Yahoo Tuning Groups Ultimate Backup tuning An idea for a 19-note keyboard layout

Regarding 19 notes/octave keyboards: From what I've read, most people take the approach of splitting the standard black keys in half, either right/left or front/back, and adding 2 more black keys. What if, instead of 7 white keys and 12 black ones, you swap white & black to get 7 black keys and 12 white ones:

| | | | | | | | || | | | | | | | | | || | |
| | | | | | | | || | | | | | | | | | || | |
| | C | | | D | | | E || F | | | G | | | A | | | B || C | |
| |___| | |___| | |___||___| | |___| | |___| | |___||___| |
| | | | | | | | | | | | | | |
| B# | C# | Db | D# | Eb | E# | F# | Gb | G# | Ab | A# | Bb | B# | C# |
| Cb | | | | | Fb | | | | | | | Cb | |
|____|____|____|____|____|____|____|____|____|____|____|____|____|____|

Has anyone thought of this before? I looked on the web, but couldn't find anything.
It has the disadvantage of octaves being too wide to play with one hand, however fifths are very playable, being the width of a standard octave (except for Bb-F and B-F#). So perhaps a good trade-off of playability vs #-of-notes-per-octave?

🔗Mike Battaglia <battaglia01@...>

On Fri, Nov 26, 2010 at 6:58 PM, kiteg <kiteg@...> wrote:
>
> Regarding 19 notes/octave keyboards: From what I've read, most people take the approach of splitting the standard black keys in half, either right/left or front/back, and adding 2 more black keys. What if, instead of 7 white keys and 12 black ones, you swap white & black to get 7 black keys and 12 white ones:
>
> Has anyone thought of this before? I looked on the web, but couldn't find anything.
> It has the disadvantage of octaves being too wide to play with one hand, however fifths are very playable, being the width of a standard octave (except for Bb-F and B-F#). So perhaps a good trade-off of playability vs #-of-notes-per-octave?

I like this idea a lot! It's very clever, and demonstrates a strength
of the Halberstadt layout that I think should be explored more. It
generalizes the Halberstadt layout to the 12+7 MOS structure instead
of the 7+5 MOS structure. I haven't ever heard of this idea, but it
sounds like a great point of departure for a different kind of
generalized keyboard layout, and one perhaps that keyboard players
might intuitively gravitate to.

What would be ridiculously awesome is to come up with a simple method
of cascading layers of keys to fit different MOS structures. That is,
7-tet could be 5 white keys and 2 black keys, and then 12-tet could be
the 7-tet layout plus an additional 5 "red" keys let's say, and then
19-tet could be the 12-tet layout plus an additional 7 "blue" keys.

This process could continue forever, but one could arbitrarily cut it
off by defining a subset of the MOS heirarchy to use. So if you're
designing the layout around meantone, you could say that you're only
going to set up the keyboard to handle meantone[7] as a primary layer
and meantone[5] as a secondary layer, and hence limit yourself to
meantone[5, 7] - Halberstadt. Or, as per your idea, you could set the
keyboard up to handle meantone[12] as a primary layer, and meantone[7]
as a secondary layer, and limit yourself to meantone[7, 12] - the
"Kiteg" layout. The Goldstein layout would be if you set mavila[9] up
as a primary layer, and mavila[7] up as a secondary layer.

And if we could devise a way to come up with a way to geometrically
pack multiple layers of keys together - an irregular tesselation of
the 2d plane, if you will - then we'd have a great approach to
generalizing the Halberstadt layout that would probably become my
favorite alternative keyboard layout ever. We could set 19-tet up as
having a primary layer of 7, a secondary layer of 5, a tertiary layer
of 3, and a quaternary layout of 2, or something.

Anyone heard of anything like this?

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, Nov 26, 2010 at 7:36 PM, genewardsmith
<genewardsmith@...> wrote:
>
> > Anyone heard of anything like this?
>
> I used to describe MOS in that manner, but not so much with an eye to actual use as a quasi-Halberstat keyboard as I'm no keyboardist.

Words cannot describe how obsessed with this idea I am!

I've always bought into the Halberstadt bashing on some level because
of the notion that I only like it because I've been playing it for 20
years - makes sense to me. And transpositional-invariant fingering is
an interesting feature that I've always sort of liked the idea of, and
the Halberstadt lacks this.

But now I'm starting to see it differently - this is one of the
strengths of the Halberstadt layout. It builds itself around the MOS
structure of a certain tuning, thus putting the most consonant scales
right at your fingertips for easy access. And it also takes advantage
of the fact that MOS scales add together to form new MOS's, i.e. that
7 white keys + 5 black keys = meantone[7] + meantone[5] = meantone[12]
(or 12-equal).

But in contrast to existing generalized keyboard layouts, this would
lead to some kind of fractal-based tesselation of the 2d plane,
though, wouldn't it?

-Mike

🔗Kalle Aho <kalleaho@...>

Yes, I have thought about it and in fact sent a picture of this to the Facebook group Xenharmonic Alliance just 10 hours ago! I mean, what is happening? Are you sure you didn't see it there?

