I am trying to figure out how to know if a note in a scale is a sharp or a flat.
So my starting point/input are the intervals of any scale. E.g. here are the Minor pentatonic intervals
Interval: 1, b3, 4, 5, b7 Semi-notes: 3 - 2 - 2 - 3 - 2 Formula: Whole and a half, Whole, Whole, Whole and a half, Whole
Now i want to know how do i get the exact sharps and flats for the notes of this scale? For example my output would be the following for Fm in the Minor pentatonic scale:
F, Ab, Bb, C, Eb, F
I understand that if a key is written as a flat or sharp is based on the half step transition, but that doesn't seem consistent in all scales, and i also don't know how to determine if a half step transition is half step higher or lower (to determine flat vs #)
For example here is the F-Mixolydian scale:
F, G, A, Bb, C, D, Eb, F
Why is Bb not written as A#?
The intervals, semi-tones and formula of Mixolydian are:
Interval: 1, 2, 3, 4, 5, 6, b7 Semi-notes: 2 - 2 - 1 - 2 - 2 - 1 - 2 Formula: Whole, Whole, Half, Whole, Whole, Half, Whole
So the A -> Bb is a Half step transition, but how do i know if it's half step lower (Bb) or half step higher (A#)?
In General is there a formula i can follow to get the correct notes in any scale with the correct sharps and flats?
I need the same formula to work for Major, Minor, Pentatonic, Mixolydian etc. so i can start from the intervals and get the correct notes.