22tet kbd example

Paul,

I wrote:
>Are there any other
> >examples, from other composers, that exhibit this one-to-one functionality
> >(serendipity?).

and you replied:

>The 22-tone keyboard mapping in my paper is an example. The "Decatonic
>Waltz" I performed at the Microthon falls right out of it.

So I went once again to check out the paper (still doesn't want to download
or view as a .pdf, and the html page came up with some of the images
missing...). In the paper you state:

>The symmetrical scale is useful as a basis for a keyboard mapping of
>22-equal. To wit: leaving every "E" on the standard keyboard out of the
>mapping gives two keyboard octaves to one acoustical octave. The black
>keys then form a maximally even scale

...which isn't exactly what I was looking for. The Diamond Marimba is both
the physical and aural manifestation of the Tonality Diamond. With a
standardized black/white kbd, you have to first ask to 'ignore' the "E"
keys (even though they are plainly there), and then there are issues of
whether something that is "maximally even" should be represented by groups
of 2's and 3's (the black key groupings).

I'm really looking for as close to a one-to-one correlation as possible,
which this scenario is not. Any other takers?

Cheers,
Jon
`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`
Jonathan M. Szanto : Corporeal Meadows - Harry Partch, online.
jszanto@adnc.com : http://www.corporeal.com/
`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`'`

Jon Szanto wrote,

>With a
>standardized black/white kbd, you have to first ask to 'ignore' the "E"
>keys (even though they are plainly there), and then there are issues of
>whether something that is "maximally even" should be represented by groups
>of 2's and 3's (the black key groupings).

Good point! Steven Rezsutek, inspired by my paper, built a keyboard which
addresses these issues. See the very bottom of
http://www.cix.co.uk/~gbreed/instrum.htm. This is the "natural" keyboard for
the decatonic system in 22, just as the standard layout is the "natural"
keyboard for the diatonic system in 12.

The images don't seem to be coming up today :( But basically, it's just like
a standard keyboard but with black keys in groups of 5 instead of
alternating 2s and 3s.

Steve Rezsutek's keyboard does seem to fit the parameter, but I'd question
whether this qualifies as a "natural" keyboard for 22tET. I admit I'm grossly
biased but the adaption of the common 12-tone keyboard to its predecessors was
not one simply of subtracting two keys to make an octave - rather it improved
upon their navigability (to an extent, independent of tuning) without
sacrificing intervallic span, neither of which does this keyboard. Not that I
have a better solution (arguably it's worse), but I chose to go the opposite
direction: less a clearly delineated "natural" scale but a pattern more familiar
and "playable".

Clark

Clark wrote,

>I admit I'm grossly
>biased but the adaption of the common 12-tone keyboard to its predecessors
was
>not one simply of subtracting two keys to make an octave - rather it
improved
>upon their navigability (to an extent, independent of tuning) without
>sacrificing intervallic span . . .

I'm not sure what the predecessors were and how their navigability was
improved upon . . . can you clarify? Anyway, Fokker's 31-tone organ took the
standard 12-tone arrangement and improved upon its navigability (all keys
are fingered the same way) while improving both its tuning and its
resources, without sacrificing intervallic span. Same goes for Bosanquet and
all of Wilson's keyboard designs. Jon, are you listening?

"Paul H. Erlich" wrote:

> I'm not sure what the predecessors were and how their navigability was
> improved upon . . . can you clarify?

I meant for precedent primarily the refined 7- and 8-note per octave keyboards,
and also the older push-pull and thumper manuals. The uniformity of these prior
layouts necessitated labelling each key for navigation, but even a single
disparate key corrects this (I think Lawrence Nalder illustrates one with a
raised Bb).

The common 12-note solution integrates four chromatic keys within the older
framework (or five including Bb) in a pattern both that emphasizes the preferred
scalar mode and reflects the sequential position of each key.

> Anyway, Fokker's 31-tone organ took the
> standard 12-tone arrangement and improved upon its navigability (all keys
> are fingered the same way) while improving both its tuning and its
> resources, without sacrificing intervallic span. Same goes for Bosanquet and
> all of Wilson's keyboard designs.

Colonna's keyboard for the Sambuca lincea also does this, but it seems likely
its genesis was based less on the 12-tone keyboard than on its modal subset -
and that of the older keyboards. My impression is that this applies to the
keyboards above as well.

