Yahoo Tuning Groups Ultimate Backup makemicromusic Re: [MMM] 3 new 22-tet KBD design rough ideas

> Whoa, those look like a nightmare to build (and play).
>
> -Carl

Eh, I'm trying to stay optimistic. Building a keyboard from scratch
isn't going to be easy at any rate. The first design is actually a
generalized design applied to a traditionally-shaped keyboard. There
are lots of uniform patterns that occur on it, since a horizontal
ascension goes up exactly 3 steps of 22 and a vertical ascenion goes
up by 1. It's either that or use a non-uniform design.

Consider also that the keys will not be "cut into each other" like on
a regular keyboard but will actually be thin keys overlayed on top of
each other in different layers, with each layer having its own anchor
point for contact switches. We haven't done any ergonomic
calculations yet, so the shapes on those designs are merely to give
an idea of the layout; they have nothing to do with actual
proportions.

And I should ask, since you are rather pessimistic about these
designs: do you have a better idea? 22 is not the easiest system to
design a keyboard for.

🔗Carl Lumma <ekin@...>

>> Whoa, those look like a nightmare to build (and play).
>
>Eh, I'm trying to stay optimistic. Building a keyboard from scratch
>isn't going to be easy at any rate. The first design is actually a
>generalized design applied to a traditionally-shaped keyboard. There
>are lots of uniform patterns that occur on it, since a horizontal
>ascension goes up exactly 3 steps of 22 and a vertical ascenion goes
>up by 1. It's either that or use a non-uniform design.

Have you looked at

http://lumma.org/stuff/carlos-keyboard.jpg

>Consider also that the keys will not be "cut into each other" like on
>a regular keyboard but will actually be thin keys overlayed on top of
>each other in different layers, with each layer having its own anchor
>point for contact switches. We haven't done any ergonomic
>calculations yet, so the shapes on those designs are merely to give
>an idea of the layout; they have nothing to do with actual
>proportions.
>
>And I should ask, since you are rather pessimistic about these
>designs: do you have a better idea? 22 is not the easiest system to
>design a keyboard for.

I don't have a scan of Bosanquet's layout for 22, but I should
look at it re. porcupine8, superpythagorean7, and pajara10...

I'd assume uniformity, which radically cuts down the number of
possible layouts -- two axes, each with increments < 5. I'd draw
most or all of them where pitch rises to the right on a rectangular
grid, and try fingering the scales of the three systems. Any time
I ran into a snag, I'd ask myself if changing the angle between
the two axes would help.

Once I'd picked a layout, I'd decide what shape of keys I wanted,
and whether I wanted them arranged on a plane or in 3-D.

Is this not the sensible way to do it?

-Carl

PS- If I explicitly didn't want uniformity, I'd use a genetic
algorithm to find a layout, based on a measure of the uniformity
of the pajara tetrads (which would tend to produce a non-uniform
overall layout).

🔗Carl Lumma <ekin@...>

🔗Kraig Grady <kraiggrady@...>

🔗Igliashon Jones <igliashon@...>

> Have you looked at
>
> http://lumma.org/stuff/carlos-keyboard.jpg

I have indeed, as well as Erv Wilson's generalized design for 22.
These work mighty fine for diatonic, but not for the others. I can't
honestly see how that design would be any easier to build or play
than any of my current ideas.

> I'd assume uniformity, which radically cuts down the number of
> possible layouts -- two axes, each with increments < 5. I'd draw
> most or all of them where pitch rises to the right on a rectangular
> grid, and try fingering the scales of the three systems. Any time
> I ran into a snag, I'd ask myself if changing the angle between
> the two axes would help.
>
> Once I'd picked a layout, I'd decide what shape of keys I wanted,
> and whether I wanted them arranged on a plane or in 3-D.
>
> Is this not the sensible way to do it?

That's actually what I've been attempting, though not so systematic.
My current favorite is the uniform one with Y axis = 1 increment and
X axis = 3. This way, diatonic scales go across a staggered
diagonal, decatonics go in a series of rising "M" shapes, and
porcupine-8 goes almost entirely horizontal with one irregularity.
Basically, this design is right in the middle of all the systems,
since decatonics are mainly 2-increment intervals and diatonics are
mainly 4-increment. 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.

This would all be much simpler if 1)we weren't worried about octaves
fitting in a one-hand reach and 2)we weren't using traditionally
shaped keys. As it is though we are trying to come up with something
that is not just for MIDI, but that could feasibly be applied to an
acoustic piano as well (albeit with heavy modifications).

