Monday, March 8, 2010

Alternative Keyboards

We all know that it was a technological accident that the piano-style musical keyboard became associated with the synthesizer. In the early 1960s when Moog and Buchla were devising the first practical analog synths, the CPU power needed to process signals from an instrument such as a guitar or a flute or a marimba, and transform them into the control voltage and gate signals necessary to control a synth, didn't exist. The keyboard presented an easy-to-implement method: conceptually, just mount pushbutton switches under the keys. And in comparison to the capacitive plate sensors and things that Buchla was experimenting with, the piano-style keyboard had the advantage of already being familiar to millions of musicians, thus lessening somewhat the rather steep learning curve for this new type of instrument. These early keyboards were neither velocity nor aftertouch sensitive, but then again, neither are most pipe organ keyboards.

This association of the keyboard with the synthesizer eased its entry into the world of music, but it also placed limitations on how the instrument is played that its designers didn't intend. The limitations of the piano keyboard have been recognized since long before the synthesizer existed. The biggest problem that the keyboard has always had is that, due to the two-row layout with all of the naturals on the bottom row and all of the accidentals on the top row, the performer must usually change fingering in order to transpose a chord from one key to another. This frustrates what should be a simple operation; the guitar player playing a barred chord can transpose it simply by moving up and down the neck, but the keyboard player must keep shifting fingers around to insure that each finger hits on the correct row. The additional manual dexterity and muscle memory requirement makes learning the different keys on the piano a slow and frustrating process. From my own experience, it also introduces the temptation to use teaching shortcuts that cause the student problems later on: a common technique is to start the beginning student out learning the C-major scale, which is played all on the white keys. This introduces a sort of fear or puzzlement at the black keys -- what are the for? When does one use them? And then when the teacher starts introducing other scales, the use of the black keys seems arbitrary and unsystematic, and the student gets a bit freaked out. By contrast, guitar pedagogy treats the accidentals as simply other notes in the chromatic scale, which they are, and the guitar student has relatively little trouble understanding how to play different scales and keys.

A number of inventors have tried to tackle this problem with "uniform" keyboards, which work by mixing the white and black keys across octaves. Paul von Jankó patented a uniform keyboard now known as the von Jankó keyboard in the USA in 1892. His keyboard uses six alternating rows of two patterns of mixed naturals: one row contains the sequence A B C# D# F G A, and the next row contains A# C D E F# G# A#. von Jankó's keyboard has six rows total (I'm not sure why; it appears that four would have done). If you go look at the diagram at the link above, you can see that, for example, if you play an E minor chord (E-G-B), you play with the index finger (or thumb) on E on one row, and the other fingers play the G and the B on either the row above or the row below, whichever is more convenient. That is admittedly harder than on the conventional piano keyboard, in which E minor is all white keys.

However: Now let's play an F# minor. This is F#-A-C#, and on the conventional keyboard it's very awkward because it's a white key in between two black keys. Unless you have good dexterous fingers, you wind up either trying to slip a finger in between G# and A# to play the neck of the A key, or you resort to bad technique and use your thumb to play the A. However, on the von Jankó keyboard, it's very easy: you take the E minor formation and just move over one column to the right. The pattern of the fingers doesn't change. Well, what about B minor? There isn't any B on the row you're on. However, if you just go up or down a row, keeping your fingers positioned as they are, and then put your index finger on B, you're playing it. And without repositioning fingers. A keyboard that has this property is called "isomorphic" because a given chord has the same fingering shape regardless of what key it is played in.


A piano fitted with a von Jankó keyboard. From an excellent page on uniform keyboards from squeezehead.com.

