Yahoo Tuning Groups Ultimate Backup tuning History of qwerty keyboard

> http://www.uh.edu/engines/epi719.htm
>
> may be of interest

Oh, the "typewriter" theory is definitely a lemon. But this
article did remind me of another important reason why QWERTY
wasn't for slowing typists down: touch-typing hadn't been
invented yet!

>Typewriter keys are arranged in the order the letters on them
>are used in print.

Looking at a QWERTY layout showing letter frequencies (available
on the web) should convince you this isn't correct.

I found a page that seems (to me) to have the correct answer;
as I remembered, it has to do with sequences of letters and the
locations of hammers inside the machine...

http://home.earthlink.net/~dcrehr/whyqwert.html

Finally, without getting too far off-topic, you can compare
Dvorak and QWERTY layouts with this nifty Java applet:

http://www.acm.vt.edu/~jmaxwell/dvorak/compare.html

Dvorak does seem close to optimal. At least, an informal
search with genetic algorithms couldn't really improve on
it (despite what the author seems to think)...

http://www.visi.com/~pmk/evolved.html

I highly recommend Dvorak. It seems to be the main factor
in the disappearance of my hand pain last year.

This appears to be the best keyboard hardware available...

http://www.typematrix.com/

-Carl

🔗prophecyspirit@aol.com

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
>
> I found a page that seems (to me) to have the correct answer;
> as I remembered, it has to do with sequences of letters and the
> locations of hammers inside the machine...
>
> http://home.earthlink.net/~dcrehr/whyqwert.html

I think that nails it! Those who have proposed alternatives to the
conventional 7+5 piano keyboard (such as Paul von Janko and his 6+6
arrangement) would have done well to heed the advice given in the
beginning of the closing paragraph:

<< It's not surprising, then, that Dvorak has failed to take hold.
No one wants to take the time and trouble to learn a new keyboard,
especially if it isn't convincingly superior to the old. ... >>

... or unless it allows you to do something that can't be done on the
old. This is very on-topic as soon as we consider keyboards for
alternative tunings.

I would counsel those who would design keyboards for microtonal
scales not to make them single-purpose (i.e., one for 19-ET, another
for 22-ET, another for 31-ET, another for 72-ET, etc.), but to use a
generalized arrangement that will accommodate multiple tunings with
the same fingering patterns in all keys. A custom keyboard is
probably the most expensive component in an electronic instrument,
and you will get much more for your money if it is able to
accommodate at least several different tunings in this way.

And even if you're doing an acoustic instrument (capable of only a
single tuning), why not use a generalized keyboard that was designed
for multiple tunings? We need to think through these things with a
broad perspective if we are going to avoid making qwerty-type
decisions that, should a new keyboard ever catch on, a lot of people
are going to regret years later.

> I highly recommend Dvorak. It seems to be the main factor
> in the disappearance of my hand pain last year.

Now there's something to be said for a superior design!

--George

🔗Haresh BAKSHI <hareshbakshi@hotmail.com>

🔗Carl Lumma <clumma@yahoo.com>

>>http://home.earthlink.net/~dcrehr/whyqwert.html
>
>I think that nails it!

It appears so. It is echoed by:

http://www.mwbrooks.com/dvorak/dissent.html#ergo

>Those who have proposed alternatives to the conventional 7+5
>piano keyboard (such as Paul von Janko and his 6+6 arrangement)
>would have done well to heed the advice given in the beginning
>of the closing paragraph:
>
><< It's not surprising, then, that Dvorak has failed to take hold.
>No one wants to take the time and trouble to learn a new keyboard,
>especially if it isn't convincingly superior to the old. ... >>
>
> ... or unless it allows you to do something that can't be done
>on the old. This is very on-topic as soon as we consider
>keyboards for alternative tunings.

I suspect you know more about this than any of us here, but the
Janko keyboard at least allows one to reach chords and voicings
not possible on the Halberstadt, even for Rachmaninov. :)

>And even if you're doing an acoustic instrument (capable of only
>a single tuning), why not use a generalized keyboard that was
>designed for multiple tunings? We need to think through these
>things with a broad perspective if we are going to avoid making
>qwerty-type decisions that, should a new keyboard ever catch on,
>a lot of people are going to regret years later.

Agreed!