Kalle

--- In tuning@yahoogroups.com, "kiteg" <kiteg@...> wrote:
>
> Regarding 19 notes/octave keyboards: From what I've read, most people take the approach of splitting the standard black keys in half, either right/left or front/back, and adding 2 more black keys. What if, instead of 7 white keys and 12 black ones, you swap white & black to get 7 black keys and 12 white ones:
>
> | | | | | | | | || | | | | | | | | | || | |
> | | | | | | | | || | | | | | | | | | || | |
> | | C | | | D | | | E || F | | | G | | | A | | | B || C | |
> | |___| | |___| | |___||___| | |___| | |___| | |___||___| |
> | | | | | | | | | | | | | | |
> | B# | C# | Db | D# | Eb | E# | F# | Gb | G# | Ab | A# | Bb | B# | C# |
> | Cb | | | | | Fb | | | | | | | Cb | |
> |____|____|____|____|____|____|____|____|____|____|____|____|____|____|
>
> Has anyone thought of this before? I looked on the web, but couldn't find anything.
> It has the disadvantage of octaves being too wide to play with one hand, however fifths are very playable, being the width of a standard octave (except for Bb-F and B-F#). So perhaps a good trade-off of playability vs #-of-notes-per-octave?
>

🔗cityoftheasleep <igliashon@...>

Man, I had to do some editing of this into a text editor to make the Ascii line up right, it displays quite messily with a monospace font if additional spaces aren't added.

Anyway, once I'd got it straightened out, I realized I've thought about this layout before for 19 before. It makes me think of Yasser, and his theory that music is evolving toward a 12-note diatonic scale. For that kind of approach, it's quite practical!

However, the interesting challenge of 19-EDO is that it has multiple MOS scales that are rich enough in concordant triads to serve as a basis for a tonality. My particular fave is the 4L+5s scale (in the LLsLsLsLs mode), once known as "hemifourths" because it's based on the ~250-cent generator. There's also the 10-note 9L+1s scale (in the LLLLsLLLL mode), as well as a few others that I haven't found too enticing. So the question in designing a layout is, which scale do you want to focus on? The 10-note 9L+1s scale has the most compact layout (simply 10 white and 9 black), but it makes other scales look like nonsense. The hemifourths scale is tough, because the large step is 3 degrees of 19-EDO and the small step is 1, so you'd need split-and-doubled black keys (or something similarly impractical). The layout you suggest is actually pretty good for hemifourths, provided you interpret it in reference to diatonic note-spellings. I don't really know which one is really overall the most versatile and ergonomic, and I'm really more of a guitarist than a keyboardist. But I'm really lovin' on 19 right now and I suspect it's the easiest alternative EDO for me to talk other musicians into playing around with, so I'd really love to know if anyone's attempted 19 on a converted halberstadt-like keyboard design.

-Igs

🔗Mike Battaglia <battaglia01@...>

🔗gregggibson <gregggibson@...>

____|
>
> Has anyone thought of this before? I looked on the web, but couldn't find anything.
> It has the disadvantage of octaves being too wide to play with one hand, however fifths are very playable, being the width of a standard octave (except for Bb-F and B-F#). So perhaps a good trade-off of playability vs #-of-notes-per-octave?
>

Nice to see somebody interested in things 19-tonic. Yeah, it's an intriguing, even ingenious idea, but Joseph Yasser had the idea before you. It's in his Theory of Evolving Tonality. The result would make the octave too wide for easy playability however, as you say.

I have tried myself to come up with a really playable 19-tone keyboard, but have never had much luck. Probably the old horizontally split accidental concept is the best, altho I think that a double manual would be advisable, so that chords playable only on accidentals could be manipulated without breaking your fingers.

There is a Mr Wraight who makes 19-tone harpsichords I believe. There's a photo of one of them on the net.

Soon after the invention of the 1/3 comma meantone in 16th century Italy, people started making 19-tone keyboards to try it out. Zarlino, Praetorius, Titelouze and above all Costeley are associated with such keyboards. Costeley tells us in no uncertain terms that he used 1/3 comma meantone on his 19-tone keyboard. And Mersenne informs us that Titelouze used the same tuning. Apparently the design used was always much the same; either splitting the accidentals horizontally or vertically.

Someone more up on generalized keyboards than I am could probably suggest something really fine. But considering that Yamaha has actually tried to PATENT the old Renaissance design, maybe people would prefer to keep any really good design a SECRET.

🔗Carl Lumma <carl@...>

Igs wrote:

> Man, I had to do some editing of this into a text editor to
> make the Ascii line up right, it displays quite messily with
> a monospace font if additional spaces aren't added.

Tried this link?

/tuning/topicId_94867.html#94867?var=0&l=1

> Anyway, once I'd got it straightened out, I realized I've
> thought about this layout before for 19 before. It makes me
> think of Yasser,

Perhaps that's because it's identical to Yasser's proposal:

http://www.musanim.com/Yasser/

> However, the interesting challenge of 19-EDO is that it has
> multiple MOS scales...

