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Looks interesting!
Open questions (or I didn't get it ? :P ): How would the row to play be represented and how are chords handled that span more than one row?

Got it!
In my head I had course = column (Tau:4, Alpha: 5) and row = horizonal...rows (Tau: 16, Alpha: 24) - as is when you hold the instrument.
So you imagined the instrument in a horizontal orientation.
Yes, this is indeed a compact representation!

1xx.. 2.... 3x... 4.... 5.... % 8xx.. 9.... 10x... |8 # chord:C

1||.. 2.... 3.... 4x... 5.... % 8||.. 9.... 10....    # chord:Csus2

1||.. 2.... 3x... 4.... 5.... % 8||.. 9.... 10x...    # chord:C

1.... 2.x.. 3.... 4xx.. 5.... % 8.... 9.x.. 10.... |4 # chord:F

A nice property of this suggestion and the way how it denotes sustaining notes would be that it is easy to add a length description to it (imho note lengths are an essential part of a notation - otherwise you just have to know the piece, so you can't use the notation to write down something actually new).
And perhaps it would be good to mark gaps in the row numbering, so you only have to watch for the first number and the numbers after the breaks instead of looking for gaps everywhere.

Just found out something interesting: For me it's much easier to read the notation when it's written upside down and mirrored, because the most difficult of the two "unwinding" steps is not necessary then anymore (now you only have to mentally turn the columns by 90 degrees but don't have to mirror them anymore) :

: tonic to 1 set

: transposition to 48 set # 4 octaves

: scale to chromatic set

: layout to horizontal set



7..... 8x.... 9.x... 10.x... 11.....      # ...until the end

7..... 8..... 9...x. 10....x 11....x |3

7x.... 8..... 9..... 10..... 11.....

7..... 8...x. 9..... 10..... 11.....

7..... 8.x... 9..... 10..... 11.....

7..... 8..... 9...x. 10..... 11.....

7..... 8..... 9.x... 10..... 11.....

7..... 8..... 9x.... 10..... 11.....

7..... 8..... 9..... 10..x.. 11.....

7..... 8..... 9..... 10x.... 11..... |2 #<--start reading here...



: tonic to 1 set

: transposition to 48 set # 4 octaves

: scale to chromatic set

: layout to vertical set

7..... 8..... 9..... 10..... 11.....

7..... 8xx... 9..... 10..... 11.x...

7xx... 8..... 9..... 10.x... 11.....

7...x. 8..... 9..... 10..... 11.....

7..... 8..... 9..... 10..x.. 11.....

7..... 8..x.. 9..... 10..... 11.....

7..... 8..... 9..... 10.x... 11.....

7..... 8.x... 9..... 10..... 11.....

7.x... 8..... 9..... 10..... 11.....

7..... 8..... 9x.... 10..... 11.....

7x.... 8..... 9..... 10..... 11..... |3

(You can also just mirror them 11... 10... etc (without turning upside down). This works equally well to read the horizontal layout but for the vertical you have to read it with 180 degrees turned now - not mirrored anymore though. So presumably mirroring and turning upwards down at the same time as shown above is the easiest to read approach for all layouts.)

Played the example with John's suggested notation with the instrument now. It's actually easier to play than to imagine :)

Very interesting discussion going on here, I had a play with all proposals and obviously came up with something myself ;-)

Here are the things I like from the previous suggestions:

• distinct points in time, but I prefer keeping those vertically as in traditional notation
  
• make the format dense if needed
  
• allow for annotations
  
• make it possible to write by hand
  
• works with existing staves
  
• works as ASCII
  
• works with any key layout or orientation
  
  
  Here are some other things that I want to highlight and incorporate:
  
  
• totally document how you're physically playing the music
  
• standard notation is good enough for musical notation
  
• work together with standard notation (same orientation, time division)
  
• has to be able to participate in a large score with other instruments
  
• provide chord charts
  
• allow for mixed-hand pieces as well as split-hand pieces
  
• allow for concurrent staves with one hand playing chords, other hand plays melody
  
• allow for concurrent staves for different splits on the Eigenharp
  
• expansion/contraction of the density when needed
  
• reuse as much of the existing musical notation elements as possible
  
• make the standard vertical layout the 'easy path' even though others are also possible
  
  
  So I set out to write down some parts of my own music and dynamically morphed into what's below.
  
