Diminished whole-half scale.
Its a weird one.
I thought ‘A’ must be diminished 7th too, because 9 semitones is a diminished 7th interval and because ‘A’ is the seventh scale degree.
Naming ‘A’ as diminished 7th would lead to interval naming ( from root note to each scale degree ) including two ‘7’ intervals.
There must be two of some interval as diminished whole-half has 8 note before the octave instead of the usual 7 notes before the octave, as in the more traditional scales.
After some time had passed I looked back at the scale formula ( 1 2 b3 4 b5 b6 6 7 8 ) and noticed that there is both a ‘b6’ ( flattened sixth ) and and ‘6’ ( Normal / Major sixth ) so instead of using diminished 7th, I went with Major sixth. Diminished 7th and Major 6th intervals both have 9 semitones. After changing it it looks like this ( I put number of semitones in this time around, in the second row ):
R W H W H W H W H
0 2 3 5 6 8 9 11 12
R M2 m3 P4 d5 m6 M6 M7 P8
1 2 b3 4 b5 b6 6 7 8
C D Eb F Gb Ab A B C
I don’t know if there is any logic to it at all, but at some point in time classical people must have decided to ‘double up’ the sixth interval in diminished scales ( rather than any interval of their choosing ). This is my assumption based on looking at the scale formula.
They want to describe everything in terms of 7 scale degrees because it fits nicely with their traditional view of music ( the seven modes ).
As diminished has 8 scale degrees before the octave, rather than seven, it was probably considered to be devilish or something.
It does sound quite ‘vampiric’ like ‘transylvania’ or something like that.
I think you are right about describing the ‘A’ as a diminished 7th in the context of a C°7 chord. With diminished meaning ‘reduced by two semitones’. The seventh degree of C Major scale is B, reduced by two semitones to Bbb, B double flat ( which is an A ). Looking at that, it makes me think my scale formula may be wrong. I’m seriously confused by this.