.photobucket.com/albums/v170/igliashon_jones/magic.gif

I haven't mapped any scales or chords yet, but if you know anything
about the mechanics of 22 you can figure them out without too much
trouble.

One thing that I'm not so certain about with this design is what
alphabet would we color-code it according to? Since it's based on
the Magic generator, color-coding it according to Diatonic
nomenclature doesn't seem like a great idea, but I have no idea what
an alphabet based on Magic would be. I'll mess around with Porcupine
and Pajara schemes to see how those work, but can anyone offer some
suggestions? Remember too that we haven't made any final decisions
yet, but we're getting close.

Gracias a todos,

-Igliashon

--- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
<igliashon@s...> wrote:
>
> > As I said in message
> > /makemicromusic/topicId_8475.html#8611
> > the easiest fingering is to cross the thumb under: 2-1-4-5
(noting
> > that this can be used in all 22 keys with the 12 duplicates I
have
> in
> > the diagram.) I also tried it with the 1-2-4-5 fingering and
found
> > it was not as difficult as doing it on a computer screen.
>
> Oh, I've tried it on paper alright, and I was actually referring to
> your suggested fingering when assessing the difficulty. Now, I
> didn't say it's not playable, but try playing a bunch of tetrads in
a
> sequence at a decent tempo; they're pretty tough to grab at speed.
> It would be learnable in time, but the whole point of having a
> generalized keyboard is that it's supposed to be EASY, and this is
> definitely not.
>
> >
> > As I said in the above message, the key dimensions would not have
> to
> > be as large as what I show, and slightly smaller keys would make
a
> > big difference in your ability to reach these chords.
>
> Actually, I think it is due to the fact that some notes are too
close
> together or at the wrong angle to each other that this design is
> difficult. Seriously, the Bosanquet design wasn't meant to
> accomodate scales based on the Pajara generator or the Porcupine.
> Strangely, I think so far Paul's tentative "Doublewide"-based
> keyboard works the best for 22; scales are only slightly more
complex
> than on the bosanquet but chords are MUCH easier. Of course I have
> no idea which other temperaments are supported by Doublewide since
> Stevie still has my copy of Paul's last paper.
>
> To see the correct versions of Paul's designs, check out
>
> http://photobucket.com/albums/v170/igliashon_jones/
>
> As soon as I get Photoshop back up and running, I'll try to flesh
> these out a bit.
> > Hmmm, sounds like you're attaching little or no importance to the
> > subminor (6:7:9) triad, which is not only better approximated in
22
> > than the major triad, but also one of the most consonant chords
> > beyond the 5-limit. And if you ever get around to utilizing the
> full
> > harmonic potential of 22 by taking it to the 11-limit, you'll
> observe
> > that 8 degrees also represents 11:14.
>
> Well, I don't mean to ignore the 6:7:9 triad, it's just in 22 my
two
> favorite tonal systems (Porcupine and Decatonic) don't really make
> use of it. It's still very important and we're certainly not going
> to ignore 22's diatonic possibilities, but we'd rather make
> decatonics and porcupine easier at the expense of diatonics than
vice-
> versa. Ideally all 4 types of triad should be playable with equal
> and minimal difficulty.
>
> > Igs, have you started looking for any commercially available
square-
> > top switches that could be used for keys? It would help a lot if
> we
> > knew what the key dimensions might be.
>
>
> It would help if I knew where to look. Can you recommend me any
> starting points?
>
> Respectfully,
> -igs

--- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
<igliashon@s...> wrote:
>
> Okay, after further consideration, we've found that Paul's design
> based on the Magic generator seems to be optimal for 22. Tetrads
> fall in a nice, neat, 4-finger row, and scales are pretty much a
> cinch. To see what I mean, go to:
>
> http://img.photobucket.com/albums/v170/igliashon_jones/magic.gif
> ...
> Gracias a todos,
>
> -Igliashon

Igs,

Paul contacted me off-list asking me to give more consideration to
his diagrams, particularly those based on periods of 1/N octaves
(i.e., Srutal/Pajara and Hedgehog). I figured out the generator
figures for the following ones. (For purposes of making an equitable
comparison, the generator numbers for Srutal/Pajara and Hedgehog are
doubled, since they have 2 chains of generators/octave and thus twice
the key-density.)

Period=11deg22, G=2deg22 (Srutal/Pajara)
Octaves ?? key-widths distant (depends on key shape)
Otonal tetrad (C-E\-G-Bb): 0G, -4G, +2G, -4G
Total spread: 6G
Utonal tetrad (C-Eb/-G-A): 0G, +6G, +2G, +6G
Total spread: 6G

G=7deg22 (Magic)
Octaves 7 key-widths distant
Otonal tetrad (C-E\-G-Bb): 0G, +1G, +5G, -10G or 0G, +1G, +5G, -12G
Total spread: 15G or 13G
Utonal tetrad (C-Eb/-G-A): 0G, +4G, +5G, -7G
Total spread: 12G

Period=11deg22, G=3deg22 (Hedgehog)
Octaves 7 key-widths distant
Otonal tetrad (C-E\-G-Bb): 0G, -10G, -6G, -10G
Total spread: -10G
Utonal tetrad (C-Eb/-G-A): 0G, +4G, -6G, +4G
Total spread: 10G

Period=11deg22, G=1deg22 (Doublewide)
Octaves ?? key-widths distant
Otonal tetrad (C-E\-G-Bb): 0G, +3G, +4G, +3G
Total spread: 4G
Utonal tetrad (C-Eb/-G-A): 0G, +1G, +4G, +1G
Total spread: 4G

From this I concluded that Magic was the *worst* one. I don't
understand your statement that "Tetrads fall in a nice, neat, 4-
finger row"? The otonal tetrad has the top note of the chord
displaced along the y-axis quite a ways from the other 3 tones; same
for the 1st-inversion utonal tetrad. Did you try these tetrads in
all of their inversions?

The two layouts that give the lowest spread have generators that are,
unfortunately, rather small (less than 1/10 of an octave), which
mandates a very short key dimension in the y-direction -- not good at
all, IMO, for playing them with the thumb (i.e., to avoid pressing 2
keys at once). For the Magic layout I gave a figure of 7 key-
widths/octave on the assumption that the keys would be considerably
narrower than what Paul shows (with the keys for 1 and 6 degrees
separating those for 0 and 7, so that the latter would not share a
common boundary), which would allow the keys to be larger in the y-
dimension (but which would also increase the distance required to
reach along the y-axis).

> --- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
> <igliashon@s...> wrote:
> >
> > > As I said in message
> > > /makemicromusic/topicId_8475.html#8611
> > > the easiest fingering is to cross the thumb under: 2-1-4-5
(noting
> > > that this can be used in all 22 keys with the 12 duplicates I
have in
> > > the diagram.) I also tried it with the 1-2-4-5 fingering and
found
> > > it was not as difficult as doing it on a computer screen.
> >
> > Oh, I've tried it on paper alright, and I was actually referring
to
> > your suggested fingering when assessing the difficulty. Now, I
> > didn't say it's not playable, but try playing a bunch of tetrads
in a
> > sequence at a decent tempo; they're pretty tough to grab at
speed.
> > It would be learnable in time, but the whole point of having a
> > generalized keyboard is that it's supposed to be EASY, and this
is
> > definitely not.

The whole point is that it's supposed to be EASIER than a
heterogeneous layout.

In the Bosanquet layout it's the diatonic things that are technically
easiest (*easier* than on a conventional keyboard) and the non-
diatonic things (which spread out into the y-dimension) that are more
difficult. The whole point of having a generalized keyboard (of
whatever sort) is that you don't have to learn anything (regardless
of whether it is technically easy or difficult) in a lot of different
keys, which gives you the time to practice the more difficult
things. With a little practice even the more difficult things become
fairly easy, because much of the "difficulty" consists in the fact
that the techniques are somewhat *different* from what keyboard
players are accustomed to. Anyone who tries the left-hand buttons of
an accordion for the first time will get the impression that their
very small size makes them maddeningly difficult, but after some
practice developing the necessary playing technique they're fairly
easy to play.

No matter how you lay out a two-dimensional (microtonal) keyboard,
some things are going to be easier than others, depending on how far
you have to reach along the y-axis. It's my feeling that, in order
for a microtonal keyboard to have any chance of getting a wider
acceptance in the musical world, the diatonic things are going to
have to be at least as easy as they are on a conventional keyboard,
because that's the comparison that most musicians will be making from
the very start. As far as I'm concerned, that, plus the fact that
the Bosanquet layout accommodates the greatest number of the "best"
octave divisions, puts it way ahead of anything else in terms of
usefulness and probable success -- particularly since I believe that
reducing the key size would make the technique a bit easier.

But if you're looking for something that will be easier for 22, I
think that you just may have to keep looking, because I don't think
you've found it.

> > > Igs, have you started looking for any commercially available
square-
> > > top switches that could be used for keys? It would help a lot
if we
> > > knew what the key dimensions might be.
> >
> > It would help if I knew where to look. Can you recommend me any
> > starting points?

Nothing specific, other than doing a websearch.

--George

> From this I concluded that Magic was the *worst* one. I don't
> understand your statement that "Tetrads fall in a nice, neat, 4-
> finger row"? The otonal tetrad has the top note of the chord
> displaced along the y-axis quite a ways from the other 3 tones;
same
> for the 1st-inversion utonal tetrad. Did you try these tetrads in
> all of their inversions?

George, have you *looked* at the diagram that I linked to? I don't
know what your calculations are based on, but I can tell you that
your statements blatantly contradict what I observe with my own two
eyes. In 22, otonal tetrad = degrees 0 7 13 18. 7 degrees =
approximately the Magic generator and is immediately adjacent to 0; 6
is right above it. 13 is adjacent to both 6 and 7, such that a
diagonal line connecting the center points of keys 0 and 13 would
pass exactly between keys 6 and 7. 18 is the only "disjoint" key but
is still within easy reach, accessible easily in one of two places.
I can post pictures highlighting this tetrad and the utonal one
(which varies only slightly in fingering) if you like. You don't
even *need* a thumb to play either of them, and the 6:7:9 triad is
only a tiny little bit more out of the way (but just as easy as on
the Bosanquet-style keyboard). Heck, we could even substantially
enlarge those keys without sacrificing playability given how close
they are. In fact, let me post some pictures comparing otonal and
utonal tetrads on some of these designs.

> It's my feeling that, in order
> for a microtonal keyboard to have any chance of getting a wider
> acceptance in the musical world, the diatonic things are going to
> have to be at least as easy as they are on a conventional keyboard,
> because that's the comparison that most musicians will be making
from
> the very start. As far as I'm concerned, that, plus the fact that
> the Bosanquet layout accommodates the greatest number of the "best"
> octave divisions, puts it way ahead of anything else in terms of
> usefulness and probable success -- particularly since I believe
that
> reducing the key size would make the technique a bit easier.

George, with all due respect, I disagree with your use of the
term "best" in reference to certain EDO's, and I think many on this
list would be inclined to concur. "Best" is all too relative to be
used here. What you really mean is that the Bosanquet design is good
for the "best" diatonic or Pythagorean EDO's, assuming that most
people who would want to play microtonally would start from the base
of traditional music. I have no problem with that; we all have our
own ambitions within this field. But I count myself a member of
the "no bad tunings" school of thought. Every tuning has its own
infinity of possible expression, within the framework of its own
unique limitations, tendencies, and colors. I tend to actually
prefer the more unusual ones, because they push my playing in a more
novel direction. And I have to ask: how can you argue "marketability"
as a reason Stevie and I should accept a design? We're not going to
mass-produce anything. The most we're hoping for is a design that
will inspire us to make novel music, which hopefully will in turn
inspire others to break out of their 12-equal shells. Who's to say
what's most likely to catch on? It all really depends on who/what
produces the most compelling music, which is defined not by us as
composers but by the public as listeners...and we all know how fickle
and unpredictable they are. If any of us really cared about
compatibility, universality, or the mass application of a design, we
probably wouldn't be here. Yes, it would be convenient to have a new
system to replace 12-equal. But as I've been told many a time by
many people on this list, that would really be making the same
mistake twice. Variety is the goal, correct? And while the
Bosanquet design does very well for a lot of temperaments, there are
others that it does very poorly for.

It is possible that the "Magic" design isn't the absolute best, but
as far as 22-equal is concerned it's a good few steps up in
versatility from Bosanquet. In fact, both the Porcupine and
Doublewide designs are improvements as well. If you recall, our
concern here is for making the best possible *22-equal* keyboard. If
it turns out to accomodate other systems, that's a plus, but it's not
a requirement.

Respectfully,

-Igliashon

it really seems like you like Paul's suggestions so much, almost universally and yet you keep asking o advice, then dismiss it. Possibly you are wasting your time since you already have the answers?

Igliashon Jones wrote:

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

> it really seems like you like Paul's suggestions so much, almost
> universally and yet you keep asking o advice, then dismiss it.
Possibly
> you are wasting your time since you already have the answers?

Ah, but you miss the point of "debate", Kraig. In order to test an
idea you have to put it up to criticism. I'm not "dismissing"
advice; I'm debating the merits of various designs. If you've paid
any attention to this you should have noted how many designs I've put
up and then taken down as a direct result of criticism from group
members. I think we're pretty close to a final idea now, but then
again I thought that in the past as well. If some point of criticism
comes up that I feel is valid or important, I take it into account.
Honestly I'm not set on anything, but to debate successfully you do
have to pick a side and argue it until the arguement is soundly
defeated. Did I mention I'm a Philosophy major? ;->

Perhaps I'm doing this on the wrong list--would this be more
appropriate over at the Tuning group? I figured since it involved
designing instruments to be used to MAKE MICRO MUSIC then this was
the place to ask, but it's been getting kind of theoretical
lately...please, if I'm getting on anyone's nerves, just tell me to
shut up or to go elsewhere.

Igliashon Jones asked,

> Perhaps I'm doing this on the wrong list--would this be more
> appropriate over at the Tuning group?

It's fine here, as far as I'm concerned. This is a place to talk about
*doing* stuff with microtuning... Seems like you're doing.