The von Jankó keyboard is neat because it's so easy to transpose things, and also because its span is a bit more compact (it's a whole step between every two keys on the same row). But, well, it's rather expensive and awkward to implement. At least on a conventional piano. But maybe reduce the number of rows a bit, and take the concept from the piano to a MIDI controller, and now you've got something that might be practical. (The controller outputs conventional MIDI note messages, and the synth that receives them doesn't know they came from an alternate-layout keyboard.) The Chromatone (most of the site is in Japanese; the link given should put you on the English home page) is a five-row uniform keyboard, of which at least a small production run has been made. Unfortunately, it's a bit tough to tell if it's still available, and the company who makes it has gone through several name changes. One problem I see is that there is absolutely no identifying info on the keys -- they're all white -- although that could be fixed.


The Chromatone Von Janko-style keyboard

The Bilinear Chromatic Keyboard is a bit more practical, but so far it's only been prototyped in a two-row version. With only two rows, you have to learn two finger patterns (an "up" pattern and a "down" pattern, according to which row the root note is on) to play a given chord in any possible key. This one also hasn't made it to production, and it appears that the Web site hasn't been updated in the past year.

H-Pi Instruments started with the concept of retaining the same fingering for a chord in all keys, but then went in a different direction with it to create the Tonal Plexus keyboard. This keyboard solves the fingering problem in a simpler manner than the von Janko keyboard -- it put all twelve tones of the equal tempered scale in a row. To ease fingering so that all of the fingers don't have to be in one line (which is difficult on account of the fingers not all being the same length), the notes are laid out in a staggered row, and the accidentals are "split" into two halves, a half-row above and a half-row below.


The Tonal Plexus TPX-2s. This is the smallest of four versions available.

Here's where it starts to get more tricky. As you know if you've studied non-equal-tempered tunings, the equally tempered scale reduces the number of possible tones in the scale by making adjacent ones "enharmonic" -- they are tuned the same. For example, in the equal tempered scale, F# and Gb are the same note. It also essentially eliminates the use of double sharps and double flats, since these are just one whole tone up or down, e.g., A-double-sharp is simply B. However, because of the mathematics of non-equal-tempered tunings that rely on "perfect" intervals, these assumptions are no longer true; F# and Gb are not the same note, and A## is not the same as B.

The Tonal Plexus keyboard accommodates just and other non-equal-tempered tunings in two ways. First, each note on the keyboard is not actually a single key. It's a column consisting of either three or four groups of related-but-not-identical notes. They are arranged so that moving diagonally up and right from a natural note gives the sharp on the next column to the right, then the double-sharp on the column to the right of that, and even the triple-sharp to the right of that. Similarly, moving to the left and down yields the flat, double-flat, and triple-flat. Using a tuning table that does not tune sharps and flats enharmonically, this in itself goes a long way towards being able to play a number of non-equal-tempered tunings. However, there is one more feature: each "note" actually consists of one main key that plays the note per the tuning table, plus two keys above and below that allow the note to be played just slightly sharp or flat (about 6 cents per each key up or down, using the default tuning table). Since, for example, just intonation is specific to the base key of the intonation, and notes have tunings that change depending on the base key, the micro-sharps and flats would allow just intonation scales to be played without the keyboard having to be tuned a priori for a specific base key. A pretty clever system, although trying to sight-read the possible fingerings makes my head hurt, to be honest.

The Tonal Plexus actually works by transmitting each MIDI note on a separate channel, and preceding it with a pitch bend message that sets up the pitch bend to accomplish the micro-tuning of the note. This depends on having a multimbral synth; all channels in use have to be set to the proper patch, and the pitch bend range has to be settable to a small enough interval so that the pitch bend can be used to tune the individual notes. So the pitch bend is not available for actual bending. It's not clear from the documentation how the keyboard actually divides up the notes; it seems to suggest that the keyboard is divided into zones, which would seem to put restrictions on the chords that can be played and the total polyphony. Maybe I'm not understanding that part right. The Tonal Plexus is available in 2-, 4-, 6-, and (incredibly) 8-octave versions, and H-Pi claims that all are shipping now. The Cortex Designs Terpstra implements a similar idea, but it doesn't appear to have made it to production.

