You are welcome. This pattern may be better for understanding the staff system 
and how LilyPond works:

Currently, LilyPond uses the M and the # as generators, and the latter is put 
on a rational number continuous variable, tied to E12, the 12-equal 
tone-system. But no matter what rational value one chooses on the horizontal 
#-line, one only gets two generators: genuine microtone notation should have 
more generators.

One can also see things like that a scale that takes up 7 adjacent staff 
positions also uses all seven note name letters, and will always do that no 
matter how transposed.


> On 21 May 2018, at 17:41, Menu Jacques <[email protected]> wrote:
> 
> Thanks Hans!
> 
> JM
> 
>> Le 20 mai 2018 à 20:56, Hans Åberg <[email protected]> a écrit :
>> 
>> Here is a two-dimensional layout fitting into the staff system (use a 
>> monospace font to view). Pitches increase by moving up or to the right. 
>> Moving vertically corresponds to changing position on the staff; moving 
>> horizontally, applying an accidental.
>> 
>> Pitches altering layout as follows:
>>      m ^  ^ M
>>        | /
>>   b <- . -> #
>>       /|
>>   -M v v -m
>> where M (resp. m) is the major (resp. minor) second, and the
>> the sharp # (resp. flat b) raises (resp lower) with the interval
>> M - m, that is, the difference between the major and minor seconds.
>> 
>> Resulting pattern, in a scale using names A B C D E F G:
>>                     Ab' A'  A#'
>>                 Gb  G   G#
>>             Fb  F   F#
>>             Eb  E   E#
>>         Db  D   D#
>>     Cb  C   C#
>>     Bb  B   B#
>> Ab  A   A#
>> For traditional interval names:
>>                 D8  P8  A8
>>                 D7  m7  M7  A7
>>             D6  m6  M6  A6
>>             D5  P5  A5
>>         D4  P4  A4
>>     D3  m3  M3  A3
>> D2  m2  M2  A2
>> D1  P1  A1
>> writing
>> P  pure
>> M  major
>> m  minor
>> A  augmented
>> D  diminished
>> plus numbers: 1st, 2nd, etc.
>> 
>> Then transpose by translating, also between the two diagrams.
>> 
>> 
>> 
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> 
> 
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