Nifty Simulation Results

[caj]

In order to test a new concertina layout, I wrote a program to simulate me playing thousands of tunes, and count all the times the fingering got awkward. Science!

 

First, I stripped an ABC tunebook of chords and ornaments, and converted all the tunes to MIDI files using abc2midi (processing MIDI is actually much easier than processing ABC, at least in this case.) Then, I wrote a program that opened each MIDI file, converted each note into a finger position, and kept track of the number of times a single finger had to hit 2 different buttons in succession, along with various other statistics.

 

My test layout was this eighteen-button monstrosity:

 

 

Each note appears exactly once, no benefit of alternate fingerings (good: my program doesn't attempt alternate fingerings, too much work,) each row is a fully chromatic octave from F up to E, and the lowest note is the F below middle C, under the left middle finger. This is essentially the core of my new layout, to which I'll add some extra buttons for low notes and ornaments.

 

The musical data consists of 1425 reels, jigs, hornpipes and polkas from Henrik Norbeck's tune archive. And boy are my virtual arms tired.

 

The results:

• There were a whopping 111 tunes---about 8 percent of the tunebook---in which virtual me was stuck playing 2 different buttons with the same finger. A grand total of 305 awkward moments, which makes sense, considering any awkward moment will occur at least twice in an AABB tune.
  
• If I add just one alternate note, a push D under the pinky or thumb, the number of awkward tunes drops to 50. I was blessed with a layout whose problems mostly revolve around this one note.
  
• The corresponding percentages for a C/G Anglo are difficult to quantify. I tried a few fingering systems, and counted the # of tunes in which you either get stuck playing 2 buttons, or must resort to an alternate fingering. The # of such tunes ranged from 33% of the tunebook and up.
   
  This surprised me at first, but after trying a dozen toons or so I found a lot more of them have conflicts than I realized.
  

Now this is by no means an accurate measure of awkwardness; it didn't account for the length of the notes, or the fact that some finger jumps are not so bad. I do feel better, tho, about the new layout: I designed it to minimize finger conflicts, and am happy to see that it does that, and better than my previous attempts. Not bad for a nineteen-button concertina!

 

Caj

 

P.S. If anyone wants me to collect other statistics (note distributions of the tunes, relative use of fingers for a given concertina, etc) let me know. I have the code now!

Edited December 9, 2003 by caj

[Richard Morse]

Very Impressive! I like your drawing too (though I find Push/Pull much easier to read).

 

Your layout seems to be tough on chords though.

 

I'd be interested to see how finger-friendly the English and Hayden systems would be in comparison. Is that fairly easy to do now that you have your code created?

[Chris Timson]

Gosh. I'd be interested in the thinking behind this layout. It certainly has, as Watson and Crick wrote in a different context, "interesting features".

 

Chris

 

Edit: Sorry, I just found your article on the Instrument forum

Edited December 9, 2003 by Chris Timson

[Dave Weinstein]

That's fascinating.

 

When I layed out the keyboard for my G/D, I designed it for the maximum number of notes in G and D with alternate fingerings in the opposite bellows directions. This opens up more chords and harmonization opportunities (and helps cope with running out of air), but it wasn't optimized for eliminating finger collisions.

 

Given that it's designed to be played with the middle three fingers, why not go with an English end layout?

 

Regards,

--Dave

[caj]

Your layout seems to be tough on chords though.

 

It is terribly bad for chords, perhaps maximally bad, because notes on each button are a fifth apart. I decided to leave this as a job for extra buttons under the pinkies. Pinky buttons will also take the range down further.

 

I'd be interested to see how finger-friendly the English and Hayden systems would be in comparison. Is that fairly easy to do now that you have your code created?

 

It is indeed easy, and I'll be happy to do it: all I need are the fingering diagrams.

