10 posts from 2007

A Critical Test passed
One of the critical little make-or-break things for any instrument is fingering.  If you can't push the keys/buttons/valves fast, consistently and easily, the shiny new instrument "jes ain't gonna make it".
The worry was small, but nagging: in any design of something new, there's always the chance something was overlooked.

Jammer Basic fingering

But! ... Its different.

For those readers trying the thing out, this what I believe works: 

The mad man thinks he's the only one in the world to truly understand the the truth. I think I understand how music works, so to prove I'm not mad (Ha! I'll show them he shouts! ;-)) I've made a minor career of the unholy challenge of explaining music to unwary passers-by. Gradually it's getting much easier to explain, as I build a portfolio of simple examples. Learning about the jammer (the generic version of Jim Plamondon's Thummer, and its Wicki-Hayden key pattern) was a major breakthrough.

Towards a layout that shows where the harmonics are
If one lays out the harmonics on a linear, piano-keyboard fashion, how they inter-relate is absolutely anything but clear:

Harmonics laid out in a line

This is roughly how the inner ear hears ("feels" is a more accurate term)  a single note. Sounds in the raw, as it were, broken down into individual harmonics touching the ear's nerves gently in a line and spacings determined by basic count-on-your-fingers arithmetic. That may be how the ear "feels" the touch, but like the feel of a pen in the hand, wherein touches across several fingers gets integrated into a single sensation; the brain sees a single "pen".

One can fold the graph above over midway at the octave change point:

Harmonics twice-folded scale

Now this only shows you the good stuff; where the consonance points are. Around each harmonic is a spot about a semi-tone flat or sharp where if a another harmonic is present then it sounds dissonant.
(an audio demo is needed & planned here)

Dissonances are important too
The dissonance can be pretty intense (one person singing 1 semi-tone flat can be heard in the choir of 100 people!). Here's a rough diagram:

Harmonics twice-folded scale plus dissonances

A better way to show how we hear sounds
If we fold it up into a 'jammer' (technical name Wicki/Hayden) layout as shown in Easier to Play, it becomes a lot clearer and closer yet to what the brain is "seeing":

Harmonics jammer-like scale plus dissonances

So the jammer layout has two added bonuses:  (1) it's much closer to the way your brain hears sounds than a linear (straight-line) layout and (2) it's much harder to sound like a fumble-fingered klutz in it.

From this, much is obvious. One can, believe it or not, deduce all the world's common musical scales - and perhaps, invent modestly exotic new ones .
Stay tuned and I will show how these scales come to be.

Why an interval sounds like it does

If one play two notes there is always a pitch interval between them (even if it's the same nominal pitch). The two sets of harmonics overlay each other and interact in simple ways to produce a complex result.

A Major Third
To give one of the simplest and commonest examples, consider playing a note (the root, i.e. C) and places a second note exactly 1/3 higher in frequency (an Interval of a "perfect (major) third", i.e. an E), then some of the harmonics in the note that's a third higher will sit right on top of the roots' harmonics, the 5th, 10th and 20th to be exact.

Harmonics Maj3rd

This will sound nice and smooth (consonant) and the overlapping harmonics will sound especially interesting. Even a small deviation in overlap either way, but especially down in pitch (flat) won't sound as good (not really bad as in evil), just louder and obnoxious.

Now, in music, everything is relative: one can aim at lots of different harmonic series in the root. Below is shown the interval of a perfect minor third, some of its harmonics overlay the strong 6th, 12th, 24th and interestingly,  the 7th and 14th harmonics of the root (these last are not well tuned).

Harmonics Min3rd

The odd thing is that it's kind of like friends: while you may get along fine with Susan, and just swimmingly with Ann, yet find Ann and Susan fight like cats that caught the same mouse; The minor third and major third just don't get along in the same chord. Yet a millisecond is all that's needed to separate them.

Making music interesting
Play a root note with a major third, then instantly switch to a minor third, and the overlaps change: we've switched to overlaps on the 6th, 12th, 24th, 7th and 14th. The ear doesn't care, but your brains goes 'hey - what happened to the root note?'. It takes about a second to figure it out, so as long as you keep changing about once a second, you're in business.
(dear reader: an audio demo is needed here - care to craft one for me?)


