38 posts from 2008

Updated Jan 7, 2009
A fool, it is said, is a person that does not know what they are doing, but does it anyway, in blissful ignorance of their incompetence.
A true fool, on the other hand, is a person that knows that he doesn't know what he is doing, but does it anyway, in willful defiance of his sorry ignorance.

I am certainly the latter. While I am waiting for my Axis-49 keyboard to arrive (my wonderful wife has granted it to me as what will be a very late Christmas present), for the edification of those amazingly dedicated souls (*) that read my postings, for my own education, and to possibly even save some time, I am attempting to work out the dynamics of the Axis keyboard strictly on theory and from my experience with the jammer keyboard's Wicki-Hayden layout.

Do not take what follows as being anywhere complete or especially insightful, and as always, all mistakes are mine. Any correct details are likely the product of chance and/or the feedback of my critics.
(*) Believe it or not: approximately weekly, some new true masochist (not a web-crawler) reads through a large portion of this site.

Harmonic Table: From elegant simplicity to surprising complexity
I've mined the web, especially the C-Thru site and Peter Davies' Opal site  for information on the Harmonic Table keyboard layout, and have found mostly tantalizing hints.

What I crave is the fine details of how to play the Axis keyboard and which nifty things that I can do, once one appears in my fevered fingers.

I'm looking for the practical working instructions, like I'd get if I went to a good guitar teacher, along with hints as to what I can do with a little practice. Jordan Rudess has a nice presentation, but it lacks the "Axis-Keyboard-for-Dummies" approach needed for keyboard novices such as I.

The raw basics
When presented with an innovative, totally new device like the Axis 64/49 and the “Harmonic Table” layout. The mind takes a while to sort out the salient new features.

First lets take a look at the key-field and get a feel for the larger features:

First, the basic unit of music - the notes in a octave as they can be grouped on an Axis keyboard. I've coloured the notes of the major scale and marked in the musician's names for the notes. 

At first the notes look a bit daunting to learn, but it's not really too bad, with a good, practical mapping to one's fingers.

Many notes that often be played together are close and can be played with one finger. (I'll talk about playing later, in a separate posting).
 
There is a slightly odd gap of notes (white on this diagram, black on the Axis keyboards) which one normally will want to avoid playing with the others. Whimsically, I call this the Gutter of Dissonance. 

Basic Axii: 

 
Right next to each note is an harmonic adjoining note, unlike on the piano, where the adjacent notes are normally almost never played at the same time.
 
The Fifth
This keyboard layout is totally nuts about the 5ths; everything pivots around them. In most music the 5th has a very special relationship with the key (the root note) of the piece. It is in many ways a secondary key center. On this keyboard simply by moving up a key row does this shift. That's all that's needed.  

The replacement of the conventional octave as the dominant musical center (paradigm) in a musician's mind may be the single greatest advantage of this keyboard. It's different, but still profoundly musical. The octave notes are so like the root note that they are boring.

To give just one example: a cool thing one can do on this keyboard is tune the fifth perfectly, rather than temper (flatten) it to fit the octave scale. (if you do this, the octave will be a bit (~2% of a semi-tone) sharp, which is not a grave musical sin, just slightly scandalous, and therefore interesting).

Another, more important example: many pieces of music involve establishing a pattern, then once it is established in the listener's ear, tweaking it in a musical way, so that the harmonics invoked change in simple ways. Thus we musicians keep our listeners interested. The trick is to do this in the aforementioned "musical way". That's the power of this keyboard, as it is wrapped around and deeply embedded in musical theory.

Tip: if you have learned a neat pattern, turn your hand 60 degrees. The same pattern should sound (mostly) musical and may (I suspect) sound interesting. You can repeat this until you have gone all the way around; in theory, 6 pieces can be learned for the price of one.

The Thirds
Also used everywhere in music is the Major Third and Minor Third intervals. If you learn a pattern and shift it diagonally one note over in any direction you will sound, quite literally, jazzy. That is what jazz musicians do in jazz (caveat alert: this is just one of several tricks used).

What I think will work: shift the hand up, down, sideways etc. for just a moment (one chord, one or two bars), then snap back.

Ridges and gutters:

There are distinct lines of consonance and dissonance (white keys and black keys) in this keyboard. Which makes sense: the consonant notes are grouped together, consequently the dissonant notes are also grouped.

In my diagrams, I've given the "white notes" a unique colour and coloured the black keys white, as this makes the coloured notes stand out better.

Based on my experience the the jammer's Wick-Hayden layout, I strongly recommend that the keys on the Axis be coloured.

Missing Axii
It's often the case that an improvement in one respect comes at an cost in other ways. So it is with the Harmonic Table layout:

The musically important intervals of Octave and Fourth are nearly "Missing In Action". This may make playing normal music harder.
Confirmation from some Axis-64 users: yup; playing inversions is indeed harder.  