Any retrospective comments on the Generalized-keyboard Scalatron?
Still playing her?

-Carl

🔗Kraig Grady <kraiggrady@anaphoria.com>

> Hello George!

I totally agree with your points here as someone who has used multiple generalized keyboards for various tunings. As there is an inner overall logic to them all , shifting from one to the other is quite easy once you understand the guiding principles. Let me add that scales will
often have more than one generalized option and have found advantages to some over others depending on the type and goals of the music that i am doing. BTW when i have had access to a keyboard, i find it easy to play.

>
> From: "gdsecor" <gdsecor@yahoo.com>
>
>
> I would counsel those who would design keyboards for microtonal
> scales not to make them single-purpose (i.e., one for 19-ET, another
> for 22-ET, another for 31-ET, another for 72-ET, etc.), but to use a
> generalized arrangement that will accommodate multiple tunings with
> the same fingering patterns in all keys. A custom keyboard is
> probably the most expensive component in an electronic instrument,
> and you will get much more for your money if it is able to
> accommodate at least several different tunings in this way.
>
> And even if you're doing an acoustic instrument (capable of only a
> single tuning), why not use a generalized keyboard that was designed
> for multiple tunings? We need to think through these things with a
> broad perspective if we are going to avoid making qwerty-type
> decisions that, should a new keyboard ever catch on, a lot of people
> are going to regret years later.
>
> > I highly recommend Dvorak. It seems to be the main factor
> > in the disappearance of my hand pain last year.
>
> Now there's something to be said for a superior design!
>
> --George
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
KXLU 88.9 fm Wed. 8-9pm PST.
live stream kxlu.com

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗prophecyspirit@aol.com

🔗Haresh BAKSHI <hareshbakshi@hotmail.com>

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "Haresh BAKSHI" <hareshbakshi@h...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> >>>> ......................
> > I would counsel those who would design keyboards for microtonal
> > scales not to make them single-purpose (i.e., one for 19-ET,
another
> > for 22-ET, another for 31-ET, another for 72-ET, etc.), but to
use a
> > generalized arrangement that will accommodate multiple tunings
with
> > the same fingering patterns in all keys. >>>>
> ................
> >>>> why not use a generalized keyboard that was designed
> > for multiple tunings? >>>>
>
> Hello George, any suggestions for the generalized keybord? I am
trying to design a harmonium keyboard, primarily for the 22-shruti
Indian scale.
>
> Thanks,
> Haresh.

Hello, Haresh.

Please refer to the (zipped) file which I have put here:

/tuning-
math/files/secor/kbds/KbScal5c.zip

This contains a diagram of the generalized keyboard that was used on
two Scalatrons that were built in the 1970s, with 31 separate tones
per octave and 5 key colors. (A third instrument was given a
keyboard with 9 colors and 55 or 56 tones per octave -- I don't know
which.) This adaptation of the Bosanquet generalized keyboard was a
collaboration between Richard Harasek (of Motorola), Erv Wilson, and
myself. The elliptical keys were made of molded plastic, but for a
harmonium you would probably find it easier to use elongated
hexagons, which is Erv Wilson's preference (see the links I have
given below).

The keyboard geometry is such that any tonal system consisting of a
single series or circle of fifths can be mapped so that any interval,
scale, or chord may be easily transposed by starting at a different
position and using exactly the same fingering pattern. You will find
C as the white key farthest to the left, and the C major scale is
played on the white keys. Five sharp keys (in each octave) are in
black, and five flat keys are in red. Immediately beyond the black
keys are blue keys, and in front of the red keys are green keys;
these are mostly double sharps and double flats, but they can also
function in other roles, depending on the tuning. (The remaining
near blue and far green and red keys were hard-wired duplicates that
were used specifically for the 31-division of the octave; in most
instances these are not used for tunings having fewer tones. It
would be best for you to ignore these.)

There are two important things to observe:

1) The key colors occur as alternating sets of 7 light-colored and 5
dark-colored keys. You do not have to use the colors that we used
for the Scalatron, but I would strongly advise you to retain the
alternating 7-light 5-dark pattern.

2) There is a vertical scale at the left side (with numbered G's,
multiples of the generating interval of a fifth) that enables you to
determine how many fifths in the series each key is located with
respect to C.