Rick

the problem with debating such ideas as a keyboard design is that we lack the " logical ' language to represent the physicality of what it is we are doing. using our hands, one of the most complex devices nature has come up with.
To George and myself keyboards are not 'ideas' they are things we use and have used over long periods of time.
What if a third party has the best keyboard idea and lacks the debating skills to put forth his argument. Musicians ( unfortunately and fortunately) tend to be more intuitive than analytical
Perhaps i am getting a bit testy and i apologize since i sense at a certain point one cannot argue which design is the best until we have the two models infront of each other. I have never built anything where something unforeseen do not manifest itself. They are all things i do not think we can get to logically except in hind sight.
these keys seem unbelievably small to me and on any practical instrument one is going to have some empty space between keys in order to prevent them from rubbing against each other.
I would suggest though of when displaying keyboards that you might include the mapping of the harmonic material in the tuning ( or since in your case the particular scales you seem to be set on ) as seen in this paper.
http://www.anaphoria.com/xen3b.PDF
which makes all the harmonic relations easier to see. although a two octave sample would be even better to really get all the inversions and such. but this paper comes from a different era

Possibly i think more would be able to grasp exactly the fingering immediately and then maybe you might get more feed back . I assume you make a 4 octave mock up and place it on a table and play with it. i can't wait till we have 3d monitors.
Igliashon Jones wrote:

> >
>>it really seems like you like Paul's suggestions so much, almost >>universally and yet you keep asking o advice, then dismiss it. >> >>
>Possibly > >
>>you are wasting your time since you already have the answers?
>> >>
>
>Ah, but you miss the point of "debate", Kraig. In order to test an >idea you have to put it up to criticism. I'm not "dismissing" >advice; I'm debating the merits of various designs. If you've paid >any attention to this you should have noted how many designs I've put >up and then taken down as a direct result of criticism from group >members. I think we're pretty close to a final idea now, but then >again I thought that in the past as well. If some point of criticism >comes up that I feel is valid or important, I take it into account. >Honestly I'm not set on anything, but to debate successfully you do >have to pick a side and argue it until the arguement is soundly >defeated. Did I mention I'm a Philosophy major? ;->
>
>Perhaps I'm doing this on the wrong list--would this be more >appropriate over at the Tuning group? I figured since it involved >designing instruments to be used to MAKE MICRO MUSIC then this was >the place to ask, but it's been getting kind of theoretical >lately...please, if I'm getting on anyone's nerves, just tell me to >shut up or to go elsewhere.
>
>
>
>
>
>
> >Yahoo! Groups Links
>
>
>
> >
>
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

Yeah, I see exactly what you mean...at this point Stevie and I are
just shooting in the dark with these ideas since we have no actual
physical model to experience playing, whereas George and yourself
both have experience playing the instruments that you are
suggesting. Plus the diagrams at this point are only vague
representations, I haven't done computer versions of the scaled
drawings I've roughed out by hand due to lacking a good program to
lay it out in. Really the only thing that comes across is the
approximate patterns that would be used, but I think that is a pretty
fair basis to compare (though there are LOTS AND LOTS of factors I've
not gotten around to taking into account). I really wish Paul would
get on here and add his two cents, since I'm a little out of my
element.

Really though this isn't a "logical" debate, it's more of a
functional debate. I.e. which design does which patterns the most
ergonomically.

>I would suggest though of when displaying keyboards that you might
>include the mapping of the harmonic material in the tuning (or since
in
>your case the particular scales you seem to be set on ) as seen in
this
> paper.

I suppose I could do that, but it'd be a lot of work since each
system based on a specific generator should have its own musical
alphabet...I don't really like naming everything in 22 according to
diatonic names since they don't work very well notating tonalities
based on other generators. That's kind of why I wanted to know if
anyone had come up with an alphabet for Magic or Doublewide, that way
I could color and name the keys to correspond to the generator that
produced them which would make the most visual sense. I mean all the
diagrams in that paper you linked to are based on a roughly diatonic
nomenclature with varying accidentals, whereas I'm coming from the
idea you should have as many letters in the alphabet as there are
notes in the generator's "natural" scale (say A-H for porcupine, A-J
for Pajara, etc. to name the obvious possibilities). Though this is
all really new territory for me and it's easy for me to miss things
that are obvious to most on this list, so I beg your patience.

Anyway, in reality the keys are going to be shaped differently than
they are in the diagram, so I shall not make any decisions until I
have the final diagrams to compare. But if you look at those
diagrams and consider them all to be on the same scale you can get a
pretty good idea of their strengths and weaknesses.

I have posted diagrams of the fingerings for the otonal and utonal
tetrads in each system (using Paul's Superpyth diagram as the
appropriate analogue to George's since they are essentially the same
layout), so maybe that will help.

Again, sorry if I'm being tiresome...I'll be more concise once I
return to school and have less time on my hands.

-igs

Igliashon Jones wrote:

> I suppose I could do that, but it'd be a lot of work since each > system based on a specific generator should have its own musical > alphabet...I don't really like naming everything in 22 according to > diatonic names since they don't work very well notating tonalities > based on other generators. That's kind of why I wanted to know if > anyone had come up with an alphabet for Magic or Doublewide, that way > I could color and name the keys to correspond to the generator that > produced them which would make the most visual sense. I mean all the > diagrams in that paper you linked to are based on a roughly diatonic > nomenclature with varying accidentals, whereas I'm coming from the > idea you should have as many letters in the alphabet as there are > notes in the generator's "natural" scale (say A-H for porcupine, A-J > for Pajara, etc. to name the obvious possibilities). Though this is > all really new territory for me and it's easy for me to miss things > that are obvious to most on this list, so I beg your patience.

I've used Magic, but never came up with a native language. The demo piece is written using a decimal notation, so that 9-limit harmony works. That's because I was using a Miracle keyboard mapping at the time, and I used about the same number of notes for Magic.

For general use, the best idea I came up with was to use diatonic names based on 19-equal. Take the simplest 19 names, from whatever center note. Fit them to Magic so that all major thirds in notation are 4:5 approximations. That leaves three more notes from 22, which should be notated with comma shifts relative to their Magic-19 enharmonies. Choosing more plain diatonic names doesn't work out.

The upshot of this in 22 is that you have a Tenney style notation where not all fifths are correct. As this isn't meantone, you can't satisfy both the fifths and thirds, and the system is biased towards thirds. Also, sharps and flats aren't consistent. Or maybe that can be fixed ... I don't have my original diagrams. What I have here are three inconsistent notes, which can be given three consistent counterparts in 22-equal.

This all makes much more sense if you're basing it on 19 rather than 22. You're probably better off starting with your favourite 22-equal notation. Unfortunately, there are no natural Magic scales between 3 and 19, which makes it difficult to notate.

What's Doublewide?

Graham

Thanks, Graham. Good thought-food. I'll try working up a bunch of
diagrams according to various languages, see how they all fit on the
diagram.

Doublewide is based on a generator of a sharp minor third (roughly in
the ballpark of 326 cents, approximated in 22 by the 6th degree. In
fact there's not a whole lot of difference between TOP doublewide and
regular 22-EDO if I'm reading this diagram right.... I have yet to
come across anyone who's used a doublewide scale in a composition,
but there is a 10-note mode of sLsLssLsLs that seems interesting.

-Igs

--- In MakeMicroMusic@yahoogroups.com, Graham Breed <gbreed@g...>
wrote:
> Igliashon Jones wrote:
>
> > I suppose I could do that, but it'd be a lot of work since each
> > system based on a specific generator should have its own musical
> > alphabet...I don't really like naming everything in 22 according
to
> > diatonic names since they don't work very well notating
tonalities
> > based on other generators. That's kind of why I wanted to know
if
> > anyone had come up with an alphabet for Magic or Doublewide, that
way
> > I could color and name the keys to correspond to the generator
that
> > produced them which would make the most visual sense. I mean all
the
> > diagrams in that paper you linked to are based on a roughly
diatonic
> > nomenclature with varying accidentals, whereas I'm coming from
the
> > idea you should have as many letters in the alphabet as there are
> > notes in the generator's "natural" scale (say A-H for porcupine,
A-J
> > for Pajara, etc. to name the obvious possibilities). Though this
is
> > all really new territory for me and it's easy for me to miss
things
> > that are obvious to most on this list, so I beg your patience.
>
> I've used Magic, but never came up with a native language. The
demo
> piece is written using a decimal notation, so that 9-limit harmony
> works. That's because I was using a Miracle keyboard mapping at
the
> time, and I used about the same number of notes for Magic.
>
> For general use, the best idea I came up with was to use diatonic
names
> based on 19-equal. Take the simplest 19 names, from whatever
center
> note. Fit them to Magic so that all major thirds in notation are
4:5
> approximations. That leaves three more notes from 22, which should
be
> notated with comma shifts relative to their Magic-19 enharmonies.
> Choosing more plain diatonic names doesn't work out.
>
> The upshot of this in 22 is that you have a Tenney style notation
where
> not all fifths are correct. As this isn't meantone, you can't
satisfy
> both the fifths and thirds, and the system is biased towards
thirds.
> Also, sharps and flats aren't consistent. Or maybe that can be
fixed
> ... I don't have my original diagrams. What I have here are three
> inconsistent notes, which can be given three consistent
counterparts in
> 22-equal.
>
> This all makes much more sense if you're basing it on 19 rather
than 22.
> You're probably better off starting with your favourite 22-equal
> notation. Unfortunately, there are no natural Magic scales between
3
> and 19, which makes it difficult to notate.
>
> What's Doublewide?
>
>
> Graham

--- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
<igliashon@s...> wrote:
>
> > From this I concluded that Magic was the *worst* one. I don't
> > understand your statement that "Tetrads fall in a nice, neat, 4-
> > finger row"? The otonal tetrad has the top note of the chord
> > displaced along the y-axis quite a ways from the other 3 tones;
same
> > for the 1st-inversion utonal tetrad. Did you try these tetrads
in
> > all of their inversions?
>
> George, have you *looked* at the diagram that I linked to?

Yes, that's what I used in making my evaluation (which I will clarify
below). Did you try these tetrads in all of their inversions? If
so, then you might have observed that they don't fall into a nice,
neat 4-finger row after all.

> I don't
> know what your calculations are based on, but I can tell you that
> your statements blatantly contradict what I observe with my own two
> eyes. In 22, otonal tetrad = degrees 0 7 13 18. 7 degrees =
> approximately the Magic generator and is immediately adjacent to 0;
6
> is right above it. 13 is adjacent to both 6 and 7, such that a
> diagonal line connecting the center points of keys 0 and 13 would
> pass exactly between keys 6 and 7.

Right -- no problem with these. As my evaluation indicates, they are
0, 1, and 5 generators distant from tone 0.

G=7deg22 (Magic)
Octaves 7 key-widths distant
Otonal tetrad (C-E\-G-Bb): 0G, +1G, +5G, -10G or 0G, +1G, +5G, +12G
Total spread: 15G or 13G
Utonal tetrad (C-Eb/-G-A): 0G, +4G, +5G, -7G
Total spread: 12G

> 18 is the only "disjoint" key but
> is still within easy reach, accessible easily in one of two
places.

This one's the problem -- in the chain of generators:

0 +1 +2 +3 +4 +5 +6 +7 +8 +9 10 11 12
0 .7 14 21 .6 13 20 .5 12 19 .4 11 18

it's +12 or -10 (not shown above) in the chain, which is about as far
displaced in the y-direction as possible. It only *appears* to be
within easy reach because:
1) It's not unreasonably far from tone 13; and
2) The keys in the picture are very (unrealistically, IMO) squat in
the y-dimension, which gives it a compressed appearance in that
direction. You would have trouble playing these keys with the thumb
unless you were to stair-step them rather steeply (and even then I
would have doubts).

If you're going to have elongated keys, it's much more useful to have
the long dimension in the y-direction, but it doesn't appear that the
Magic geometry would allow that. (And the same goes for
Srutal/Pajara and Doublewide.) Paul has come up with some clever and
imaginative layouts, but I fail to see how any of them would be
better than the Bosanquet geometry.

> I can post pictures highlighting this tetrad and the utonal one
> (which varies only slightly in fingering) if you like. You don't
> even *need* a thumb to play either of them, and the 6:7:9 triad is
> only a tiny little bit more out of the way (but just as easy as on
> the Bosanquet-style keyboard). Heck, we could even substantially
> enlarge those keys without sacrificing playability given how close
> they are. In fact, let me post some pictures comparing otonal and
> utonal tetrads on some of these designs.

I'm looking at them as I write this. If you draw a line parallel to
the x-axis between two keys for tone 0 (an octave apart), you'll
notice how much of a reach tone 18 really is, particularly in the
direction you specified for playing this chord. Essentially what you
have are 3 tones reasonably lateral from one another and the fourth
at a relatively large y-displacement from the other 3. With the
Bosanquet layout you have the same thing (actually a little better in
terms of generators!), with tones 0, 13, and 18 in a lateral
placement (better than Magic) and tone 7 with a larger y-displacement
(but smaller than Magic, in terms of generators):

G=13deg22 (Bosanquet)
Octaves 6 key-widths distant
Otonal tetrad (C-E\-G-Bb): 0G, +9G, +1G, -2G
Total spread: 11G
Utonal tetrad (C-Eb/-G-A): 0G, +14G, +1G, +3G or 0G, -8G, +1G, +3G
Total spread: 14G or 11G

> > It's my feeling that, in order
> > for a microtonal keyboard to have any chance of getting a wider
> > acceptance in the musical world, the diatonic things are going to
> > have to be at least as easy as they are on a conventional
keyboard,
> > because that's the comparison that most musicians will be making
from
> > the very start. As far as I'm concerned, that, plus the fact
that
> > the Bosanquet layout accommodates the greatest number of
the "best"
> > octave divisions, puts it way ahead of anything else in terms of
> > usefulness and probable success -- particularly since I believe
that
> > reducing the key size would make the technique a bit easier.
>
> George, with all due respect, I disagree with your use of the
> term "best" in reference to certain EDO's, and I think many on this
> list would be inclined to concur. "Best" is all too relative to be
> used here. What you really mean is that the Bosanquet design is
good
> for the "best" diatonic or Pythagorean EDO's, assuming that most
> people who would want to play microtonally would start from the
base
> of traditional music.

By "best" (notice that I did put the word in quotes) I mean those
divisions that most accurately approximate the small-number ratios of
just intonation (especially above the 5-limit) and which thereby
offer the widest range of consonance to dissonance. This does not
necessarily restrict one to an expansion of traditional harmony. For
example, 17 (one of my favorites) offers 13-limit harmony *without*
the 5-consonances.

Divisions such as 15-ET were, to the best of my knowledge, never
seriously considered for harmony until Easley Blackwood wrote his
electronic etudes around 1975. In many different cultures and
localities, over many centuries, those divisions that have generally
been considered "best" are those that represent the fifth, 2:3, (and
after that, the next most consonant ratios) most accurately, an
observation that I don't consider "all too relative."

> I have no problem with that; we all have our
> own ambitions within this field. But I count myself a member of
> the "no bad tunings" school of thought. Every tuning has its own
> infinity of possible expression, within the framework of its own
> unique limitations, tendencies, and colors. I tend to actually
> prefer the more unusual ones, because they push my playing in a
more
> novel direction.

While I understand (and somewhat agree) with your opinion that there
are no "bad" tunings, I would say that some are "better" than others
(for whatever purpose). ;-) -- but each to one's own taste.

> And I have to ask: how can you argue "marketability"
> as a reason Stevie and I should accept a design? We're not going
to
> mass-produce anything.

That thought was presented as part of my response to your objection:

<< > It would be learnable in time, but the whole point of having a
> > generalized keyboard is that it's supposed to be EASY, and this
is
> > definitely not.

The whole point is that it's supposed to be EASIER than a
heterogeneous layout. >>

> The most we're hoping for is a design that
> will inspire us to make novel music, which hopefully will in turn
> inspire others to break out of their 12-equal shells. Who's to say
> what's most likely to catch on? It all really depends on who/what
> produces the most compelling music, which is defined not by us as
> composers but by the public as listeners...and we all know how
fickle
> and unpredictable they are.

Very true!

> If any of us really cared about
> compatibility, universality, or the mass application of a design,
we
> probably wouldn't be here.

I can confidently disagree with you on that point, because that's one
of the main reasons I'm here.

I, for one, would dearly love to see alternate tunings break out of
its niche and begin to catch on with a wider group of listeners.
That, in turn, would bring more musicians into our midst who would
desire to get involved. First thing they ask: what tuning(s) do I
use? If I commit to one and learn an instrument and notation for it,
what if I decide to use a different sort of tuning later on? Will I
need another instrument? Will the other notation have anything in
common with the first one, or will they conflict? In other words,
are there already any standard ways of doing things, or is everyone
pretty much doing one's own thing, which means that I'm going to have
to sort through it all and perhaps (re-)invent my own wheel before I
get around to making any music.