Making the simplest chord
Here you can kinda see the overylay pattern of a Major Chord (root position):

Harmonics MajChord

The thumb-unit is still to be completed, but I now have a "Piano 2.0"; a jammer.

All the keys are just like a piano in action and feel. (Not surprising, as they are piano keys with a special overlay)

A very playable jammer

If you want to build your own, please let me know and I'll help - I can show the design, how it was made, offer tips for improvement, and if you don't have all the hardware to make it, I can help make the wood and keys. (For the last I would expect a significant donation to my charity, the Vancouver Walk For Breast Cancer)

Ken.

PS. Here's how the keys are mapped to notes.

Portable Jammer note layout

When one is faced with limited options, sometimes the limitations spur innovation.
In other words, any idiot can make perfection with perfect tools and gadgets, but it takes a real idiot to fake success successfully.
 
With the M-audio unit, the PC board does not split evenly in half, instead there's a row of 49 and a row of 39 keys.
This means there are 39 keys that can be paired up, with 10 left over.
39 keys is pretty good, - that gives almost 20 keys for each side (actually more, if one is clever with programming). the extra 10 can be either used as more notes, or as I've elected, special keys.

The layout I've elected is to make each side into separate logical keyboards, one for each hand. the default setting is for them to work together as a single piano keyboard, with the right hand C being C3 - "middle C" and the left-hand main-row C being C1. The rows above are of course the octave above. (The top row and bottom row are, alas, the same note as the upper middle and lower middle row - I just put in an extra row of keys onto the M-Audio's physical keys, I figured they'd still be handy for keying)

This only gives a measly 4 or 5 octaves - not too impressive when you started off with 7 and a bit. Not too much compensation that they are great octaves, really easy to play.
However, there are those extra control keys at the side
- can we use them to improve the keyboard?

ZipEx2 Special Keys

- access to the rest of the octaves - all of them
- an easy way to do a halftone modulation
- a way to do a "one-line" shift
- a simple way to switch to any key.
- an easy way to reset.  

ZipEx2 split

Here's how the keyboard divides into a left and right logical (virtural) keyboard, each of which can be  independently assigned a instrument, and/or a desired octave range. I'm hoping it will make contrapuntal motion in the same octave really easy.

A brief comment on better key design. We don't have to be slaves to tradition - or even geeky geometry.
For example,  how about a heart shape?

Part 1 - What is the optimum width and shape?

Finger tip & key spacing

• rounded corners is best
• The key spacing (on a jammer derived from a regular keyboard is too far apart to be ideal, but still useful for learning
•   A round/hex hybrid shape for the keys would be better
  
• Possibly a more complex shape.but we can give it a sexier shape, as long as it interlocks fairly well.

- also see ways to add a Wii to it. and Connectiing a joystick to MaxMSP/Jitter 

-          Acceleration (brightness) (2^nd differential) would be good to have., although most midi does not support it easily. - piano players plainly use it: to quote an expert "using the flat of the finger gives a brighter sound" presumably the flat finger gives a higher initial acceleration, loading the hammer head with speed, but lowering its effective mass, so it bounces off more quickly.

-          Piano key width or a bit less would be good;  The lower limit would be the computer keyboard spacing

-          Color scheme is useful and fun! It also seems to be increasing my weak sense of perfect pitch.

-          Dimpled/scooped surface might be better; it would help keep one centered.

-      with my current large, flat key, it's easy for the fingers to drift - there's no tactile clues preventing it, until one hits a neighboring key.

 A lot of things become possible if there is a modest community of jammer enthusiasts that specialize somewhat – for instant, one could build PCBs – or know a shop that can build them for the community, and one could build the keys – the ideal would be a plastic mold

Giving keys a fun shape

Gavin Healy, one of the first people ever to learn a jammer wrote:

"I can recall the first time sitting down with the Capel. I didn’t know much about the Thummer at all, especially the layout. For me it was not having any preconceptions of the Capel. I simply plugged it in and started experimenting with an open mind, which is when I realized the same pattern fingering for scales and melodies. I found this absolutely amazing and exciting.