Indeed. And the same is true of most good ETs. Building
a physical halberstadt-style keyboard for each one does
seem impractical. Also, octaves will be unreachable in any
of these interesting systems with a 1-D keyboard and I
think that's a real problem.

The middle ground is a 2-D keyboard but with a non-isomorphic
mapping... I've been thinking about this possibility lately.

-Carl

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Nov 26, 2010 at 7:36 PM, genewardsmith
> <genewardsmith@...> wrote:
> >
> > > Anyone heard of anything like this?
> >
> > I used to describe MOS in that manner, but not so much with an eye to actual use as a quasi-Halberstat keyboard as I'm no keyboardist.
>
> Words cannot describe how obsessed with this idea I am!

My approach to these virtual keyboards was to start with p+q = number of notes in a period. So, for 19, you might have 12+7 = 19. Then take the continued fraction convergents for 7/12, with penultimate convergent 3/5. Now take the ratio of numerators and compare to the ratio of denominators: 5/12 < 3/7. Fill in the mediant: (5+3)/(12+7) = 8/19. The 12 note MOS using the 8/19 generator gives you your white keys, and the 7 note MOS filling out the circle using the 8/19 generator gives the black keys. This way of analyzing an et I was calling white keys-black keys for a while.

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

Mike wrote:

> What do you mean by a "non-isomorphic" mapping? Is that the
> same thing I was trying to get at?

A mapping that doesn't have transpositional invariance, but
does use a 2-D array of keys to shrink the octave span.
More to come perhaps...

> Paul also just pointed out to me that this approach might
> in some cases be isomorphic to a Fokker layout, but with the
> keys slanted so as to give transpositional invariance.

Yes, that sounds like the same thing I'm talking about.
Look at the photo!

> I'm not sure exactly what I'm saying yet, so I don't know
> if there are any subtle differences I might be missing.
> But what is a Carlos keyboard - how does that differ from
> a Fokker layout?

I've never seen the Fokker layout up close. I'm told it's
identical to Bosanquet but without the column offsets (i.e.
a Bosanquetian zero-order keyboard). The Carlos keyboard has
the first-order column offsets, so it essentially is
Bosanquet's design, but with keys of a slightly different
shape and shown in a perspective illustration. Ever since
I saw her illustration in the late '90s, I've thought of it
as basically perfect.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Fri, Nov 26, 2010 at 9:46 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > What do you mean by a "non-isomorphic" mapping? Is that the
> > same thing I was trying to get at?
>
> A mapping that doesn't have transpositional invariance, but
> does use a 2-D array of keys to shrink the octave span.
> More to come perhaps...

That's what I was saying! But you didn't seem to like it.

Well, that and to steal the feature of the Halberstadt - to set a
tuning up around several sub-MOS's of the scale you're designing the
keyboard around, and take advantage of the fact that in meantone, 7
and 5 are both MOS's, and also 5+7 = 12, which is also an MOS, etc.

Setting three layers up without having stupid unergonomic split black
keys seems tough, but there's probably some insight here that maybe
you have that I don't. Are you suggesting to just take a Wilson
keyboard and shift everything to mimic a Halberstadt?

> > I'm not sure exactly what I'm saying yet, so I don't know
> > if there are any subtle differences I might be missing.
> > But what is a Carlos keyboard - how does that differ from
> > a Fokker layout?
>
> I've never seen the Fokker layout up close. I'm told it's
> identical to Bosanquet but without the column offsets (i.e.
> a Bosanquetian zero-order keyboard). The Carlos keyboard has
> the first-order column offsets, so it essentially is
> Bosanquet's design, but with keys of a slightly different
> shape and shown in a perspective illustration. Ever since
> I saw her illustration in the late '90s, I've thought of it
> as basically perfect.

Here's a Fokker layout:
http://monxmood.free.fr/fokker/fokker.html

Does that look the same to you?

-Mike

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> My approach to these virtual keyboards was to start with p+q = number of notes in a period. So, for 19, you might have 12+7 = 19.

I should note that this sort of thing can have more than one interpretation, depending on the period. For instance, starting from 11+8=19, we get a penultimate convergent to 8/11 of 3/4. Now looking at the numerators and denominators, we have 4/11 < 3/8, and inserting the mediant, 4/11 < 7/19 < 3/8. Brave souls may want to try out the 7/19 generator with an 11+8 white-black pattern, which gives a sensi temperament tuning not so optimal as the one 46et provides. However, we can just as well consider that the period is 2^(1/9), in which case we are looking at 4/99 < 7/171 < 3/72 generators cycling around 1/9 octave, and we have the 99+72 virtual halberstadt keyboard for 171 notes of ennealimmal temperament. Which is how, incidentally, ennealimmal and some other temperaments were first discovered.

🔗Carl Lumma <carl@...>

Mike wrote:

> > A mapping that doesn't have transpositional invariance, but
> > does use a 2-D array of keys to shrink the octave span.
> > More to come perhaps...
>
> That's what I was saying! But you didn't seem to like it.

