Re: Intervals between various B pitches

[Hans Åberg]

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.