So I think the best way to start with a Thummer Jammer or ZipEx is to simply have fun experimenting with it, not trying to learn songs, melodies or patterns, but just simply banging it and letting the brain develop the motor skills needed. After sometime banging and playing with it, melodies, scales, songs and patterns naturally occur from simply having fun with it."

Sage advice, I've found.

I can add a bit to that - remember that Gavin already knows how to play an instrument, so he is transfering a skill already learned into a new system. for those of us whose instrument is singing, its perhaps a bit slower.

1) Grab some children's music books - the ones in C - just practice the melodies.

2) Useful to practice C maj, F maj inversion (keeping C in common) - this is the basis of 50% of music.

Odd things about the instrument:

 The separation of close natural vs flat or sharp intervals by such a gap is odd at first. Then the fingers get used to it very quickly.

 There is at least some transference of skills from the right to the left hand, speeding up learning times.   

Nick Allott, who tested the Thummer as well:

I also like how the button layout is symmetrically opposite for each hand, making every pattern the same in both hands. This is great because you can then have your stronger hand teach your weaker hand (which is a very effective way to learn). This way of playing is quite different to both piano and guitar (which have higher notes on the left and lower notes on the right). With the Thummer, it’s more a case of lower notes are towards the centre of the body and higher notes are away from the centre. I am still not used to this way of thinking, but I can see logically that it will make more sense over time.

What if there was a musical instrument that was easier to learn, faster to play and best of all, provided a special insight into how music comes into being?

Herein I present the “jammer”, an innovative musical keyboard design, and why it’s so cool.

The 12 notes of the scale

First, let’s design a music keyboard from scratch, as if you’d never seen one before.
There are 12 notes in an octave,
     spaced apart by a semitone. 
     Two semitones steps make a wholetone.

Step 1: Lay out the keys in one row all equally spaced by semi-tones, like this, and you have the layout of a harp's strings.

Twelve notes on two rows

But unlike in a harp, we don't have to be linear, and we don't have to base our design on a early harp-like instrument that only had the C-major scale's notes.
Next: It makes sense to stagger notes so they alternate: 

And slam them closer together:

Notes of the major scale

So far so simple. If you play all in sequence all 12 notes you get a chromatic scale, presumably so named because it has every color of note on the scale. Most musical scales are whole tone based, with the type defined, largely, by the notes they skip, and when they sneak in a semitone jump. With this layout, a major scale goes as shown right:

If you add a third row on top, then you can play any scale, in any key using the same pattern.

Playing major scale on jammer

You have much less to learn – 1/12th (!) as many patterns as on a standard piano keyboard.

This is the Janko pattern and is over a century old.

It's also a trifle bulky, as you can see if you click the above link.

The technical term, used (I suspect) to either scare off non-geeks or to sound intellectual is isomorphism. I prefer the term consistent-interval, or simply consistent. (Personally I bet we'll one day hear the term in a science fiction show: "he's gone isomorphic, Jim")

Compare to learning the piano as show here:

Playing major scales on piano

It was first designed without black notes,
and its totally designed around the C-major scale. 

Other scales are fiendishly hard to play.

It's rumored that the Janko pattern was scuttled, despite being favored by noted pianists, by piano teachers. Bad people!

That’s easier to learn – what about easier to play?

While the Janko pattern is cool, it flopped a century ago, and perhaps not all the blame lies in greedy piano teachers. After all, pianos are hard to lug around, and an reduction from learning 12 (!) fingering patterns to just 1 streamlines only one part of the playing experience. After all, the simple alternative is to just learn one pattern as was often done.

Can we do better? Can we take advantage of the fact that some notes are physically adjacent? Normally on a piano you’d seldom play adjacent (Black and white) notes.

The patterns the thing

Lets look at the important notes in the scale. In all scales there’s a special note, the Root, it’s odd twin the Octave,  shown in green on the right.

They have special partners the 5^th and the 4^th, also know as the dominant and  sub-dominant. 

Practically every musically useful chord pairs a root or the octave with the 4^th or 5^th. With a linear layout, the useful notes are spread out and you have to bop around a lot: great, big hand motions are needed, and the piano keys are big and heavy because the thumb also has to be able to play them.
And ... you can’t wear a piano, or even carry it to your next gig.