I don't like layouts where some intervals in the tuning
can't be reached with a single hand. I do wonder if
transpositional invariance is so important, and I've written
extensively on that since a long time now.

Western music compositions pretty much stayed in one key
for several centuries, and a majority still do. Personally,
I transpose like crazy in 12-ET, but only to get novelty.
In a completely new system, optimizing for one key might
not be so bad.

http://lumma.org/temp/AXiS-49_ideal.png

Given the AXiS digitals in the orientation you see here,
I consider this mapping ideal for the right hand to play

|| 7/4..12/7 ||
|| 3/2...3/2 o||
|| 5/4...6/5 o||
|| 1/1...1/1 ||

Of course it's impossible for an isomorphic layout to
support this. More to come...

> Are you suggesting to just take a Wilson
> keyboard and shift everything to mimic a Halberstadt?

I'm suggesting the Carlos keyboard does what you want
while maintaining transpositional invariance.

> Here's a Fokker layout:
> http://monxmood.free.fr/fokker/fokker.html
>
> Does that look the same to you?

No.

-Carl

🔗kiteg <kiteg@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, Nov 26, 2010 at 10:13 PM, genewardsmith
<genewardsmith@...t> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> > My approach to these virtual keyboards was to start with p+q = number of notes in a period. So, for 19, you might have 12+7 = 19.
>
> I should note that this sort of thing can have more than one interpretation, depending on the period. For instance, starting from 11+8=19, we get a penultimate convergent to 8/11 of 3/4. Now looking at the numerators and denominators, we have 4/11 < 3/8, and inserting the mediant, 4/11 < 7/19 < 3/8. Brave souls may want to try out the 7/19 generator with an 11+8 white-black pattern, which gives a sensi temperament tuning not so optimal as the one 46et provides. However, we can just as well consider that the period is 2^(1/9), in which case we are looking at 4/99 < 7/171 < 3/72 generators cycling around 1/9 octave, and we have the 99+72 virtual halberstadt keyboard for 171 notes of ennealimmal temperament. Which is how, incidentally, ennealimmal and some other temperaments were first discovered.

Right, and what I think would be useful would be to generalize this to
three tiers - let's say white keys, black keys, and blue keys. The
thing is, how do you generalize this to three tiers? The split-black
key solution is awkward. Maybe if we represented key position as just
dots in space, we could come up with some kind of irregular
tesselation scheme that would do the trick.

What I think would be ultimately useful is some way to come up with a
"meta-Halbersdadt" that could be defined for some infinite series of
MOS's/convergents/etc, either proper or improper, and then find a way
to pick a subset of it for actual keyboard implementation. So the 7+5
Halberstadt layout would be one subset, kiteg's 12+7 layout would be
another, and you could also pick a 7+5+3+2+1+1 layout or something if
you wanted, or maybe make it 7+5+5+2, or 7+5+7, etc. If there's a
clever way to arrange the infinite series in 2d space in
pseudo-Halberstadt fashion (maybe in such a way that doesn't use
weirdly-shaped "white" and "black" keys, but using something more like
a fractal-ish hexagonal arrangement), then you'd be able to set up a
lot of interesting "tertiary-layered" structures that wouldn't use
stupid split black keys, etc.

Rearranging the Carlos or Fokker layouts seem to be a decent step in
that direction, if you rearrange things so that they aren't
transpositionally invariant but rather reflect this MOS-based
heirarchy.

-Mike

🔗kiteg <kiteg@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, Nov 26, 2010 at 10:25 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > > A mapping that doesn't have transpositional invariance, but
> > > does use a 2-D array of keys to shrink the octave span.
> > > More to come perhaps...
> >
> > That's what I was saying! But you didn't seem to like it.
>
> I don't like layouts where some intervals in the tuning
> can't be reached with a single hand. I do wonder if
> transpositional invariance is so important, and I've written
> extensively on that since a long time now.

I wouldn't expect anything in the layout I suggest to be unreachable
with a single hand unless it's an exceptionally wide interval. I
prioritize melodic over harmonic function, so perhaps that's a
personal choice I'm making. The intervals would increase roughly
linearly with pitch to the right.

> Western music compositions pretty much stayed in one key
> for several centuries, and a majority still do. Personally,
> I transpose like crazy in 12-ET, but only to get novelty.
> In a completely new system, optimizing for one key might
> not be so bad.

It's like a "middle path" for keyboard layouts or something. Maybe a
more apt analogy is a "well temperament." I also think it would be
great for beginners in that the tuning is laid out according to its
most useful sub-MOS scales, so diatonic music is easily playable by
just messing with the white keys. Setting the heirarchy up around
porcupine instead of meantone, for example, would be awesome.

I also think it would prove to be fairly intuitive for existing
keyboard players to make the switch.

> http://lumma.org/temp/AXiS-49_ideal.png
>
> Given the AXiS digitals in the orientation you see here,
> I consider this mapping ideal for the right hand to play
>
> || 7/4..12/7 ||
> || 3/2...3/2 o||
> || 5/4...6/5 o||
> || 1/1...1/1 ||
>
> Of course it's impossible for an isomorphic layout to
> support this. More to come...

