I'm going through Larry Teal's daily studies for an alto saxophone (E-flat instrument). I'm practicing D sharp minor and I am seeing a B sharp and a C double sharp. Is B sharp a C? and the C double sharp a D? Please advise. Thanks
yes, it is!
If you transpose the piece of d# minor to the enharmonic eb minor, C double sharp will change to D and B# will change to C.
In this key you can better identify the two notes in question as the lead tone (D for C##) and C for B# as the natural 6th of the melodic minor scale.
The melodic minor scale is borrows the second tetrachord of the parallel major scale: the 6th and the 7th step are augmented:
Mi Fa So La -> Mi Fi Si La
5, 6, 7, 8 -> A#, B#, C##, D#
5, 6, 7, 8 -> Bb, C, D, Eb
as on the keyboard of the piano where you have to play for both scales the same keys it will be analog on the sax:
B# = C, C## = D
Yes, they are. A sharp raises a note by one semitone.
So, a B sharp is one semitone above B, so this is (broadly speaking) played as a C.
A C double sharp is two semitones above C, so this is correspondingly played as a D.