Spaced out notes!

If we slide the notes in the second row over a bit, the 4^th and the 5^th can be put right above the root.

Consequences both simple and a bit bizarre:

• On the third row above, the octave naturally appears above the root, between the 4^th and 5^th. All the important notes touch.
• The design is brilliant. My thanks go to the inventor, Brian Hayden.
• We can play the commonest useful pairs of notes with one finger.
• Thus suddenly almost every chord needs one less finger - often two!
  

  Less 'Spacey' notes
• Add a few more rows and the hand movement needed to switch octaves drops from feet to mere inches.
• Instead of moving the hand a lot left and right, just the fingers have to move a bit up and down
  
• Bizarre side effect #1; it gets harder to play wrong notes, as the dissonant pairs have been pushed apart. 
• Bizarre side effect #2; you can play new patterns with your hand turned sideways.
• Since the keys are closer, one can play more exotic and interesting chords with one hand - you can jam!

And there's more:

• The thumb is free to do cool things to the sound, as is shown at thummer.com.
• The human brain is wired to think in this pattern, so players understand it deeply.
  

So there you have it – here’s an instrument that you can play in any key, significantly faster, and as I show in the next segment, also allows you to jam, improvise, arrange, understand and therefore teach music far faster.

So how do you get one? You either join the ThumClub, and lobby for a Thummer(tm) (joining does not seem to get you more than 2 emails a year, for those spam-shy), or build one. I, naturally, recommend both.

Thirds are OK too

* We'll deal with thirds later; they are a fully a topic on their own.

* Also note the this idea is not unique, a guitar's strings mostly go up in fourths (4th, 4th, 4th, 3rd & 4th to be precise), and some guitarists tune all their strings up in perfect fourths, violins strings are always tuned up in perfect 5ths. Finally, European accordions (concertinas) have this precise layout, known formally as Wicki-Hayden.

Downside:

Thus far, I don't know of much in the way of problems with this system, except that its a touch more complex (at first) than the Janko system. Even playing a chromatic scale (ascending semi-tones) is easier than on a piano.

Gavin Healy, one of the world's first jammer players, wrote:

"What I found amazing is that the Thummer taught me patterns of intervals like this one: whole-tone, whole-tone, semi-tone; whole-tone, whole-tone, whole-tone, semi-tone – which defines the major scale. This to me was like a revelation; I could simply remember this pattern and automatically transfer it to my instrument of choice. I felt like this was a hidden secret of music theory. Instead of learning all these different fingerings for scales, chords, progressions etc on the piano or whatever instrument when I was a kid, I could have been taught the geometry of music which actually makes more sense." 

The wearable ZipEx is a 4-row musical jammer keyboard I built because (1) one can't buy a Thummer yet and (2) it happens to be surprisingly easy to build from a "regular" keyboard. Jammers have several advantages over a traditional keyboard.

This design is also a living illustration that one can make a virtue out of necessity; when forced to make do (e.g. can only make 4 rows), then the "making do" forces interesting innovation (e.g. use tricks to make the thing have 8 rows - take that Thummer!), and with the dementia that comes of gadget-building obsession.

This unit has 4 rows of 15-20 keys, arranged thus, when playing in "laptop" mode:

ZipEx Playing- Hands on Same Side

And in "guitar" mode:

ZipEx Playing-hands on alternate sides

The black keys at the side are pitch and octave-shifting function keys, used to make it pretend to have more rows and keys. In effect one can have a 96-key keyboard that pretends, if you want it to, be two keyboards, one for each hand.

So there you have it, the music geek's newest fashion accessory: 

A bit more portable than a Piano?

I've actually had multiple people stop me and say: "what the hell is that?" - no finer accolade can a geek get.

Just fold it over

How to make a “ZipEx” style jammer*

Riddle: How do you make a 4-row hexagonal-key instrument from a 2-row piano-key one? 
Answer: you fold it over and replace the keys!

Background:

Update: I've since made a second generation version, the ZipEx Mark II, the basics are still the same. This rebuild-from-the-PC-board-up way was much harder but resulted in a smaller, wearable version. The Mark II is heavier, but much easier to build. Ken.