 

There are two caveats: the first is that I only have archives of Irish trad music (for which huge and well-maintained collections exist in ABC format.) These are heavily biased towards G and D. In fact, here's a graph of key signatures:

 

 

And here is a graph of tonic notes for each tune:

 

 

If you play music heavily centered in other keys, maybe we could cheat by transposing the archive. This is very easy to do the data is converted to MIDI format; just throw a "-2" somewhere in the source code and you've just transposed everything from G to F.

 

The second caveat is that my program can not simulate any grabbing for alternate buttons or alternate fingerings, unless there is a very very simple rule I can code in. Basically, every musical note is assigned to one button, which is assigned to one finger. So, an "awkward moment" is either two buttons under the same finger in succession, or any other necessary deviation from the strict pattern.

 

Caj

[caj]

Given that it's designed to be played with the middle three fingers, why not go with an English end layout?

Hi,

 

Since its major weakness is the inability to play chords, I think some extra buttons will wind up under the pinkies. I'd rather avoid using pinkies for playing melody notes, but I think they're ideal for chords. This will probably keep me stuck to the Anglo form factor.

 

Caj

[Dave Weinstein]

The second caveat is that my program can not simulate any grabbing for alternate buttons or alternate fingerings, unless there is a very very simple rule I can code in. Basically, every musical note is assigned to one button, which is assigned to one finger. So, an "awkward moment" is either two buttons under the same finger in succession, or any other necessary deviation from the strict pattern.

Is there any chance you can make the source available? I'd be interested in taking a whack at it just to see if I can get it to analyze tunes and make fingering suggestions for me.

 

--Dave

[BruceB]

The second caveat is that my program can not simulate any grabbing for alternate buttons or alternate fingerings, unless there is a very very simple rule I can code in. Basically, every musical note is assigned to one button, which is assigned to one finger.

This isn't going to work at all for an english concertina as the buttons aren't assigned to one finger. It's very common for two different fingers to hit the same button, and sometimes even three, possibly all in one tune. It's even possible that mister pinky could get involved and all four fingers might press the same button, though I can't think of any examples.

 

I use mostly my index finger for the first column of buttons. Column two would be index & middle finger, index first choice, but middle finger anytime it would make things easier or if the index was already busy. Column three it's almost equally likely I'd use my middle or ring finger, but it's possible that a situation could arise where I'd use any of my four fingers. Column four is most likely my ring finger, but I sometimes use my pinky here, and I'd consider using my middle finger too.

 

I was just reading about Simon Thoumire's technique, which would really require program flexibility. On one hand he mostly uses just his index & middle fingers across all four columns, unless he needs the others for chords. He also does his rolls (which he describes as central to his playing style) with just his index & middle fingers. Less fingers=more speed?!?

 

bruce boysen

[Richard Morse]

I'd be interested to see how finger-friendly the English and Hayden systems would be in comparison. Is that fairly easy to do now that you have your code created?

It is indeed easy, and I'll be happy to do it:  all I need are the fingering diagrams. 

A note chart for the Hayden system can be found here but I can't seem to find one for the English on the web. Very Strange! I hope someone else has better luck searching for one than I had. If no one comes forth with one soon, I can make one up.

[caj]

A note chart for the Hayden system can be found here but I can't seem to find one for the English on the web. Very Strange!  I hope someone else has better luck searching for one than I had. If no one comes forth with one soon, I can make one up.

Thanks,

 

I need to know how you apply your fingers to the buttons. It looks like you place your fingers differently for different key signatures, which is fine: I can scan the key signature out of the MIDI header (abc2midi puts it there!) But for a given key, say a tune in G major, which fingers are typically applied to which buttons?

 

What I can tell you easily is how often two buttons in the same "column" are played sequentually; but if it is typical to compensate for this by moving fingers from column to column, all I'm really telling you is how often your fingers move out of "assigned" columns.

 

That being said, I can also give you all sorts of other useful statistics, such as which buttons are hit the most often, or which button/note transitions are the most likely. However you use your fingers, this information will be objectively useful.

