Axis-49 at a good price, August 2

[MusicScienceGuy]

Hi gang,

As you may know I'm using the "harmonic table" keyboard made by C-Thru
Music called the Axis 49, tricked out to play as a Wicki-Haden
(Thummer) keyboard. It works with both my pc, I hear, macs as a midi
keyboard.
If you're interested in alternative keyboard controllers or music
notation in general I recommend checking it out, as it teaches music
theory like nothing else, and in the hands of a non-music novice like
myself is fast to learn and play.. It is velocity sensitive, albeit
with a touch more like a guitar than a piano.

They just added a forum post with the details of 50% off the regular
price ($250). The post says the sale is only happening on August 2nd
and requires purchase via a paypal account. I'm not sure what they are
up to, but there is a chance that this will be as they say, truly a
"one-time only" offer.

see http://www.c-thru-music.com/cgi/?page=prod_axis-49 for the gory
details.

Why am I posting this? Two reasons:
1) I don't want them fail to fail, like Thumtronics: this is one on
the most unique and cool keyboards that's been built since the piano
came onscene, and ... it isn't vaporware. I'd much rather they do well
and inspire competition.

2) I'd really like to have more buddies with an Axis so I can trade
ideas.

Cheers!
Ken Rushton, @ MusicScienceGuy.vox.com

[John]

Oh man, I'm going to be on that as fast as you can transpose on an
isomorphic layout!

Thanks big time Ken

John

[Paul W Morris]

Wow, thanks Ken, that's a great tip!  It'll be hard not to buy one at that price.  How hard was it to re-map the keys to the Wiki-Hayden layout?    Very cool that you can reprogram it that way.

I wonder if they may be clearing inventory for a new model coming out?  

Paul (Morris)

[Doug Keislar]

http://forum.c-thrumusic.com/viewtopic.php?f=6&t=118
seems to be the post that Ken was referring to. The offer's timing
seems to be measured in Pacific Standard Time (PST), which is 7 hours
behind GMT/UTC and 8 hours behind London (British Summer Time).

Doug

[Ken on Google Rushton]

I'm tempted to buy two ;)

- Seriously!, one for my left hand, and the other as my experimental machine - I want to make the action more like a piano's, but this is low priority, so I will probably only get one.  

 

Remapping the keyboard is done externally, via max/MSP, an expensive midi delelopment system with a simple program I created. To make it more convenient for everyone, I put together a runtime that reads an editable table so one can customize the remapping and made it publically available. The programming could be done in Bridle or PD, if one has the time to load it these tools and learn to use them - I don't.

 

There are limits to what I can do with the Axis-49 until (if) a firmware upgrade come out - it has 2 banks of 7x7 keys, each bank has the same set of midi note value output, with no way of distinguishing them,

 

What they are up to I have not a clue - I doubt they are clearing stock for a new model, as the current one is only 3 months old. Their marketing has been minimalist - no ads in EM or elsewhere, no presence at NAMM, no friendly chatter in their forum.

Perhaps they are "old-school British" or just quietly working.

 

Ken.

[Paul W Morris]

On Mon, Jul 27, 2009 at 2:36 PM, Ken on Google Rushton <bogru...@gmail.com> wrote:

Remapping the keyboard is done externally, via max/MSP, an expensive midi delelopment system with a simple program I created.

Hi Ken,  This is all good to know.  Just to clarify, it sounds like the program you made will run on its own, so there's no need for others to buy the expensive max/MSP, right? 

Thanks for making your program available and editable!  I don't suppose it runs on macs?  (There would be ways to get it running on a mac if not: windows emulators, dual-booting, WINE/Cross-over, etc.)

I'd be curious how the two 7x7 key banks are set up.  Are they left-and-right or top-and-bottom?  It really would be nice to get a firmware update to get past this limitation. 

Thanks again!
Paul

[Paul W Morris]

On Mon, Jul 27, 2009 at 4:08 PM, Paul W Morris <paulw...@gmail.com> wrote:

I'd be curious how the two 7x7 key banks are set up.  Are they left-and-right or top-and-bottom?