Now to address your question more specifically, I will assume that
the 22 shrutis can be assigned the following ratios (and would 1/1 be
Sa?):

0 1/1
1 256/243
2 16/15
3 10/9
4 9/8
5 32/27
6 6/5
7 5/4
8 81/64
9 4/3
10 27/20
11 45/32
12 729/256
13 3/2
14 128/81
15 8/5
16 5/3
17 27/16
18 16/9
19 9/5
20 15/8
21 243/128
22 2/1

There are two possible ways to map these onto the Bosanquet
keyboard. If the srutis are treated as a 22-division of the octave,
then they could be mapped the same way as 22-ET, in which the fifth
is 13 degrees. An octave of keys would then consist of the following
degrees:

blue keys: 2, 6, 10, 11, 15, 19, 1
black keys: 3, 7, 12, 16, 20
white keys: 0, 4, 8, 9, 13, 17, 21, 22
red keys: 1, 5, 10, 14, 18
green keys: 20, 2, 6, 7, 11, 15, 19

This is also the 22-ET mapping by Erv Wilson to which Kraig Grady
referred you here on page 13:

http://www.anaphoria.com/xen3a.PDF

Notice that some of the blue and black keys are duplicate pitches of
the green and red ones. Also, any two adjacent keys along any row or
column in any direction will be separated by the same number of
degrees. Thus, like intervals in the system of shrutis will be
played with like patterns. However, like patterns will not always
give you like intervals, since shrutis of the same number of degrees
vary considerably in size.

For this reason I would recommend mapping these onto the keyboard in
a different way:

blue keys: -, -, -, 10, -, -, -
black keys: 2, 6, 12, 15, 19
white keys: 0, 4, 8, 9, 13, 17, 21, 22
red keys: 1, 5, 11, 14, 18
green keys: -, 3, 7, -, -, 16, 20

This is also the way Erv Wilson mapped it. If you go here, you will
see how he employed the hexagonal key shape (page 5):

http://www.anaphoria.com/xen2.PDF

Here the shrutis are treated as a series of fifths (rather than a
circle), so that there are no duplicate keys. As before, like
intervals will be played with like patterns, but like patterns will
also give you like intervals (or very nearly so, since two of the
fifths in the series are false by a schisma).

Since this is the same pattern in which 41-ET and 53-ET would be
mapped, any two keys with the same lateral placement will differ in
pitch by a comma (80:81), with the key farther from the player having
the higher pitch.

All of this has assumed that C would be 1/1, but you could just as
easily choose another key, as long as you moved everything else so
that the relative positions were maintained. Or you could tune the
shrutis as a schismic temperament, which would give you the option of
adding as many more tones to the series as you wish. This would
allow you to have a "movable" 1/1 (or movable Sa) so that the
instrument could accompany singers with different vocal ranges (or is
there now a pitch standard of some sort?). (Or would this be of any
use?)

I hope that this information will be helpful to you. Also, please
look for a response that I will be making to Carl Lumma to learn more
about how this keyboard was used on the Scalatron.

--George

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> Any retrospective comments on the Generalized-keyboard Scalatron?
> Still playing her?
>
> -Carl

Yes, but time has taken its toll. The instrument is now 27 years old
and there are a few things here and there that don't work anymore --
probably due to solder joints that have crystallized. One of these
days I'm going to have to open the thing up and remelt some of them.

As for retrospective comments, I have quite a few.

I am often given most of the credit for the application of the
generalized keyboard to the Scalatron, but the truth is that Erv
Wilson and Dick Harasek (president of Motorola Scalatron) had as much
to do with it as I did (not to mention our dependence on the prior
work of Bosanquet and Fokker). In collaboration, we carefully
considered all of the details and got everything right: the size and
shape of the keys, the use of slightly convex key surfaces and
placement of all the keys in a single plane (which together make it
very easy to play a glissando anywhere in any direction), the proper
front-to-back slant (17 degrees) of the keyboard (to minimize arm
fatigue), employment of touch coding on the sharp and flat keys, and
effective use of color (on which I received quite a bit of positive
feedback). To this day, I can't think of a single thing that we
should have done differently.

I found that anyone sufficiently familiar with the conventional
keyboard could perceive diatonic patterns on the new keyboard within
a matter of seconds, so that it was possible to play simple
conventional pieces with the tuning in either 12, 19, or 31-ET in
almost no time at all. And having the same fingering patterns in
every key made learning the new microtonal intervals simple and
straightforward.