 

Caj

[Richard Morse]

A note chart for the Hayden system can be found here

I need to know how you apply your fingers to the buttons.  It looks like you place your fingers differently for different key signatures

Your fingers are "homed in" on the key you're playing in. The scale (of virtually any mode - maybe ALL modes in ANY key within the range of the instrument?) is a pattern of alternating 3 and 4 buttons rows played sequentially with the fingers.

 

For instance, on the right side, the major scale (in numbers) would be

    Numbers of major scale:      For example:           Fingers used:

       (1) (2) (3)              (G) (A) (B)             (1) (2) (3)  
      4   5   6   7            C   D   E   F#          1   2   3   4
        1   2   3                G   A   B               1   2   3

The exact same fingers would be used for various scale modes though the "beginning" of the scale would start on another finger other than your 1st (index) finger.

 

The most common minor key is what I call the "2" minor (Dorian?) which "starts" with your 2nd (middle) finger in the 3 note long rows. The "6" minor (Aeolian?) starts with your 3rd (ring) finger in the 4 note long rows. Modal tunes (mixolydian?) would start on the 5 of the major scale which would be your 2nd finger (middle) in the 4 note long rows. Other modes are similar. Fingers used for modes of

         Dorian:                    Aeolian:              Mixolydian:

        1  (2) (3)                1   2  (3) (4)          1  (2) (3) (4) 
      1   2   3   4                 1   2   3               1   2   3 
       (1)  2   3                (1) (2)  3   4          (1)  2   3   4

The left side can be identically fingered but in mirror image, so the 3 note rows would use fingers 3rd, 2nd, 1st, and 4 note rows 4th, 3rd, 2nd, 1st.

 

Of course there are times when the fingering doesn't work out and you have to adjust here and there, but how often is what your about to tell us!

Edited December 12, 2003 by Richard Morse

[Richard Morse]

What I can tell you easily is how often two buttons in the same "column" are played sequentually; but if it is typical to compensate for this by moving fingers from column to column, all I'm really telling you is how often your fingers move out of "assigned" columns.

 

What do you mean by "columns"? Had you meant "rows"?

[David Barnert]

What I can tell you easily is how often two buttons in the same "column" are played sequentually; but if it is typical to compensate for this by moving fingers from column to column, all I'm really telling you is how often your fingers move out of "assigned" columns.

 

What do you mean by "columns"? Had you meant "rows"?

I think he meant two different notes that would ordinarily be played by the same finger, that is, using "column" to refer to the domain of any given finger, which are generally vertically oriented. In the Hayden, the "columns" are oriented in a vertical zig-zag.

[Richard Morse]

The [Hayden] scale is a pattern of alternating 3 and 4 buttons rows played sequentially with the fingers.

I forgot to mention that sometimes when there's a note included in a tune which is NOT in that mode it is usually the 4# (four sharp) note. IOW, if you're playing in G major, that note would be a C#.

 

Being that that is the row that is normally 3 buttons long, that out-of-mode 4th button note would be played with the 4th (pinky) finger. This seems to hold true for all the modes. The most common out-of-mode note is an additional note to the right of the 3 note row to be played with the 4th finger.

[caj]

Thanks for all that information! It's just what I need, and I'll get right to work.

 

I have one point of confusion, tho: on the right side of the instrument, the fourth finger is the pinky. What of the left side? According to the note chart, the left side is not reversed. So would you play a major scale on the left side like

 

   R   M   I           OR           p   R   M
p   R   M  I          OR         p   R   M   I
  R   M   I           OR           p   R   M
p   R   M  I          OR         p   R   M   I

 

Furthermore, that extra out-of-key sharp is still to the right. In that first fingering, you use the index finger more and the pinky less, but now you must move your index finger for that extra sharp. In that second fingering, the extra sharp falls naturally under the index finger, just as it naturally falls under the pinky on the right side.