So would you say that harmonic accessibility is something you
prioritize over melodic accessibility then?

> > Are you suggesting to just take a Wilson
> > keyboard and shift everything to mimic a Halberstadt?
>
> I'm suggesting the Carlos keyboard does what you want
> while maintaining transpositional invariance.

For ease of remapping to different MOS substructures, I'd say you're
right. However, the thought of having an 8+7 porcupine keyboard seems
like it would be an awesome way to conceptualize porcupine, as well as
an intuitive way for people used to the Halberstadt. 22 would probably
make the most sense in a three tiered structure, something like 8+7+7.

(Or you could take advantage of the fact that 22 is divisible by 2 and
come up with a Janko-ish layout for it, but that's another story).

> > Here's a Fokker layout:
> > http://monxmood.free.fr/fokker/fokker.html
> >
> > Does that look the same to you?
>
> No.

I think it's just the Carlos keyboard turned upside down. Note that
from top to bottom, you have B#-C-Dbb in the first column. B# is the
same thing as Cv by Fokker's names, and Dbb is the same thing as C^
(where ^ and v are 1/31).

-Mike

🔗gdsecor <gdsecor@...>

--- In tuning@yahoogroups.com, "gregggibson" <gregggibson@...> wrote:
> ...
> I have tried myself to come up with a really playable 19-tone keyboard, but have never had much luck. Probably the old horizontally split accidental concept is the best, altho I think that a double manual would be advisable, so that chords playable only on accidentals could be manipulated without breaking your fingers.

What problem do you have with 19-equal mapped on Bosanquet's generalized keyboard (or, as I prefer, something closer to Erv Wilson's hexagonal key shape)? I've used this on my Scalatron for the past 35 years, and my experience is that, because of transpositional invariance, it's as easy to play as anything could possibly be -- far easier than 12-equal on the conventional Halberstadt arrangement. Because you learn to play intervals as vectors and scales & chords as patterns, once you learn something in one key, you've automatically learned it in all the (18) other keys.

You don't need a double manual to facilitate fingering, because the generalized keyboard has more than 19 keys/octave, which allows for pitches to map to duplicate keys (e.g., the E# and Fb keys play the same pitch). Your thumb doesn't have to reach into the farthest rows, because they're duplicated 3 rows closer.

--George

🔗Carl Lumma <carl@...>

Mike wrote:

> I wouldn't expect anything in the layout I suggest to be unreachable
> with a single hand unless it's an exceptionally wide interval. I
> prioritize melodic over harmonic function, so perhaps that's a
> personal choice I'm making. The intervals would increase roughly
> linearly with pitch to the right.

Octaves are unreachable on the Yasser layout - I thought
it was an example of your proposal here.

> So would you say that harmonic accessibility is something you
> prioritize over melodic accessibility then?

It's just harder to hit notes together than in sequence.
So chords are the natural priority.

This is the best I can do for an isomorphic pajara layout on
the AXiS (still assuming right hand, horizontal orientation):

http://lumma.org/temp/AXiS-49_pajara.png

The whole numbers are 22-ET degrees, with pajara members
in red. The letters are decatonic pitch classes on the
keys I think you'd usually finger an ascending run.
The ratios show the shapes of the major and minor tetrads.

I would probably mirror this for the left hand (i.e. pitch
descending from the middle to the left) in the 7 blank
columns there. Probably better would be two AXeS in the
vertical orientation.

The criteria I used for this are:

1. fingering of major and minor tetrads be as similar
as possible
2. root-position pitches for these fall as close as possible
on a semicircle of radius 2

I dunno if it's optimal for these but it's what I came up
with just now.

> > I'm suggesting the Carlos keyboard does what you want
> > while maintaining transpositional invariance.
>
> For ease of remapping to different MOS substructures, I'd
> say you're right.

No, I meant preserving the 7+5 structure of the Halberstadt.

> However, the thought of having an 8+7 porcupine keyboard seems
> like it would be an awesome way to conceptualize porcupine, as
> well as an intuitive way for people used to the Halberstadt.

There should always be a tiered 2-D isomorphic layout for
any MOS structure, like the Carlos layout for 7+5, which is
isomorphic. But you'd need a separate keyboard for each.
A flat keyboard might be colored to indicate the structure.
With OLED keycaps (ala Maximus keyboard)...

> 22 would probably make the most sense in a three tiered
> structure, something like 8+7+7.

I should say I think MOS are over-rated. In pajara, Paul's
preferred scales (the pentachordal scales) aren't MOS.

> > > Here's a Fokker layout:
> > > http://monxmood.free.fr/fokker/fokker.html
> > >
> > > Does that look the same to you?
> >
> > No.
>
> I think it's just the Carlos keyboard turned upside down.

The column offsets are different. But contrary to what
I'd heard about Fokker being zero-order, it looks like the
offsets are 1/2-key-height or something. So it winds up
being zero-order since 12 is divisible by 2. Anyway, it's
not optimal for the systems Fokker was interested in.
Have another look at the Carlos illustration.