Here's an interesting anecdote. I have always kept the instrument
covered with a bedsheet when it's not being used. After I had it for
several months, I thought it would be fun trying to play it with the
sheet on it. To my surprise (and great delight), it was almost as
easy as playing it without the sheet. Sometimes when I had a guest
at the house who had not seen the instrument before, I would first
play it with the sheet on it without revealing what was underneath,
which made for a rather surrealistic experience to say the least.

I would also like to make a few comments about the keyboard layout
and dimensions, for which you should also refer to this (zipped) file:

/tuning-
math/files/secor/kbds/KbScal5c.zip

The lateral keys are spaced 7/8 inch (center to center) as on the
piano keyboard, but since there are only 6 lateral keys to an octave,
the octave distance is one key closer (good news for all you Scriabin
fans). After using it for a short time I realized that the keys
would not even have to be that large. On the piano keyboard one must
be able to fit a finger between two black keys to depress the narrow
part of a white key, but on the generalized Scalatron keyboard that
problem does not occur.

The duplicate keys are important, not only to permit uniform
fingering patterns in all keys, but to provide an option so that the
thumb does not have to reach for the more distant keys, which would
produce a strain on the hand (which is the reason why piano keys are
so long). As the number of tones in the octave is increased, the
duplicate keys get farther apart and become less useful. In my
judgment, anything above 31 tones/octave is too far to reach (both
for duplicate keys and for harmonically extended chords) with keys of
this size, so unless the keys were made smaller, I would not
recommend this keyboard for larger divisions of the octave. (The
physical size of the key switches used on the generalized keyboard
Scalatron did not make a closer distance possible.)

For 41-ET or 72-ET (which is not possible to map on the Bosanquet
arrangement), I would instead advise using a generalized decimal
keyboard arrangement (which will also handle 31; also see my posting
#37151):

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

The only thing wrong with the Scalatron was that it was too
expensive; there would be more customers if the price were lower, but
the price could be lower only if there were more customers, so
Motorola pulled the plug on the Scalatron venture after only a few
years.

--George

🔗Carl Lumma <clumma@yahoo.com>

>As for retrospective comments, I have quite a few.

Thanks, George, for the update!!

>On the piano keyboard one must be able to fit a finger between
>two black keys to depress the narrow part of a white key, but
>on the generalized Scalatron keyboard that problem does not occur.

On the piano this is important because the middle fingers are
longer than the thumb. 'Playing' Wilson's drawings, I find
my middle finger is often forced too far under the palm to reach
many chords (ie minor triads in root position). What has been
your experience with this on the generalized Scalatron?

>The duplicate keys are important, not only to permit uniform
>fingering patterns in all keys, but to provide an option so that
>the thumb does not have to reach for the more distant keys, which
>would produce a strain on the hand (which is the reason why piano
>keys are so long).

Ah. The keys aren't marked on KbScal5C.bmp, so I can't see the
dupes.

>In my judgment, anything above 31 tones/octave is too far to
>reach (both for duplicate keys and for harmonically extended
>chords) with keys of this size, so unless the keys were made
>smaller, I would not recommend this keyboard for larger divisions
>of the octave.

That's ok, up to 31 tones should keep us busy for quite a while!

>For 41-ET or 72-ET (which is not possible to map on the Bosanquet
>arrangement),

To be fair, Bosanquet gives positive and double-positive
mappings...

>I would instead advise using a generalized decimal keyboard
>arrangement (which will also handle 31; also see my posting
>#37151):

Looks cool. IIRC the Fokker organ is left-rising.

One question: Why are the ovals on the generalized Scalatron
right-pointing?

-Carl

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> >As for retrospective comments, I have quite a few.
>
> Thanks, George, for the update!!
>
> >On the piano keyboard one must be able to fit a finger between
> >two black keys to depress the narrow part of a white key, but
> >on the generalized Scalatron keyboard that problem does not occur.
>
> On the piano this is important because the middle fingers are
> longer than the thumb. 'Playing' Wilson's drawings, I find
> my middle finger is often forced too far under the palm to reach
> many chords (ie minor triads in root position). What has been
> your experience with this on the generalized Scalatron?