 

Caj

[Richard Morse]

The bass side fingering example would be as you indicate on the *left* with the 3 note rows using R,M,I (from left to right). I hadn't considered your right example, but just now did try it and find it considerably harder than your left example probably because my pinky is pretty slow and stupid compared to the other digits.

 

That extra out-of-key sharp *would* be played by moving your index finger out of position which is not great. But OTOH, that note almost never comes up on the bass side of the instrument as it's usually a melody thing, played on the treble side - and those out-of-key sharps are easy to grab with the pinky.

 

I realize that your "digial efficiency" (or whatever we're calling it) index is a bit brutal, and like Englishes which currently are tough to index due to the ease at which fingers can hit most any key, duets have about an octave of the SAME notes on each side which allows one to grab one of those "alternate" notes if there is some particularly tough fingering sequence.

[David Barnert]

Note: Everything below was written before I noticed Rich's response, immedeately above.

 

-------------------------------------------------------------------------------------------------------

 

I have one point of confusion, tho:  on the right side of the instrument, the fourth finger is the pinky.  What of the left side?  According to the note chart, the left side is not reversed.  So would you play a major scale on the left side like

 

   R   M   I           OR           p   R   M
p   R   M  I          OR         p   R   M   I
  R   M   I           OR           p   R   M
p   R   M  I          OR         p   R   M   I

Rich probably would (my guess would be the pattern on the left, although playing only three notes in the starting row, and four in the next). I tend to use my pinkies a lot less than Rich and spend more time moving my hands around as a result. His way is undoubtedly better. He also uses his left thumb occasionally to catch the D# at the right end of the left hand buttons when playing in Bb (whose buttons, all but the missing Eb, are near the right edge of the field). I wouldn't be surprised if he has found a way to use his toes as well.

Furthermore, that extra out-of-key sharp is still to the right.  In that first fingering, you use the index finger more and the pinky less, but now you must move your index finger for that extra sharp.  In that second fingering, the extra sharp falls naturally under the index finger, just as it naturally falls under the pinky on the right side.

The sharp 4 and the flat 7 (both commonly used accidentals) are both adjacent to notes at the ends of the row of three notes in the first line of a major scale. Depending on the context, reaching either might be a trivial matter of just using the next finger (whether it be the index or the pinky) or it might require sliding your hand sideways one notch at some convenient time in the preceding notes. Edited December 11, 2003 by David Barnert

[caj]

Thanks very much for the info on playing the Hayden, that's all I need to know.

 

Unfortunately, it will take quite a bit more work to account for grabbing notes from the other side. In the mean time, I have a very preliminary result for playing a melody only on the right hand.

 

In this case, I ignored any problems with notes being out of reach horizontally, and just assumed you have, like, a dozen fingers on one hand. If you don't have to worry about reaching right or left, then there are only two ways to play each melody: with the same finger playing the notes C and G, or with the same finger playing the notes G and D. I figured I'd count the number of double-buttons in each case, and report the best of the two. The actual number of conflicts is going to be higher than this, but at least it gives a lower bound.

 

1141 tunes out of 1425 have at least one conflict---what one would expect because half of all fifths are going to present a conflict. Here's a breakdown:

 

60 tunes --- 1 conflict

202 tunes --- 2 conflicts

52 tunes --- 3 conflicts

155 --- 4 conflicts

65 --- 5 conflicts

117 --- 6 conflicts

39 --- 7 conflicts

77 --- 8 conflicts

21 --- 9 conflicts

78 --- 10 conflicts

 

Now, bear in mind two things: first, this is the # of conflicts that occurs when playing an entire tune, including all repeats and additional variations. That's why you see even numbers of conflicts being very popular: usually the offending notes are played twice.

 

The other thing to bear in mind is that I must check my work. I checked the results by hand against a couple tunes, but I encountered some subtle errors on the last program too. More to come...

 

Caj