If we aren't ready with some acceptable answers to these questions,
then we're going to be caught with our collective pants down if
ever/whenever) this happens, and many are going to be turned away
with the idea that we haven't been able to get it together. So I'm
determined to do my best to ensure that others aren't confronted with
the same obstacles that I've had to face over the past 42 years.

Sure, you can go ahead and design your own keyboard or whatever, but
with a standard generalized solution you're not required to do that.
Or with a generalized microtonal notation, instrumentalists wouldn't
be required to learn a new system for every tuning (or even multiple
systems for the same tuning, as has often been the case). In case
you're not aware of it yet, Dave Keenan and I have spent the past 3
years on such a notation:

http://dkeenan.com/sagittal/

(And please check out the *mythical introduction* for a discussion of
relevant issues.)

> Yes, it would be convenient to have a new
> system to replace 12-equal. But as I've been told many a time by
> many people on this list, that would really be making the same
> mistake twice. Variety is the goal, correct? And while the
> Bosanquet design does very well for a lot of temperaments, there
are
> others that it does very poorly for.

But I still don't believe that 22 is one of them. :-)

> It is possible that the "Magic" design isn't the absolute best, but
> as far as 22-equal is concerned it's a good few steps up in
> versatility from Bosanquet. In fact, both the Porcupine and
> Doublewide designs are improvements as well. If you recall, our
> concern here is for making the best possible *22-equal* keyboard.
If
> it turns out to accomodate other systems, that's a plus, but it's
not
> a requirement.

Having said about as much as (and perhaps more than) I ought, let me
wish you and Stevie well in your quest for the best. Although I'll
continue to follow the developments in this thread, I need to get
back to other things (such as working on my latest composition), so
I'll chime in only if asked for my opinion, or if there's something
important that hasn't already been said. (Or if I think that you've
gotten it oh, so right! :-)

Best,

--George

--- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
<igliashon@s...> wrote:
>
> Yeah, I see exactly what you mean...at this point Stevie and I are
> just shooting in the dark with these ideas since we have no actual
> physical model to experience playing, whereas George and yourself
> both have experience playing the instruments that you are
> suggesting. Plus the diagrams at this point are only vague
> representations, I haven't done computer versions of the scaled
> drawings I've roughed out by hand due to lacking a good program to
> lay it out in. Really the only thing that comes across is the
> approximate patterns that would be used, but I think that is a
pretty
> fair basis to compare (though there are LOTS AND LOTS of factors
I've
> not gotten around to taking into account). ...

Ah, one more thing. Once you get past the paper designs, make a
mockup of the keyboard with wooden key surfaces glued down to a flat
panel, or perhaps first make wooden keys that you can move around and
experiment with. A quick way to get round keys is to cut a dowel rod
into uniform cross-sections -- not the optimum shape, but just
something to get more of a feel for the real thing.

--George

I'm going to withhold judgement on these keyboard layouts until I've
had time to work up more accurate diagrams of them. As you've noted,
it is difficult to tell how playable they actually are when the key
sizes are so much smaller than they'd be in reality.

I thank you for donating your time and effort to helping us figure
this whole design thing out, and I think we're pretty much to the
point where the life-size diagrams will make the decision for us.
Your criticisms have been invaluable, and I wish you luck in your
endeavors. I'll keep posting as we make more progress,.

-Igs.

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Igliashon Jones"
> <igliashon@s...> wrote:
> >
> > > From this I concluded that Magic was the *worst* one. I don't
> > > understand your statement that "Tetrads fall in a nice, neat,
4-
> > > finger row"? The otonal tetrad has the top note of the chord
> > > displaced along the y-axis quite a ways from the other 3
tones;
> same
> > > for the 1st-inversion utonal tetrad. Did you try these tetrads
> in
> > > all of their inversions?
> >
> > George, have you *looked* at the diagram that I linked to?
>
> Yes, that's what I used in making my evaluation (which I will
clarify
> below). Did you try these tetrads in all of their inversions? If
> so, then you might have observed that they don't fall into a nice,
> neat 4-finger row after all.
>
> > I don't
> > know what your calculations are based on, but I can tell you that
> > your statements blatantly contradict what I observe with my own
two
> > eyes. In 22, otonal tetrad = degrees 0 7 13 18. 7 degrees =
> > approximately the Magic generator and is immediately adjacent to
0;
> 6
> > is right above it. 13 is adjacent to both 6 and 7, such that a
> > diagonal line connecting the center points of keys 0 and 13 would
> > pass exactly between keys 6 and 7.
>
> Right -- no problem with these. As my evaluation indicates, they
are
> 0, 1, and 5 generators distant from tone 0.
>
> G=7deg22 (Magic)
> Octaves 7 key-widths distant
> Otonal tetrad (C-E\-G-Bb): 0G, +1G, +5G, -10G or 0G, +1G, +5G, +12G
> Total spread: 15G or 13G
> Utonal tetrad (C-Eb/-G-A): 0G, +4G, +5G, -7G
> Total spread: 12G
>
> > 18 is the only "disjoint" key but
> > is still within easy reach, accessible easily in one of two
> places.
>
> This one's the problem -- in the chain of generators:
>
> 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 10 11 12
> 0 .7 14 21 .6 13 20 .5 12 19 .4 11 18
>
> it's +12 or -10 (not shown above) in the chain, which is about as
far
> displaced in the y-direction as possible. It only *appears* to be
> within easy reach because:
> 1) It's not unreasonably far from tone 13; and
> 2) The keys in the picture are very (unrealistically, IMO) squat in
> the y-dimension, which gives it a compressed appearance in that
> direction. You would have trouble playing these keys with the
thumb
> unless you were to stair-step them rather steeply (and even then I
> would have doubts).
>
> If you're going to have elongated keys, it's much more useful to
have
> the long dimension in the y-direction, but it doesn't appear that
the
> Magic geometry would allow that. (And the same goes for
> Srutal/Pajara and Doublewide.) Paul has come up with some clever
and
> imaginative layouts, but I fail to see how any of them would be
> better than the Bosanquet geometry.
>
> > I can post pictures highlighting this tetrad and the utonal one
> > (which varies only slightly in fingering) if you like. You don't
> > even *need* a thumb to play either of them, and the 6:7:9 triad
is
> > only a tiny little bit more out of the way (but just as easy as
on
> > the Bosanquet-style keyboard). Heck, we could even substantially
> > enlarge those keys without sacrificing playability given how
close
> > they are. In fact, let me post some pictures comparing otonal
and
> > utonal tetrads on some of these designs.
>
> I'm looking at them as I write this. If you draw a line parallel
to
> the x-axis between two keys for tone 0 (an octave apart), you'll
> notice how much of a reach tone 18 really is, particularly in the
> direction you specified for playing this chord. Essentially what
you
> have are 3 tones reasonably lateral from one another and the fourth
> at a relatively large y-displacement from the other 3. With the
> Bosanquet layout you have the same thing (actually a little better
in
> terms of generators!), with tones 0, 13, and 18 in a lateral
> placement (better than Magic) and tone 7 with a larger y-
displacement
> (but smaller than Magic, in terms of generators):
>
> G=13deg22 (Bosanquet)
> Octaves 6 key-widths distant
> Otonal tetrad (C-E\-G-Bb): 0G, +9G, +1G, -2G
> Total spread: 11G
> Utonal tetrad (C-Eb/-G-A): 0G, +14G, +1G, +3G or 0G, -8G, +1G, +3G
> Total spread: 14G or 11G
>
> > > It's my feeling that, in order
> > > for a microtonal keyboard to have any chance of getting a wider
> > > acceptance in the musical world, the diatonic things are going
to
> > > have to be at least as easy as they are on a conventional
> keyboard,
> > > because that's the comparison that most musicians will be
making
> from
> > > the very start. As far as I'm concerned, that, plus the fact
> that
> > > the Bosanquet layout accommodates the greatest number of
> the "best"
> > > octave divisions, puts it way ahead of anything else in terms
of
> > > usefulness and probable success -- particularly since I believe
> that
> > > reducing the key size would make the technique a bit easier.
> >
> > George, with all due respect, I disagree with your use of the
> > term "best" in reference to certain EDO's, and I think many on
this
> > list would be inclined to concur. "Best" is all too relative to
be
> > used here. What you really mean is that the Bosanquet design is
> good
> > for the "best" diatonic or Pythagorean EDO's, assuming that most
> > people who would want to play microtonally would start from the
> base
> > of traditional music.
>
> By "best" (notice that I did put the word in quotes) I mean those
> divisions that most accurately approximate the small-number ratios
of
> just intonation (especially above the 5-limit) and which thereby
> offer the widest range of consonance to dissonance. This does not
> necessarily restrict one to an expansion of traditional harmony.
For
> example, 17 (one of my favorites) offers 13-limit harmony *without*
> the 5-consonances.
>
> Divisions such as 15-ET were, to the best of my knowledge, never
> seriously considered for harmony until Easley Blackwood wrote his
> electronic etudes around 1975. In many different cultures and
> localities, over many centuries, those divisions that have
generally
> been considered "best" are those that represent the fifth, 2:3,
(and
> after that, the next most consonant ratios) most accurately, an
> observation that I don't consider "all too relative."
>
> > I have no problem with that; we all have our
> > own ambitions within this field. But I count myself a member of
> > the "no bad tunings" school of thought. Every tuning has its own
> > infinity of possible expression, within the framework of its own
> > unique limitations, tendencies, and colors. I tend to actually
> > prefer the more unusual ones, because they push my playing in a
> more
> > novel direction.
>
> While I understand (and somewhat agree) with your opinion that
there
> are no "bad" tunings, I would say that some are "better" than
others
> (for whatever purpose). ;-) -- but each to one's own taste.
>
> > And I have to ask: how can you argue "marketability"
> > as a reason Stevie and I should accept a design? We're not going
> to
> > mass-produce anything.
>
> That thought was presented as part of my response to your objection:
>
> << > It would be learnable in time, but the whole point of having
a
> > > generalized keyboard is that it's supposed to be EASY, and this
> is
> > > definitely not.
>
> The whole point is that it's supposed to be EASIER than a
> heterogeneous layout. >>
>
> > The most we're hoping for is a design that
> > will inspire us to make novel music, which hopefully will in turn
> > inspire others to break out of their 12-equal shells. Who's to
say
> > what's most likely to catch on? It all really depends on
who/what
> > produces the most compelling music, which is defined not by us as
> > composers but by the public as listeners...and we all know how
> fickle
> > and unpredictable they are.
>
> Very true!
>
> > If any of us really cared about
> > compatibility, universality, or the mass application of a design,
> we
> > probably wouldn't be here.
>
> I can confidently disagree with you on that point, because that's
one
> of the main reasons I'm here.
>
> I, for one, would dearly love to see alternate tunings break out of
> its niche and begin to catch on with a wider group of listeners.
> That, in turn, would bring more musicians into our midst who would
> desire to get involved. First thing they ask: what tuning(s) do I
> use? If I commit to one and learn an instrument and notation for
it,
> what if I decide to use a different sort of tuning later on? Will
I
> need another instrument? Will the other notation have anything in
> common with the first one, or will they conflict? In other words,
> are there already any standard ways of doing things, or is everyone
> pretty much doing one's own thing, which means that I'm going to
have
> to sort through it all and perhaps (re-)invent my own wheel before
I
> get around to making any music.
>
> If we aren't ready with some acceptable answers to these questions,
> then we're going to be caught with our collective pants down if
> ever/whenever) this happens, and many are going to be turned away
> with the idea that we haven't been able to get it together. So I'm
> determined to do my best to ensure that others aren't confronted
with
> the same obstacles that I've had to face over the past 42 years.
>
> Sure, you can go ahead and design your own keyboard or whatever,
but
> with a standard generalized solution you're not required to do
that.
> Or with a generalized microtonal notation, instrumentalists
wouldn't
> be required to learn a new system for every tuning (or even
multiple
> systems for the same tuning, as has often been the case). In case
> you're not aware of it yet, Dave Keenan and I have spent the past 3
> years on such a notation:
>
> http://dkeenan.com/sagittal/
>
> (And please check out the *mythical introduction* for a discussion
of
> relevant issues.)
>
> > Yes, it would be convenient to have a new
> > system to replace 12-equal. But as I've been told many a time by
> > many people on this list, that would really be making the same
> > mistake twice. Variety is the goal, correct? And while the
> > Bosanquet design does very well for a lot of temperaments, there
> are
> > others that it does very poorly for.
>
> But I still don't believe that 22 is one of them. :-)
>
> > It is possible that the "Magic" design isn't the absolute best,
but
> > as far as 22-equal is concerned it's a good few steps up in
> > versatility from Bosanquet. In fact, both the Porcupine and
> > Doublewide designs are improvements as well. If you recall, our
> > concern here is for making the best possible *22-equal*
keyboard.
> If
> > it turns out to accomodate other systems, that's a plus, but it's
> not
> > a requirement.
>
> Having said about as much as (and perhaps more than) I ought, let
me
> wish you and Stevie well in your quest for the best. Although I'll
> continue to follow the developments in this thread, I need to get
> back to other things (such as working on my latest composition), so
> I'll chime in only if asked for my opinion, or if there's something
> important that hasn't already been said. (Or if I think that
you've
> gotten it oh, so right! :-)
>
> Best,
>
> --George

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor" <
gdsecor@y...> wrote:

> G=7deg22 (Magic)
> Octaves 7 key-widths distant
> Otonal tetrad (C-E\-G-Bb): 0G, +1G, +5G, -10G or 0G, +1G, +5G, +12G
> Total spread: 15G or 13G
> Utonal tetrad (C-Eb/-G-A): 0G, +4G, +5G, -7G
> Total spread: 12G

Hi folks -- I'm snowed in, just checking in real quick . . . not sure if anyone
caught this, but it's a mathematical impossibility for the otonal and utonal
tetrads to have different spreads >:-)

I sent many of you my new paper, if anyone else wants it just send me your
snail-mail address. The tables in that paper tell you how primes 2, 3, 5, and (if
applicable) 7 are generated by each system. This is a general paper, not
specific to 22. I actually don't have a copy of the paper outside my office!

And when assessing spread, remember to multiply the number of generators
required by the number of periods per octave (where's the tuning-math
gang?) -- so it should be all even numbers for Hedgehog and Doublewide
just like Pajara. In my preliminary keyboard diagrams, which are not intended
to be taken literally but rather should be skewed and distorted to taste, each
note forms a square gird with its unison and octave duplicates. So each key
occupies 1/22 the area of the square. The square can be deformed to a
parallelogram of any desired size and shape, and the keys themselves can
and should be completely altered in shape. And best of all, we have three
dimensions to work with in reality. That's why I called them "preliminary!"