I'm not sure which tuning this was for, but by process of elimination
I would guess that it's 22, where the minor third above C would be on
the green key vertically below E (F-flat) in the diagram in this
(zipped) file:

/tuning-
math/files/secor/kbds/KbScal5c.zip

In 22 it would be better to play this with the index finger on the
duplicate blue key vertically above D (C-double-sharp).

But suppose that this is a schismic temperament (i.e., series of
fifths, not a circle) and there are no duplicate keys. That C triad
using the F-flat key would now be a major triad, the green keys being
a comma lower than the white keys (so that this is now E\). The
major triad is not too difficult to play in its inversions, but in
root position bending the middle finger downward is not the best way
to do it. Instead, play the C with your index finger (observing that
C and G aren't as far apart as they are on the Halberstadt) and cross
your thumb under to get the E\.

This is the exact same technique that I would use on my decimal
keyboard layout for both the major and subminor triads:

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

Notice that my decimal keyboard design is right-rising. This puts
both the major and subminor thirds, 5/4 and 7/6, (vertically) below
the root and fifth, 1/1 and 3/2, of their triads. If the keyboard
were left-rising, they would be (vertically) above the root and
fifth, so that this technique could not be employed. One unintuitive
consequence of this is that the tones in vertical columns *drop* in
pitch as you go *up* the column, but on the other hand, the generator
scale at the left (the generating interval being a ^secor^) *does* go
up the way you would expect, and the 3/2 is in the *positive*
direction, so it^s not completely unintuitive to do it this way.

> >The duplicate keys are important, not only to permit uniform
> >fingering patterns in all keys, but to provide an option so that
> >the thumb does not have to reach for the more distant keys, which
> >would produce a strain on the hand (which is the reason why piano
> >keys are so long).
>
> Ah. The keys aren't marked on KbScal5C.bmp, so I can't see the
> dupes.

The extreme top and bottom red, green, and blue keys are the hard-
wired duplicates for 31-ET, so you can easily match these with their
duplicates, because they have the same colors.

For most divisions less then 31 (one exception is 29, and another is
my 19+3 temperament described in message #38287), I stay within the
green-blue color boundaries, so that only 31 keys per octave are
used. For 19 tones there are thus 12 duplicates, for 17 there are 14
duplicates, and for 22 there are 9 duplicates. Of course, the more
duplicates the better (up to a point), but this amount of duplication
works reasonably well, even for 22.

Like the Microzone keyboard, the colored key tops of the generalized
Scalatron keyboard can be easily switched around to form different
patterns, but I've never found it necessary to do that, because all
of the intervals, scales, and chords are played according to fixed
patterns, including the keyboard vector for a (unison) duplicate
key. Once the patterns are learned, you do quite a lot by touch, so
you don't have to look at the keyboard that often, which doesn't make
it all that necessary to have something like lights in the keys that
would change color with the tuning (as Mats suggested; by the way
Mats, the key switches that were used for the Scalatron actually did
have a provision for lighted keys, and we did briefly discuss the
possibility of doing something like this with an on/off lighted
pattern that would change with the tuning). Of course, in a single-
tuning acoustic instrument (such as the 19+3 accordion that I
proposed in the message referenced above), it would make sense to
have all duplicate pairs of keys the same color.

Getting back to your question about seeing the duplicates, if you
again look at the diagram in the (zipped) file:

/tuning-
math/files/secor/kbds/KbScal5c.zip

Go to the leftmost white key, which is C, and observe that the small
cross in its center is in vertical alignment with the zero G mark in
the scale just to the left. If you want to find its duplicate in 19-
ET, just go up to the +19 marker in that scale and find the key
center that is at the same height. In this case it's a green key
that's beyond the blue-green color boundary, so it's not valid on
this 31-tone hard-wired keyboard. But at least you've found the
keyboard vector for duplicates in 19, so if you start at the red D-
flat adjacent to C (at -5G) and go up 19 marks, you'll come to its
duplicate at +14G, the blue key vertically aligned with D. In
essence, what we're doing is going through a series of fifths 19
places, which brings us around a circle of 19 back to our starting
tone.

You can do the same thing with any other division of the octave that
will map onto this keyboard. The point here is that, the larger the
division, the farther apart (vertically) will be the duplicates.