-Carl

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Right, and what I think would be useful would be to generalize this to
> three tiers - let's say white keys, black keys, and blue keys. The
> thing is, how do you generalize this to three tiers?

As I say, I've mostly thought about this sort of thing as a mathematical convenience, not being a keyboardist. That was brought home by my first posting on this list, which was about a five-color system in your terms. A 7+5+7+5+7 arrangement for 31edo, which met with general lack of favor and interest.

Since we start with a rank one system, it's not hard to make the idea work in theory. We have some generator, say 11/19. Since we are rank one and octave equivalent, this cycles in a circle of generators. Hence three equal divisions with generators close to 11/19, such as 7, 7, and 5, will work. Hence you can go around the circle, 7 white keys, 5 black keys, 7 blue keys, giving a 7+5+7 three-layer system.

🔗cityoftheasleep <igliashon@...>

🔗Carl Lumma <carl@...>

Igs wrote:

> The perspective I'm coming from, Carl, is "how can I turn
> a cheap, readily-available MIDI controller into something my
> keyboardist friends won't balk at." It's quite easy and
> extremely cheap to "re-key" a halberstadt-based MIDI controller
> to fit a variety of other intonations. The 16-EDO 9 white-7
> black layout, for instance, is pretty awesome, and is used by
> Ron Sword, Elaine Walker, and "Tetra F". Low EDOs are ripe
> for Halberstadt-esque designs, though around 19 they become
> a bit difficult.

From my perspective, if you can't afford an AXiS you should
look for a new line of work. To get any kind of MIDI controller
for 400 beans is pretty great. I think the es88 was more than
that when it came out. I see it's now $230. That's just nuts.

Octaves are already too wide on the Halberstadt in 12. I was
convinced of that after spending a weekend with a room full
of 7/8-scale "DS Keyboard" pianos.

That's not to say great things can't be done with a 9+7 or
other linear keyboard, and the ones I saw Elaine and Ron
posing with on facebook looked rad. But we're talking about
a revolution here. At some point you need a Kalashnikov.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Sat, Nov 27, 2010 at 12:02 AM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > I wouldn't expect anything in the layout I suggest to be unreachable
> > with a single hand unless it's an exceptionally wide interval. I
> > prioritize melodic over harmonic function, so perhaps that's a
> > personal choice I'm making. The intervals would increase roughly
> > linearly with pitch to the right.
>
> Octaves are unreachable on the Yasser layout - I thought
> it was an example of your proposal here.

No, the proposal is just what sparked my train of thought. I think
that 12+7 is too many white notes to be useful. I think that if you could
come up with a three-tiered system that was ergonomic and didn't
involve any goofy split black keys or anything like that, then it
would become really easy to come up with meta-Halberstadt-ish layouts
for 19, 22, etc.

Or in short, the concept of dividing xx-tet into two sub-MOS's (or
non-MOS scales that are complementary) is really what defines the
Halberstadt layout, and I think that it's a good approach to explore
as an alternative to the more common "topographically neutral"
generalized keyboard layouts.

So rather than make 19-tet 12+7, you could make it 7+5+7, or 7+5+5+2,
or any of the other random options you can think of. Yes, it would
lead to multiple layouts for each tuning - you could build a 22 layout
off of superpyth diatonic, or porcupine[8], or pajara (or the SPM
scales), etc.

> The whole numbers are 22-ET degrees, with pajara members
> in red. The letters are decatonic pitch classes on the
> keys I think you'd usually finger an ascending run.
> The ratios show the shapes of the major and minor tetrads.
>
> I would probably mirror this for the left hand (i.e. pitch
> descending from the middle to the left) in the 7 blank
> columns there. Probably better would be two AXeS in the
> vertical orientation.
>
> The criteria I used for this are:
>
> 1. fingering of major and minor tetrads be as similar
> as possible
> 2. root-position pitches for these fall as close as possible
> on a semicircle of radius 2
>
> I dunno if it's optimal for these but it's what I came up
> with just now.

That's a new paradigm for me, although I could probably get used to
it. The fact that you naturally put 6/5 right below 5/4 (vertically)
and 12/7 right below 7/4 suggests that the vertical axis -> pitch
height cue is fairly intuitive for you, and the fact that you set the
upper notes of the chord to increase in pitch to the right suggests
that the horizontal axis -> pitch height cue is also just as intuitive
(unless you mirror it on the other hand, in which case it's replaced
by a thumb to pinky axis -> pitch height cue).

To me, cues like that are more important than transpositional
invariance, unless the layout also preserves most of those cues (e.g.
Bosanquet/Fokker). But I guess it depends on if you're focusing more
on harmonic relationships or melodic ones.

> > However, the thought of having an 8+7 porcupine keyboard seems
> > like it would be an awesome way to conceptualize porcupine, as
> > well as an intuitive way for people used to the Halberstadt.
>
> There should always be a tiered 2-D isomorphic layout for
> any MOS structure, like the Carlos layout for 7+5, which is
> isomorphic. But you'd need a separate keyboard for each.
> A flat keyboard might be colored to indicate the structure.
> With OLED keycaps (ala Maximus keyboard)...