  Here's an attempt at describing where I'm at now:
  
  
  
• the notation is written horizontally from left to right, just as in standard notation
  
• vertical positions correspond to a moment in time
  
• horizontal space between the vertical positions indicates a new moment in time
  
• surrounding space can be used for manual annotations
  
• vertical positions can be glued together without horizontal spacing to indicate simultaneous notes
  
• the horizontal lines correspond to the rows across the Eigenharp (2 on Pico, 4 on Tau, 5 on Alpha)
  
• the rows are oriented so that bottom to top corresponds to physically nearest towards the furthest
  
• the natural blocks of 4 keys that subdivide the Eigenharp keyboard are used to further locate where you are (2x4 on Pico, 4x4 on Tau, 5x4 on Alpha)
  
• above each letter you use that location system: first number indicates the block, second the column in the block (block|column, b|c notation)
  
• this goes 1|1, 1|2, 1|3, 1|4, 2|1, 2|2, ... until 6|4 on the Alpha and on the Pico only until 2|4
  
• each key that's played is placed on the row it's played on and you write down the finger you play it with
  
• this uses the standard fingerstyle guitar convention: (thumb: p, index: i, middle: m, ring: a, little: c)
  
• lower-cased letters are played with the left hand, upper-cased latters are played with the right hand
  
• optionally only the changes in b|c are notated so that it's clear when this doesn't change
  
• optionally the column can be left out, only writing the block, this then uses a grid of 4 columns, which is an expanded layout
  
• other expanded layouts can be used as long as the b|c properly notates the top-left reference point
  
• the expanded layouts can be used for chord diagrams, even within note-based music
  
  
  Examples, best to copy/paste to a fixed-width font text editor to remove the spurious empty horizontal lines:
  
  "Same Place Again", dense, hands combined:
  
  

   2     3     2     3  2  3     2         
  
   1  4  1  4  1  4  1  4  4     2  4  3 
  
   .  .  .  .  .  .  .  .  .  .  .  .  . 
  
   .  .  .  C  .  .  .  .  .  .  .  .  . 
  
   .  c  I  .  .  .  .  .  .  A  m  .  . 
  
   i  .  .  .  .  c  I  c  .  .  .  c  a 
  
   .  .  .  .  i  .  .  .  P  .  .  .  . 

  
  
  "Same Place Again", expanded, hands combined:
  
  

   2           3           2           3     2     3           2         
  
   ....  ....  ....  ....  ....  ....  ....  ....  ....  ....  ....  ....  .... 
  
   ....  ....  ....  ...C  ....  ....  ....  ....  ....  ....  ....  ....  .... 
  
   ....  ...c  I...  ....  ....  ....  ....  ....  ....  ...A  .m..  ....  .... 
  
   i...  ....  ....  ....  ....  ...c  I...  ...c  ....  ....  ....  ...c  ..a. 
  
   ....  ....  ....  ....  i...  ....  ....  ....  ...P  ....  ....  ....  .... 

  
  
  "Same Place Again", section with chords, hands combined:
  
  

   2     3     2     3     2  3     23  3  2  2     3     2     3     2  2       
  
   1  4        1  4  1     3  3     22  2  3  1  4        1  4  1     3  2  4  3
  
   .  .  ....  .  .  ....  .  .  .  ..  .  .  .  .  ....  .  .  ....  .  .  .  .
  
   .  .  ...C  .  .  ....  .  .  .  .M  .  .  .  .  ...C  .  .  ....  .  .  .  .
  
   .  c  I..C  .  .  M..C  .  .  A  m.  A  .  .  c  I..C  .  .  M..C  .  m  .  .
  
   i  .  ....  .  c  I...  .  P  .  ..  .  .  i  .  ....  .  c  I...  .  .  c  a
  
   .  .  ....  i  .  ....  a  .  .  ..  .  A  .  .  ....  i  .  ....  A  .  .  .

  
  
  
  "What If", different staff for each hand:
  
  

            5                                   5                 5          
  
            1                                   2                 3          
  
   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
  
   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
  
   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
  
   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
  
   .  .  .  M  .  .  .  .  .  M  .  .  .  .  .  A  .  .  .  .  .  C  .  .  . 
  