> >In my judgment, anything above 31 tones/octave is too far to
> >reach (both for duplicate keys and for harmonically extended
> >chords) with keys of this size, so unless the keys were made
> >smaller, I would not recommend this keyboard for larger divisions
> >of the octave.
>
> That's ok, up to 31 tones should keep us busy for quite a while!

If you want JI that includes pairs of tones separated by a comma, I
find that a 29-tone mapping is particularly useful. The hard-wired
duplicate keys are one key to the right of their proper locations,
but their color coding is correct, which somewhat compensates for
that.

> >For 41-ET or 72-ET (which is not possible to map on the Bosanquet
> >arrangement),
>
> To be fair, Bosanquet gives positive and double-positive
> mappings...

I meant that 72-ET is not possible, since it is not a single circle
or series of fifths.

> >I would instead advise using a generalized decimal keyboard
> >arrangement (which will also handle 31; also see my posting
> >#37151):
>
> Looks cool. IIRC the Fokker organ is left-rising.
>
> One question: Why are the ovals on the generalized Scalatron
> right-pointing?

It's just the most efficient way to use up the available space when
the tones 12G's apart are kept vertically aligned. If you want to
see an example of a circular key sharp, here's a diagram for the
treble (right-hand) buttons for my 19+3 accordion design, where the
vertical alignment is not maintained:

/tuning-
math/files/secor/kbds/KbAc19p3.gif

You will be happy to see that I did label the buttons (this being for
an instrument with a fixed, albeit, multi-purpose tuning).

--George

🔗Carl Lumma <clumma@yahoo.com>

>>On the piano this is important because the middle fingers are
>>longer than the thumb. 'Playing' Wilson's drawings, I find
>>my middle finger is often forced too far under the palm to reach
>>many chords (ie minor triads in root position). What has been
>>your experience with this on the generalized Scalatron?
>
>I'm not sure which tuning this was for,

Many I've seen from Erv's xh articles (duplicates don't usually
appear on these diagrams).

>But suppose that this is a schismic temperament (i.e., series of
>fifths, not a circle) and there are no duplicate keys. That C
>triad using the F-flat key would now be a major triad, the green
>keys being a comma lower than the white keys (so that this is now
>E\). The major triad is not too difficult to play in its
>inversions, but in root position bending the middle finger downward
>is not the best way to do it. Instead, play the C with your index
>finger (observing that C and G aren't as far apart as they are on
>the Halberstadt) and cross your thumb under to get the E\.

Ah....!

>Like the Microzone keyboard, the colored key tops of the
>generalized Scalatron keyboard can be easily switched around
>to form different patterns,

Cool! You really did get a lot right.

>Getting back to your question about seeing the duplicates, if
>you again look at the diagram in the (zipped) file:
//
>Go to the leftmost white key, which is C, and observe that the
>small cross in its center is in vertical alignment with the zero
>G mark in the scale just to the left. If you want to find its
>duplicate in 19-ET, just go up to the +19 marker in that scale
>and find the key center that is at the same height. In this case
>it's a green key that's beyond the blue-green color boundary, so
>it's not valid on this 31-tone hard-wired keyboard. But at least
>you've found the keyboard vector for duplicates in 19, so if you
>start at the red D-flat adjacent to C (at -5G) and go up 19 marks,
>you'll come to its duplicate at +14G, the blue key vertically
>aligned with D. In essence, what we're doing is going through a
>series of fifths 19 places, which brings us around a circle of 19
>back to our starting tone.

Ah, ok, cool. Still might be nice to have a labeled-version, say
of the layout you use most often, for people to gaze upon.

>>One question: Why are the ovals on the generalized Scalatron
>>right-pointing?
>
>It's just the most efficient way to use up the available space
>when the tones 12G's apart are kept vertically aligned.

Couldn't the ovals be straight, long axis perpendicular to the
player? Not sure how that would waste space or threaten vert.
alignment...