Oops, should have looked at the layout before asking as it looks like it must be one bank left and one right.   

I wish the hexagon's were aligned differently (I think I went into this in an earlier post.)  The rows are like this:

<=><=><=><=>  which spaces them out horizontally.

When I'd rather this:  

|^|^|^|^|^|    which is more horizontally compact.

...if that's clear.  Here's the layout for reference:

http://www.c-thru-music.com/cgi/?page=layout_49map

I think this would be better for either a Wiki-Hayden or Janko-type layout.   They probably prefer the current hexagon alignment since it makes it easy to play a triad with one finger in the default Tonnetz layout.

Seems you could rotate the whole instrument 90 degrees and then remap the pitches to achieve this re-alignment of the hexagons, but then your button field is twice as tall as it is wide, which may or may not be as useful.  (And you might run into issues remapping the two banks of 7x7 keys since they are now top-bottom instead of left-right.)

-Paul M

[Ken on Google Rushton]

Bingo - I'll comment later.

Ken.

I wish the hexagon's were aligned differently (I think I went into this in an earlier post.)  The rows are like this:

<=><=><=><=>  which spaces them out horizontally.

When I'd rather this:  

|^|^|^|^|^|    which is more horizontally compact.

....

[Ken on Google Rushton]

The remapping program runs on Macs in native mode too, I'm pleased to say.
I plan to upgrade it considerably.
.
Wicki/Hayden and native axis mode can be turned on/off with a mouse.

In wicki -hayden mode, you have two banks of keys turned sideways, making a tall kayboard.

One day I hope for a firmware upgrade, but first they have to sell enough to make it worthwhile.

Ken.

[Paul W Morris]

2009/7/28 Ken on Google Rushton <bogru...@gmail.com>:

> The remapping program runs on Macs in native mode too, I'm pleased to say.
> I plan to upgrade it considerably.

> Wicki/Hayden and native axis mode can be turned on/off with a mouse.

Ken, this all sounds excellent!

> In wicki -hayden mode, you have two banks of keys turned sideways, making a tall kayboard.

Hmmm... this makes it a harder decision, as 7 is not a very wide
range of keys horizontally. And sounds like we're really talking 7x7
usable button field, given the current firmware. I guess this is why
you want one for your left hand...

> One day I hope for a firmware upgrade, but first they have to sell enough to make it worthwhile.

I may send them an email. If the firmware was upgraded you could turn
the unit on a diagonal axis and remap the keys based on that to get
the hexagons aligned right. Still far from perfect...

Paul M

[Paul W Morris]

I worked up a diagram to help me visualize just what you'd get with
the Axis-49 + Ken's Wiki-Hayden Remapping program. See the attached
image.

As you can see, you get a four octave range (7x7=49, 48/12=4) in two
sonically identical 7x7 banks of keys one 'north' and the other
'south'.

Paul M

[Ken on Google Rushton]

I find that in practice, a 7x7 array works OK - note that even a 6-6 would do, but a 7x7 is better.  The other bank is not very useful, unless i want to work out the left hand fingering - I'd much rather mirror image the bank, and use the same fingering for the left hand as the right. I've tried mirror-keys on my earilier jammers and it is indeed good.

 

Each row is a whole tone scale, and an octave is therefore 6 tones wide. The notes therefore wrap on the 7th note-column. The 7th column adds flexibilty.

Most notes played cluster around the major scale,

 

Without note shifting I can play in C, G and D. F, Bb, and Eb,  Ab and Db are a bit of a stretch, because you lose easy access to the more important minor notes, and the hand has to (horrors!) actually move to play them.

 

With a semitone shift key (not implemented yet)  I could play in all the keys, even "hard" keys like C# and Db.

 

I need access to all keys so I can play the other bank mirror-imaged, including on my chest.

 

What features do you want in the next version of my program?

 

ken.

