Theory
Introduction
My aim is not to write an harmony handbook in few rows and I apologise in advance o everyone more expert than me. My purpose is to give few basic information and some samples about the chords order using in an arpeggio.
Many times I found generic indications concerning guitar accompainment simply signaling to "play an arpeggio", sometimes suggesting the right hand movement required.
Anyway, there are some rules in the "classical" or "tonal" harmony, briefly that harmony used (more or less) from XVI century chorals up to almost all the XIX century, and still today, knowingly or not, in a lot of the pop music, that might still be observed, just to be a little bit rigorous and, at the same time, to obtain more convincting effects for the most sensitive ears of some listener.
So, in the first part I will try to explain the rules in a nutshell (at least the ones concerning the note selection of two consecutive chords), in the second part I will show a series of chord progressions so that these rules are actually observed (I will limit myself to the most used tonalities).
The major scale
The major scale (let's take the C major scale as an example) is the scale everyone know how to sing (C-D-E-F-G-A-B-C). Following what I said above, between C and D there is one tone, between D and E one tone, between E and F half tone, between F and G one tone, between G and A one tone, between A and B one tone and finally, to come full circle, between B and C half tone.
In harmony, the first note is said tonic (C), the fourth is said subdominant (F), the fifth is said dominant (G), the seventh is said Leading-tone (and it is half note below the tonic).
This sequence of intervals is the same for each major scale.
If we start, for example, from an A, the second note must be one tone from the first, so it will be a B, the third will be one more tone above, so it will be a C# as B and C are half tone distant, and going on we will find D, E F# and G#.
The minor scale
The minor scale (let's take the A minor scale as an example) is made by the tonic (A), followed by the second that is one tone above (B), the third is an half tone above (C), the fourth (subdominant) one tone above (D), the fifth (dominant) one tone above (E), the sixth is one half tone above (F) and the sventh (leading-tone) is three half-tones above (G#). So the leading-tone is half tone below the tonic. Sometimes the seventh may not have any alteration (so loosing its leading.tone function) and sometimes the sixth too may be alterated (it means F#).
The most frequent cases concern the descending scale that usually needs the two notes not altered (see the sequence below)
The intervals
An interval is said harmonic when you have two notes played at the same time, melodic when you have two notes played in sequence.
Starting from any note (i.e. C) you can have the following intervals:
Unison.
Unison can be perfect (i.e. C – C), augmented (C – C#), diminished (C – Cb ). There could be other definitions that go far beyond these few rows.
Second
The interval of second can be major (C – D), minor (C – Db ), augmented (C – D#), diminished (C – Dbb )
Please, pay attention: writing C – C# or C – Db , from an harmonic point of view is not the same although it id the same sound (the intervals are said enharmonics).
Third
Same as the second, it can be major (C – E), minor (C – Eb ), augmented (C – E#), diminished (C – Ebb )
Fourth
Same as unison, it can be perfect (i.e. C – F), augmented (C – F#), diminished (C – Fb ).
Fifth
Same as unison, it can be perfect (i.e. C – G), augmented (C – G#), diminished (C – Gb ).
Sixth
Same as the second, it can be major (C – A), minor (C – Ab ), augmented (C – A#), diminished (C – Abb )
Seventh
Same as the second, it can be major (C – B), minor (C – Bb ), augmented (C – B#), diminished (C – Bbb )
is a triad (C-E-G-C). From the intervals point of view we will say that E is the third (it is a third distant from the root) and G is the fifth third (it is a fifth distant from the root).
We will take into account chords built "on third" that is placing above the first note of the chord (i.e. C), a second note that is a third above, a third note that is a third above the second note and, in case, a fourth note that is a third above the third note).
Type of chords
A major chord is a chord whose second note is a major third distant from the first note and whose third note is a minor third distant from the second note.
A minor chord is a chord whose second note is a minor third distant from the first note and whose third note is a major third distant from the second note.
Note
Following what we wrote, to build an A major chord I have to take an A, the note that is a major third above, that is a C# and the note that is a minor third above the C#, that is an E.
To build an A minor chord I have to take an A, the note that is a minor third above, that is a C and the note that is a major third above the C, that is an E.
You can see easily that the two chords are equal except for the intermediate note that has an half tone variation and is said mediant and its variation identify major mode and minor mode.
A diminshed chord is a chord in which the second note is a minor third distant from the first and the third note is a minor third distant from the second note.
An augmented chord is a chord in which the second note is a major third distant from the first and the third note is a major third distant from the second note.
A four sound chord is built as over but adding a minor or a major third as the fourth note. I will not describe it for now.
The degrees
Starting from a scale, the chord built on the triad starting from the first note is said first degree chord (or tonic). For instance in C major it is formed by C-E-G.
The chord built on the triad starting from the second note is said second degree chord. For instance in C major it is formed by D-F-A.
Going on we will find the third degree, fourth degree (or subdominant), fifth degree (or dominant), sixth and seventh degree.
Chords are built following the specific alterations of the scale of the choosen tonality.
In a major tonality, the first degree is - obviously - a major chord (i.e. C-E-G), the second degree a minor chord and the third is minor too, the fourth and the fifth are major chords, the sixth is a minor chord and the seventh is a diminished chord.
In a minor tonality, the first degree is - obviously - a minor chord, the second degree a diminished chord, the third is major, the fourth is a minor chord, the fifth is usually a major chords (with alteration of the leading-tone), the sixth is a major chord and the seventh is a diminished chord (with alteration of the leading-tone).
Example: A major (F#, C# and G# in cleff) A minor (no alteration in cleff)
I degree: A-C#-E A-C-E
II degree: B-D-F# B-D-F
III degree: C#-E-G# C-E-G
IV degree: D-F#-A D-F-A
V degree: E-G#-B E-G#-B (rare E-G-B)
VI degree: F#-A-C# F-A-C
VII degree: G#-B-D G#-B-D
As you can see, there are only two identical chords and they are on the V and on the VII degree.