Sure, but what about if you're doing 7+5+3 or something?

> > 22 would probably make the most sense in a three tiered
> > structure, something like 8+7+7.
>
> I should say I think MOS are over-rated. In pajara, Paul's
> preferred scales (the pentachordal scales) aren't MOS.

I guess you could set it up around any complementary set of scales. So
if you were going to set up 22, you could then set it up like 10+7+5
or something. Perhaps you could make it so that the 10 is one of
Paul's decatonic scales, and the 7+5 is a superpyth chromatic scale,
or a sort of 5-limit chromatic scale, or whatever. I'm not sure how to
make them complement each other.

> > I think it's just the Carlos keyboard turned upside down.
>
> The column offsets are different. But contrary to what
> I'd heard about Fokker being zero-order, it looks like the
> offsets are 1/2-key-height or something. So it winds up
> being zero-order since 12 is divisible by 2. Anyway, it's
> not optimal for the systems Fokker was interested in.
> Have another look at the Carlos illustration.

Er, what does zero-order mean...?

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

Mike wrote:
> No, the proposal is just what sparked my train of thought.
> I think that 12+7 is too many white notes to be useful. I think
> that if you could come up with a three-tiered system that was
> ergonomic and didn't involve any goofy split black keys or
> anything like that, then it would become really easy to come up
> with meta-Halberstadt-ish layouts for 19, 22, etc.

That'd be cool. Sounds like Gene had something like this
figured out.

> > http://lumma.org/temp/AXiS-49_pajara.png
> >
> > The criteria I used for this are:
> > 1. fingering of major and minor tetrads be as similar
> > as possible
> > 2. root-position pitches for these fall as close as possible
> > on a semicircle of radius 2
>
> That's a new paradigm for me, although I could probably get used
> to it. The fact that you naturally put 6/5 right below 5/4
> (vertically) and 12/7 right below 7/4 suggests that the vertical
> axis -> pitch height cue is fairly intuitive for you,

Not at all, I wanted the two 7th chords to be a similar
as possible. Since these pairs are both separated by
semitones in 22, I knew that one of the two axes would
have to be a semitone. Then I just tried to get everything
on the semicircle. I'm not thinking about pitch height
at all.

> To me, cues like that are more important than transpositional
> invariance,

Well, this has that too. It's hard to resist in a
flat hex layout. Really the ultimate beginner's
pajara keyboard is just ten white notes with no
chromatic notes at all.

> But I guess it depends on if you're focusing more
> on harmonic relationships or melodic ones.

I just want the chords to be playable. Note I'm assuming
the AXiS will be close to the body, so the arms will be
coming in at 45 degree angles (from bent elbows). So the
3:2 should be about parallel with the knuckles.

> Sure, but what about if you're doing 7+5+3 or something?

Draw it up! The AXiS blank is available on the c-thru site.

> > > I think it's just the Carlos keyboard turned upside down.
> >
> > The column offsets are different. But contrary to what
> > I'd heard about Fokker being zero-order, it looks like the
> > offsets are 1/2-key-height or something. So it winds up
> > being zero-order since 12 is divisible by 2. Anyway, it's
> > not optimal for the systems Fokker was interested in.
> > Have another look at the Carlos illustration.
>
> Er, what does zero-order mean...?

I think you were driving to Miami when we were discussing
this just now. Do a last 30-days on author lumma and read
the thread.

-Carl

🔗Graham Breed <gbreed@...>

🔗Carl Lumma <carl@...>

🔗gregggibson <gregggibson@...>

--- In tuning@yahoogroups.com, "gdsecor" <gdsecor@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "gregggibson" <gregggibson@> wrote:
> > ...
> > I have tried myself to come up with a really playable 19-tone keyboard, but have never had much luck. Probably the old horizontally split accidental concept is the best, altho I think that a double manual would be advisable, so that chords playable only on accidentals could be manipulated without breaking your fingers.
>
> What problem do you have with 19-equal mapped on Bosanquet's generalized keyboard (or, as I prefer, something closer to Erv Wilson's hexagonal key shape)? I've used this on my Scalatron for the past 35 years, and my experience is that, because of transpositional invariance, it's as easy to play as anything could possibly be -- far easier than 12-equal on the conventional Halberstadt arrangement. Because you learn to play intervals as vectors and scales & chords as patterns, once you learn something in one key, you've automatically learned it in all the (18) other keys.
>
> You don't need a double manual to facilitate fingering, because the generalized keyboard has more than 19 keys/octave, which allows for pitches to map to duplicate keys (e.g., the E# and Fb keys play the same pitch). Your thumb doesn't have to reach into the farthest rows, because they're duplicated 3 rows closer.
>
> --George
>

Thanks for your opinion. I will have to look into Wilson's design. Do you have a link with more info on it?