[Doug Keislar]

Wow! Thanks for the diagram, Paul; that makes the discussion much more
concrete.

I see that the leftmost and rightmost buttons of the Thummer are missing
in this remapped Axis-49 layout. (The Thummer has 9 or 10 buttons in
each row, whereas its reincarnation on the Axis-49 has 7). In 12-tone
equal temperament, there are fortunatlye no pitches missing, because the
leftmost and rightmost buttons are enharmonically equivalent. (That
doesn't mean it wouldn't be convenient to have more buttons, so that
more patterns can be transposed intact without refingering.) For things
like 19-TET, some pitches would be missing.

I assume that since Ken's remapping from the Axis harmonic layout to the
Wicki layout is "a simple matter of software" using Max/MSP, someone who
was able to tweak the Max patch could create other, arbitrary pitch
mappings, such as a Janko layout (12-TET), or a partial Bosanquet or
partial Fokker layout (microtonal). Right, Ken? But until there's a
firmware upgrade (if there ever is), the range would be limited to ust
one octave for 6-6 layouts like Janko. The Axis-49 would seem more
useful for Wicki, where the pitch increases in two dimensions instead of
one.

"Unless I'm missing something."

Doug

[Doug Keislar]

Oops.  My posting crossed with Ken's, where he explained more and basically answered most of my questions below.

[Ken on Google Rushton]

Doug,

You got it. One can remap to anything. With janko you are pretty limited, as it goes side-ways - although you can fold it by octave.

 

With W/H and full key remapping, and 2 axis-49, you'd have 2 complete 7-octave keyboards under each hand. and little need to look at the keys.

It's pretty "Wickied" ;)

 

Ken.

[Doug Keislar]

Ken on Google Rushton wrote:
> Doug,
> You got it. One can remap to anything. With janko you are pretty
> limited, as it goes side-ways - although you can fold it by octave.

I see. So for Janko, you could have one 3-row octave plus one 4-row
octave, or possibly (if the Max patch would allow specifying a zero MIDI
velocity for certain keys) two octaves of a 3-row 6-6 layout with an
inactive row in between. There would be something like 25 distinct
pitches (two octaves).

Not a great solution for someone who wants only Janko or a similar
layout, but much nicer for someone who either wants Wicki only, or wants
to experiment with several layouts, especially ones like Wicki where
pitch is arranged in two dimensions and all or most pitches are unique.
With Wicki you get three and a half octaves: 42 distinct pitches for
12-TET or up to 49 distinct pitches for a non-12-TET tuning.

Per Axis-49, of course. One could use two or more (as you mention) to
get more pitches.

Doug

[Evan Lenz]

I like the sound of that.

If you had two, would you make the second Axis-49 a mirror of the first
to correspond to the fact that the left hand is a mirror of the right
hand? For example, playing "toward your pinky" would always go upward in
pitch?

Evan

Ken on Google Rushton wrote:

[Ken on Google Rushton]

Hi,
I've toyed with the notion of using tricks to extend the range - imagine playing the bottom bank. Assuming that one does not play the bottom 2 rows of the 7x7 at the same time  as the top two rows would allow one to dynamically switch the pitches when one is playing in the top 2 rows to pretend the notes in the top bank are other than the default.

---------------------

I've fair experience with 4-row W/H (2 octaves) and that is just too confining. 3.5 octaves seems fine for most songs.

But I'm looking to the future, now that the only-7-rows-wide issue is resolved. With 2 Axis-49's fully reprogrammed to play 7-octaves, one for each hand, plus a Nano pad under the thumb, and a patch for duplex sustain pedal, I think this might just be a rather serious instrument, indeed. Total cost under $1000.

Not quite a Thummer perhaps, but getting there.

Ken.
Perhaps the Motto of the DIY music community should be: "making a virtue out of necessity".

[Ken on Google Rushton]

Absolutely. I tried it, it works. (my pianist wife just does not, not understand)
That's the advantage of building prototypes. 
Theory is good, but nothing beats testing and experiment.

K.