-Carl

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> >>On the piano this is important because the middle fingers are
> >>longer than the thumb. 'Playing' Wilson's drawings, I find
> >>my middle finger is often forced too far under the palm to reach
> >>many chords (ie minor triads in root position). What has been
> >>your experience with this on the generalized Scalatron?
> >
> >I'm not sure which tuning this was for,
>
> Many I've seen from Erv's xh articles (duplicates don't usually
> appear on these diagrams).
>
> >But suppose that this is a schismic temperament (i.e., series of
> >fifths, not a circle) and there are no duplicate keys. That C
> >triad using the F-flat key would now be a major triad, the green
> >keys being a comma lower than the white keys (so that this is now
> >E\). The major triad is not too difficult to play in its
> >inversions, but in root position bending the middle finger downward
> >is not the best way to do it. Instead, play the C with your index
> >finger (observing that C and G aren't as far apart as they are on
> >the Halberstadt) and cross your thumb under to get the E\.
>
> Ah....!
>
> >Like the Microzone keyboard, the colored key tops of the
> >generalized Scalatron keyboard can be easily switched around
> >to form different patterns,
>
> Cool! You really did get a lot right.
>
> >Getting back to your question about seeing the duplicates, if
> >you again look at the diagram in the (zipped) file:
> //
> >Go to the leftmost white key, which is C, and observe that the
> >small cross in its center is in vertical alignment with the zero
> >G mark in the scale just to the left. If you want to find its
> >duplicate in 19-ET, just go up to the +19 marker in that scale
> >and find the key center that is at the same height. In this case
> >it's a green key that's beyond the blue-green color boundary, so
> >it's not valid on this 31-tone hard-wired keyboard. But at least
> >you've found the keyboard vector for duplicates in 19, so if you
> >start at the red D-flat adjacent to C (at -5G) and go up 19 marks,
> >you'll come to its duplicate at +14G, the blue key vertically
> >aligned with D. In essence, what we're doing is going through a
> >series of fifths 19 places, which brings us around a circle of 19
> >back to our starting tone.
>
> Ah, ok, cool. Still might be nice to have a labeled-version, say
> of the layout you use most often, for people to gaze upon.

I jump back and forth from one tuning to another much of the time,
and what I use most often at any given time depends on what I'm
concentrating on at the time. Why don't I just give you the 31-ET
mapping, which is the tuning that I used most when I first got the
instrument:

/tuning-
math/files/secor/kbds/KbScal31.zip

> >>One question: Why are the ovals on the generalized Scalatron
> >>right-pointing?
> >
> >It's just the most efficient way to use up the available space
> >when the tones 12G's apart are kept vertically aligned.
>
> Couldn't the ovals be straight, long axis perpendicular to the
> player? Not sure how that would waste space or threaten vert.
> alignment...

There's no way to do it without making the keys much smaller and
wasting a lot of space between them. Just try mentally rotating the
D and E-flat keys counter-clockwise slightly, and you'll see that the
bottom of one will bump into the top of the other. You'd have to
make all of the keys shorter, which would leave a lot of space
between D and D-flat, E and E-flat, etc.

--George

🔗Carl Lumma <clumma@yahoo.com>

🔗prophecyspirit@aol.com

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> [George Secor wrote...]
> > I jump back and forth from one tuning to another much of the
time,
> > and what I use most often at any given time depends on what I'm
> > concentrating on at the time. Why don't I just give you the 31-
ET
> > mapping, which is the tuning that I used most when I first got
the
> > instrument:
> >
> > /tuning-
> > math/files/secor/kbds/KbScal31.zip
>
> Excellent, thanks! My vote for putting a gif version on the main
> page. :)

Thank you for your kind words of appreciation (and you too, Joseph).
This is a diagram that I did last year for my book-in-progress, and I
tried to give the keys a 3-D appearance with subtle changes in color
to illustrate the slightly convex key surfaces. When I tried saving
this as a gif file, not only did the subtleties disappear, but the
blue and green keys came out looking very different (too garish), and
I wasn't able to fix them to my satisfaction, hence the zipped file.

> >>Couldn't the ovals be straight, long axis perpendicular to the
> >>player? Not sure how that would waste space or threaten vert.
> >>alignment...
> >
> >There's no way to do it without making the keys much smaller and
> >wasting a lot of space between them. Just try mentally rotating
> >the D and E-flat keys counter-clockwise slightly, and you'll see
> >that the bottom of one will bump into the top of the other. You'd
> >have to make all of the keys shorter, which would leave a lot of
> >space between D and D-flat, E and E-flat, etc.
>
> If you turn your head you'll see that it's possible. The octaves
> will no longer be equidistant from the player, which must be what
> you meant by vert. alignment...