The transpositional equivalence these embody (I think) doesn't lend itself to
navigation as specifically as the 12-tone; in the same manner as Reszutek's only
relative navigation is embedded so necessitating (again) the labelling of keys.

Clark

>The transpositional equivalence these embody (I think) doesn't lend itself
>to navigation as specifically as the 12-tone; in the same manner as
>Reszutek's only relative navigation is embedded so necessitating (again)
>the labelling of keys.

Clark, it is true that the design of the conventional keyboard allows for
easy navigation by touch. However, I believe transpositional invariance is
a far greater asset, and what's wrong with color-coded keys, or tactile
patterns on the keys (US 5515763)?

Rezsutek's keyboard would probably, in practice, have plenty enough feel
abouts for one to find his way. It has other problems, though. Noticably,
the lack of transpositional invariance. However, I personally think
there's one thing worth giving up TI for: easy access to the scale, and a
consistent fingering pattern for its chords (it seems that TI rules out
uniform fingering for the chords of a generalized diatonic scale...).
However, Rezsutek's keyboard puts the easiest decatonic on all black keys,
which is bass ackward.

But foremost among my problems with this keyboard is my inability to reach
an octave on it. According to my calculations, the average octave span
would be 28" if standard key width was assumed. The good folks over at DS
Keyboards (www.dskeyboards.com) have shown that this width need not be
assumed --- the minimum workable key width turning out an octave span of
about 24". Still too long for your average bear. Reaching an octave is,
in my book, a requirement for any serious xen keyboard, and so the
conclusion: you need more than two ranks of keys!

-Carl

I wrote...

>But foremost among my problems with this keyboard is my inability to reach an
>octave on it. According to my calculations, the average octave span would be
>28" if standard key width was assumed. The good folks over at DS Keyboards
>(www.dskeyboards.com) have shown that this width need not be assumed --- the
>minimum workable key width turning out an octave span of about 24". Still
>too long for your average bear. Reaching an octave is, in my book, a
>requirement for any serious xen keyboard, and so the conclusion: you need
>more than two ranks of keys!

Whoops! All that was cm, not inches!

-Carl

Clark wrote,

>The transpositional equivalence these embody (I think) doesn't lend itself
to
>navigation as specifically as the 12-tone; in the same manner as Reszutek's
only
>relative navigation is embedded so necessitating (again) the labelling of
keys.

On Fokker's keyboard, color (white, black, and blue keys) and on Reszutek's
keyboard, the position of adjacent white keys allow absolute navigation so
no labelling is necessary.

Carl Lumma wrote,

>However, Rezsutek's keyboard puts the easiest decatonic on all black keys,
>which is bass ackward.

That of course follows from my paper. What's wrong with that? The standard
keyboard puts the easiest pentatonic on all black keys -- seems like a great
feature.

>Reaching an octave is,
>in my book, a requirement for any serious xen keyboard, and so the
>conclusion: you need more than two ranks of keys!

Ideally, I'd agree, but for now, unfortunately, most of us have to make do
with standard keyboards. Rather that sit around and wait for multi-rank
keyboards to become affordable, we play with what we can.

Transpositional invariance is a great asset, but especially with large layouts
finding a single note immediately could present problems. My colleague here at
the shop has a hard enough time with the finite, non-repeating computer
keyboard which is still labelled, has tactile cues, and in this case is split.
;)

Paul wrote:

> on Reszutek's
> keyboard, the position of adjacent white keys allow absolute navigation so
> no labelling is necessary.
>
Do they? The 12-tone keyboard likewise has two groups of raised notes, but one
has more than the other: this, on the other hand, has a symmetrical arrangement
and without explicit cues, those of body position, key position from the ends
or position relative to non-keyboard instrument road marks must come into play.

Color and tactile cues seem to work best in conjunction with other means of
differentiating keys. Ivory, ebony, pearwood and rosewood, for instance, all
feel _and_ look different - arranged in tiers of different key sizes and
shapes, they are fairly navigable, too.

