I'm still thinking about Valencia's question about the names to give chords (and perhaps the notes in the chords as well). Some answers have been given already. I want to try an answer as well. To set the stage, I want to talk about intervals first.
I want to talk about intervals because I want to be able to say: a major triad is a major third and a perfect fifth above the root. A dominant 7 chord (e.g. C7: CEGBb) adds a minor seventh, while a major 7 chord (e.g. Cmaj7: CEGB) adds a major seventh. A dominant 7 chord resolves to the chord whose root is a fifth below. E.g C7 resolves to F. That information implicitly contains all (or almost all) the needed information about when to choose sharps or flats.
The key about intervals is that there is sound, and there is the names (or notation on the staff) that we use for that sound. Naming intervals has to do not only with sound, but also with the names, or staff notation, that we use for that sound.
Major thirdsPlay a note, and the note 4 half-steps higher. Play them together, and also one after the other. That sound (the same as the first two notes of "Oh When the Saints") is the same sound whatever we call the notes. For example, start on C. The sound is the same whether we call the two notes CE or CFb or B#E or B#Fb or B#D## (to think of successively more unlikely things that we might call it!). For another example, start on F#. The sound is the same whether we call the two notes F#A# or F#Bb or GbA# or GbBb or GbCbb or E##A#, etc. (I'm having fun running through all the crazy names we could give a note...)
But when we give that sound of "four half steps" an interval name and call it a major third, that implies a particular way of notating it. In particular, a major third is notated on two neighbouring line notes, or two neighbouring space notes. For ilustrations of thirds, see p. 9 of Jason Sifford's guide to intervals
Interval, Schminterval.
So in our first example starting on C, the note a major third up is called and notated E -- not D##, not Fb. If we were to call the first note B#, then the note a major third up would be called some type of D: D## to be exact. Take out a piece of staff paper (or draw five lines to be a staff) and draw these, to see what's going on.
Notice that this matches up with what keystring said earlier in the thread: an interval of a third means the third letter over, starting from the first letter. For example, C, D, E. Or B#, some type of C, some type of D (D## to be exact).
Look at the second example, from the first of the group of three black keys to the last of that group. Suppose we call the first note F#. Draw this on your staff paper. Let's say we're doing this on the first space of the treble clef. The note a third higher needs to be notated on the next space of the treble clef: the second space. So it's a type of A. We can see on the keyboard that it's the black key to the right of A natural, hence A#.
Suppose instead we call that first note Gb. Draw this on your staff paper. Let's say we're doing this on the second line of the treble clef. The note a third higher needs to be notated on the next line of the treble clef: the third line. So it's a type of B. We can see on the keyboard that it's the black key to the left of B natural, hence Bb.
Minor thirdsThe same thing is true of minor thirds: they are notated on two neigbouring lines, or two neighbouring spaces. This matches up with the rule for thirds (of any type), that they be the third letter. Also they are three half-steps. For example, counting off letters C 1, D 2, Eb 3 gives that CEb is a third. What kind of third? Check the number of three half-steps from C to Eb: C to Db, 1. Db to D, 2. D to Eb, 3. So CEb is a minor third.
So by just a quick glance at the staff you can detect thirds: two neighbouring lines, or two neighbouring spaces. Then you have to either check the sound, or count the half-steps, or use other remembering devices, to know what kind of third it is.
Perfect fifthsSimilarly, there is a pattern on the staff for fifths (of any type, perfect or otherwise). They are either two lines with a line in between, or two spaces with a space in between. See p. 3 of the aforementioned
Interval, Schminterval. To be a perfect fifth, there must be 7 half-steps from the first note to the second note.
Suppose we start on B, on the middle line of the treble clef. That means the note a perfect fifth higher must be on the top line of the treble clef, hence a type of F. Checking half-steps, we find that it must be F#. Notice that this matches up counting letters: the letter for a fifth must be the fifth letter over from the starting letter. E.g. B, a type of C, a type of D, a type of E, F#. So a perfect fifth starting on B is notated as BF# --
not BGb.
Diminished fifthsDiminished fifths are also a type of fifth. They are 6 half-steps: one half-step smaller than a perfect fifth. Being a type of fifth, they are also notated on two lines with a line in between, or two spaces with a space in between. For example the interval BF is a diminished fifth.
Major and minor seventhsA seventh is notated... well, ugh, I can't eyeball sevenths easily. It's notated on the line or space below where the octave would be notated. (Thinks about it a bit). This turns out that sevenths are notated either on two lines with two lines in between, or on two spaces with two spaces in between.
A major seventh is 11 half-steps; a minor seventh is 10 half-steps. But double-ugh, I hate counting half-steps, so I remember that a major seventh is a half-step down from an octave, and a minor seventh is a whole-step down from an octave.
So a major seventh above C is B, and a minor seventh above C is Bb. Note that the letter for a seventh is the seventh letter over (for example C D E F G A B, B is the seventh letter from C). So, for example, the note a major seventh above G is called F#, not Gb.
Remember what I said about sound? The sound is exactly the same whether we call it GF# or GGb. But when we start naming it as a major seventh, we are implying a particular choice of note name (and notation): GF#.
See p.7 of
Interval, Schminterval.
I hate countingNow for a secret: I hate counting half-steps. My limit for patience with counting half-steps is about 2 half-steps. I've just described for sevenths how I avoid counting 10 or 11 half-steps, and just back down 2 half-steps or 1 half-step from the octave instead.
Here are some other tricks that I use to avoid counting half-steps.
For major thirds, I remember the major triads, and a major third is always the first two notes of a major triad in root position.
For minor thirds, I remember the major thirds, and a minor third is a half-step smaller than that. I could remember the minor triads instead: a minor third is always the first two notes of a minor triad in root position. I don't happen to do it that way, but you might find that helpful.
For perfect fifths, I could remember them as the outside of either a major or minor triad, but actually I just have these memorized. (For a long time I used a mnemonic BEADGCF (pronounced beed-guh-cuf), which gives descending fifths, or ascending fifths when read backwards. This is a mental quirk of mine that this works for me: easily reading a mnemonic backwards in my head. This may not work for everyone.) If I'd known about the "two lines with a line in between, or two spaces with a space in between" when I was learning these, I could have visualized them on the staff instead of using the mnemonic.
For diminished fifths, I remember the perfect fifths, and a diminished fifth is always a half-step smaller than that. For example GDb. I remember "GD is a perfect fifth, so GDb must be a diminished fifth."
For major and minor sevenths, as mentioned, I count them back one or two half-steps back from the octave.
I have some other ways of finding intervals also, involving keys and inverted intervals, but I'll talk about those later, since it involves more material than we need yet and I don't want to overload the information (as if this post isn't perhaps too much information already).
Other intervalsThere are other intervals smaller than an octave: seconds, fourths, and sixths. You can read about them in
Interval, Schminterval. I'll post about them at some other time; we don't need them yet.
When we start to talk about extended chords (chords bigger than a sevenths), we get into extended intervals like ninths, elevenths, thirteenths (and there are tenths, twelfths, etc.) I'll talk about those at some later time, when we start to really need those chords.
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