The major scale is the basic reference point for all scale and chord formulas. Because it is so fundamental it is worthwhile to review its structure. Based on the white notes of the piano starting on C and playing every white note up to the next C the structure is W W H W W W H where W=Whole Step and H=Half Step. This structure can be recreated starting on any key black or white and it makes one's life much easier if one has all of the major scales memorized on whatever instrument is primary.
We also need to address a bit of nomenclature here. Each note in the scale is assigned a number referred to as the scale degree. The first note of the scale is referred to as the root or the "tonic." The second note is two or the second scale degree and so on. These definitions will be very important moving forward so feel free to download the PDF below if you need something to refer to.
The triad is a "stack" of three notes, it is the smallest stack of notes that can technically be called a chord. Two-note "stacks" are called dyads but are often referred to as chords and that is not something to get hung up on.
Triads are composed of three elements, a Root, from which the triad derives its name, a third, and a fifth. (If you are new to this information please download the PDF below to accompany this description.) They have these names because if you look at the piano and start on a note, in this case, C, skip over a note, which would be 2, and then land on the next note you will end up on 3.
We start with the Major Triad which is built by starting on a root note also called the tonic, in our example C and going up a Major 3rd (4 H.S.) this is also called the root of the chord and a Minor 3rd (3 H.S) also called the 5th of the chord. Sometimes these are called Major Minor chords.
Next is the Minor Triad which is constructed from a root note (tonic) and a Minor 3rd and then a Major 3rd sometimes called a Minor, Major chord. (Imagine that!)
Moving on is the less common Diminished Triad which is constructed of a Root, Minor 3rd and another minor third. Sometimes called, you guessed it, a Minor Minor chord.
The least common triad is the Augmented Triad which consists of a Root, Major 3rd and Major 3rd. (Yep, Major Major chord)
OK OK I know I just used a scary music theory word, but it is not scary and it is fundamental to understanding the use of the major scale when building harmonies and progressions.
Simply put if you take the major scale, in our example C, start on the root note (tonic) and stack up thirds you get a major chord...the I chord.
Start on the 2nd scale degree, D and stack up thirds you get a minor chord, the ii chord.
Start on the 3rd degree, stack up 3rds, you get a minor chord, the iii chord.
Start on the 4th degree stack up 3rds you get a Major chords, the IV chord.
Start on the 5th degree, stack up 3rds you get a Major chord, the V chord
Start on the 6th degree, stack up thirds you get a minor chord, the vi chord.
Start on the 7th scale degree, stack up thirds, and you get a diminished chord, the vii chord.
It is customary to use Roman Numerals to denote scale degrees and they also indicate chord function. Upper case Roman Numerals indicate Major and lower case minor.
In their basic form, 7th chords are created by adding another note either a Major or Minor 3rd on top of a triad. (See and download PDF below)
Before we go on a note (pun intended) about nomenclature. There is much confusion and sometimes conflict about how jazz or extended harmonies are notated.
Major 7 = Maj7 or the somewhat old-fashioned Δ7
Minor 7 = Min7 or m7 or -7
Dominant 7 = (The dominant 7 is denoted by simply adding 7 to the Root i.e. C7)
Half diminished = 7b5
Fully diminished = °7
It is also important to note that in most jazz charts the 7 designation implies higher extension i.e. 9, #11, 13...etc.
I believe it is more satisfying and less boring to put concepts to work right away. A relatively simple way to jump in is to play blues progressions using shell voicings. For this application a shell voicing is the Root of the chord and the minor 7th above. The minor 7th is 10 half-steps above the root, but a super easy way to think of it is that the minor 7th is a whole step below the root. So find it a whole-step below and then transpose it an octave and there you go! Brilliant.
Rootless Chord Voicings A smooth and popular type of chord voicing are called (Bill Evans style) Rootless Chord Voicings. As the name suggests, these chord voicings exclude the root note. Instead of the root (and sometimes the 5th) we play chord tensions. This gives us a jazzy sound (because of the tensions) while not being too crowded (you only ever play 4 notes because we drop the root). Even though we are allowed to omit the root note in a chord, if you’re playing in a band often the bass player will play the root note. Otherwise, there’s nothing wrong with just leaving it out. The root note isn’t really all that important, harmonically speaking.