[Paul W Morris]

Hi everyone,

So I've been experimenting with other button-field layout
possibilities here, as I contemplate getting an Axis-49.

There's a lot to like about the Wiki-Hayden. My only reservation is
the half-step intervals. They may just take getting used to. (I've
been playing guitar for years, so used to the half steps between
guitar frets.) So I tried a couple of other layouts that have
half-steps rather than whole steps for their "east-west" horizontal
axis, as this is similar to guitar strings.

I started with the "Tonnetz" or "Harmonic Table" or whatever the
default Axis-49 layout is called, but turned it 90 degrees so that the
hexagons are aligned differently and the east-west horizontal rows of
buttons are closer together. (see attachments for each of these)

Then I experimented with two other possibilities that ascend by
fourths moving either diagonally up-left or up-right in each version.
Since I'm familiar with the guitar, I like how the fourths are similar
to it -- 4ths being the interval between open guitar strings (except
for one where it breaks its isomorphism for easier chord playing...).

Of the two I think I like the fourths ascending up and to the right.
See the row of E A D G... on the left hand side, which is the same as
the open strings of the guitar... This would be nice for seeing the
same patterns on both instruments.

I also include an updated Wiki-Hayden image.

Haven't thought too much about these, just trying them out...

Paul

[John]

> There's a lot to like about the Wiki-Hayden.  My only reservation is
> the half-step intervals.

As it was mine. But I've been practicing with the wicki/hayden layout
on my computer keyboard using the TransFormSynth (albeit with huge
latency and low sound quality, it's all the fault of my computer)
which is available here
http://www.dynamictonality.com/spectools.htm
and I've found that the half step, although the farthest interval
other than the tritone, is very easily accessible. Although not
intuitive in the 12-edo mindset, one is not physically limited by the
distance.

> Of the two I think I like the fourths ascending up and to the right.
> See the row of E A D G... on the left hand side, which is the same as
> the open strings of the guitar...  This would be nice for seeing the
> same patterns on both instruments.

It certainly is neat that there are so many possible layouts, each
corresponding more or less to specific musical genres or instrumental
tendencies. Every possible two dimensional layout has been identified
and explored by someone by somewhere, it would be nice to have them
all publicly accessible so that each individual didn't have to create
his own diagrams when exploring their possibilities as you and I, as
well as many others I'm sure, have done. So thanks for putting so many
up for all to see.

Still, the other layouts all require more buttons/octave than wicki/
hayden if one intends to explore outside our standard 12-edo. Because
it reflects the method of tuning in the syntonic temperament, stacked
fifths with reduced octaves, it can be used for any tuning including
those that have more notes per octave than an instrument (like the
thummer) has buttons per octave. This has to do with the fact that in
any tuning there are only so many notes that one uses in tonal music
for a given tonic and the wicki/hayden layout puts these pitches
closest together.

So the advantages in over all versatility of the wicki/hayden layout
are in my opinion completely unmatched. Some layouts work well as
chordal instruments, some work well for melodic performance. The
wicki/hayden layout compromises reasonably large access to both melody
and harmony with the *huge* benefit of the possibility of exploration
of tunings. This may not be important to most but it certainly could
be in the future.

> Absolutely. I tried it, it works. (my pianist wife just does *not*,
> *not *understand)

Was this referring to the mirroring of the layouts? Because I was just
about to ask you myself if you had tested this with success and if it
was all done with your software. Have you already created your mark 2
software?
I was curious because...
I just bought two axis-49 units today =D
I look very much so forward to discussing experiences with the
instrument and your software.

[Paul W Morris]

Ken, I think I'm going to get an Axis-49 on Sunday with the discount
(and maybe 2, if their 30 day return policy is in effect...). I saw
on your blog that you found a way to rearrange the keys so the colors
align more with the Wiki-Hayden layout. How'd you do it, and was it
easy to do? That would really put the icing on the cake if that can
be easily done.

