To start off, take a look at the grand staff with all the different pitches notated. While they are all different with their placement vertically on the staff – heck, some utilize ledger lines, those extra lines above/below the staves – all of those pitches do have something in common: they are all C. That means this collection of pitches are in the same pitch class, or notes that are octave-related and have the same letter name.
Remembered how we numbered pitches before from left to right on a keyboard, which is how we got C4 to be middle C? This is the act for naming registers. Starting with the first C and naming it C1, everything above and below the consecutive C is in the 1 category for their letter name. And this continues on and on. Any pitches before C1 will be numbered with a 0.
So, if I was to write a G between C4 and C5 vertically on the grand staff, it would be called G4 because it is higher than C4, but lower than C5.
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