SF's harmony tutorials

[Sascha Franck]

OK, along with my (still to be finished) guitar voicing thread I thought it'd make sense to finally start some harmony thread - some people allready asked me to do so, so here we go.

Before we really get into the stuff, there's some fundamental knowledge to be cleared up, basically it comes down to two things:
- Knowing the notes on your instrument (in case I'm posting some examples, those will usually be using a piano keyboard).
- Knowing intervals. Intervals describe how far one note is away from each other. This is important to understand certain functionalities.

Notes in our western music are all made up by 7 notenames. In case you'd start with A, they're just like the alphabet: A, B, C, D, E, F, G. As it will help for a lot of explanations, we will start with the C though, so the most basic tonal material is looking like this: C, D, E, F, G, A, B (note: some german traditions have screwed up the pretty much logical alphabet stuff, our B is called H, for whatever stupid reason, in international notation fortunately the B is used).
When you look at piano keys, the C is the white key left from the "group" of two black keys. Starting at this C, playing all possible white keys up will give you exactly what I mentioned before: C, D, E, F, G, A, B. After that, the "octave" (see intervals) is reached and the same pattern starts to repeat.
At the same time, this is our C-major scale.

Now you will notice that there's some "occasional" black keys between some white ones. In fact, there's only two steps which don't have a black key between them (E and F, B and C). The step from one key to the next is called "halftone" while the step from one key to the "overnext" (wtf do you call it in english???) is called a "wholetone" step. Assuming that all the white keys define our C major scale, this gives some insight into the structure of it (and any major scale therefor).
The steps are:
C-D = Wholetone
D-E = Wholetone
E-F = Halftone
F-G = Wholetone
G-A = Wholetone
A-B = Wholetone
B-C = Halftone
So, if we give our scale "degrees" numbers (C = 1, D = 2 and so on), which is quite the usual thing, we will see that there wholetones from each note inside C major to the next apart from the steps between 3 to 4 and 7 to 8.
This is valid for ANY major scale! More on this a few sentences below...

Now, for the black keys that haven't been covered yet, those have names as well, deriving from our "basic" note names. They are either indicated by a "b" or by a "#", following the basic note name. A "b" is lowering the note by a halftone, a "#" is raising it. "b" is called "flat" and "#" is called "sharp". For each black key there's two possibilities to be named, either by a "b" or by a "#", this is depending on the harmonical context, but we're not there yet.
Possible namings for the black keys:
between C and D = C# or Db (C sharp or D flat)
between D and E = D# or Eb (D sharp or E flat)
between F and G = F# or Gb (F sharp or G flat)
between G and A = G# or Ab (G sharp or A flat)
between A and B = A# or Bb (A sharp or B flat)

Back to the scale thing: In all our most used western scales (I won't explain them for now, more on them later), each note name is used EXACTLY once. So, if notated/spelled correctly, you won't find, say, an A and an Ab in the same scale, instead of the Ab it would be named G#. Note: there is some exceptions, caused by either notational needs, harmonical "weirdness" or due to using non-7-note scales. But in general this rule applies though:
Each note name only ONCE!

With this knowledge, we should now be able to construct a major scale with correct note names in every key.
Let's do some example. We would like to build a D major scale.
The basic note names would still remain the same, we'd just start with D this time, so the scale only constructed by "basic" note names would look like: D, E, F, G, A, B, C and the octave D.
Now, you may have allready noticed that this by no means is a D major scales, because the steps aren't identical to the whole/halftone formula presented above. So, the basic note names are correct allready (each one is used once), but the steps between them are wrong. What we want is wholetones between all degrees but 3-4 and 7-8.
Easy, all we need to adjust is the wrong steps. In the case of D major those would be the F (which is only a halftone away from the E, but it should be a wholetone away, at the same time it's a wholetone away from the 4th degree G, but it should only be a halftone away, following the major scale formula) and the C, both will have to be raised by a halftone, thus getting "sharpened" with a "#".
With those sharps applied, our D major scale will look like: D, E, F#, G, A, B, C# and the octave D, perfectly suiting the major scale formula.

I would like to do another example, say, an Eb major scale: Basic note names would be E, F, G, A, B, C, D and the octave E.
In this example, even our first step (the root of the scale) doesn't fit, so this has to be lowered as the very first step. E is becoming Eb. Now, when applying our major scale formula, we will find out that keys A and B will have to be lowered as well to fit into the formula. Therefor our Eb major scale will look like: Eb, F, G, Ab, Bb, C, D and the octave Eb.

You may by now allready have noticed one of the reasons to use either sharps or flats. For the record, with out standard scales it's allways that either flats OR sharps are used, they never occur at the same time (as said, only valid for standard scales, there's exceptions...). I'll get into that a bit more detailed in further posts.

One could also construct scales by learning things such as the cycle of fifths, but for now I wanted to concentrate on the structure of a major scale, and for that the "scalestep" approach IMO fits best.