A typical electronic keyboard has 2 parts, one is the music control thingy, I’ll call it the controller, and the second the key holder assembly itself.

I have examined just 2 keyboards, A Yamaha DjX, and a Technics P50, but I suspect most are pretty similar.

The key board electronics is on two loooong printed

DjX keyboard PC boards extracted

circuit boards (PCB) clamped into the key assembly. The two boards are connected to each other by a single 6-inch, 12-lead wire, and one of the boards in turn connected by a 10 inch or so, 6-lead connector to the controller.

Each long PCB has clamped onto it a bunch of rubber buttons which make a little dome about 2-3 mm over the PCB. These buttons are depressed when the plastic keys of the keyboard assembly are depressed (I'm not sure what makes them happy).

The underside of the little dome buttons, the part clamped to the PCB, has a little bit of conductive black graphite paint on it, and when it hits the PCB, it closes a circuit, and the circuit generates a signal that the controller interprets.

DjX Keyboard PC board

On the Technics keyboard, each key has two buttons it depresses, presumably at slightly different times to denote a key's velocity.  The Yamaha has a double contact set within each button and the contacts are of slightly different length, thus also hinting at the key's velocity. The important thing here is that you don't need to know further detail on how it works, or electronics.

In my design, I used just the pc boards and the rubber buttons, and rebuilt the key holder assembly.

List of materials

• A keyboard to cannibalize - I used a second-hand Yamaha DjX,  $60
  
• Clear plastic about 3 mm thick for the base – I used a piece from a vinyl window. One should be able to get this from a glass window shop.
• 70 plastic or metal posts – allow extra 10 for wastage - a set of 19 mm nylon spacers for PCB boards worked well here. 
• Material to make 70 plastic or wooden keys. I used Douglas fir for Practice, and settled on Maple rather than Oak
• 35 springs – I cut them in half, as they were expensive, @ 80 cents each. Drop a comment if you need a supplier.  
• 70 key caps.  – made from thick plastic sheets – I have some extras I can send to you. 
• The keys caps were attached to the key-tops with double–sided tape.
• Lots of bolts to attach the posts to the base and to cap the posts
• A tap to thread the posts so the bolts could screw onto them.

Tools

• Drill press with depth control
• 

  ZipEx Half Built
  Drill bits in 1/64" gradations
• Sander is handy
• A protractor, ruler and a compass.
• Several colors of fine-tipped Felt pens to mark up the plastic
• Table Saw to make the keys
  

Software

• Needed is some way to remap the keys to different notes. I used MAX/MAP, an expensive program @ $500 (I have other uses in mind for it, so felt it's price justified). One might be able to use Java, or in a pinch, I can compile my Max version and send you a runtime.  

Layout – the pattern is drawn on the [plastic with fine-tipped felt marker pens.
The spacing between key is determined by the average inter-key spacing of the switches on the PCB, and simple geometry.

The key spacing on the PCB is slightly irregular, due to the irregular placement of black keys. This made things a bit complicated, as the buttons didn't line up with the jammer keys.

ZipEx key

.

There are two ways discovered thus far to mount the circular or hexagonal keys for the jammer:

• mount them on posts - this is fairly fiddly, as 60 sets of holes have to be drilled, and each set is of 8 or so individual holes in addition to making the keys themselves. There were also problems removing friction.
  
• Mount them on little arms - I have not tried this way, but will use this for my mark II version. 
  

Update: Johannes Drinda asked how I made the keys.

====================================

ZipEx Finished

Here's the end product. In addition, the pitch-bend wheel was mounted in the corner and a brass rod attached. 

The black keys at the sides (one PCB was 6 notes longer than the other, so there was overhang) are octave-shifting function keys, used to make it pretend to have more rows and keys. In effect I have a 96-key keyboard that pretends, when needed, to be two keyboards, one for each hand. The blue-black keys in the center divide the two sides of the instrument, and are dynamically assigned to whichever hand is playing near them.

With the special function keys, it's surprisingly easy to play in pretty much any key.

The case was easily made out of brass angle-iron and the leather strap bought at a guitar shop.