Re: Intervals between various B pitches

[Hans Åberg]

> On 20 May 2018, at 11:45, Menu Jacques <address@hidden> wrote:
> 
> Working on intervals, I bump into this question.
> 
> How is the right column below to be filled?
> 
> Downward interval between B## and:
> 
>       B#:    augmented unison or minor second?
>       B:     major second or ...?
>       Bb:    minor third or ...?
>       Bbb:   major third or ...?



Use the keyboard layout below, which I made for a ChucK program. Take 
two-dimensional pattern and transpose between the two diagrams. 


The keyboard layout is altering pitches as follows:
           ^ #
          /
         . -> M
        / \
     b 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 key pattern, in a scale using names A B C D E F G:
      C#  D#  E#
    C   D   E   F#  G#  A#  B#
  Cb  Db  Eb  F   G   A   B
            Fb  Gb  Ab  Bb  C'
In terms of traditional interval names, writing
  P  pure
  M  major
  m  minor
  A  augmented
  D  diminished
plus numbers: 1st, 2nd, etc., this is
      A1  A2  A3
    P1  M2  M3  A4  A5  A6  A7
  D1  m2  m3  P4  P5  M6  M7  A8
    D2  D3  D4  D5  m6  m7  P8
                          D2