Next installment will cover intervals, perhaps I'll even find the time to write it down today.

As usual, comments and questions are more than welcome, I've got plans to compile all this and whatever will follow into one doc, so it'd only make sense if everybody's possible questions are answered.

[Sascha Franck]

Allright, on to the next step, which would be understanding intervals.

As said before, an interval is describing the distance between one note and another.
The basic procedure is rather simple, we just take our "basic notenames" (the alphabet stuff again) and count through them, the first note being numbered "1" and the rest to follow.
Let's take our C major scale as an example again:
C = 1
D = 2
E = 3
F = 4
G = 5
A = 6
B = 7
C' = 8
D' = 9
E' = 10
F' = 11
G' = 12
A' = 13
B' = 14
C'' = 15

Those are the ones that might be important for harmonic explanations. You may wonder about the ones above an octave (because you could just say, hey C to D is a second, eventually with an octave in between) but it's important for some functional point of view.

There's different descriptions for certain intervals, they come in certain flavours, based on their functionality:
- "plain/pure" (sorry, I might miss the proper english word here, in german "rein", as in "reine Quinte" which would approx. be "plain fifth").
- augmented or diminished
- major or minor
Sometimes they are also reffered to as "sharped" (thus indicated with a "#") or "flat" (indicated by a "b"), just as with notes.
The system isn't exactly 100% consistent, especially when it comes to intervals appearing in chord symbols, so it might be the best way to learn the following list, which should be more or less comprehensive in terms of analyzing harmonic or scalar contents.

I will use C as our starting point and describe every possible interval inside our 2 octave range in the form:
C - other interval note | amount of halftonestepe | functional name | possible appearance in chord symbol (explanations for those namings later).

C - C | 0 | first | chord root name
C - C# | 1 | augmented first | never seen that one in a chord
C - Db | 1 | minor second | b2, add b2 (hardly ever found)
C - D | 2 | second | 2, add2, sus2
C - D# | 3 | augmented or sharp second | #2 add #2 (hardly ever found)
C - Eb | 3 | minor third | describing minor chords, found as C-, Cm, Cmin, Cminor
C - E | 4 | major third | not mentioned in chord names. In case you don't find a min/m/minor it's automatically major
C - F | 5 | fourth | sus4, add4
C - F# | 6 | augmented or sharp fourth | add#4 (rarely found)
C - Gb | 6 | diminished or flat fifth | b5, 5-, dim5, dim (without the 5, the dim implies a dimished chord with minor third and diminished 6th)
C - G | 7 | fifth | not mentioned in chord symbol, obvious interval in chords.
C - G# | 8 | augmented or sharped fifth | #5, 5+, +, aug5, aug (without the 5, "aug" and "+" imply an augmented chord with major third and augmented 5th)
C - Ab | 8 | minor sixth | b6, addb6 (not found too often)
C - A | 9 | sixth, sometimes major sixth | 6, add6
C - Bb | 10 | seventh, sometimes (rare but confusingly) minor 7th | 7
C - B | 11 | major seventh | j7, maj, maj7, j, major, major7, sometimes a small triangle (can be confusing, not recommended, best to read would be maj7)
C - C' | 12 | octave | not mentioned in chord symbols
C - C#'| 13 | augemented octave | never seen that one
C - Db'| 13 | minor or flatted ninth | b9, addb9
C - D' | 14 | ninth | 9, add9
C - D#'| 15 | augmented or sharped ninth | #9, add#9
C - Eb'| 15 | minor tenth | only mistakenly written down in some sheets, it's allways the #9 that is meant.
C - E' | 16 | majort tenth | not to be found
C - F' | 17 | eleventh | 11, add11
C - F#'| 18 | augmented or flat eleventh | #11, add#11
C - Gb'| 18 | diminished twelveth | not found
C - G' | 19 | twelveth | not found
C - G# | 20 | augmented or sharped twelveth | not found
C - Ab'| 20 | minor thirteenth | b13, addb13
C - A' | 21 | thirteenth | 13, add13
C - Bb'| 22 | fourteenth | not mentioned
C - B' | 23 | major fourteenth | not mentioned
C - C''| 24 | two octaves | not mentioned.

Some notes:
If you want, strip out all the not mentioned ones, they're irrelevant for any harmonic analysis and description.
There's some room for confusion, especially when it comes to thirds and sevenths. In case a chord has nothing indexed, it's a major chord. In case a chord has some "maj" indexed, it allways means the seventh - there's even minor chords with major sevenths. On the other hand, in case a chord is indexed "min" or "minor", it's allways the third that is meant. Yes, confusing.
Also, in case you're ever dealing with sheets, expect to find quite some suspicious stuff, such as the "b10" bollocks.

OK, after those two posts only covering very basic ground I hope to start with the interesting stuff in my next installments. Might take some time... we'll see.

[Mighty_Hero]

Nice posts mate, keep them coming.

[declassified]

Wow!
Looks great, though I don't think I'll get into it soon; lack of time, etc.