🔗gdsecor <gdsecor@...>

--- In tuning@yahoogroups.com, "gregggibson" <gregggibson@...> wrote:
>
> --- In tuning@yahoogroups.com, "gdsecor" <gdsecor@> wrote:
> >
> > --- In tuning@yahoogroups.com, "gregggibson" <gregggibson@> wrote:
> > > ...
> > > I have tried myself to come up with a really playable 19-tone keyboard, but have never had much luck. Probably the old horizontally split accidental concept is the best, altho I think that a double manual would be advisable, so that chords playable only on accidentals could be manipulated without breaking your fingers.
> >
> > What problem do you have with 19-equal mapped on Bosanquet's generalized keyboard (or, as I prefer, something closer to Erv Wilson's hexagonal key shape)? I've used this on my Scalatron for the past 35 years, and my experience is that, because of transpositional invariance, it's as easy to play as anything could possibly be -- far easier than 12-equal on the conventional Halberstadt arrangement. Because you learn to play intervals as vectors and scales & chords as patterns, once you learn something in one key, you've automatically learned it in all the (18) other keys.
> >
> > You don't need a double manual to facilitate fingering, because the generalized keyboard has more than 19 keys/octave, which allows for pitches to map to duplicate keys (e.g., the E# and Fb keys play the same pitch). Your thumb doesn't have to reach into the farthest rows, because they're duplicated 3 rows closer.
> >
> > --George
>
> Thanks for your opinion. I will have to look into Wilson's design. Do you have a link with more info on it?

See the following, especially page 5, which includes a mapping for 19:
http://anaphoria.com/xen1.PDF

Here Erv develops the size & shape of the digitals:
http://anaphoria.com/xen2.PDF

Page 6 of the following is a diagram of a clavichord keyboard that was actually built for Scott Hackleman:
http://anaphoria.com/xen456.PDF

This is a photograph of my Scalatron keyboard (built in 1975), which is based on Erv Wilson's designs (except that the keys are elliptical). Note the 7+5+7+5+7 pattern (colored top-to-bottom: blue, black, white, red, green; duplicate keys were hard-wired for 31-equal):
/tuning/files/secor/GenKbd.jpg
The lateral spacing of the keys, center-to-center, is the same as on the piano, making the octave distance the same as C to B on the piano, or one key less than a piano octave. The tenth is therefore an easy reach (I can reach a twelfth with one hand).

--George

🔗Graham Breed <gbreed@...>

🔗gregggibson <gregggibson@...>

Thanks for the links. Never having played a Scalatron, I cannot say whether this is the ideal design, but I suspect that keys that mix sharps and flats would sometimes be a problem, necesiitating the middle finger to be tucked under, while the thumb and pinkie strain to reach an upper rank of keys. Additional ranks would perhaps solve this problem, though.

Wilson's designs are quite like my own from the 90s, when I still had time for them. I suspect that musicians would be comforted by having traditional keys present in some order. It is a pity that Yasser's design results in too wide an octave. I am thinking that some sort of three dimensional structure might solve this problem, a la Bosenquet.

Of course, one can also bevel the keys, just as accidentals are slightly beveled in the traditional 7+5 design, so that the white keys are still playable, even if much narrower.

The possibilities are endless. Somewhere out there is the perfect 19-tone keyboard.

🔗gdsecor <gdsecor@...>

--- In tuning@yahoogroups.com, "gregggibson" <gregggibson@...> wrote:
>
>
> Thanks for the links. Never having played a Scalatron, I cannot say whether this is the ideal design, but I suspect that keys that mix sharps and flats would sometimes be a problem, necesiitating the middle finger to be tucked under, while the thumb and pinkie strain to reach an upper rank of keys. Additional ranks would perhaps solve this problem, though.

Yes, additional rows or ranks are essential, not only for fingering facility, but also to achieve transpositional invariance. (I am quite disappointed that the Wilson clavichord has only 2 keys duplicated in each octave.) For a 19-tone mapping I found that 12 duplicates (or 31 total keys/octave) are sufficient. Also, the duplicate keys make a longer key shape (such as Bosanquet used) unnecessary, and the keys do not have to be as narrow.

> Wilson's designs are quite like my own from the 90s, when I still had time for them. I suspect that musicians would be comforted by having traditional keys present in some order. It is a pity that Yasser's design results in too wide an octave. I am thinking that some sort of three dimensional structure might solve this problem, a la Bosenquet.
>
> Of course, one can also bevel the keys, just as accidentals are slightly beveled in the traditional 7+5 design, so that the white keys are still playable, even if much narrower.

On the generalized keyboard Scalatron the keys are all in a single plane. The key surfaces are slightly convex, which enables the player to feel the location of the finger on the surface with respect to the center. Another consequence is that a glissando is extremely easy to execute on any part of the keyboard in any direction.

You might think that the relative lack of 3-dimensionality in having the keys in a single plane would require the player to rely on sight more than touch in navigating the keyboard, but I found that this is not the case, 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.

> The possibilities are endless. Somewhere out there is the perfect 19-tone keyboard.

Somewhere in my house, I think.

--George