Semi-tones and Whole-Tones:

Weirdly, the notes that are close together on a standard piano are stretched out. Fortunately, they can still be reached by the fingers in under the hand without undue movement or stretching, a key requirement for speed and ergonomics. This is partly due to the smaller keys.

 

Major (and Minor) scales :

The major Scale and it's close cousin, the Minor Scale have profound reasons for existing (one day I will get up the nerve to try to explain it - it's not that hard).. Besides, western music is written around it and imbeds it totally, and that's what the instrument must play.

How does it do?

Not bad; not bad at all. To the right I show, I hope clearly, what I guess is the commonest way to play these scales, showing a numbered ascending sequence on the left side, and the fingers needed on the right.

This pattern must be utterly become a part of the soul of a musician playing this instrument well.

Note that the distance traveled to play is measured in millimeters and scant centimeters, while on a piano, it is a factor of 10 greater or more. This should translate to a huge improvement in playing speed.

Other observations;
Octave Units :

Around the octave one is playing, is clustered other clusters of octaves, but because an octave unit on the Axis is 6.5 notes wide and less than 2 notes high, the octave units abut in a different way.

The thumb seems to be seldom needed. The thumb has an awkward shape and is awkwardly placed (except to play bass, perhaps) to be used on the smallish hexagonal keys of the board. Note that Jordan Rudess' in his demos seldom uses his thumb. Addendum: Jordan confirms this.

"You are right that it is harder to play the instrument with your 
thumb. I sometimes will use it though for certain musical situations."

I believe this is actually an great advantage. Jordan loves using the mod wheels but has to stop playing with his left hand to use them - amazingly bad ergonomics.

Imagine what he could do with a better thumb-control such as I prototyped here:

  

One can also "slice up" the notes in other ways.
Zones: 

Here's another way to group the notes. On the Axis-64, the key-field can be broken up into 3 Zones, each 7 columns wide.

How does the Harmonic Table system; the heart of the Axis keyboard, work? 

 

To the left is my attempt at showing how harmonics are laid out and inter-relate as explained in the basis of harmony and a jammer sound-byte.

This is a "twice folded scale" whereupon we have notes evenly spaced out, in intervals called a major second, and fold them twice, first by octave, and then again, so that the octave family of harmonics(1, 2, 4, 8, 16, & 32), the green circles, are next to the Perfect Fifth family(3, 6, 12, 24), the Red circles. 

This is the basis of the Wicki-Hayden (Wicki for short) key layout and design of the jammer keyboard. One big advantage is that one can press the two notes most used together in music with a single finger straddling the two.

The jammer has other advantages as well.

But can we do "better", at least in terms of fingers-per-musically-useful notes than the jammer? Yes, we can! The Axis keyboard uses the Harmonic table layout.

The Harmonic table is fairly closely related to the Wicki, as I hope to show (in my addled-geek way). For one thing they are consistently laid out, so one only has to learn one finger pattern to play them instead of 12.
Cast your eyes on the harmonics in the little diagram above. Is there a way to put the blue circles right next to the red and green ones? Yes, but it's not a free lunch. Instead, it's a meal that's reasonably priced, yet with some intriguing spices.

Step 1: Note the Axii of Fifths 

Key to the tranformation is the concept of tonal axii (what's the plural of axis? axes? axises?). You can see that the Wicki layout has a row of keys ascending to the right. This is the Axis of Fifths, with the keys numbered 1, 5, 9, 13 (why do they go up by 4s? 'tis a quirk of musical arithmetic). There is also a flanking set of parallel axii that are up and down in pitch by a relative whole-tone (a.k.a. major second, or 1/6th of an Octave).

We can remove the parallel axiI and keep the vital consistency that a simple-to learn instrument must have.

Step 2: Identify the pesky intervening notes,

They have been colored white.

 

Step 3: Pull the intervening axii out

 

 

 

 

 

Step 4: Re-assemble them: 

 

 

 

 

Step 5: Add the discarded axii back in

You still need them. On this layout, they have
a place to go that's reasonable for playing.  

 

 

 

Step 6:  Rotate it so the major Fifth Axis is vertical  

And we are done.

This design at first looks bizarre - the octave is way off to the side, and the fifths (and thirds) become the dominant musical principle on this keyboard, instead of the octave. 

 

But it does have advantages, especially to a musician looking for a new way of viewing music. Just look at the way the harmonics fit together. (!)

That, however, is a discussion all on it's own.

 

Ken, the Music Science Guy.  

C-Thru's Axis 49 is in production (Updated March 2009)

Last summer at a company called C-Thru Music announced that it would be making a smaller-scale version of its Axis-64 pro midi Controller , an interesting keyboard that had several major drawbacks.
(As always this is from my perspective – your mileage likely varies).

