Play a major scale from the bottom up all the way through.
Ok. How many notes did you play? If you are like me, then you would play 8, not 7.
Because a scale is 7 intervals, not 7 notes. So, for example, the interval of a half step between the major 7th and the octave is part of the melodic contour and sound of that scale, just as much any of the other six intervals. So to get those seven intervals you need 8 notes. (As against the view that the scale simply starts over again at the octave.)
Surely this is wrong, in a book on Lorca and Falla I am reading:
"The Phrygian, according to Falla's personal jottings, contains the notes E-F#-G-A-C#-D. The Lydian includes F-G-A-Bb-C-E. The Doric [sic] holds D-E-F-B-C-E."
First of all, why are there only six notes in these modes? Secondly, isn't Phrygian EDFGABCDE? And the Lydian FGABCDEF? The Dorian DEFGABCD? I know there's a Phrygian dominant, but it still has the flat second. What he has for Lydian is an F major scale missing the sixth.
I don't know why he defines an interval by saying, "a seventh signifies a difference of seven notes..." So would a second be a difference of two notes? Actually it would be one note different, right?
I don't think "modulation" is "the transposition of a melody from one key to another." I'm not trying to be super-pedantic here. The modal transcription could be a typo. I'm just trying to figure out whether to trust the source. It's hard to get things accurately, even in the definition of a simple term like modulation, which is the way that music piece shifts harmonically into another key, not the transposition of a melody.
Flattening a note is not taking it down "half an interval," but taking it down a half-step, or a very specific interval.