Here's the image where you can see the rearranged keys/colors:
http://musicscienceguy.vox.com/library/photo/6a00cd972aa36b4cd50110184134b6860f.html

Thanks!
Paul M

[Ken on Google Rushton]

On Sat, Aug 1, 2009 at 5:45 PM, John <jlmo...@gmail.com> wrote:

> There's a lot to like about the Wiki-Hayden.  My only reservation is

I've found that the half step, although the farthest interval
other than the tritone, is very easily accessible. Although not
intuitive in the 12-edo mindset, one is not physically limited by the

distance. and the wicki/hayden layout puts these pitches
closest together.

Jim Plamondon spent years evaluating options, in his quest  for careful domination of the music world. If he said is was good, then I was prepared to believe him, and get on with using the thing. My concern was that there is often a gap between theory and practice, and my impression was that Jim leaned towards theory, I've been working through practice (although too busy to blog about it, natch.) I'm happy (deeply relieved actually), to report that there are no hidden gotchas (only one mild kinesthetic glitch so far). I've even found the thumb is going to be useful, especially on the left hand. In other words, the fingering works. Semitone spacing is getting to be automatic.

The reading of Traditional Notation also works,  with some reservations. The uneven spacing of the TN makes it tougher than it should be, but there are ways of working around it and teaching the fingers how to know when an interval is a minor vs a major third.  The fold on the 5th in the W/H keyboard maps pretty easily to TN, while I've found the Harmonic axis does not map as well.

So the advantages in over all versatility of the wicki/hayden layout
are in my opinion completely unmatched. Some layouts work well as
chordal instruments, some work well for melodic performance.  The
wicki/hayden layout compromises reasonably large access to both melody
and harmony with the *huge* benefit of the possibility of exploration
of tunings.  This may not be important to most but it certainly could
be in the future.

> Absolutely. I tried it, it works. (my pianist wife just does *not*,
> *not *understand)

Was this referring to the mirroring of the layouts? Because I was just
about to ask you myself if you had tested this with success and if it
was all done with your software.  Have you already created your mark 2
software?

 
To Marilyn, the notes always go up in one direction, to the right. Playing a parallel scale with the left hand starting on the little finged and going to the thumb and the right hand going thumb => little finger are totally natural. Going up to the left is unthinkable, literally.

I was curious because...
I just bought two axis-49 units today =D
I look very much so forward to discussing experiences with the
instrument and your software.

See my blog and a posting on the forum to come shortly.

Ken.

[Ken on Google Rushton]

Hi Paul

On Sat, Aug 1, 2009 at 9:36 PM, Paul W Morris <paulw...@gmail.com> wrote:

I saw on your blog that you found a way to rearrange the keys so the colors
align more with the Wiki-Hayden layout.  How'd you do it, and was it
easy to do?  That would really put the icing on the cake if that can
be easily done.

Not hard to do. Just take it apart as described here.  Note the instructions on doing it gently, and take off the top with it right-side up with the
The key-caps are stuck in a thumb-tack-like plastic fastener. Just pull the fasters off gently, and re-arrange & color the keys.
I'd suggest putting a dab of glue on the C's too, so you can touch-play

Ken.

[Ken on Google Rushton]

Ps. I got my second one.
Ken.

[Jim_Plamondon]

On Aug 1, 7:45 pm, John <jlmori...@gmail.com> wrote:
> It would be nice to have [all isomorphic note-layouts]

> publicly accessible so that each individual didn't have to create
> his own diagrams when exploring their possibilities as you and I, as
> well as many others I'm sure, have done.

You can generate any note-layout, in any tuning, using this
spreadsheet:
www.igetitmusic.com/papers/JIMS_Note.xls

Each "note" in JIMS Isomorphic Music System (JIMS) is defined by a
vector [a, b].
- alpha is the width of a first interval in cents (the period, often
an octave, c. 1200 cents)
- beta is the width of a second interval in cents (the generator,
often a tempered perfect fifth, c. 700 cents)

A given note[a, b] is ((a * alpha) + (b * beta)) cents away from the
reference pitch, which is any pitch you want it to be. Changing the
reference pitch effects a modulation. All of the structures of
tonality are independent of the reference pitch (with the exception of
some physiologically-based effects, such as the ear's frequency-
dependent critical band, combination tones, etc.).