While the Axis-64 had the critical 2-dimensional hexagonal, finger-sized keys needed to make an truly player-friendly keyboard, in early 2007 the Axis-64 had these hindrances:

1.   It was expensive - initially over $2000 Canadian, and available only from England.
The problem is not so much the price; $1500-$2000 is cheap for a good keyboard.
The problem is that the personal value of the unit was a total unknown.

2.   It used the 'somewhat different' keyboard note layout, the harmonic table , which I understood only to a limited degree, and did not explain it or demo it well.

3.   The initial website, late 2006/early 2007 was really geeky (worse than mine!) (this may have been the website of the inventor, now set up for a related company Shape of Music).
For example, it gave not one hint that I could find that the keyboard was velocity sensitive. Imagine a website advertising monitors, with every single picture in black and white.
[correction: apparently it was here all along - I missed it.]

In other words, two years ago my thoughts were "So close, yet So far - Rats!".

The Axis-49 midi Controller , on the other hand, has the potential to be a true industry changer.  
Consider:

1.     It’s one fourth the price: $500 US, and available from the US. The price hits the crucial musical-hobbyist entry range, with room to grow. (It's a bit high; $300 would further triple the market, IMO). $500 for a unique keyboard can be worth it to us music geeks simply for the musical education it provides (and to be honest, the sheer geek bling).

2.     While it uses the harmonic table layout, it’s now easy with simple tools (i.e. Max/MSP) to remap keys from one layout to another. I have done so.

3.     The website has really improved from the “invent it and they will understand it” ancestry. They now mention prominently the crucial “velocity sensitive” phrase. And the demos have improved, although still a tad esoteric and some use boring Rolland midi sounds.

    4.     They have also added a forum, an excellent way to get feedback
    5.      They are gathering many fine testimonials.

In other words, if I buy it, can I play ‘Doe-Rae-Me” on it to my friends that night?

(update: Actually, I played Happy Birthday to my wife on the second night, using the Wicki layout.)

At last the dream keyboard looks within reach

The smaller size of the Axis-49 turns out to be an advantage over the larger Axis-64. If the first Axis-49 works out, I'll buy a second as a practice machine to take everywhere.

Twisting on the Axis.

As an example of the flexibility, with 2 of these units and a couple of Wii-sticks,  one could make a not half-decent two-handed Thummer  or jammer, quite easily.

Perhaps, at long last the quest for the fabled practical "isomorphic' (I hate that geeky term) keyboard has found it's first major goal. 

____________________________________________________

Does this mean that my work creating my own keys is a waste? No! I'll tell why later.

 

I've glued together, sanded, inspected and corrected 120 of the blinking things. The only things left to do are: drill excess glue out of the spring holes; and actually mount them in a keyboard. Oh-yah - and make the key caps.

The key caps can be of two shapes:
 Rectangular (or "click-let", for Janko-layout,
 Hexagonal, for Wicki-Hayden or Harmonic-table. Chicklets are easier to make.

Now, what am I going to do with these funny keys?
Convert 2 or 3 M-Audio keyboards, specifically the oxygen-49 or the Oxygen-61 to Janko layout, like the Chromatone.

This will be do a couple of things:
1) prove I'm not mad (odd perhaps; very slightly loopy upon occasion, but no way mad-scientist mad, I'm past that now; I take my medication ;))
2) let me know how if the new keys will fit into the M-audio case properly. It's not good enough to have it work, in our fussy world, it's got to look dang near perfect.
 
Once they are done I'll be looking for people to try them out, with a view to moving forward.

Finally, I'm getting somewhere.

I've managed to make 8 good moulds and about 100 key pairs so far (I had more but went over them and culled them drastically). With 8 moulds in service, I can make 16 keys (32 halves) at a time.

Mixing and pouring the casting compound takes about an half an hour - I have to make up 3 batches of compound, as it gels in about 4-5 minutes, tops. Pouring a liquid that dynamically changes viscosity is an art. (BTW, if you want to do this yourself, I'll write up and post the gory details. You don't have to re-invent the wheel!)

I've also overcome the latest snag: gluing the halves together.  I was told that 5-minute epoxy would do the job, but instead found that it did not quite bond to the Por-a-Cast (sic) polymer quite well enough. - the forces on the spring end are quite high.  The release agent that allows the cast to come out of the Por-a-Mold material does a good job of weakening the bond to the glue (duh! - I should have foreseen this). For this reason, I've largely gone over to silicone moulds, except for my best 2 old Por-a-Mold moulds, which helps. Silicone moulds are the way to go for this job. But even silicone leaves a thin no-stick, almost teflon-like residue.

The secret: Dip the spring end of the key in anhydrous (i.e. 99.9% pure) methyl hydrate (methanol) or acetone - available at any hardware store. This removes the release agent and "opens the pores" of the plastic.