:=>

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <paul@s...>
wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "George D. Secor" <
> gdsecor@y...> wrote:
>
> > G=7deg22 (Magic)
> > Octaves 7 key-widths distant
> > Otonal tetrad (C-E\-G-Bb): 0G, +1G, +5G, -10G or 0G, +1G, +5G,
+12G
> > Total spread: 15G or 13G
> > Utonal tetrad (C-Eb/-G-A): 0G, +4G, +5G, -7G
> > Total spread: 12G
>
> Hi folks -- I'm snowed in,

Hi, Paul. Hope the temperature goes up and starts melting some of
that. I survived the blizzard of '79 in Chicago, when we got a total
accumulation of around 80 inches of snow (or was it 90?). During
that time there was no significant melting, because the temperature
got above freezing for only about 4 hours over a period of 9 weeks.
I remember shoveling snow every day for days on end and recall after
a week or so being thankful that it had snowed *only* 4 inches on
that particular day. The snow in both our front and back yards was
piled up way over my head. In order to get some of the snow off our
(unheated) garage roof, I laid a ladder down (horizontally) on top of
the snow and climbed up on top of it, using it like a giant snowshoe,
which enabled me to stand on top of the accumulation. The garage
gutters were at the same height as my ankles as I shoveled as much
snow off the roof as I could reach. There were numerous parked cars
buried in the snow, but in many cases it was impossible to tell that
they were even there.

> just checking in real quick . . . not sure if anyone
> caught this, but it's a mathematical impossibility for the otonal
and utonal
> tetrads to have different spreads >:-)

Sorry about that, Paul -- you're right. Otonal tonal spread should
have been 15G or 12G in the above example. Likewise the following
one is now corrected to:

G=3deg22 (Porcupine)
Octaves 7.5 key-widths distant
Usable divisions of the octave: 15, 22, 23, 29, 31, ...
Otonal tetrad (C-E\-G-Bb): 0G, -5G, -3G, +6G
Total spread: 11G
Utonal tetrad (C-Eb/-G-A): 0G, 2G, -3G, -9G or 0G, 2G, -3G, +9G, -13G
Total spread: 11G or 15G

> And when assessing spread, remember to multiply the number of
generators
> required by the number of periods per octave (where's the tuning-
math
> gang?) -- so it should be all even numbers for Hedgehog and
Doublewide
> just like Pajara.

Yep, right again. In my haste it appears that I forgot to multiply
by 2 for Doublewide.

> In my preliminary keyboard diagrams, which are not intended
> to be taken literally but rather should be skewed and distorted to
taste, each
> note forms a square gird with its unison and octave duplicates. So
each key
> occupies 1/22 the area of the square. The square can be deformed to
a
> parallelogram of any desired size and shape, and the keys
themselves can
> and should be completely altered in shape. And best of all, we have
three
> dimensions to work with in reality. That's why I called
them "preliminary!"

From the figures for total spread I thought that Srutal/Pajara would
seem to be the clear winner, but I'm put off by the difficulty that I
anticipate in arriving at a reasonable key shape. I just went back
to look at the diagram to take another look, but found that it's no
longer there. :-<

--George

Hiya Paul,

>And when assessing spread, remember to multiply the number of generators
>required by the number of periods per octave (where's the tuning-math
>gang?)

Waaay behind on this list.

>In my preliminary keyboard diagrams, which are not intended to be taken
>literally but rather should be skewed and distorted to taste, each note
>forms a square gird with its unison and octave duplicates. So each key
>occupies 1/22 the area of the square. The square can be deformed to a
>parallelogram of any desired size and shape, and the keys themselves can
>and should be completely altered in shape. And best of all, we have
>three dimensions to work with in reality. That's why I called them
>"preliminary!"
>
>:=>

Hey, I somehow misplaced your paper (I'm pretty sure it's around here
somewhere), but I did get a chance to read it. But I don't recall
any keyboard diagrams of the type described above. Am I wrong, or
is there another source for these?

Enjoy the snow! I miss it dearly.

-Carl

[Rich Holmes wrote...]
>> Normal triads are
>> alright, but extending the chords by adding those extra 7-limit notes
>> requires a pretty awkward fingering, one that would be very difficult
>> to reach in the context of performance.
>
>Hmm, I am not a keyboardist of any more than minimal skill, on any
>sort of musical keyboard, so maybe I need some further explanation...
>but putting my fingers on the screen I get a different impression. A
>major tetrad is e.g. degrees 0, 7, 13, 18, and where I think that
>feels awkward is on the 7.

I assume we're talking about GKbd22s1.gif?

I think I'd play this 2 / 1 or 3 / 4 / 5 in the right hand, and
5 / 3 / 2 / 1 in the left. I balked at first, but then realized:

() This was designed to be actual size at 72dpi, I think. My
monitor is 133dpi. I resampled the image in Photoshop.

() The keyboard would not be perpendicular to the ground! I bent
my laptop screen back as flat as it would go, and things got a lot
easier!

>The minor tetrad is 0, 6, 13, 17 and is worse;

I think this can be played 5 / 3 / 1 / 1 in the left hand and
1 / 2 / 5 / 5 in the right...

>I notice the tetrads on 2 (2, 9, 15, 20 and 2, 8, 15, 19) are easier
>if I use 2 in the lower cyan row and the 15, 19, and 20 in the upper
>cyan and black rows. The minor tetrad especially. But crossing that
>many rows would make for difficult scales, I'd think.

All the more reason to add more duplicates, which I believe George
is in favor of?

>> It seems that your current design, while not
>> prohibitive of different scales, is fairly biased toward diatonic
>> scales, favoring meantone temperaments and scales with 7-note LLsLLLs
>> scales. Do you have any different types of mapping up your sleeve
>> that might be more suited to a decatonic or "porcuponic" approach?
>
>The Bosenquet-style design seems to me to be biased not so much toward
>diatonic scales as toward scales composed mainly of "major seconds",
>i.e. steps of about 200 cents. Scales with smaller intervals then
>necessarily have notes fairly far out of line with one another. I
>guess I could imagine a Bosenquet-like layout with adjacent notes
>differing by something closer to 100 cents, with a 22-note layout
>looking very roughly something like (view this in a monospaced font)
>
> 1 3 5 7 ...
> 13 14 16 18 20 0 2 4 6 ...
> 1 3 5 7 9 11 13 15 17 19 21 1 3 5 ...
> 0 2 4 6 8 10 12 14 16 18 20
> 21 1 3 5 7 9
>
>(tilted to put octaves on a horizontal line and with notes added to or
>subtracted from columns as needed); but this not only involves a lot
>of duplicate notes, it also nearly doubles the octave stretch.

Yeah, seems maybe 2 and 3 or more would be advisable.

-Carl

>Igliashon, I already replied to Paul off-list before I read your
>message, and I'll forward a copy to you. It addresses some other
>issues relating to non-Bosanquet generalized layouts.

Say: could you forward this to the list?

-Carl

>Okay, after further consideration, we've found that Paul's design
>based on the Magic generator seems to be optimal for 22. Tetrads
>fall in a nice, neat, 4-finger row, and scales are pretty much a
>cinch. To see what I mean, go to:
>
>http://img.photobucket.com/albums/v170/igliashon_jones/magic.gif

This gives me a 'not found'. :(

-Carl

George,

>Paul contacted me off-list asking me to give more consideration to
>his diagrams, particularly those based on periods of 1/N octaves
>(i.e., Srutal/Pajara and Hedgehog). I figured out the generator
>figures for the following ones. (For purposes of making an equitable
>comparison, the generator numbers for Srutal/Pajara and Hedgehog are
>doubled, since they have 2 chains of generators/octave and thus twice
>the key-density.)
>
>Period=11deg22, G=2deg22 (Srutal/Pajara)
>Octaves ?? key-widths distant (depends on key shape)
>Otonal tetrad (C-E\-G-Bb): 0G, -4G, +2G, -4G
>Total spread: 6G
>Utonal tetrad (C-Eb/-G-A): 0G, +6G, +2G, +6G
>Total spread: 6G
>
>G=7deg22 (Magic)
>Octaves 7 key-widths distant
>Otonal tetrad (C-E\-G-Bb): 0G, +1G, +5G, -10G or 0G, +1G, +5G, -12G
>Total spread: 15G or 13G
>Utonal tetrad (C-Eb/-G-A): 0G, +4G, +5G, -7G
>Total spread: 12G
>
>Period=11deg22, G=3deg22 (Hedgehog)
>Octaves 7 key-widths distant
>Otonal tetrad (C-E\-G-Bb): 0G, -10G, -6G, -10G
>Total spread: -10G
>Utonal tetrad (C-Eb/-G-A): 0G, +4G, -6G, +4G
>Total spread: 10G
>
>Period=11deg22, G=1deg22 (Doublewide)
>Octaves ?? key-widths distant
>Otonal tetrad (C-E\-G-Bb): 0G, +3G, +4G, +3G
>Total spread: 4G
>Utonal tetrad (C-Eb/-G-A): 0G, +1G, +4G, +1G
>Total spread: 4G
>
>From this I concluded that Magic was the *worst* one.

Does that mean you made diagrams for all of them? ;)

-Carl

>I have posted diagrams of the fingerings for the otonal and utonal
>tetrads in each system (using Paul's Superpyth diagram as the
>appropriate analogue to George's since they are essentially the same
>layout), so maybe that will help.

You have?

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Okay, after further consideration, we've found that Paul's design
> >based on the Magic generator seems to be optimal for 22. Tetrads
> >fall in a nice, neat, 4-finger row, and scales are pretty much a
> >cinch. To see what I mean, go to:
> >
> >http://img.photobucket.com/albums/v170/igliashon_jones/magic.gif
>
> This gives me a 'not found'. :(
>
> -Carl

Sorry, Carl. I took Paul's preliminary designs down because I'm
working on more "realistic" versions. I'll get those up tomorrow
morning, they'll give a more equal basis for comparison (at least for
my purposes).

-Igs

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >I have posted diagrams of the fingerings for the otonal and utonal
> >tetrads in each system (using Paul's Superpyth diagram as the
> >appropriate analogue to George's since they are essentially the
same
> >layout), so maybe that will help.
>
> You have?
>
> -Carl

Don't worry, they'll be back.

-Igs

>> >I have posted diagrams of the fingerings for the otonal and utonal
>> >tetrads in each system (using Paul's Superpyth diagram as the
>> >appropriate analogue to George's since they are essentially the
>> >same layout), so maybe that will help.
>>
>> You have?
>
>Don't worry, they'll be back.

Cool. Take your time. Just let us know when (and where) they are.

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Igliashon, I already replied to Paul off-list before I read your
> >message, and I'll forward a copy to you. It addresses some other
> >issues relating to non-Bosanquet generalized layouts.
>
> Say: could you forward this to the list?
>
> -Carl

Only part of it. Some of it was a bit personal, so I've deleted that
from the following:

--- wallyesterpaulrus <...> wrote:
> ...
> On another note, I've been discussing keyboards very intensely with
> Igliashon and Stevie of MMM, and I think it would be most valuable
> for them to see (and play around with) transpositionally invariant
> keyboards for 22, not only one using the Superpyth (Bosanquet)
> geometry as you have, but also one using Porcupine geometry (since
> he's planning to use 15 too), one using Srutal/Pajara geometry
(since
> it's more efficient than Bosanquet/Superpyth in either 5-limit or 7-
> limit), and others including Magic and Hedgehog. How hard would it
be
> for you to prepare diagrams of such keyboards?

Determining appropriate angles and dimensions for a "pretty and
proper" keyboard layout in which all of the rows or columns slant is
pretty time-consuming, involving a bit of trial and error,
particularly if you're constrained to using a particular (i.e.,
square) key shape. In this particular case I've taken the time to do
it, because I felt very strongly that Igs and Stevie were heading in
the wrong direction.

But I guess if you only need something quick and dirty to experiment
with, it might not be too hard to do a few of these. My main problem
is that my time is going to be very limited the rest of this year, so
it might be better to tell you how I prepared these diagrams (without
using any special or expensive software) so that you or Igs could do
them yourselves. (As Terry Pratchett put it, "Build a man a fire and
you'll keep him warm the rest of the day; set a man on fire and
you'll keep him warm the rest of his life." ;-)

I believe that, in general, you'll find that any transpositionally
invariant keyboard in which the octaves are laterally positioned at a
reasonable distance will be fairly easy to use, as long as there are
a sufficient number of duplicate keys. The only application I've
found in which the requirements are more critical is for the left
hand of an accordion, where the thumb cannot be used (making cross-
over fingering both clumsy and difficult), in which case the solution
is a special arrangement of buttons that works well for the left hand
(but would work very poorly for the right hand, unless it were mirror-
imaged).

> Like you yourself said
> on this list last year, 4 different tuning systems can and should
be
> enough for a lifetime of exploration, so I really think we can't
give
> the particularities of systems like 22 and 15 short shrift here.

By "4 different tuning systems" I meant 4 *completely* different
*tunings*. By my reckoning, Superpythagorean, Porcupine, and
Decatonic in 22-ET count as one, not three. [Paul subsequently
replied that he agreed with me about this.] Other possibilities
would be a tuning in the meantone family or a JI set (or some sort of
temperament very close to just). Sure, one alternate tuning could
last you a lifetime or more, but having the experience of working
with several tunings gives you the opportunity to take time off from
one tuning to work with another and then return afresh to the first
with a broader perspective -- as when one spends a few weeks in a
foreign land, upon returning taking notice of things about which one
was previously unaware.

I would not be one to encourage the building of alternate keyboards
not based on the Bosanquet (fifth-generator) geometry for tunings
that can already be accommodated on the Bosanqet, for a couple of
reasons:

1) One would end up investing time, money, and effort building and
learning a keyboard that very likely no one else will ever have. It
would be wiser to invest in the microtonal keyboard most likely to
become the standard one (provided, of course, that it's a very good
one).

2) There are important tunings that would not be accommodated on
these alternates. You think, perhaps, that you can always build
another keyboard, but then you get married, start a family, and then
wonder when you'll ever have the time, money, and energy to go
through all of that again. ...

Personal circumstances do not always turn out the way you
expect. ... Through all of this I'm often surprised that I even have
a chance to think about microtonality (I'm trying to make some
headway on a new composition) -- but then I count myself fortunate in
that I haven't had to experience anything on the order of a tsunami.

Anyway, getting back to the subject, I wouldn't consider 15-ET
important enough to warrant a non-Bosanquet keyboard. If you've
already gone ahead and built the Bosanquet, you can, in a pinch, use
8deg15 (a narrow false 5th) as the generating interval and have
transpositional invariance. A lot of the intervals may turn up as
rather strange vectors, but it will be playable.

I don't even consider 72-ET important enough to warrant a non-
Bosanquet keyboard, even my decimal keyboard design (at least at the
present time). If you want Blackjack, Canasta, or Stud-loco, you can
play them in a 31 or 41 mapping on the Bosanquet.

Just some advice from someone who's been there and done that (which
you may pass along to Igs and Stevie, if you think it will be
helpful).

Best,

--George

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> George,
>
> >Paul contacted me off-list asking me to give more consideration to
> >his diagrams, particularly those based on periods of 1/N octaves
> >(i.e., Srutal/Pajara and Hedgehog). I figured out the generator
> >figures for the following ones. ...(Srutal/Pajara) ...
(Magic) ... (Hedgehog) ... (Doublewide) ...
> >
> >From this I concluded that Magic was the *worst* one.
>
> Does that mean you made diagrams for all of them? ;)
>
> -Carl

No, I was just using the y-spread numbers for a rough comparison of
the amount that one would have to reach in the y-direction to play 7-
limit tetrads.

