> Here's how I approach it: forget about all the historic naming like "perfect fifths" and just think in terms of the modern 12-note equal temperament.
You actually want to learn these names, because they characterize the diatonic scale. Basically, pick seven contiguous notes on the circle of fifths, you get the pitch-class set of a diatonic scale. Then put the notes in the set in pitch order, and pick a tonal center. The default, naïve choice (pick the "flattest" note as your tonal center) is called Lydian mode. It can be interesting, but it has a drawback in that it forgoes the subdominant relationship. Picking the next-to-'flattest' note gives you Ionian, which solves this (the fourth scale degree forms a "perfect fourth" with the tonic, which is the flip side of a perfect fifth. Having more notes that can be related to the tonic makes for more musical possibilities). This is one simple explanation of the diatonic scale we ordinarily use.
One other quirk that also explains the "weird historic names": in traditional music theory, sharps and flats are definitely not treated equally, the way that would be implied by 12-equal temperament. The musically-relevant distinction is simple enough to explain: taking one example, F# "wants" to step up to G, whereas Gb "wants" to step down to F. This means that the "circle of fifths" turns into more of a helix of sorts that can be extended in both directions, in principle indefinitely. This difference cannot be "heard" directly; it's all about characterizing how the notes "work" in a piece of music.
After learning about the diatonic scale degrees, the next sensible step would be to start learning about counterpoint, which is based on simple definitions of consonance and dissonance between scale degrees. Then move on to thoroughbass and harmony.
Yes, the names are important for "interop" reasons and yes, historically they mattered because the temperament was different and C# was totally different from Db. And yes, not all modern music is based on the 12-note equal temp. But for a beginner, I would advocate avoiding them and thinking in terms of semi-tones as I've described. It's simpler, and it's the way guitars and pianos and DAWs and whatnot work, so it's a good way of thinking for a beginner. I know for sure I didn't appreciate being bombarded with names like "augmented fourth" or "diminished seventh" when "+6“ or "+9" would make more sense in terms of piano keys/frets that beginners usually have in front of them.
> But for a beginner, I would advocate avoiding them and thinking in terms of semi-tones as I've described.
For a total beginner, I might agree. But thinking about the scale degrees (Do, Re, Mi etc.) is also a totally viable approach (even as a starting point), and it's extremely helpful to learn about how the two relate ASAP so you aren't left holding a mess of seemingly-contradictory "theories" in your head!
Historically, they sounded different, so they wouldn't even be acoustically in-tune w/ the same notes. Each would only be in tune with its nearby notes on the "extended" cycle of fifths.
Yes, and it means that songs actually sound different when played in different keys. It's not just a shift up or down, the intervals within the song shift, if only slightly.
Indeed "slightly different", as opposed to "totally different", which they are not.
And apparently the human ear can be train to ignore this slight difference (which everybody does because we are used to 12-TET). And this, for me, kind of throws the whole "simple integer fraction ratio == pleasing harmony" a bit into question. It's probably not wrong, but there's definitely more to it. But it's hard to explore, because you need the exposure to get used to the new microtonals if you want to experiment with it. Definitely very hard to test scientifically because it depends so much on a particular person's musical background and education.
> taking one example, F# "wants" to step up to G, whereas Gb "wants" to step down to F.
Uhhh....no? A flat or sharp can be the tonic, which does not lead to any other note. A note is named flat or sharp to maintain proper interval distance without repeating letters within the scale. A flat is typically not a leading tone because of interval distance, but can still want to resolve up or down. Any note can be consonant or dissonant, leading or resolved depending on the context.
> A flat or sharp can be the tonic, which does not lead to any other note.
You're right, and this is most often seen with flats; when Bb is the tonic, it doesn't "want" to resolve to A. --Of course, a modulation to F - the next-sharpest key in the cycle of fifths - is enough to change that. A "stable" sharp note is seen starting from the key of D, where F# is a stable third. But in the context of enharmonic notes, what I said generally holds. F# and Gb, to take the most common example, are so far in the 'extended' cycle of fifths that whenever both appear in the same piece, one can generally assume that the rule holds.
> A note is named flat or sharp to maintain proper interval distance without repeating letters within the scale.
Notes are not just named flats or sharps; at least in principle, there can be double, triple etc. sharps, and double, triple etc. flats. This is done in order to properly notate modulations in the cycle of fifths; one does not arbitrarily "switch" from sharps to flats, but just keeps adding to them.
I took a few years of music lessons (granted light on theory) but I never heard this idea.
Is this exclusive to notes that are not in the current key? For example the f# in Gmaj doesn't want to step up to G any more than B wants to step up to C in Cmaj.
Because historically, a "sharp" note was thought of as a leading tone (Ti), whereas a "flat" note was thought as a fourth scale degree (Fa), tending to step down to the third (Mi).
(Actually, this was thought of most often in terms of hexachords, where there is no Ti and one would always use Mi-Fa for a half-step interval. I rewrote it in terms of scale degrees to avoid confusion.)
I.e. the F# in Gmaj does "want" to step up to G, in basic structural terms. We call the places where this happens most properly "cadences", and they are among the main structuring elements in a piece of music. (This Ti-Do - F#-to-G or B-to-C motion is then called a "cantizans", since it appears most prominently as a "canto" or "sopran" cadence. It's most typically seen as Do-Ti-Do, where the first appearance of Do is first "prepared" in a context that makes it a consonance, but then sounds as a dissonance as the other parts shift to a dominant chord (Sol and Re), so it's allowed to resolve to the leading tone.)
Yes. (The local tonic, at least. It's no coincidence that the structural feature which most often results in "extra" sharps and flats, outside the key signature, is known as "tonicization".)
You've never heard of this because it's not true. A note wants to resolve up or down based on it's relative distance from tonic. This had nothing to do with what it's named, the most important part of naming notes is not repeating letters in an 8-note scale.
You actually want to learn these names, because they characterize the diatonic scale. Basically, pick seven contiguous notes on the circle of fifths, you get the pitch-class set of a diatonic scale. Then put the notes in the set in pitch order, and pick a tonal center. The default, naïve choice (pick the "flattest" note as your tonal center) is called Lydian mode. It can be interesting, but it has a drawback in that it forgoes the subdominant relationship. Picking the next-to-'flattest' note gives you Ionian, which solves this (the fourth scale degree forms a "perfect fourth" with the tonic, which is the flip side of a perfect fifth. Having more notes that can be related to the tonic makes for more musical possibilities). This is one simple explanation of the diatonic scale we ordinarily use.
One other quirk that also explains the "weird historic names": in traditional music theory, sharps and flats are definitely not treated equally, the way that would be implied by 12-equal temperament. The musically-relevant distinction is simple enough to explain: taking one example, F# "wants" to step up to G, whereas Gb "wants" to step down to F. This means that the "circle of fifths" turns into more of a helix of sorts that can be extended in both directions, in principle indefinitely. This difference cannot be "heard" directly; it's all about characterizing how the notes "work" in a piece of music.
After learning about the diatonic scale degrees, the next sensible step would be to start learning about counterpoint, which is based on simple definitions of consonance and dissonance between scale degrees. Then move on to thoroughbass and harmony.