an example of trouble with the standard keyboard. formally genralized keyboard?

Since the last discussion of the generalized and the conventional keyboard was on this list. i am keeping it here.
On my hammer dulcimer i tune it to Erv Wilson's Meta Mavila. Those who have my Without R & R recording can hear this scale also on the hammer dulcimer in question
Recently someone asked if i had an organ to play along with which i have done with other tunings in the past.
here is what one has to do to place it on a conventional keyboard.

for those that don't know off hand Meta -Mavila is a recurrent sequence which can be expressed by 2A+B=E. more on it can be found in the Wilson Archives

in this example which might make the series clearer i seeded it with harmonics
15
20
27
37
so if 15 (times 2) is A and 20 is B we get 50'as E Next we take 20 (times 2) which gives us 40 plus 27 gives us 67 etc.
we started (where i liked the series the best by experiment/ear) with 37. below i add the cents to the next fourth along with how i have it tuned up in relation to 12 ET. all my recurrent tuning are based on F below A440 to possibly allow common tones modulations if they occur between other recurrent tunings. I decided to place tuned reeds into a pump organ and the follow situation developed ( and how i answered it)

again i added to the below the cents to the next 'forth' (including the closing one to 37) as well as the cent's deviation from 12 ET
37 531.26 G# -35
50 506.7 C# -17.7
67 530 F# -7 91 535.7 B +23
124 515.4 E +58.7 or F -41.3
167 516.1 A +74.1 or A# -25.9
225 (474) D +90.2 or D# -9.8

from high to low using it closest letter names if i place the reed in a series of fourth. included in the cents to the next highest note
C# to D 203.9
D to E 158.5
E to F# 134.3
F# to G# 172
G# to A 209
A to B 148
D to C# 163

one can see how C# to D is actually bigger than D to E and if i continued the series one more place too the next key G would actually be higher that G# key. Also the closing four which is the smallest looks larger as a tritone. This was not my option from the beginning not what one would what i ended up doing and i used the alternate which also keeps the reeds with 50 cents of where they would normally be

C# to D# 203.9
D# to F 158.5
F to F# 134.3
F# to G# 172
G# to A# 209
A# to B 148
B to C# 163

So one has to periodically has to change what would look like a fourth on the keyboard to what looks like a Tritone. hence with only 7 tones we have ran into trouble with the conventional keyboard. doable but with a Generalized Keyboard we would not have to concern ourselves with this.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
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