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.

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.

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.

* 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."