Comment by seanhunter

> Does picking E minor somehow give you fewer options than C major (I'm not a musician)?

Short answer: No. No matter what note you start on you have exactly the same set of options.

Long answer: No. All scales (in the system of temperament used in the vast majority of music) are symmetrical groups of transpositions of certain fundamental scales.[1] These work very much like a cyclic group if you have done algebra. In the example you chose, E minor is the "relative minor" of G Major, meaning that if you play an E Aeolean mode it contains all the same notes as G Major), and G major gives you the exact same options as C Major or any other Major Scale. What Messiaen noticed is that there are grouped sets of "Modes of limited transposition" which all work this way. So the major scale (and its “modes”, meaning the scales with the same key signature of sharps or flats but starting on each degree of the major scale) can be transposed exactly 11 times without repeating. There are 3 other scales that have this property (Normally these are called the harmonic minor, melodic minor and melodic major[2]). There are also modes of limited transposition with only 1 transposition (the chromatic scale), 2 (the whole-tone scale), 3 (the "diminished scale") and so on. Messiaen explains them all in that text if you're interested.

[1] This theory was first written out in full in Messiaen's "The technique of my musical language" but is usually taught as either "Late Romantic" or "Jazz" Harmony depending on where you study https://monoskop.org/images/5/50/Messiaen_Olivier_The_Techni...

[2] If you do "classical" harmony, your college may teach you the minor scales wrong with a descending version that is just a mode of the major scale. You may also not have been taught melodic major but it's awesome. (By “wrong” here, I mean specifically Messiaen and Schoenberg would say it’s wrong because a scale is a key signature/tonal area and so can’t have different notes when a melody ascending from descending. If there are two sets of different notes, Messiaen would say they are two scales and I would agree.)