--George

George D. Secor wrote:

>
> Just some advice from someone who's been there and done that (which
> you may pass along to Igs and Stevie, if you think it will be
> helpful).
>
> Best,
>
> --George

George,

I've come 'round to the viewpoint that appeals to experience ("been there and done that") or authority of any other sort have limited mileage in the alternative tuning community. In fact, a great deal of the attraction to our common interest comes from the process of discovering things for yourself (even if it means considerable amounts of re-invention) and a fundamental mistrust of received authority. After all, the exploration of alternatives does come in response to a sense that the received patterns are [you fill in the blank: exhausted, flawed, restricting etc.]. Personally, I have little patience for an overproduction of terminology which I sense in the community, feeling that it often puts private ambitions in from of communication based on a shared heritage. But I do understand the impulse (and have, indeed, been guilty of the same) and as long as I'm not forced to adopt a given set of terms, let a thousand flowers bloom. In general, I certainly hope that we're moving in the direction of variety rather than conformity. (I recently did a set of etudes in equal temperaments, just to shake my just intonation tree a bit).

Erv Wilson has, like Lou Harrison had, a very good touch with beginners. He'll listen closely to try and figure out what the musician has been up to, and then make some gentle suggestions, albeit with powerful arguments. But even Erv will put some musicians off, usually because they have come to him with programs of their own that are already finished products, complete packages. It's often easy for me to see that the loss of not considering Erv's advice is great, but the investment of musical-intellectual time and energy into the program is simply too far advanced to start again. (I'm so glad that I met Erv at 17!) But the other essential element in Erv's teaching is his constant readiness for the possibility that he might learn something himself - Larry Hanson's keyboard geometry, or a few terms from real maths (I remember David Feldman mentioning freshman sums to him).

Daniel Wolf

"George D. Secor" <gdsecor@...> writes:

> By my reckoning, Superpythagorean, Porcupine, and Decatonic in 22-ET
> count as one, not three.

Probably a FAQ but I can't find the answer: What's Superpythagorean?

- Rich Holmes

--- In MakeMicroMusic@yahoogroups.com, Daniel Wolf <djwolf1@a...>
wrote:
> George D. Secor wrote:
>
> > Just some advice from someone who's been there and done that
(which
> > you may pass along to Igs and Stevie, if you think it will be
> > helpful).
> >
> > Best,
> >
> > --George
>
> George,
>
> I've come 'round to the viewpoint that appeals to experience ("been
> there and done that") or authority of any other sort have limited
> mileage in the alternative tuning community.

Of which I am well aware. Nevertheless, within that "limited
mileage" there are factors to be taken into account that will, more
likely than not, be highly relevant to one's situation. In this
particular context, "been there and done that" refers to selecting
tools or hardware that will not severely restrict one's creative
choices; more specifically: my having participated in the design,
building, and use of a new keyboard -- only to discover that
subsequent circumstances were not what I imagined they would be.
After 2 or 3 years I found myself preferring tunings that I
subsequently created, tunings quite different from the ones that I
had expected to use. Fortunately, the keyboard was readily able to
accommodate these. But had I chosen a different (more restrictive)
keyboard geometry, that would probably not have been the case, and I
would have found myself a victim of my own creativity, stuck with a
keyboard that locked me into a very limited choice of tunings, with
no opportunity to retrace my steps and do it over again.

That, however, has not been the case with some of the other important
decisions I've made over the years, and I only wish that I had sought
the advice of someone else who had "been there and done that" to
allow me to make better-informed decisions.

> In fact, a great deal of
> the attraction to our common interest comes from the process of
> discovering things for yourself (even if it means considerable
amounts
> of re-invention) and a fundamental mistrust of received authority.

Undoubtedly one of the best ways to learn. :-)

> After
> all, the exploration of alternatives does come in response to a
sense
> that the received patterns are [you fill in the blank: exhausted,
> flawed, restricting etc.].

And inability to explore those alternatives may come in response to
the realization that you are [fill in the blank: exhausted, trapped,
restricted, etc. by one of your prior decisions]. :-(

> Personally, I have little patience for an overproduction of
terminology
> which I sense in the community, feeling that it often puts private
> ambitions in from of communication based on a shared heritage. But
I do
> understand the impulse (and have, indeed, been guilty of the same)
and
> as long as I'm not forced to adopt a given set of terms, let a
thousand
> flowers bloom. In general, I certainly hope that we're moving in
the
> direction of variety rather than conformity. (I recently did a set
of
> etudes in equal temperaments, just to shake my just intonation tree
a bit).

Terminology is something you are relatively free to discard and re-
invent at will and whim (as long as you're willing to accept the
prospect that you might not be properly understood), but special
tools and hardware (and the technique one has developed to make use
of them) can become a foolish investment of time, money, and effort
for which there is a very limited market, should you come to realize
that they did adequately suit your purposes for very long.

The bottom line is: choose carefully and wisely.

--George

--- In MakeMicroMusic@yahoogroups.com, Rich Holmes<rsholmes@m...>
wrote:
> "George D. Secor" <gdsecor@y...> writes:
>
> > By my reckoning, Superpythagorean, Porcupine, and Decatonic in 22-
ET
> > count as one, not three.
>
> Probably a FAQ but I can't find the answer: What's Superpythagorean?
>
> - Rich Holmes

It's the tonality or scale in 22-ET generated by a chain of fifths.
Because these fifths are tempered rather wide, the resulting diatonic
scale contains supermajor and subminor intervals (approximating
ratios of 7) rather than major and minor intervals (approximating
ratios of 5).

--George

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"

> The bottom line is: choose carefully and wisely.

With all the talk about how important it is to choose the right
keyboard design the first time around, I thought I'd forward this
hint of a new world to come, in which any conceivable 2-D keyboard
arrangement can be realized at no additional cost:

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>>This guy is a bit of a dweeb, but he seems to like the
>>virtual keyboard...
>>
>>http://tinyurl.com/6unkm?__VKB_Review
>
>It would be nice to have a virtual midi keyboard for any
>EDO just on the table!
>
>Lorenzo

You betcha. Even for 12-equal; hauling a keyboard around is
one of my least-favorite things. But this technology might
be especially useful for microtonalists, since it seems it
would be possible to project different key layouts at the
push of a button!

As for polyphony, it can apparently do two-key combinations
like Shift+, Ctrl+, etc... whether it could be coaxed into
working for polyphonic music... whether it could function
quickly enough for musical applications... whether the
anomalies would be as easy to avoid in musical playing as
this reviewer found them in typing... I don't know.

-Carl
--- End forwarded message ---

--- In MakeMicroMusic@yahoogroups.com, Daniel Wolf <djwolf1@a...>
wrote:

> Personally, I have little patience for an overproduction of
terminology
> which I sense in the community, feeling that it often puts private
> ambitions in from of communication based on a shared heritage.

In front of? For my part, no way -- I tried to stick with Erv
Wilson's names, and names of those with historical priority, wherever
possible in my new paper (which informed Igliashon, to whom George
was responding). There are some distinguished systems Erv seems to
have missed (such as that based on 2025:2048 as unison vector, useful
for example for 34-equal where the Bosanquet is useless), each of
which implies a new 2-D keyboard layout. Many more of these,
especially those for higher harmonic limits, have been discussed on
the tuning-math list but were not in my paper because of limited
space. Years of work (largely by Graham Breed and Gene Ward Smith) on
tuning-math have filled in the holes in the knowledge of such
systems, and also put the theory on a firm mathematical footing (of
Grassmann, or exterior, or multilinear algebra) for the first time.
And all this was largely inspired by the rediscovery, on the tuning
list, of a system George Secor had published in Xenharmonikon 3.
Shared heritage seems to the running thread in this community, and
private ambitions conspicuously absent.

> But I do
> understand the impulse (and have, indeed, been guilty of the same)
and
> as long as I'm not forced to adopt a given set of terms, let a
thousand
> flowers bloom.

I've tried to stay as close as possible to the language in Erv
Wilson's published writings and the xenharmonic literature in
general. And Igliashon is drawing on my paper. So who's guilty of
what here (in this particular case)?

> But the other essential element in Erv's teaching is his constant
> readiness for the possibility that he might learn something
himself -
> Larry Hanson's keyboard geometry,

Hanson is of course one of the systems in my new paper, and the
keyboard design implied by it looks very much like Larry's own -- no
surprise there. I'd be happy to make preliminary keyboard designs for
any of the 2-D systems in my paper and/or from the tuning-math list,
if anyone's interested.

> or a few terms from real maths (I
> remember David Feldman mentioning freshman sums to him).

George Secor was kind enough to send my paper to Erv but his response
so far has been so oblique that we have no idea if Erv was learning
something new, or if he already knew of the systems in my paper, what
he's called them before. Maybe if I had included all the implied
keyboard layouts, he would have responded more informatively?

P.S. If I haven't gotten a copy of the paper to you yet, send me your
snail-mail address and I'll do so immediately.

C,

{you wrote...}
> > The bottom line is: choose carefully and wisely.
>
>With all the talk about how important it is to choose the right keyboard >design the first time around, I thought I'd forward this hint of a new >world to come, in which any conceivable 2-D keyboard arrangement can be >realized at no additional cost:

There is a cost: expressivity. People can go on and on about the wonderful world of no velocity sensing whatsoever, but go out and propose a flute, or a violin, or a drum, or ... that doesn't respond to the human breath, the human touch. Feh. If it is a new world, it needs to encompass more options, not fewer.

Funny how this all comes around right now: just last night, during the lengthy stretches between playing in "Die Fledermaus", I was reading stories by T. C. Boyle. There is a great one that involved whole-body condoms. In most scenarios - save for playing an organ somewhere (noting all those stops you can fiddle with) - that is exactly what it would feel like to me.

Organs and condoms - a perfect combo!

Cheers from the other bleachers,
Jon

--- In MakeMicroMusic@yahoogroups.com, "Jonathan M. Szanto"
<JSZANTO@A...> wrote:
> C,
>
> {you wrote...}
> > > The bottom line is: choose carefully and wisely.
> >
> >With all the talk about how important it is to choose the right
keyboard
> >design the first time around, I thought I'd forward this hint of a
new
> >world to come, in which any conceivable 2-D keyboard arrangement
can be
> >realized at no additional cost:
>
> There is a cost: expressivity. People can go on and on about the
wonderful
> world of no velocity sensing whatsoever, but go out and propose a
flute, or
> a violin, or a drum, or ... that doesn't respond to the human
breath, the
> human touch. Feh. If it is a new world, it needs to encompass more
options,
> not fewer.

Excuse me, Jon, but I was envisioning a future with more
expressivity, not less. If this technology were used for a musical
keyboard, of course I'd want as many means of controlling expression
as possible -- with the breath, with the feet (as on an organ), etc.
Perhaps you're confusing me with someone else.

>George Secor was kind enough to send my paper to Erv but his response
>so far has been so oblique that we have no idea if Erv was learning
>something new, or if he already knew of the systems in my paper, what
>he's called them before. Maybe if I had included all the implied
>keyboard layouts, he would have responded more informatively?

Erv is very oblique. :)

-Carl

>C,
>
>{you wrote...}
>> > The bottom line is: choose carefully and wisely.
>>
>>With all the talk about how important it is to choose the right keyboard
>>design the first time around, I thought I'd forward this hint of a new
>>world to come, in which any conceivable 2-D keyboard arrangement can be
>>realized at no additional cost:

That was Paul, not me.

>There is a cost: expressivity. People can go on and on about the
>wonderful world of no velocity sensing whatsoever, but go out and
>propose a flute, or a violin, or a drum, or ... that doesn't respond
>to the human breath, the human touch. Feh. If it is a new world, it
>needs to encompass more options, not fewer.

Oh Jon, what *are* we going to do with you?

-Carl

I know that Hanson went quite a bit over the territory covered by his keyboard, once Erv showed him the full extension of what he had inadvertently created. when i tuned up a set of hebdomekontany taken out to 72, it was Hanson layout that i used. the 2025/2048 is not that far out to spot. then again i don't recall a name for this comma.
for the record it should be pointed out that Hanson and Erv worked quite a bit for quite a period of time, meeting in person on a weekly basis, to augment their phone conversations.
most of the support books and documents pertaining to the recurrent sequences, along with computer runnout of series was done by Hanson for Erv.
All his Hanson musical papers are in a file cabinet at Erv's house that hopefully will see more of a light of day than so far.

Paul Erlich wrote:

>--- In MakeMicroMusic@yahoogroups.com, Daniel Wolf <djwolf1@a...> >wrote:
>
> >
>>Personally, I have little patience for an overproduction of >> >>
>terminology > >
>>which I sense in the community, feeling that it often puts private >>ambitions in from of communication based on a shared heritage.
>> >>
>
>In front of? For my part, no way -- I tried to stick with Erv >Wilson's names, and names of those with historical priority, wherever >possible in my new paper (which informed Igliashon, to whom George >was responding). There are some distinguished systems Erv seems to >have missed (such as that based on 2025:2048 as unison vector, useful >for example for 34-equal where the Bosanquet is useless), each of >which implies a new 2-D keyboard layout. Many more of these, >especially those for higher harmonic limits, have been discussed on >the tuning-math list but were not in my paper because of limited >space. Years of work (largely by Graham Breed and Gene Ward Smith) on >tuning-math have filled in the holes in the knowledge of such >systems, and also put the theory on a firm mathematical footing (of >Grassmann, or exterior, or multilinear algebra) for the first time. >And all this was largely inspired by the rediscovery, on the tuning >list, of a system George Secor had published in Xenharmonikon 3. >Shared heritage seems to the running thread in this community, and >private ambitions conspicuously absent.
>
> >
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

Hello George, and all. This message got lost in my outbox when
I was at NAMM. But I've updated it...

>> I never know what the term 'Bosanquet geometry' meant. Is it
>> just that fifths should.... do what?
>
>A Bosanquet keyboard geometry or layout is simply a generalized
>keyboard that uses the fifth as the generating interval. The
>location of a particular key along the y-dimension is a direct
>function of the location of its pitch in the chain of fifths.

Aha!

>Erv judged the shape of Bosanquet's keys as relatively inefficient,
>because the back half of each key surface can be played only by
>putting the finger or thumb between two adjacent keys that are
>higher in elevation (which can get a bit tricky).

The multi-tiered aspect does offer tactile feedback about what's
going on (reduces the symmetry of the keyboard). And fitting
fingers between keys on the piano hasn't been fatal to the art,
though piano technique doesn't involve turning the hand (at all)
or curling fingers (as much) as any generalized design is likely
to require.

The rectangular aspect potentially gives more ways to reach a
multi-note target (chord or sequence). In the simplest case...

| | | | | | |
| a | c | | | | |
| | | | | | |
\ / \ / vs. | d |---| f |
\ / \ / | | | |
| b | | | e | |
| | | | | |

...without turning the hand, curling the fingers or using the
thumb, d & e can be reached from more places than a & b. The
player can sustain d & e while moving his hand into better position
for the next target. Rectangular keys do have to be made thinner,
but with multiple tiers we make it easier to select subsets of the
keyboard, even if the keys are thin (by creating empty holes around
targets).

Another approach is to ask which motions are faster and/or more
accurate and/or less stressful to the body: finger extensions/curls,
or depressing a sequence of different fingers? Clearly the latter.
This suggests our keys should be long and narrow rather than
short and fat.

Michael Zarkey, who built a multi-tiered 19-tone harpsichord
based on Erv's design (like the layout on the left), felt that for
muli-tiered keyboards at least, rectangular was better. After
playing his instrument for 2-3 hours, I agreed. But I could have
been wrong (2-3 hours ain't nothin').