If you've read my early paper on isomorphic note-layouts (http://
www.thummer.com/thummusic12.asp), then you've seen how it defines H
and V in terms of semi-tones. The problem with this approach is that
the "semi-tone" is an artifact of 12-tone equal temperament, with no
meaning outside of that temperament.

The JIMS_Note system, as described in the JIMS_Note.xls spreadsheet,
generalizes the H & V approach to describing/defining isomorphic note-
layouts by defining H and V as [a, b] vectors instead of semi-tones.

The "Variables" sheet of the spreadsheet contains six highlighted
cells, which are the only ones that should be changed directly.

The top two variables allow you to change the widths of alpha (the
period) and beta (the generator). Unless you're into microtonality,
you should leave these alone; the default values are 1200 and 700
cents respectively, which give you 12-tone equal temperament.

The next four variables allow you to specify the [a, b] vectors for H
and V. There's a table on the lower-right side of the same sheet that
contains the H & V vectors for common isomorphic note-layouts --
Wicki, Triad (aka "harmonic table"), Chromatic Button Accordion B-
System, Chromatic Button Accordion C-System, and Wesley. Just plug
those vector values into the corresponding highlighted fields on the
Variables sheet, and all of the later sheets will update to reflect
the chosen note-layout.

For your convenience, here's a list of vectors for common intervals in
the syntonic temperament (which is what you've almost certainly been
using all your life, except for Doug, who's exceptional):

m2: [4, -7]
M2: [-1, 2]
m3: [2, -3]
M3: [-2, 4]
d4: [5, -8]
P4: [1, -1]
A4: [-3, 6]
d5: [4, -6]
P5: [0, 1]
A5: [-4, 8]
...and P8: [1, 0]

In 12-tone equal temperament, some of these intervals are enharmonic
(e.g., M3 and d4), but that's an artifact of the tuning, not of the
underlying syntonic temperament (which is described in more deplth
here: http://en.wikipedia.org/wiki/Syntonic_temperament).

It's the definition of "notes" as being two-dimensional entities that
makes Dynamic Tonality possible (http://en.wikipedia.org/wiki/
Dynamic_tonality).

Different note-layouts have different strengths and weaknesses; one of
the advantages of the Wicki layout is that it is optimal for Dynamic
Tonality in the syntonic temperament (http://www.thummer.com/ThumTone/
Tuning_Invariant_Layouts_Last_Draft.pdf).

For a bit of theoretical background...In the JIMS_Notes spreadhseet,
the "Rect-note Indices" sheet shows the rectangular, canonical form of
a 2D isomorphic note-layout. In it, the note [a, b] is at cartesian
location [x, y], with x = a and y = b. All other isomorphic note-
layouts are just regular mappings of these rectangular coordinates to
geometric locations -- for example, to a hexagonal-lattice button-
arrangement

If I understood the mathematics of Voronoi diagrams (http://
en.wikipedia.org/wiki/Voronoi_diagram), which I don't, then I could
describe, in general terms, the mapping from this canonical
rectangular grid to any regular Voronoi diagram, which would include
all possible hexagonal and semi-hexagonal arrangements of physical
buttons. The Thummer's physical arrangement of buttons is only semi-
hexagonal, for example; the column spacing (between major seconds) is
wider than the row spacing (between P5/P4's), to make it easier to
play P5's without accidentally playing a sus2 or a sus4 by pressing an
adjacent M2, too. Strictly regular hexagonal keyboards such as the
AXiS, with no gaps between buttons, make such layout-specific
optimizations impossible.

...which is all much more than you probably wanted to know! ;-)

--- Jim

[Paul W Morris]

Wow Jim! This is really cool. I'll have to check this out more
thoroughly when I get the chance...

Paul M