Here “modes” include anything that has a weird scale. Modes are usually taught as a scale beginning on a white key and using only white keys. This yields C major, A minor, and five modes. The one that starts on B, Locrian, is hostile in the extreme and rarely employed.
But there is no need to stick to these scales. Any seven notes will do, or any other number. There are several hundred possible. My composition teacher seems to like to fool with these sorts of scales.
A Sharp Scale
Just what it says, A normal C scale with A sharp instead of A: “C D E F G A# B”
The Tuareg Scale
This scale in C has D and A flat: “C Db E F G Ab B” It was concocted my my daughter and her friend, who named it and played it incessantly to stress-test any nearby adults.
For my standard modal exercises, I decided to have them all be in the key of C, so C Dorian, C Phyrigian, etc. Here they are…
The normal major scale. “C D E F G A B”
The all white key version would starts on D. Here I use “C D Eb F G A Bb”
Start a white key scale on E. Scale used here is “C Db Eb F G Ab Bb”
Then an F white scale. Scale here is “C D E F# G A B”
Then G. Scale used is “C D E F G A Bb”
The normal minor scale. Scale used is “C D Eb F G Ab Bb”
The white scale version starts from B. Scale used here is “C Db Eb F Gb Ab Bb” Composing in Locrian is a musical migraine headache.