What's next
Next I finish gluing the keys together. grind them flat with my table sander.
 and make up enough for 2 keyboards. 

Ken, the Music Science Guy

At long last, production of keys has begun.

To the right you can see the masters mounted on a 6 mm plastic sheet. The dark parts are areas built up with balsa wood, and or tape - some areas were ground down too. Fiddly work it was.

However fiddly, it's done. Now the next stage begins.

To the below left, is the masters clamped onto the molding box:

The liquid resin is poured in the top, the bubbles are shaken and tilted out (hence the clear acrylic sheet. It's about 15 minutes to do, and the thing sets overnight.

BTW: If you should be possessed of the whim to do this your self, Write on the resin containers ""lube??" to tell you to spray on the special lubrication that allows the mould to unstick from the master, or the cast items to unstick from the mould - I forgot to do this for the second set of key casting, and boy, were they hard to get out, despite the presence of lubricant from the first casting.

I can't say it's efficient or fast.  The first pair of keys took over an hour to make. 

However, once a mold is made, mixing and pouring the resin into the mold is fast. I'm going to make many molds - several a week. Once I have 6 or 8 , I should have the ability to make a keyboard conversion kit or three.

Ken.

An important milestone: the masters of the new keys are in from Diversions Inc.(Thanks, Kevin).
Update - with all the redesign some dimensions are off - I'm sanding, hand-carving (with the help of various tools), and filling in with balsa wood.
I'm almost finished the re-re-re-design.
Whatever M-Audio pays it's designers, it's not enough. This is hard work, working in .05 mm increments - I used a piece of thin paper to adjust the depth of the grinding, for example.
Ken.
Further update, Sep 8: Finished the masters, and have begun making the keys.
Ken

These are the start

Here's my rough plan:
1) Check them over v.e.r.y carefully.
2) Polish, sand, and enhance where needed
3) A-fix them to a thick sheet of clear acrylic
4) build mold boxes and make many molds
(These will be available for purchase if you can't wait for me)
5) run off n keys.
6) buy a M-audio Keyboard with n keys and convert it.
7) test it, then sell it.
7b) refine the design as needed.
8) Once my time and material costs are known, I will be able to estimate the sales volume and timings.
Then I'll be open for business.
Ken.

Hi,
Here's my first dry run at making a resin cast mold. (trust me, I'll need more)

The two halves were screwed and glued to a plastic sheet:

Sorry to have not blogged for a while!   I hope your summer is as busy and happy as mine. Currently I have my son and grandson visiting from Montreal, so jammer keys is pretty low on my priorities list. Greater Vancouver during the summer is a wonderful place.

But enough of petty distractions. I'd like to let you know about my findings thus far. In 2 weeks, I'll have more time to devote to this, so I promise the pace will pick up.

If the key is cut into 2 halves, down the long axis, then the following happens to the parts from a molding perspective:

So there's probably a gotcha - there always seems to be -  but this should put me nearer to $2-3 grand for injection molding molds. To see the keys in more detail, here's the ProtoMold rendering

It also gives me a fallback to resin molding.
For resin molding, I need to get the time per key way down.
Can I get it under say 3 hours per set of 88 or 66 keys? (I like my keyboard friends on the net, but I neglect my wife at my extreme peril)  Time will tell, but I think I have a way to skip the vacuuming step, using sonic de-bubbling. If I can do say 12 keys at a time, then it starts getting feasible for running off a few prototypes or more. 

So I've asked Kevin the Plastic Design Guru to 3D to print one each of the two kinds of keys.
I will take them, split them in half with a razor, and try making some resin casting molds out of RTV. 

2) I've also asked for an estimate of his charge for the redesign of the 2 keys into 4 half-key injection molding. Injection molding design is an art form.

So, comments are welcome. Resin molding experts help is needed too.

Ken.

Hi loyal readers. You sure are a varied lot.  See: my site monitor  .

While work goes forth on the Generalized Keyboard conversion kit, I'm refining the design of the jammer.
I had to take it apart to analyse the keys and to show to plastic makers. Now I'm improving it as I put it back together.

The main change is invisible: I've tuning the keys to the same, much lighter weight, so that I have more hope of learning to play it well. when first constructed I was happy to have a working instrument with all keys that worked and had pianoforte. Now, as I learn the details of construction and the mechanics of playing, I'm getting more fussy. When I measured the pressures required, I found they were way out of spec. The good part is that, now that I've found this out, others are saved the work.

But enough of technicalities. On to the important things: gadgetry.
Can you guess what I'm going to do with these items?

The first correct answer gets a free jammer conversion kit (when finally I start making them).

Ken.

Update: Here's what it looks like after the 1st assembly, but before refinement and styling.