Carl wrote:

> [...]there's one thing worth giving up TI for: easy access to the scale, and a
> consistent fingering pattern for its chords[...]
>
That's its purpose in the usual configuration; along with doubled keys, at
least a partially TI keyboard might be possible, and as Steinbuhler's keyboards
show the octave span could be reduced - with the 165mm standard reduced by 7/8
and applied to a 10-note scale, the span would be about 206mm.

The 12-tone keyboard crystallized practically. It allows 1/2" spacing for
unison strings and action parts still with decently sized keys. It maps a scale
nicely for one key, however, with the others compromised, but this is not
wholly objectionable considering that each note is identifiable.

I agree with Carl that for 22-tET two tiers is not enough; I honk my own _horn_
with four. Reszutek's arrangement better reflects the symmetrical decatonic
scale, but I think with too many other compromises for me to consider it
practical.

Clark

Paul wrote:

> Rather that sit around and wait for multi-rank
> keyboards to become affordable, we play with what we can.
>
Yessirree, we do!

Clark

>Paul wrote:

>on Reszutek's
>keyboard, the position of adjacent white keys allow >absolute
navigation so
>no labelling is necessary.

>Do they? The 12-tone keyboard likewise has two groups of raised >notes, but
one has more than the other: this, on the other hand, has a >symmetrical
arrangement and without explicit cues, those of body >position, key position
from the ends or position relative to non->keyboard instrument road marks
must come into play.

Yes, but this is not very different from the problem of finding the correct
octave on a standard keyboard.

To clarify: The Reszutek keyboard looks the same every half-octave, much as
the standard one looks the same every octave.

>I agree with Carl that for 22-tET two tiers is not enough; I honk my own
>_horn_ with four. Reszutek's arrangement better reflects the >symmetrical
decatonic scale, but I think with too many other >compromises for me to
consider it practical.

I've seen your design and it seems absolutely unnavigable beyond one or two
"keys" -- diatonic ones which don't even work in 22-tET. On the other hand,
Wilson's designs afford transpositional invariance so that any scale, once
learned, could be moved around easily. Much as on the guitar, a couple of
inlays would be the only thing required to allow easy position-finding.

>On Fokker's keyboard, color (white, black, and blue keys)

Keeping in mind this does little for the sight-reader...

>Do they? The 12-tone keyboard likewise has two groups of raised notes, but
>one has more than the other: this, on the other hand, has a symmetrical
>arrangement

Judging from my experience on the Halberstadt, there's plenty of distance
in a period of this keyboard to get the right one with your arm alone.

>>However, Rezsutek's keyboard puts the easiest decatonic on all black keys,
>>which is bass ackward.
>
>That of course follows from my paper. What's wrong with that? The standard
>keyboard puts the easiest pentatonic on all black keys -- seems like a great
>feature.

As an extra, sure. But the Halberstadt isn't used for pentatonic music.
Nobody would put the ur-scale on the smaller, farther-away rank.

>>Reaching an octave is, in my book, a requirement for any serious xen
>>keyboard, and so the conclusion: you need more than two ranks of keys!
>
>Ideally, I'd agree, but for now, unfortunately, most of us have to make do
>with standard keyboards. Rather that sit around and wait for multi-rank
>keyboards to become affordable, we play with what we can.

Multi-rank keyboards can be made for dollars a pop on an assembly line.
They can even be made by hand -- even for acoustic instruments -- by the
average woodworker in the average American garage for insubstantial cost.

If you mean, "wait for somebody else to make one for me," then yes, I'm all
using what we've got in the meantime!

-Carl

Some of the pictures on my web page for this are Java applets, because
they have shorter download times than GIFs. I think this is a bit silly
now, and will be replacing them with GIFs or PNGs ... sometime.

Also, I'll add photos of my instruments, which I've already uploaded for
those interested:

http://x31eq.com/pics/DX21.jpg
http://x31eq.com/pics/guitar.jpg

Carl Lumma wrote

>>On Fokker's keyboard, color (white, black, and blue keys)

>Keeping in mind this does little for the sight-reader...

Well, there are plenty of ways around that, like the nipples on computer
keyboards.

The poor orientability is one of the problems I have with my rebuilt DX21.
Also, that it isn't touch sensitive and is quite heavy.

Carl/Paul/Carl:

>>>However, Rezsutek's keyboard puts the easiest decatonic on all black
keys,
>>>which is bass ackward.
>>
>>That of course follows from my paper. What's wrong with that? The
standard
>>keyboard puts the easiest pentatonic on all black keys -- seems like a
great
>>feature.