   
  
   2     3  2     3  1  2     1  2     2        2        1  2     1  2    
  
   2  4  1  2  4  1  4  2  3  4  2  3  1  3  4  1  3  4  3  1  3  3  1  3 
  
   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
  
   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
  
   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 
  
   i  .  c  i  .  c  i  .  c  i  .  c  i  .  c  i  .  c  i  .  c  i  .  c 
  
   i  a  .  i  a  .  i  a  .  i  a  .  i  a  .  i  a  .  i  a  .  i  a  . 

I like it, Geert. Particularly the fingering. It also has enough white space for scribbling on a printed version.

An automated capture could print an "O" in which the fingering could be added in pencil or by editing the file.

It would be interesting to place this above the standard staff for the music which would, if nothing else, establish the flow of the moments in time

After first experiments: Geert's proposal is really nice! Experimented with typing in the ASCII text as lyrics into a staff in MuseScore - works wonderful! (just use a nonproportional font and use verses to add rows. Trick: Always click on the note with the shortest length in a polyphonic piece, so you can add a diagram or short-type notation to really each note, not only those from the first voice)
Fortunately there is a scripting facility in MuseScore, so what would be cool:
* MuseScore to EigenD bridge - step-playback with lights (probably we would have to go down to the C++ level in MuseScore for this feature - not sure whether QtScript can be extended by just throwing a dll into the proper directory - probably not - yet :) )
* automatically generating and updating score from a tab
* automatically generating and updating tabs from any existing score based on John N's EigenTab keyfinding algorithm
* as soon as tab->score works probably a low hanging but very worthwhile fruit - step entry and continuous playing entry of scores into MuseScore by playing the Eigenharp

Made a few minor changes to the (as said really nice) notation system:
1) block|column became column|block (so the columns info is now above the block to get the block closer to the tab - this is nicer for change 2)
2) in the expanded view only the block is notated - at the position of the first line of this block. E.g.:

 3

....

I.A.

.M..

....

....

(index finger is one position above block 3 marker)

Embedded into a normal staff this is probably all you might want - would still like to have a possibility to notate note durations in the ASCII only view. Perhaps one could paint musical time divided by shortest note in bar (e.g. 3/4 / 1/4 = 3) number of diagrams for each bar and use John's proposal for expressing note durations with '="? (In order to see the duration of one diagram one just has to count the number of diagrams in the bar - together with the musical time you know the value of one diagram then.

 3

.... .... .... | .... 

I.A. =.=. =... | .... 

.M.. .... .... | .... 

.... .... .... | .... 

.... .... .... | .... 

When you know that the musical time is 3/4 each diagram has to be one quarter. That leads to I=dotted half, M=quarter and A=half.
The block or column numbers shouldn't change in between - what is mostly the case because your hand is nonetheless "pinned" to the sustained key. And for most pieces the hands will probably be notated in separate staffs. (For rare exceptions where a finger stretches out of the 2x4/4x4/5x4 field while sustaining notes inside it you can still use the "stitched" notation suggested by Geert).

Will continue to write my test piece tomorrow, so I get a better feeling for the concept.

Oh, for me it's the opposite - each of the suggestions makes sense in one way or the other:
* my suggestion works with normal staff paper and has fully proportional intervals for the horizontal layout (making it easier to "see" the musical progression than even with conventional notation)
* John's approach has the beauty of having events in time in lines so you can rearrange easier with your normal editor. And it would be easier to have a 1:1 mapping to belcanto phrases to write (and since recently: speak ;) )
* Geert's approach has the advantage that you can see the fingering and has a really nice location system.

Currently Geert's approach has in my eyes the highest probability to find acceptance, so I support it (I slightly regret not having proportional intervals for my favourite layout anymore ;) But this will not be a major selling point for many, so I see slim chances to get this established)

Looking forward with what you will come up with! :) (We are still in brainstorming phase, so many suggestions are good!)

Can you please go a little bit more into detail, am not sure whether I got all aspects of your proposal. Do you assume that the reader knows the note pitch to key mapping?
(This can be a little bit difficult for Eigenharps, because layouts and scales can be changed - even inside the piece.
For most existing instruments there is a fixed position on string to pitch mapping so standard notation works - at some point you just know where to touch the instrument to get the notated pitch.
So a notation system for Eigenharp should give you a positional information - otherwise normal notes (perhaps with fingering) would probably be sufficient.
Optimizing notation for easier approaching the musical information is a different topic. Many tried, many succeeded in being better than standard notation (not so difficult...) none got a broader spread, because of all the existing literature and people already knowing standard notation.)