C-Thru Music
took yet another tack towards the generalized keyboard. Discarding both the duplicate key rows of the von Janko keyboard and the microtonal playing capability of the Tonal Plexus, they went with a very unusual-looking layout using hexagonal-shaped keys in their Axis-64 controller. (A smaller and less expensive version, the Axis-49, is also available.) Starting from the bottom of each column, the keys play a Pythagorean circle of fifths as you go up the column. The next column to the right starts such that, for any given key, the key that is up and to the right of it is a major third above. So, playing two keys that are in a lower-left-to-upper-right diagonal plays a major third interval. If the key that is directly above the lower key is then added, the result is a major chord. Three adjacent keys, very easy to play.


C-Thru Axis-64. It isn't clear to me whether the note legends on some of the keys are a standard feature or not; I've seen photos without them. Photo from Steelberry Clones.

As the mathematics of it works out, for a given key, the key that is up and to the left of it plays a minor third above, so then adding the fifth plays a minor chord. Adding sevenths is another adjacent key; the C-Thru Web site gives the shapes for many common chords, and as it happens, in many cases the major and minor chords are mirror images of each other about the vertical axis, which makes them easy to remember.







The tradeoff is that it makes some other common chords a bit weird:



But it does neatly accommodate the tritone!


All of these devices offer alternates for those who either aren't facile or feel constrained by the normal chromatic piano keyboard. There is a lot to be said for having isomorphism of chords, as any guitar player can tell you. However, there are also tradeoffs, not the least of which is that all of these devices are considerably more expensive than a standard semi-weighted keyboard. The C-Thru Axis hexboards look like the most accessible (and most affordable), and should open up new possibilities by making certain things such as large-span chords a lot easier, plus the fact that the chord shapes can help with learning music theory. If you have a desire to play in non-equal-tempered intonations, and a lot of patience, you might want to check out one of the Tonal Plexus keyboards.

6 comments:

MusicScienceGuy said...

Nice summary about some alternate keyboards. I particularly liked the summary of the Tonal Plexus, an instrument that has looked intriguing.

I'm creating a new website on alternate keyboards, and all the things that are needed to make them useful instruments (fingerings, lessons, virtual instruments etc.) See:
http://sites.google.com/site/altkeyboards/ for my ough draft.

Be warned that I will be pestering you for help.

Ken Rushton, aka MusicScienceGuy

Dave Cornutt said...

Thanks! I'll take a look.

hugo said...

hi dave was looking for your email but cant seem to find it. i have a question and maybe u can help.
i did buy a juno 106 from a guy today not working.
problem with it is this. hope u can maybe tell me whats wrong...

when i turn it on here is what i get.
key transpose and poly 1 and 2 leds are on.
subject group a and b leds are on
save , verify and load leds are on.
nothing displays on the screen its blank and thats all. those leds are on the whole time and pressing things dont do anything...dead.

MusicScienceGuy said...

I've been posting stuff about alternate keyboards at MusicScienceGuy.vox.com for quite a while. Have you not seen my blog?
Ken.

Dave Cornutt said...

Hugo, that doesn't sound good. On the 106, whenever one of the cassette interface functions (save/load/verify) is in use, it normally blanks out the rest of the panel. The fact that they are all on at once indicates some kind of CPU board problem. I've never seen a 106 have a problem with the control CPU, so I'm not sure where to start. The only thing I can think of is to check the power supply voltages; maybe the +5 is off and it's preventing the CPU from running properly.

Ken, I must admit I had not come across your blog before. But I'll be sure to keep an eye on it now.

MusicScienceGuy said...

Hi, this is just a note to advise all that my new altKeyboards website, at http://sites.google.com/site/altkeyboards/ is up and running. It gives information about alternate/novel & easy to play keyboards and attempts to make it all a simple process. Comments and article contributions are eagerly ask for.