> As an extra, sure. But the Halberstadt isn't used for pentatonic music.
> Nobody would put the ur-scale on the smaller, farther-away rank.

If I'm playing a pentatonic scale, I use the black keys. Further away
isn't a problem: move the keyboard closer. Size isn't a problem either:
the black keys are smaller, but they're widely spaced, so there's less
chance of hitting two accidentally. Some keyboards are designed to favour
the white notes, but that's not a big problem.

I also find it much easier to play these extended mappings, where an
octave is more than 12 notes, centering on the black keys.

Carl:

>Reaching an octave is, in my book, a requirement for any serious xen
>keyboard, and so the conclusion: you need more than two ranks of keys!

Or two hands. Or smaller keys: you can get MIDI keyboards with mini keys.
I haven't tried any, for playing or rebuilding. But if you were taking
this *seriously*, it might be an option.

>As an extra, sure. But the Halberstadt isn't used for pentatonic music.

Even in the conservatory repertoire, some Chopin and Debussy might surprise
you.

>Nobody would put the ur-scale on the smaller, farther-away rank.

Maybe the dodecatonic, rather than the decatonic, scale is the "ur-scale."
Anyway, it's quite easy to adjust to orienting yourself around the black
keys instead of the white keys. Plus, on the non-Reszutek mapping, the ~3/2
from a D# to the F# an "octave" above is easier to play than that from a D
to the F an "octave" above.

[Graham Breed wrote...]
>>>On Fokker's keyboard, color (white, black, and blue keys)
>>
>>Keeping in mind this does little for the sight-reader...
>
>Well, there are plenty of ways around that, like the nipples on computer
>keyboards.

Did you check out the patent I referenced in my previous post?

http://www.patents.ibm.com/details?&pn=US05515763__

>>Reaching an octave is, in my book, a requirement for any serious xen
>>keyboard, and so the conclusion: you need more than two ranks of keys!
>
>Or two hands. Or smaller keys: you can get MIDI keyboards with mini keys.
>I haven't tried any, for playing or rebuilding. But if you were taking
>this *seriously*, it might be an option.

As I said, after visiting the DS keyboard factory and showroom, the
narrowest keys workable on a 2-rank keyboard, by average hands, are about
1.9cm wide, on average (with about 0.15cm space between keys). This puts
the octaves on Rezsutek's keyboard out of reach of the average hand. You
can make the keys narrower, and the space between them wider, but if you
make the center-to-center distance much less than 2cm, you start to run
into problems (like getting stuck between the blacks).

Two hands, eh? Why didn't I think of that! Who needs four-part harmony,
anyway! (There's no doubt that a helluva lot could be done on a
no-octave-reaching keyboard. There's also no doubt that a helluva lot
_couldn't_ be done.)

-Carl

In-Reply-To: <947320174.21660@onelist.com>
Carl Lumma, digest 480.2, wrote:

> >>Reaching an octave is, in my book, a requirement for any serious xen
> >>keyboard, and so the conclusion: you need more than two ranks of keys!
> >
> >Or two hands. Or smaller keys: you can get MIDI keyboards with mini
> keys.
> >I haven't tried any, for playing or rebuilding. But if you were taking
> >this *seriously*, it might be an option.
>
> As I said, after visiting the DS keyboard factory and showroom, the
> narrowest keys workable on a 2-rank keyboard, by average hands, are
> about
> 1.9cm wide, on average (with about 0.15cm space between keys). This
> puts
> the octaves on Rezsutek's keyboard out of reach of the average hand.
> You
> can make the keys narrower, and the space between them wider, but if you
> make the center-to-center distance much less than 2cm, you start to run
> into problems (like getting stuck between the blacks).

According to the website, DS only make piano keyboards. So those findings
aren't applicable to MIDI keyboards, let alone when they have more than 12
keys to the octave. Steve rebuilt a MIDI keyboard, not a piano.