Another approach would be just to make tiny round buttons really
close together, like the bass keys on an accordion. Any reason
why this wouldn't be optimal? Does it exile the thumb?

>> inclined slightly up and away from the player, right?
>
>Right. An angle of about 17 degrees allows a natural arm motion as
>one moves along the y-direction.

Anything that angles my wrists up/back (computer mice, keyboard racks
with an inclined upper tier) winds up putting the hurt on my tendons.
It seems to me that Derek Sherinian has the right idea, angling his
keyboards down and away from the player, so the hands can be flat with
the arms when playing in a standing position.

How do you move your hands along y? From the shoulders only, or
with elbows too? I don't see how the arm motion would be an arc...

>> But I have Bosanquet's book.
//
>> But I don't remember this term.
>
>It's not in his book. He simply named his keyboard a generalized
>keyboard because it possesses these very desirable characteristics:
>
>1) It accommodates multiple tunings (as opposed to being a
>specialized keyboard for a single tuning);
>2) It does not require special fingering patterns for different keys.
>
>Since that time, others, such as Erv Wilson, have observed that
>various other generating intervals may be used to define a keyboard
>layouts having the above characteristics. Some of these will
>accommodate divisions not possible on the Bosanquet layout; e.g.,
>using a hemi-fifth as generator will accommodate 10, 14, and 24 (in
>addition to 17, 31, and 41), but not 19, 22, 29 or 46, while using a
>hemi-fourth as generator will accommodate 10, 14, 24 (in addition to
>19 and 29), but not 17, 22, 31, 41, or 46.
>
>Since many different kinds of generalized keyboard layouts (or
>geometries) are possible, I employed the term "Bosanquet layout" to
>specify the one that Bosanquet originated -- the one using a fifth as
>the generating interval. The Bosanquet geometry is the closest thing
>to a "universal" layout, because it accommodates more of the "best"
>divisions than any other, and it's the easiest to learn, because it
>allows one to retain many fingering patterns used on the conventional
>keyboard.

Aha. Thanks for the explanation.

-Carl

>There is a cost: expressivity. People can go on and on about the
>wonderful world of no velocity sensing whatsoever, but go out and
>propose a flute, or a violin, or a drum, or ... that doesn't
>respond to the human breath, the human touch.

? A keyboard is not a flute, violin, or drum, and I wouldn't
want it to be.

>If it is a new world, it needs to encompass more options, not fewer.

An insta-layout keyboard generator doesn't seem to you to offer
new options?

>Funny how this all comes around right now: just last night, during
>the lengthy stretches between playing in "Die Fledermaus", I was
>reading stories by T.C. Boyle. There is a great one that involved
>whole-body condoms. In most scenarios - save for playing an organ
>somewhere (noting all those stops you can fiddle with)

Save? Maybe you don't like organ music. Is that what you're
trying to say?

Somewhere? Don't forget the Hammond organ, which is hardly
obscure.

Stops? Ever note all those knobs you can fiddle with on a
synthesizer?

>that is exactly what it would feel like to me.

With the limitations of MIDI and the lack of decent velocity
implementations in most synthesizer patches and programming
environments, modern keyboards are hardly velocity-sensitive
anyway.

-Carl

>Another approach would be just to make tiny round buttons really
>close together, like the bass keys on an accordion. Any reason
>why this wouldn't be optimal? Does it exile the thumb?

Does chromatic accordion and/or bayan technique employ the thumb
on the right hand?

-Carl

C,

{you wrote...}
>? A keyboard is not a flute, violin, or drum, and I wouldn't want it to be.

Duh. The point is that if you proposed to virtually any other instrumentalist that they lose the expressive nature of the interface, you'd be laughed off the block. That kbds encompass a number of different performance cultures is not disputed; what is is the idea that someone has a great new option, when in doing so they lop of a huge percent of the musical extension of the performer.

>An insta-layout keyboard generator doesn't seem to you to offer new options?

Yeah, it's easy to carry around. We're a loooong way from something as flexible as you are thinking about; in the meantime, how would you play in a well-lit room?

>Save? Maybe you don't like organ music. Is that what you're trying to say?

I like organ music. But if one is looking for an all-around solution for creating new musics, I wouldn't choose that mode as the interface.

>Somewhere? Don't forget the Hammond organ, which is hardly obscure.

Currently going through a rennaisance, but it has had it's ups and downs. And, don't forget, you are the one that didn't want to lug a kbd to a gig! And a Hammond is nothing if you can't be yanking on the drawers and smearing your hands on the keys.

>Stops? Ever note all those knobs you can fiddle with on a synthesizer?

Do it all the time, on my touch-sensitive, multi-slider, multi-knob controller. I wonder how they'd implement sliders and knobs...

>With the limitations of MIDI and the lack of decent velocity >implementations in most synthesizer patches and programming environments, >modern keyboards are hardly velocity-sensitive anyway.

They are a lot more so than NO sensitivity. I think that - for the most part - the only people that a non-sensitive keyboard controller for microtonality would appeal to are people that are interested in harmony (and maybe some contrapuntalism) uber alles. Who needs phrasing, expression, and all that stuff when you're blissing out on chord progressions?

That's over the top, but an extreme version of what I'm trying to get at. I have a very, very hard time seeing static, non-expressive actuators being peddled as a panacea. But YMMV, as always.

Cheers,
Jon

>They are a lot more so than NO sensitivity. I think that - for the most
>part - the only people that a non-sensitive keyboard controller for
>microtonality would appeal to are people that are interested in harmony
>(and maybe some contrapuntalism) uber alles.

That's an... interesting opinion.

Ever play a Minimoog?

>I like organ music. But if one is looking for an all-around solution
>for creating new musics, I wouldn't choose that mode as the interface.

Pianos have had velocity sensitivity for 200 years. What's new about
that?

>We're a loooong way from something as flexible as you are thinking
>about;

I said it's unclear if it could ever be adapted to musical applications.

>I wonder how they'd implement sliders and knobs...

They could be carried separately (pedals would be even better).
Or, something like Roland's D-Beam could be added.

>in the meantime, how would you play in a well-lit room?

It works in normal lighting.

>That's over the top, but an extreme version of what I'm trying to get
>at. I have a very, very hard time seeing static, non-expressive
>actuators being peddled as a panacea. But YMMV, as always.

I didn't say it was a panacea. In the two years I've been following
this thread, I've never called it anything more than an exciting
option.

Really... stand clear of the reality distortion field.

-Carl

John, Carl...it may be that there is something under the surface that
I'm not aware of, but this seems like a very silly thing to be
debating. I'm sure Carl is not AGAINST velocity sensitivity, but as
far as keyboard instruments are concerned it is not a NECESSARY thing
to have. Yes, it's nice. But if someone offered a keyboard like
that crazy infrared deal that could be re-arranged completely
according to whim, I wouldn't quibble over velocity sensitivity.
Take things for what they are and what they are capable of. Everyone
has different needs and different desires, and this whole debate is
really a matter of personal preference. In fact, I'd hesitate to
even call this a debate because there are no real arguments, just two
people with different preferences. If John wants velocity
sensitivity on his instruments, that's his choice. Likewise, if Carl
doesn't find it necessary, that's his choice. Let the rest of the
world make up their own minds, because that's what will happen
anyway. Developers will develop and consumers will consume. There's
nothing to be gained from all this quarelling, no one will change
their minds and people will just get frustrated and by and large the
rest of the group will get sick of seeing the same arguments over and
over again.

Please guys, give it a rest.

-Igliashon

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >They are a lot more so than NO sensitivity. I think that - for the
most
> >part - the only people that a non-sensitive keyboard controller
for
> >microtonality would appeal to are people that are interested in
harmony
> >(and maybe some contrapuntalism) uber alles.
>
> That's an... interesting opinion.
>
> Ever play a Minimoog?
>
> >I like organ music. But if one is looking for an all-around
solution
> >for creating new musics, I wouldn't choose that mode as the
interface.
>
> Pianos have had velocity sensitivity for 200 years. What's new
about
> that?
>
> >We're a loooong way from something as flexible as you are thinking
> >about;
>
> I said it's unclear if it could ever be adapted to musical
applications.
>
> >I wonder how they'd implement sliders and knobs...
>
> They could be carried separately (pedals would be even better).
> Or, something like Roland's D-Beam could be added.
>
> >in the meantime, how would you play in a well-lit room?
>
> It works in normal lighting.
>
> >That's over the top, but an extreme version of what I'm trying to
get
> >at. I have a very, very hard time seeing static, non-expressive
> >actuators being peddled as a panacea. But YMMV, as always.
>
> I didn't say it was a panacea. In the two years I've been following
> this thread, I've never called it anything more than an exciting
> option.
>
> Really... stand clear of the reality distortion field.
>
> -Carl

Paul Erlich wrote:

>
> I've tried to stay as close as possible to the language in Erv
> Wilson's published writings and the xenharmonic literature in
> general. And Igliashon is drawing on my paper. So who's guilty of
> what here (in this particular case)?
>
I was just mentioning a particular annoyance of mine, then diminished it by noting my own inconsistancy. Judiciously (or so I thought), I didn't name names, and if I had, I wouldn't have named yours. But I stick to my opinion that too much new terminology is unwarranted. Names for commas, for example. I just want the ratio, and I can figure out the rest by myself; a new name for a comma is unnecessary baggage, bound to scare away the uninitiated or alienate those with different backgrounds.

> George Secor was kind enough to send my paper to Erv but his response
> so far has been so oblique that we have no idea if Erv was learning
> something new, or if he already knew of the systems in my paper, what
> he's called them before. Maybe if I had included all the implied
> keyboard layouts, he would have responded more informatively?
>
(a) The more illustrations the better, (b) Erv may well be still cogitating over your paper, (c) he always has something on his desk or growing in his fields (literally), so that a serious response has been back-burnered, or (d) it's always best to sit down in person with Erv at his dining table -- that's where he really shines. Looks like you could use some better weather right now -- why not take a flight to LA?

> P.S. If I haven't gotten a copy of the paper to you yet, send me your
> snail-mail address and I'll do so immediately.
>
Until mid-June, it's Galgoczy utca 8, 1125 Budapest. After that, back to Frankfurt. Thanks in advance!

DJW

C,

{you wrote...}
>That's an... interesting opinion.

Pretty empirical though. I've based it mainly on watching what has come out of the work of people who utilize a non-velocity interface.

>Ever play a Minimoog?

Not in a long time. But, while I still love the instrument, it is hard to play my Prophet V - I keep wanting it to do things with my hands besides turn on and off.

>Pianos have had velocity sensitivity for 200 years. What's new about that?

You're right, that's an evolution. I don't propose to roll back those advances.

>I said it's unclear if it could ever be adapted to musical applications.

Yes, true.

>It works in normal lighting.

That's fairly impressive.

>I didn't say it was a panacea. In the two years I've been following this >thread, I've never called it anything more than an exciting option.
>
>Really... stand clear of the reality distortion field.

Well, I did say I was being colorful in the extreme. And I guess I don't share your excitement for the null keyboard.

However, I too would appreciate if you ever find a keyboard, and most especially a controller (I don't need the sound generation facilities) that you felt had a good response for touch. I'm disappointed in them, but I'm also not a real pianist/kbdist, and I know you put your hands on more of them (especially these days) than I do. Virtually every one of them feel either clunky or sproingy to me. And I don't get that sitting at the Steinway down at symphony hall.

Cheers,
Jon

Igs,

Sorry if it went on too much. I guess Carl and I have had our last say today (I guess I do). And yes, there is a tie-in to past musical issues on this list.

Also, bear in mind we've been very patient as you've hashed out the pluses and minuses of George's (and others) various 'universal' kbd layouts.

Peace,
Jon

Igliashon Jones wrote:

>There's >nothing to be gained from all this quarelling, no one will change >their minds and people will just get frustrated and by and large the >rest of the group will get sick of seeing the same arguments over and >over again.
>
>Please guys, give it a rest.
>
You alls new around here, aren't you?

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

>>Ever play a Minimoog?
>
>Not in a long time. But, while I still love the instrument, it is hard to
>play my Prophet V - I keep wanting it to do things with my hands besides
>turn on and off.

You have a Prophet V?! I thought they were velocity-sensitive, at least
the rev2 and 3s. ?

>>I didn't say it was a panacea. In the two years I've been following
>>this thread, I've never called it anything more than an exciting option.
>>
>>Really... stand clear of the reality distortion field.
>
>Well, I did say I was being colorful in the extreme.

That's true.

>However, I too would appreciate if you ever find a keyboard, and most
>especially a controller (I don't need the sound generation facilities)
>that you felt had a good response for touch. I'm disappointed in them,
>but I'm also not a real pianist/kbdist, and I know you put your hands
>on more of them (especially these days) than I do. Virtually every one
>of them feel either clunky or sproingy to me. And I don't get that
>sitting at the Steinway down at symphony hall.

None compare to a good piano. I love the synth action on my
Kawai K5000 (out of production). It's light, even from front to
back, has textured blacks, and the attached synth can do amazing
things with the velocity numbers.

The new Access Virus TI has a keyboard that's very similar. It
isn't shipping yet, though, and is very buggy.

The Kurzweil PC2 with semi-weighted action is about my favorite.

The new M-Audio stage piano (not yet on their website last I
checked) gets the action of the Keystation 88, which I wasn't
fond of, but adds textured blacks and the attached synth has
good response to velocity and I liked it pretty well at NAMM.

The best thing to do is to go to one of the few remaining big shops
and play as many different 'boards as you can, for as long as you can.

-Carl

C,

Ta for the feedback!

{you wrote...}
>You have a Prophet V?! I thought they were velocity-sensitive, at least >the rev2 and 3s. ?

I got one of the last revs, still in mint condition. No v-s.

>None compare to a good piano.

!

>The Kurzweil PC2 with semi-weighted action is about my favorite.

I've often wanted to just pick up a PC88, as it felt about the most workable for me, with enough tactile feedback to influence/inform my playing.

>The new M-Audio stage piano (not yet on their website last I checked) gets >the action of the Keystation 88, which I wasn't fond of, but adds textured >blacks and the attached synth has good response to velocity and I liked it >pretty well at NAMM.

Boy, I wanted that K..88 to be the end-all, but I couldn't begin to like the action, and it seemed like a LOT of people had production quality problems with it. I'll keep an eye out for the new one anyway.

>The best thing to do is to go to one of the few remaining big shops and >play as many different 'boards as you can, for as long as you can.

Yeah, I take my headphones out to Guitar Center every so often to do just that. I'll keep looking (and touching)...

Cheers,
Jon

--- In MakeMicroMusic@yahoogroups.com, Kraig Grady <kraiggrady@a...>
wrote:

> the 2025/2048 is not that far
> out to spot. then again i don't recall a name for this comma.

It's called the diaschisma.

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> ...
> >Erv judged the shape of Bosanquet's keys as relatively
inefficient,
> >because the back half of each key surface can be played only by
> >putting the finger or thumb between two adjacent keys that are
> >higher in elevation (which can get a bit tricky).

To elaborate on this, it requires much more lateral accuracy to avoid
hitting an adjacent key, in contrast to his hexagonal keys, which are
much wider, yet do not increase playing distances along either the x
or y axis.

> The multi-tiered aspect does offer tactile feedback about what's
> going on (reduces the symmetry of the keyboard). And fitting
> fingers between keys on the piano hasn't been fatal to the art,
> though piano technique doesn't involve turning the hand (at all)

I've never had to do that.