> PS- If I explicitly didn't want uniformity, I'd use a genetic
> algorithm to find a layout, based on a measure of the uniformity
> of the pajara tetrads (which would tend to produce a non-uniform
> overall layout).

You lost me on that one. Genetic algorithm? Measure of the
uniformity of pajara tetrads? I have no idea how I'd do that.
Please remember that I have no background in math or science (or even
music theory for that matter; in this field I am completely
unschooled!).

🔗Carl Lumma <ekin@...>

>> Have you looked at
>>
>> http://lumma.org/stuff/carlos-keyboard.jpg
>
>I have indeed, as well as Erv Wilson's generalized design for 22.
>These work mighty fine for diatonic, but not for the others. I can't
>honestly see how that design would be any easier to build or play
>than any of my current ideas.

I referred you to the above only re. the shape/design of the keys.

>> I'd assume uniformity, which radically cuts down the number of
>> possible layouts -- two axes, each with increments < 5. I'd draw
>> most or all of them where pitch rises to the right on a rectangular
>> grid, and try fingering the scales of the three systems. Any time
>> I ran into a snag, I'd ask myself if changing the angle between
>> the two axes would help.
>>
>> Once I'd picked a layout, I'd decide what shape of keys I wanted,
>> and whether I wanted them arranged on a plane or in 3-D.
>>
>> Is this not the sensible way to do it?
>
>That's actually what I've been attempting, though not so systematic.
>My current favorite is the uniform one with Y axis = 1 increment and
>X axis = 3. This way, diatonic scales go across a staggered
>diagonal, decatonics go in a series of rising "M" shapes, and
>porcupine-8 goes almost entirely horizontal with one irregularity.
>Basically, this design is right in the middle of all the systems,
>since decatonics are mainly 2-increment intervals and diatonics are
>mainly 4-increment. 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.

Oh, so you're now in favor of uniform. Sorry, didn't catch that!

>This would all be much simpler if 1)we weren't worried about octaves
>fitting in a one-hand reach and 2)we weren't using traditionally
>shaped keys. As it is though we are trying to come up with something
>that is not just for MIDI, but that could feasibly be applied to an
>acoustic piano as well (albeit with heavy modifications).

Cool. If you're interested in microtonal piano, you might like to
see Norman Henry's project in Oakland. Write me off-list or give
me a call -- (510) 306-7305.

>> PS- If I explicitly didn't want uniformity, I'd use a genetic
>> algorithm to find a layout, based on a measure of the uniformity
>> of the pajara tetrads (which would tend to produce a non-uniform
>> overall layout).
>
>You lost me on that one. Genetic algorithm?

First, you find a way to describe a layout with 'genes'. In the
uniform case, it'd be a string like 90,+1,-3 that tells the angle
between axes and then the increment for each axis. You then define
a rule for combining two of these strings into a child string (like
component-wise addition) and. . .

>Measure of the uniformity of pajara tetrads? I have no idea how
>I'd do that.

. . .You find all the tetrads in the decatonic scale on the keyboard
and see how alike their fingering patterns are. Like, to play the
triads in a C-major scale on a piano, you can pretty much make a
claw-hand and move your arm. My thinking goes: if there's some
advantage to not having uniformity in pitch space ("generalized" or
whatever you want to call it), you might as well have uniformity in
scale space -- the Halberstadt (the name of the traditional 7/5
layout) seems to do fairly well at this for the diatonic scale.

To "see how alike their fingering patterns are" you might lay the
chords' key patterns on a grid (in root position, say). Then
average the patters per-note (imagine them overlapping) and finally
use some "measure of central tendency" (statistics) to describe
the deviations from the average.

So for the genetic algorithm, you start with a population of random
strings... 45,+2,-4 etc etc. and breed them, round after round,
killing of the ones for which the pajara tetrads are very different.
At the end, you have pure gold. :)

[In practice, as I've described this, you might wind up with
something where the pajara tetrads are all very similar, but
impossible to finger. So rather that making a rule that measures
their similarity, you might instead decide on an ideal chord
shape in advance and use a rule that measures the total deviation
from that (it's an easier computation, too).]

>Please remember that I have no background in math or science (or
>even music theory for that matter; in this field I am completely
>unschooled!).

Yes, well I'm entirely self-taught and slightly crazy. Let me
know if I lost you. Or maybe you don't care. But if you do, I'm
happy to explain further, on- or off-list.

-Carl