Comment by nilirl

No you have an equal number of options (minor and major are effectively transpositions/rotations...e.g. the chord progressions are "m dim M m m M M" for minor (m-minor, M-major, dim-diminished) chord progression, vs "M m m M M m dim" for major).

The post is likely getting to the point that, for english-speaking/western audiences at least, you are more likely to find songs written in C major, and thus they are more familiar and 'safer'. You _can_ write great songs in Em, but it's just a little less common, so maybe requires more work to 'fit into tastes'.

edit: changed 'our' to english/western audiences

> 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.)

It...depends.

If you're working in a continuous environment rather than discrete (choirs and strings can fudge notes up or down a bit, but pianos are stuck with however they're tuned), you'll often find yourself wanting to produce harmonies at perfect whole-number ratios -- e.g., for a perfect fourth (the gap between the first and second notes in "here comes the bride") you want a ratio of 4:3 in the frequencies of the two notes, and for a major third (the gap between the first and second notes in "oh when the saints, go marching in...") you want a ratio of 5:4. Those small, integer ratios sound pleasing to our ears.

Those ratios aren't scale-invariant though when you move up the scale. Here's a truncated table:

Unison (assume to be C as the key we're working in): 1

Major Second (D): 9/8

Major Third (E): 4/3

However, E is also a major second above D, so in the key of D for a "justly tuned" instrument, you would want the ratio D/E to also be 9/8. Let's look at that table though: (4/3)/(9/8) is 32/27 -- 5.3% too big (too "sharp").

When tuning something like a piano then where you can't change the frequency of E based on which key you're playing in, you have to make some sort of compromise. A common compromise is "equal temperament." To achieve scale invariance in any key you need an exponential function describing the frequencies, and the usual one we choose is based on 2^(1/12) since an octave having exactly twice the fundamental frequency is super important and there are 12 gaps in normal western music as you move up the scale from the fundamental frequency to its octave.

Doing so makes some intervals sound "worse" (different anyway, but it makes direct translations hard) than they would in, e.g., a choir. A major third, for example, is 0.8% sharp, and a perfect fourth is 0.1% sharp in that tuning system.

Answering your question, at first glance you would expect the scale invariance to therefore not limit your choices. Every key is identical, by design.

That's not quite right though for a number of reasons:

1. True equal temperament is only sometimes used, even for instruments like pianos. A tuner might choose a "stretched" tuning (slightly sharpening high notes and flattening low notes) or some other compromise to make most music empirically sound better. As soon as you deviate from a strict exponential scale, you actually live in a world where the choice of key matters. It's not a huge effect, but it exists.

2. Even with true equal temperament or in a purely vocal exercise or something, there are other issues. Real-world strings, vocal folds, etc aren't spherical cows in a frictionless vacuum. A baritone voice doesn't sound different just because their voice is lower, but because of a different timbre. When you choose a different key, you'll be moving the pitch of the song up or down a bit, exercising different vocal regions for singers, requiring different vocal types, or otherwise interacting with those real-life deviations from over-simplified physics. Even for something purely mechanical like piano strings, there's a noticeable difference in how notes resonate or what overtones you expect or whatnot. Changing the key changes (a little) which of those you'll hear.

3. Related to (2), our ears also aren't uniform across the frequency spectrum, and even if they were our interpretations of sounds also depends on sounds we've heard before, leading to additional sources of variation in the "experience" of a slightly lower or slightly higher key.