No, that's horizontal (or lateral) alignment. By vertical alignment
I mean that lines connecting the centers of corresponding black and
red keys (sharps and flats) are exactly vertical. So we're keeping
keys aligned in both directions. This was Erv Wilson's idea, and I
am in complete agreement.

In my right-hand accordion keyboard diagram (with circular buttons) I
eliminated the vertical alignment, which shifted the sharps leftward,
relative to the flats. For the tuning used in this particular
instance (19-tone well temperament) the sharps are lower in pitch
than the flats, so it's not inappropriate to do this. On the
Scalatron they could be either lower or higher (depending on the
tuning), so it is best to have the vertical alignment.

> I'm guessing this can be solved
> in the mapping, but I'll spare you the claim until I can
> demonstrate it.

Now that I think about it, Erv Wilson also dispensed with the
vertical alignment in his 19-tone clavichord design (beginning on
page 6):

http://www.anaphoria.com/xen456.PDF

There he retained his elongated hexagons but gave them a vertical
axis. As I recall he was rather delighted at how well the Bosanquet
geometry worked for a 19-tone octave.

> I guess my question is, isn't the space wasted
> somewhat anyway, since unless one turns the hand his fingers do
> not move along the long axis of the keys?

You can depress a key near either end of its surface (handy if you
have to stretch) without turning the hand, so I wouldn't consider it
wasted space.

--George

🔗Carl Lumma <clumma@yahoo.com>

>Thank you for your kind words of appreciation (and you too,
>Joseph). This is a diagram that I did last year for my book-
>in-progress, and I tried to give the keys a 3-D appearance
>with subtle changes in color to illustrate the slightly convex
>key surfaces. When I tried saving this as a gif file, not
>only did the subtleties disappear, but the blue and green keys
>came out looking very different (too garish), and I wasn't able
>to fix them to my satisfaction, hence the zipped file.

With enough colors in the gif palette and/or the right amount
of dither, it can look nearly flawless. Also FYI, there are
filters in Kai's Power Tools (and elsewhere, I'm sure) that can
do pretty-good instant concave and convex surfaces.

>>If you turn your head you'll see that it's possible. The
>>octaves will no longer be equidistant from the player, which
>>must be what you meant by vert. alignment...
>
>No, that's horizontal (or lateral) alignment. By vertical
>alignment I mean that lines connecting the centers of
>corresponding black and red keys (sharps and flats) are exactly
>vertical. So we're keeping keys aligned in both directions.
>This was Erv Wilson's idea, and I am in complete agreement.

Hmm...

>>I guess my question is, isn't the space wasted somewhat
>>anyway, since unless one turns the hand his fingers do
>>not move along the long axis of the keys?
>
>You can depress a key near either end of its surface (handy
>if you have to stretch) without turning the hand, so I wouldn't
>consider it wasted space.

Geez, you're right.

-Carl

History of qwerty keyboard

🔗Robert Walker <robertwalker@ntlworld.com>

🔗Carl Lumma <clumma@yahoo.com>

🔗prophecyspirit@aol.com

🔗gdsecor <gdsecor@yahoo.com>

🔗Haresh BAKSHI <hareshbakshi@hotmail.com>

🔗Carl Lumma <clumma@yahoo.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗prophecyspirit@aol.com

🔗Haresh BAKSHI <hareshbakshi@hotmail.com>

🔗gdsecor <gdsecor@yahoo.com>

🔗gdsecor <gdsecor@yahoo.com>

🔗Carl Lumma <clumma@yahoo.com>

🔗gdsecor <gdsecor@yahoo.com>

🔗Carl Lumma <clumma@yahoo.com>

🔗gdsecor <gdsecor@yahoo.com>

🔗Carl Lumma <clumma@yahoo.com>

🔗prophecyspirit@aol.com

🔗gdsecor <gdsecor@yahoo.com>

🔗Carl Lumma <clumma@yahoo.com>

🔗Jon Szanto <JSZANTO@ADNC.COM>

🔗Carl Lumma <clumma@yahoo.com>

🔗Jon Szanto <JSZANTO@ADNC.COM>

🔗gdsecor <gdsecor@yahoo.com>

🔗Jon Szanto <JSZANTO@ADNC.COM>