Musical nomenclature has been cobbled together over the centuries like a medieval city. Different systems leave their imprint in convention, later developments try to be compatible with accepted names, and the whole thing ends up confusing and contradictory.
Take enharmonic equivalents, for example. G# and Ab are the same note on the piano, the black key between G and A. So why do you sometimes call that note by one name, and sometimes by the other? The answer actually leads to some deep realizations about music, and it comes back to just intonation. In untempered or just music, G# and Ab are not the same note, and which one you choose becomes important. It’s important in ET too — the music establishes a context, and the ear figures out which note it’s supposed to be. But if you grew up with ET, and have no idea that there used to be two different notes there, the names can be confusing. How do you imply one note or the other? Which one is right in a given situation? Why bother? It’s a huge part of writing chord progressions that make sense, but ET by itself isn’t going to tell you what to do. You have to dig deeper for that.
I’ve slowly evolved a personal system I’m very happy with. It’s based on the lattice.
The great advantage of this approach is that it’s entirely unambiguous. Every note on the infinite lattice has a unique name, and that name tells you exactly what its pitch is, and where it is on the map.
The seven notes I’ve covered so far form the core of the system. I’ve dropped all the word names and just use numbers:
1 — the tonic, 1/1
2 — the major second, 9/8
3 — the major third, 5/4
4 — the perfect fourth, 4/3
5 — the perfect fifth, 3/2
6 — the major sixth, 5/3
7 — the major seventh, 15/8
The rest of the notes are named by adding accidentals to modify the pitches. I’ll quantify these later, and explain how they work, but approximately they are:
b — flat by about 2/3 of an equal-tempered semitone
# — sharp by about 2/3 of a semitone
– — flat by about 1/5 of a semitone
+ — sharp by 1/5 semitone
7 — flat by 1/2 semitone.
The basic notes occupy the center of the lattice. These seven notes form the major scale.
Next: The Major Scale