> or curling fingers (as much) as any generalized design is likely
> to require.

I was long accustomed to doing that on the accordion with the left
hand, so the technique was not new to me. Don't guitarists have to
do that as well, in order to play chords?

> The rectangular aspect potentially gives more ways to reach a
> multi-note target (chord or sequence). In the simplest case...
>
> | | | | | | |
> | a | c | | | | |
> | | | | | | |
> \ / \ / vs. | d |---| f |
> \ / \ / | | | |
> | b | | | e | |
> | | | | | |
>
> ...without turning the hand, curling the fingers or using the
> thumb, d & e can be reached from more places than a & b. The
> player can sustain d & e while moving his hand into better position
> for the next target. Rectangular keys do have to be made thinner,
> but with multiple tiers we make it easier to select subsets of the
> keyboard, even if the keys are thin (by creating empty holes around
> targets).

There is another a trade-off: Rectangular keys will have 2 adjacent
neighbors on each side, while hexagonal keys will have 3.

> Another approach is to ask which motions are faster and/or more
> accurate and/or less stressful to the body: finger extensions/curls,
> or depressing a sequence of different fingers? Clearly the latter.
> This suggests our keys should be long and narrow rather than
> short and fat.

Another trade-off with long and narrow keys is that distances in the
y-direction will tend to be farther, which seems to negate much of
the advantages offered by their length.

> Michael Zarkey, who built a multi-tiered 19-tone harpsichord
> based on Erv's design (like the layout on the left), felt that for
> muli-tiered keyboards at least, rectangular was better. After
> playing his instrument for 2-3 hours, I agreed. But I could have
> been wrong (2-3 hours ain't nothin').

I have found that shorter & fatter keys eliminate the need for
multiple tiers, so the keys (or buttons) can all be in a single
plane, as on the Scalatron and left hand of the accordion.

> Another approach would be just to make tiny round buttons really
> close together, like the bass keys on an accordion. Any reason
> why this wouldn't be optimal? Does it exile the thumb?

Yes, they're too small for the thumb.

> >> inclined slightly up and away from the player, right?
> >
> >Right. An angle of about 17 degrees allows a natural arm motion
as
> >one moves along the y-direction.
>
> Anything that angles my wrists up/back (computer mice, keyboard
racks
> with an inclined upper tier) winds up putting the hurt on my
tendons.
> It seems to me that Derek Sherinian has the right idea, angling his
> keyboards down and away from the player, so the hands can be flat
with
> the arms when playing in a standing position.
>
> How do you move your hands along y? From the shoulders only, or
> with elbows too?

Both shoulders and elbows.

> I don't see how the arm motion would be an arc...

It's not an arc; it's a flat plane inclined around 17 degrees. If
you put your hands into playing position and then move your arms
forward in a natural, comfortable manner without changing the angle
at which your hands are positioned (without any wrist movement), your
fingertips should remain at a fairly constant distance above the
plane of the keyboard.

When I tried the Archiphone (electronic instrument with Fokker's
keyboard) at Webster U. in St. Louis, I immediately noticed that the
angle of incline of the keys was large enough, as I found myself
unbending my arms too much to reach the farthest rows.

--George

--- In MakeMicroMusic@yahoogroups.com, "Jonathan M. Szanto"
<JSZANTO@A...> wrote:

> >Somewhere? Don't forget the Hammond organ, which is hardly
>>obscure.
>
> Currently going through a rennaisance, but it has had it's ups and
downs.
> And, don't forget, you are the one that didn't want to lug a kbd to
a gig!
> And a Hammond is nothing if you can't be yanking on the drawers and
> smearing your hands on the keys.

And most importantly, using the volume pedal for expression (at least
my Hammond has one . . .)

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
>
> When I tried the Archiphone (electronic instrument with Fokker's
> keyboard) at Webster U. in St. Louis, I immediately noticed that
the
> angle of incline of the keys was large enough,

Sorry, that should have been:

I immediately noticed that the angle of incline of the keys was *not*
large enough, ...

> as I found myself
> unbending my arms too much to reach the farthest rows.
>
> --George

--- In MakeMicroMusic@yahoogroups.com, Daniel Wolf <djwolf1@a...>
wrote:

> Names for
> commas, for example. I just want the ratio, and I can figure out
the
> rest by myself; a new name for a comma is unnecessary baggage,
bound to
> scare away the uninitiated or alienate those with different
backgrounds.

You'll be glad to know that I don't name any commas in my paper -- I
just give the ratios and, in some cases, their prime-factorizations.
And I don't refer to them as "monzos" either.

> (a) The more illustrations the better,

I'll get to work!

>(d) it's always best to sit down in person with Erv at
> his dining table -- that's where he really shines. Looks like you
could
> use some better weather right now -- why not take a flight to LA?

There's nothing I'd rather do (between my frequent gigs, that
is) . . . anyone who can facilitate such a meeting should contact me
off-list. Perhaps Gene, Kraig, and other CA folks can be in on it
too . . . (?)

> > P.S. If I haven't gotten a copy of the paper to you yet, send me
your
> > snail-mail address and I'll do so immediately.
> >
> Until mid-June, it's Galgoczy utca 8, 1125 Budapest.

Hungary it is! Licking envelope now . . .

>>The new M-Audio stage piano (not yet on their website last I checked) gets
>>the action of the Keystation 88, which I wasn't fond of, but adds textured
>>blacks and the attached synth has good response to velocity and I liked it
>>pretty well at NAMM.
>
>Boy, I wanted that K..88 to be the end-all, but I couldn't begin to like
>the action, and it seemed like a LOT of people had production quality
>problems with it. I'll keep an eye out for the new one anyway.

Yeah, it was a bit rickety. The new one (at least the prototype they
had at NAMM) was a *lot* more solid.

-Carl

Daniel wrote...

>I just want the ratio, and I can figure out the
>rest by myself; a new name for a comma is unnecessary baggage, bound to
>scare away the uninitiated or alienate those with different backgrounds.

There's some truth to this, but many of the commas we deal with
have unmanageably-long ratios. Prime factor notation is an
alternative.

-Carl

>> The multi-tiered aspect does offer tactile feedback about what's
>> going on (reduces the symmetry of the keyboard). And fitting
>> fingers between keys on the piano hasn't been fatal to the art,
>> though piano technique doesn't involve turning the hand (at all)
>
>I've never had to do that.

Never had to play at the back of the keyboard on a piano? Or...?

>> or curling fingers (as much) as any generalized design is likely
>> to require.
>
>I was long accustomed to doing that on the accordion with the left
>hand, so the technique was not new to me. Don't guitarists have to
>do that as well, in order to play chords?

Dunno. There's nothing wrong with it, but it is a different
type of hand-use.

>> Another approach is to ask which motions are faster and/or more
>> accurate and/or less stressful to the body: finger extensions/curls,
>> or depressing a sequence of different fingers? Clearly the latter.
>> This suggests our keys should be long and narrow rather than
>> short and fat.
>
>Another trade-off with long and narrow keys is that distances in the
>y-direction will tend to be farther, which seems to negate much of
>the advantages offered by their length.

It's just like, where do you want the extra notes: in front and
back, or left and right?

>> Michael Zarkey, who built a multi-tiered 19-tone harpsichord
>> based on Erv's design (like the layout on the left), felt that for
>> muli-tiered keyboards at least, rectangular was better. After
>> playing his instrument for 2-3 hours, I agreed. But I could have
>> been wrong (2-3 hours ain't nothin').
>
>I have found that shorter & fatter keys eliminate the need for
>multiple tiers, so the keys (or buttons) can all be in a single
>plane, as on the Scalatron and left hand of the accordion.

Yes, my guess is that round/hex keys work best on a plane, though
I've never actually played a planar hex keyboard (aside from
Accordion left hand). Note: In 2001, I asked Scott Hackleman if
the multi-tiered aspect was a problem on his hex-keyed clavichord,
and he said no, he was absolutely satisfied with his keyboard.

>> Another approach would be just to make tiny round buttons really
>> close together, like the bass keys on an accordion. Any reason
>> why this wouldn't be optimal? Does it exile the thumb?
>
>Yes, they're too small for the thumb.

Is the trade-off of lots and lots of close-packed keys worth
omitting the thumb?

>> >> inclined slightly up and away from the player, right?
>> >
>> >Right. An angle of about 17 degrees allows a natural arm motion
>> >as one moves along the y-direction.
>>
>> Anything that angles my wrists up/back (computer mice, keyboard
>> racks with an inclined upper tier) winds up putting the hurt on my
>> tendons. It seems to me that Derek Sherinian has the right idea,
>> angling his keyboards down and away from the player, so the hands
>> can be flat with the arms when playing in a standing position.
>>
>> How do you move your hands along y? From the shoulders only, or
>> with elbows too?
>
>Both shoulders and elbows.
>
>> I don't see how the arm motion would be an arc...
>
>It's not an arc; it's a flat plane inclined around 17 degrees. If
>you put your hands into playing position and then move your arms
>forward in a natural, comfortable manner without changing the angle
>at which your hands are positioned (without any wrist movement), your
>fingertips should remain at a fairly constant distance above the
>plane of the keyboard.

Hmm... if I move my arms at the shoulder with my elbows and
wrists locked, my hands move in an arc. If I use my elbows too,
I can get my hands to move along a plane at any angle, but
parallel to the floor seems most natural.

[Oh man, I'd kill for a web site on the Generalized Scalatron,
with a few pictures and some brief technique hints. . .]

>When I tried the Archiphone (electronic instrument with Fokker's
>keyboard) at Webster U. in St. Louis, I immediately noticed that the
>angle of incline of the keys was large enough, as I found myself
>unbending my arms too much to reach the farthest rows.

Hmm.....

I wasn't aware of the Archiphone, for one thing!

-Carl

>And most importantly, using the volume pedal for expression (at least
>my Hammond has one . . .)

You have a Hammond!!!! Which model? Leslie?

-Carl

Carl Lumma wrote:

> Daniel wrote...
>
> >I just want the ratio, and I can figure out the
> >rest by myself; a new name for a comma is unnecessary baggage, bound to
> >scare away the uninitiated or alienate those with different backgrounds.
>
> There's some truth to this, but many of the commas we deal with
> have unmanageably-long ratios. Prime factor notation is an
> alternative.
>
> -Carl

Factors are fine, I'm happy with numbers in any form. But watch out for Grothendieck primes, please.

DJW

>>(d) it's always best to sit down in person with Erv at
>> his dining table -- that's where he really shines. Looks like you
>>could use some better weather right now -- why not take a flight
>>to LA?
>
>There's nothing I'd rather do (between my frequent gigs, that
>is) . . . anyone who can facilitate such a meeting should contact me
>off-list. Perhaps Gene, Kraig, and other CA folks can be in on it
>too . . . (?)

I'm all for it! I could drive a bunch a folks down.

My impression, though, is that this would overwhelm Erv. Maybe
I'm wrong about that...

But Paul, you should definitely visit. There's a JI Network
anniversary concert coming up... not sure if they've fixed
the date yet. Though if I were you I'd make LA my main target.
But you're always welcome at my place, and perhaps Kurt
could put you up even more comfortably...

-Carl

>> >I just want the ratio, and I can figure out the
>> >rest by myself; a new name for a comma is unnecessary baggage, bound
>> >to scare away the uninitiated or alienate those with different
>> >backgrounds.
>>
>> There's some truth to this, but many of the commas we deal with
>> have unmanageably-long ratios. Prime factor notation is an
>> alternative.
>
>Factors are fine, I'm happy with numbers in any form. But watch out
>for Grothendieck primes, please.

Now who's using intimidating terminology!

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >And most importantly, using the volume pedal for expression (at
least
> >my Hammond has one . . .)
>
> You have a Hammond!!!! Which model?

I'm told it's a "Portable B3". It only says "Hammond". I must have
shown it to you when you visited.

> Leslie?

My solid-state Leslie perished in a fire in Dec. 1998. My Hammond
won't work with tube Leslies because the connecting wire uses a
different number of pins.

C,

{you wrote...}
>Yeah, it was a bit rickety. The new one (at least the prototype they had >at NAMM) was a *lot* more solid.

Hey, that's promising!

Cheers,
Jon

>> >And most importantly, using the volume pedal for expression (at
>> >least my Hammond has one . . .)
>>
>> You have a Hammond!!!! Which model?
>
>I'm told it's a "Portable B3". It only says "Hammond". I must have
>shown it to you when you visited.

Er, I don't remember you having any keyboards other than
an upright piano.

There's something called a Portable B3 currently in production,
but it's very new (last year I think). But it's quite possible
there's something older with the same name that I don't know
about.

>> Leslie?
>
>My solid-state Leslie perished in a fire in Dec. 1998.

Hmm, I visited post-fire, so I must be forgetting.

>My Hammond won't work with tube Leslies because the connecting
>wire uses a different number of pins.

Yeah, those proprietary connectors are teh sux. There is maybe
a way to convert it... our B3 guy, Steve Fortner, has an external
box made by some guy in Florida that did something... I should
find out what that was. . .

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >And most importantly, using the volume pedal for expression (at
> >> >least my Hammond has one . . .)
> >>
> >> You have a Hammond!!!! Which model?
> >
> >I'm told it's a "Portable B3". It only says "Hammond". I must have
> >shown it to you when you visited.
>
> Er, I don't remember you having any keyboards other than
> an upright piano.

> Hmm, I visited post-fire, so I must be forgetting.

After the fire, I put the Hammond in the back bedroom (pretty useless
without a Leslie -- no 1/4-inch jacks or anything), so maybe you
never saw it, though I liked to show it to all musical visitors . . .

> There's something called a Portable B3 currently in production,
> but it's very new (last year I think). But it's quite possible
> there's something older with the same name that I don't know
> about.

This thing is ancient.

> Yeah, those proprietary connectors are teh sux. There is maybe
> a way to convert it... our B3 guy, Steve Fortner, has an external
> box made by some guy in Florida that did something... I should
> find out what that was. . .

If you do, let me know . . . off-list. This is all off-topic now!

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> The multi-tiered aspect does offer tactile feedback about what's
> >> going on (reduces the symmetry of the keyboard). And fitting
> >> fingers between keys on the piano hasn't been fatal to the art,
> >> though piano technique doesn't involve turning the hand (at all)
> >
> >I've never had to do that.
>
> Never had to play at the back of the keyboard on a piano? Or...?

Never had to turn my hand to play anything.

> >> or curling fingers (as much) as any generalized design is likely
> >> to require.
> >
> >I was long accustomed to doing that on the accordion with the left
> >hand, so the technique was not new to me. Don't guitarists have
to
> >do that as well, in order to play chords?
>
> Dunno. There's nothing wrong with it, but it is a different
> type of hand-use.

Yes, and it's one of the things you learn to do when you play a 2-
dimensional keyboard.

> ...
> >Another trade-off with long and narrow keys is that distances in
the
> >y-direction will tend to be farther, which seems to negate much of
> >the advantages offered by their length.
>
> It's just like, where do you want the extra notes: in front and
> back, or left and right?

Yes. Decisions, decisions!

> ...
> >> Another approach would be just to make tiny round buttons really
> >> close together, like the bass keys on an accordion. Any reason
> >> why this wouldn't be optimal? Does it exile the thumb?
> >
> >Yes, they're too small for the thumb.
>
> Is the trade-off of lots and lots of close-packed keys worth
> omitting the thumb?