My old PSR keyboard has white keys 1.8 cm center-center. I found that
playable, but not convenient. A Rezsutek octave with this spacing would
be 21.6 cm, plus the width of the key. Playable melodically, but I
wouldn't be able to hold an octave with one hand. Someone with larger
hands would, but would also have more trouble with the keys being small.
Unfortunately, the spacing of a rebuilt keyboard would be greater than
this, as it's the chromatic spacing that's the limiting factor. I make it
a 26cm octave (counting 23 keys).

When you say "getting stuck between the blacks" does that mean you're
deliberately playing the top end of the white notes? This is possible
with mini-keys, but not easy. I'd prefer to write music that doesn't
require such tricks. With a custom-built keyboard, the blacks could be
thickened, and the keyboard made playable with a smaller span. But then a
custom-built keyboard could have more than two ranks.

Like I said, I haven't tried this with a MIDI keyboard, and so can't be
sure how it would work with an extended mapping. Also, the keyboard I've
used isn't velocity sensitive.

> Two hands, eh? Why didn't I think of that! Who needs four-part
> harmony, anyway!

Well, you may prefer playing against a drone, but the chords are there if
you want them. I can play progressions of 4-note chords with 29 notes to
the octave, it shouldn't be too difficult with 29.

> (There's no doubt that a helluva lot could be done on a
> no-octave-reaching keyboard. There's also no doubt that a helluva lot
> _couldn't_ be done.)

That's better, you're not talking about pre-requisites for "any serious
xen keyboard" any more.

Paul wrote:

> [...]your design [...] seems absolutely unnavigable beyond one or two
> "keys" -- diatonic ones which don't even work in 22-tET.
>

Fair enough. Parts of this are true and this is what I found interesting both
in our correspondence and in the course of this thread - namely which
compromises can be found unacceptable.

My 3-octave and a fourth, 22-tone keyboard to which I alluded and Paul mentions
above has a 12-tone basis - in a class which Douglas Keislar terms
'accretional': it resembles a meantone keyboard, splitting all sharps and five
naturals, excepting D and A (physical constraints and social pressure finalized
this format).

I think any keyboard that allows a broader choice of harmony than 12 notes is
brilliant - Wilson's designs are excellent, certainly they fit the bill of the
'serendipity' that started this.

For me there is no question that instruments influence the kind of music they
can produce, and likewise I think that this music should be considered in
designing the means of playing these instruments, no better exemplified than by
the layout of keys finally to some extent which must be compromised by the
number and size of our fingers.

I will also note that the design of keyboards for mechanical instruments
differs greatly from that of electronic ones; even the 7/8 reduction made by
the 12-tone DS piano keyboard is afforded only by rather an extreme
re-engineering of traditional practice, while a similar (full) xenharmonic
application would necessitate much further departure - I'd venture too much for
any manufacturer even to consider anymore, even for low tension instruments.

Cheers,

Clark

>According to the website, DS only make piano keyboards. So those findings
>aren't applicable to MIDI keyboards, let alone when they have more than 12
>keys to the octave. Steve rebuilt a MIDI keyboard, not a piano.

It is true that DS only makes piano keyboards. But the findings (at least
the ones I've mentioned) are applicable to any keyboard with Halberstadt
topology.

>My old PSR keyboard has white keys 1.8 cm center-center. I found that
>playable, but not convenient.

Too narrow for my fingers. There'd be too much strain playing runs, having
to ball up my hand. And, how thick were your blacks?

>When you say "getting stuck between the blacks" does that mean you're
>deliberately playing the top end of the white notes? This is possible
>with mini-keys, but not easy. I'd prefer to write music that doesn't
>require such tricks.

Such as music entirely in the key of C maj?

>With a custom-built keyboard, the blacks could be thickened, and the
>keyboard made playable with a smaller span.

Thickening the relative size of the blacks only makes the getting stuck
problem worse -- or isn't that what you meant?

>But then a custom-built keyboard could have more than two ranks.

Well, that's the thing.

>That's better, you're not talking about pre-requisites for "any serious
>xen keyboard" any more.

Yes I am. You could spend your life playing wonderful music on a xen
keyboard where you could only reach a 5/3. But I wouldn't call it a
serious alternative to the Halberstadt-12 keyboard, considering the types
of voicings you'd be giving up. I wouldn't pay money for a full-sized
Halberstadt anymore either, after playing various scaled-down versions over
at DS. But I do have a relatively small hand, and I am a bit of a nut.

-Carl