No. I gave the reason in message #8722:

<< The only application I've found in which the requirements [for a
generalized keyboard] are more critical is for the left hand of an
accordion, where the thumb cannot be used (making cross-over
fingering both clumsy and difficult), in which case the solution is a
special arrangement of buttons that works well for the left hand (but
would work very poorly for the right hand, unless it were mirror-
imaged). >>

In other words, it would be extremely difficult to design a keyboard
that would work well for both hands if you couldn't use your thumbs.
(And you would have one less digit to play with.)

> >> >> inclined slightly up and away from the player, right?
> >> >
> >> >Right. An angle of about 17 degrees allows a natural arm motion
> >> >as one moves along the y-direction.
> >>
> >> Anything that angles my wrists up/back (computer mice, keyboard
> >> racks with an inclined upper tier) winds up putting the hurt on
my
> >> tendons. It seems to me that Derek Sherinian has the right idea,
> >> angling his keyboards down and away from the player, so the hands
> >> can be flat with the arms when playing in a standing position.
> >>
> >> How do you move your hands along y? From the shoulders only, or
> >> with elbows too?
> >
> >Both shoulders and elbows.
> >
> >> I don't see how the arm motion would be an arc...
> >
> >It's not an arc; it's a flat plane inclined around 17 degrees. If
> >you put your hands into playing position and then move your arms
> >forward in a natural, comfortable manner without changing the
angle
> >at which your hands are positioned (without any wrist movement),
your
> >fingertips should remain at a fairly constant distance above the
> >plane of the keyboard.
>
> Hmm... if I move my arms at the shoulder with my elbows and
> wrists locked, my hands move in an arc. If I use my elbows too,
> I can get my hands to move along a plane at any angle, but
> parallel to the floor seems most natural.

It sounds like the keyboard would be at a rather low height -- no
higher than your waist. The 17-degree determination was made seated
in front of the actual cabinet in which the Scalatron generalized
keyboard was going to be built, which was about the same height as a
piano keyboard. Carl, do you always play the piano while standing?

--George

>> >> The multi-tiered aspect does offer tactile feedback about what's
>> >> going on (reduces the symmetry of the keyboard). And fitting
>> >> fingers between keys on the piano hasn't been fatal to the art,
>> >> though piano technique doesn't involve turning the hand (at all)
>> >
>> >I've never had to do that.
>>
>> Never had to play at the back of the keyboard on a piano? Or...?
>
>Never had to turn my hand to play anything.

By turning, I mean keeping the hand flat and pointing it to the
left or right, so that the fingers are no longer in line with
the forearm. It looks like some of the chords on the generalized
keyboard would require the fingers to be non-perpendicular to
the chest... am I wrong or do you turn out your elbows to accomplish
this?

> >> or curling fingers (as much) as any generalized design is likely
> >> to require.
>>
>> There's nothing wrong with it, but it is a different
>> type of hand-use.
>
>Yes, and it's one of the things you learn to do when you play a
>2-dimensional keyboard.

Wow. Ok.

>> >> Another approach would be just to make tiny round buttons really
>> >> close together, like the bass keys on an accordion. Any reason
>> >> why this wouldn't be optimal? Does it exile the thumb?
>> >
>> >Yes, they're too small for the thumb.
>>
>> Is the trade-off of lots and lots of close-packed keys worth
>> omitting the thumb?
>
>No. I gave the reason in message #8722:
>
><< The only application I've found in which the requirements [for a
>generalized keyboard] are more critical is for the left hand of an
>accordion, where the thumb cannot be used (making cross-over
>fingering both clumsy and difficult), in which case the solution is a
>special arrangement of buttons that works well for the left hand (but
>would work very poorly for the right hand, unless it were mirror-
>imaged). >>
>
>In other words, it would be extremely difficult to design a keyboard
>that would work well for both hands if you couldn't use your thumbs.
>(And you would have one less digit to play with.)

Huh, I imagine a huge bank of buttons like an accordion left hand,
on a table, with fairly large intervals on the axes -- maybe even
octaves and fifths, as on Bill Wesley's "array" instruments --
that you play eight fingers.

I guess I'm wondering aloud how much good the thumb does us.
Early harpsichordists didn't use the thumb (much)...

>> >> >> inclined slightly up and away from the player, right?
>> >> >
>> >> >Right. An angle of about 17 degrees allows a natural arm motion
>> >> >as one moves along the y-direction.
>> >>
>> >> Anything that angles my wrists up/back (computer mice, keyboard
>> >> racks with an inclined upper tier) winds up putting the hurt on
>> >> my tendons. It seems to me that Derek Sherinian has the right
>> >> idea, angling his keyboards down and away from the player, so
>> >> the hands can be flat with the arms when playing in a standing
>> >> position.
>> >>
>> >> How do you move your hands along y? From the shoulders only, or
>> >> with elbows too?
>> >
>> >Both shoulders and elbows.
>> >
>> >> I don't see how the arm motion would be an arc...
>> >
>> >It's not an arc; it's a flat plane inclined around 17 degrees. If
>> >you put your hands into playing position and then move your arms
>> >forward in a natural, comfortable manner without changing the
>> >angle at which your hands are positioned (without any wrist
>> > movement), your fingertips should remain at a fairly constant
>> >distance above the plane of the keyboard.
>>
>> Hmm... if I move my arms at the shoulder with my elbows and
>> wrists locked, my hands move in an arc. If I use my elbows too,
>> I can get my hands to move along a plane at any angle, but
>> parallel to the floor seems most natural.
>
>It sounds like the keyboard would be at a rather low height -- no
>higher than your waist. The 17-degree determination was made seated
>in front of the actual cabinet in which the Scalatron generalized
>keyboard was going to be built, which was about the same height as a
>piano keyboard. Carl, do you always play the piano while standing?

Never. I try to sit with my thighs and forearms parallel to the
floor. If I put my fingertips on my desk here, I can use my
shoulders and elbows to slide them straight across the desk.
You're saying this is more natural if my desk is at 17deg.?

This is a hard topic to discuss in e-mail...

-Carl

Carl Lumma wrote:

> >> >I just want the ratio, and I can figure out the
> >> >rest by myself; a new name for a comma is unnecessary baggage, bound
> >> >to scare away the uninitiated or alienate those with different
> >> >backgrounds.
> >>
> >> There's some truth to this, but many of the commas we deal with
> >> have unmanageably-long ratios. Prime factor notation is an
> >> alternative.
> >
> >Factors are fine, I'm happy with numbers in any form. But watch out
> >for Grothendieck primes, please.
>
> Now who's using intimidating terminology!
>
> -Carl
>

It's a joke. Google "Grothendieck prime". DJW

>> >> >I just want the ratio, and I can figure out the
>> >> >rest by myself; a new name for a comma is unnecessary baggage, bound
>> >> >to scare away the uninitiated or alienate those with different
>> >> >backgrounds.
>> >>
>> >> There's some truth to this, but many of the commas we deal with
>> >> have unmanageably-long ratios. Prime factor notation is an
>> >> alternative.
>> >
>> >Factors are fine, I'm happy with numbers in any form. But watch out
>> >for Grothendieck primes, please.
>>
>> Now who's using intimidating terminology!
>
>It's a joke. Google "Grothendieck prime".

It was still intimidating. :)

-C.

Carl Lumma <ekin@...> writes:

> >It's a joke. Google "Grothendieck prime".
>
> It was still intimidating. :)

And then there's the infinite set of even primes, and the Converse
Goldberg Conjecture:

<http://people.cs.uchicago.edu/~dinoj/crantz.htm>

- Rich Holmes

On Friday 04 February 2005 03:03 am, Carl Lumma wrote:
> >> >> >I just want the ratio, and I can figure out the
> >> >> >rest by myself; a new name for a comma is unnecessary baggage, bound
> >> >> >to scare away the uninitiated or alienate those with different
> >> >> >backgrounds.
> >> >>
> >> >> There's some truth to this, but many of the commas we deal with
> >> >> have unmanageably-long ratios. Prime factor notation is an
> >> >> alternative.
> >> >
> >> >Factors are fine, I'm happy with numbers in any form. But watch out
> >> >for Grothendieck primes, please.
> >>
> >> Now who's using intimidating terminology!
> >
> >It's a joke. Google "Grothendieck prime".
>
> It was still intimidating. :)

Guys, please, take this stuff to metatuning, and please, change the subject
heading, ok? Jeez....there's nothing here to do with 22-tet keyboards
whatsoever.

Aaron Krister Johnson
http://www.akjmusic.com
http://www.dividebypi.com

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >> The multi-tiered aspect does offer tactile feedback about
what's
> >> >> going on (reduces the symmetry of the keyboard). And fitting
> >> >> fingers between keys on the piano hasn't been fatal to the
art,
> >> >> though piano technique doesn't involve turning the hand (at
all)
> >> >
> >> >I've never had to do that.
> >>
> >> Never had to play at the back of the keyboard on a piano? Or...?
> >
> >Never had to turn my hand to play anything.
>
> By turning, I mean keeping the hand flat and pointing it to the
> left or right, so that the fingers are no longer in line with
> the forearm. It looks like some of the chords on the generalized
> keyboard would require the fingers to be non-perpendicular to
> the chest... am I wrong or do you turn out your elbows to accomplish
> this?

Okay, I guess sometimes I do turn my hands slightly to do some of the
fingering (but not the elbows -- ugh!)

> ...
> >> >> Another approach would be just to make tiny round buttons
really
> >> >> close together, like the bass keys on an accordion. Any
reason
> >> >> why this wouldn't be optimal? Does it exile the thumb?
> >> >
> >> >Yes, they're too small for the thumb.
> >>
> >> Is the trade-off of lots and lots of close-packed keys worth
> >> omitting the thumb?
> >
> >No. I gave the reason in message #8722:
> >
> ><< The only application I've found in which the requirements [for
a
> >generalized keyboard] are more critical is for the left hand of an
> >accordion, where the thumb cannot be used (making cross-over
> >fingering both clumsy and difficult), in which case the solution
is a
> >special arrangement of buttons that works well for the left hand
(but
> >would work very poorly for the right hand, unless it were mirror-
> >imaged). >>
> >
> >In other words, it would be extremely difficult to design a
keyboard
> >that would work well for both hands if you couldn't use your
thumbs.
> >(And you would have one less digit to play with.)
>
> Huh, I imagine a huge bank of buttons like an accordion left hand,
> on a table, with fairly large intervals on the axes -- maybe even
> octaves and fifths, as on Bill Wesley's "array" instruments --
> that you play eight fingers.
>
> I guess I'm wondering aloud how much good the thumb does us.
> Early harpsichordists didn't use the thumb (much)...

That's news to me.

Anyway, why don't you try printing out a generalized keyboard on
paper with the keys reduced to button size and try playing a diatonic
scale with just the 4 fingers of one hand. You'll be twisting one
finger around another every time you come to a half-step. :-( You
need the thumbs to accomplish the cross-under smoothly -- unless you
have a keyboard that will remedy that problem. But such a keyboard
doesn't usually work well with both hands.

An exception may be the Hayden concertina keyboard:
http://www.maccann-duet.com/hayden/Hayden-The-Hayden-System.pdf
but this one would introduce a different problem if one were to use
it as you suggested. Your right hand would end up sitting right on
top of your left hand much of the time, e.g., if you tried playing a
major scale with each hand, an octave apart.

> >> ...
> >> Hmm... if I move my arms at the shoulder with my elbows and
> >> wrists locked, my hands move in an arc. If I use my elbows too,
> >> I can get my hands to move along a plane at any angle, but
> >> parallel to the floor seems most natural.
> >
> >It sounds like the keyboard would be at a rather low height -- no
> >higher than your waist. The 17-degree determination was made
seated
> >in front of the actual cabinet in which the Scalatron generalized
> >keyboard was going to be built, which was about the same height as
a
> >piano keyboard. Carl, do you always play the piano while standing?
>
> Never. I try to sit with my thighs and forearms parallel to the
> floor. If I put my fingertips on my desk here, I can use my
> shoulders and elbows to slide them straight across the desk.
> You're saying this is more natural if my desk is at 17deg.?

Just to make sure you're not supporting the weight of your hands or
arms by your fingers touching the desk, start with your fingertips in
playing position right at the near edge of the desk, just above the
surface. Now close your eyes and move your hands forward in the most
natural or comfortable motion using both your shoulders and elbows.
Now open your eyes and observe how far above the surface of the desk
your fingertips are.

> This is a hard topic to discuss in e-mail...

But we manage -- somehow. ;-)

--George

>> >Never had to turn my hand to play anything.
>>
>> By turning, I mean keeping the hand flat and pointing it to the
>> left or right, so that the fingers are no longer in line with
>> the forearm. It looks like some of the chords on the generalized
>> keyboard would require the fingers to be non-perpendicular to
>> the chest... am I wrong or do you turn out your elbows to accomplish
>> this?
>
>Okay, I guess sometimes I do turn my hands slightly to do some of
>the fingering (but not the elbows -- ugh!)

People do it at the conventional keyboard -- to play things
like A Major, first inversion with the right hand. But it's
a good way to get injuries, and it's much faster just to play
them straight-on.

>> I guess I'm wondering aloud how much good the thumb does us.
>> Early harpsichordists didn't use the thumb (much)...
>
>That's news to me.

My friend (a harpsichordist) showed me once... scales are
fingered in an entirely different way. It's a totally different
technique, with lots of vertical bounce in the wrists. I've
read that Bach played a key role in adding the thumb, though I'm
not sure how true this is.

>Anyway, why don't you try printing out a generalized keyboard on
>paper with the keys reduced to button size and try playing a diatonic
>scale with just the 4 fingers of one hand. You'll be twisting one
>finger around another every time you come to a half-step. :-( You
>need the thumbs to accomplish the cross-under smoothly -- unless you
>have a keyboard that will remedy that problem. But such a keyboard
>doesn't usually work well with both hands.

I think the idea is to arrange things so scales consist of
'walking' an alternating pair of fingers over the keyboard
by moving the arm. I think this can be done by using larger
intervals on x and y...

>An exception may be the Hayden concertina keyboard:
>http://www.maccann-duet.com/hayden/Hayden-The-Hayden-System.pdf
>but this one would introduce a different problem if one were to use
>it as you suggested. Your right hand would end up sitting right on
>top of your left hand much of the time, e.g., if you tried playing a
>major scale with each hand, an octave apart.

Hmm...

>>>> The 17-degree determination was made seated in front of the
>>>> actual cabinet in which the Scalatron generalized keyboard was
>>>> going to be built, which was about the same height as a piano
>>>> keyboard. Carl, do you always play the piano while standing?
>>
>> Never. I try to sit with my thighs and forearms parallel to the
>> floor. If I put my fingertips on my desk here, I can use my
>> shoulders and elbows to slide them straight across the desk.
>> You're saying this is more natural if my desk is at 17deg.?
>
>Just to make sure you're not supporting the weight of your hands or
>arms by your fingers touching the desk, start with your fingertips in
>playing position right at the near edge of the desk, just above the
>surface. Now close your eyes and move your hands forward in the most
>natural or comfortable motion using both your shoulders and elbows.
>Now open your eyes and observe how far above the surface of the desk
>your fingertips are.
>
>> This is a hard topic to discuss in e-mail...
>
>But we manage -- somehow. ;-)

Hmm... maybe so. . .

-Carl