Learn to improvise. 2003-2004. Lesson 03: fifth, third, triad, key of C.

When two tones sound together, extra combination tones sound also which cause a complex pattern of waves, dependent on the distance (interval) between the two tones.

Important intervals are: (The names octave, fifth, etc are originated from our Western scale).
A stack of two intervals makes a triad:
A major third and a minor third makes a 'major triad', e.g. the chord C = c-e-g.
A minor third and a major third makes a 'minor triad', e.g. the chord Am = a-c-e.

(If the character m, which stands for 'minor', is left out in the name of the chord, it always is a major triad.)

A stack of two minor thirds makes a 'diminished triad', e.g. the chord Cdim = c-eb-gb.
A stack of two major triads makes an 'augmented triad', e.g. the chord Caug = c-e-g#.

(We will use the latter two chords only after we have mastered the world of the major and minor chords)

Remark: though the word 'triad' points to three, a triad may have more notes by doubling.
Fast procedure to make chords by counting keysteps:
The fastest procedure to make a chord, e.g. a major triad, is by counting of the keysteps (half steps or semitones are the common ways to put it, but the real things you are to deal with are keys).
If you want to make e.g. the chord G, you take the tone g (called the root) and add to it the tone 4 keysteps to the right (b), and another 3 keysteps (d). In less than a second you can create a major triad. In this case the chord G = g-b-d.

To make a major triad count 4+3 keysteps.
To make a minor triad count 3+4 keysteps.
To make a dim. triad count 3+3 keysteps.
To make an aug. triad count 4+4 keysteps.

The chords we make this way are in the root position, as the root is the bottom note. For the sake of fingering and sound we often modify it to an inversion, which means that another of the three notes of the triad are at the bottom, e.g.
C = c-e-g is in the root position,
C = e-g-c is in the 1st inversion,
C = g-c-e is in the 2nd inversion.
A key has an accompaniment with 3 chords, a fifth apart:
The fifth is the most important interval. It not only plays a part in the tuning of instruments but also in the relationship between chords.

Notably, three chords, a fifth apart, form a so called 'key' (the thing you hit on the piano is also called a key, but that's not we are talking about). As long as the accompaniment is restricted to these three chords, the music has a particular air. This structure is called a key.
The key of C:
For didactical reasons we will explain as much as possible with the key of C. This key is determined by the tree chords C, F and G. These chords are a fifth apart, which you can see when you write them in the order: F-C-G.
A song, accompanied by these three chords is made in the key of C.
It is a major key as all three chords are major triads.
HOMEWORK:

1) Practice in making chords (C, C#, D, etc) by counting keysteps. Do this in two steps:
-make the chord in the root position,
-arrange the notes in a practical position (e.g. an inversion).

2) Play in the key of C.
The accompaniment doesn't hit any black keys as it only plays notes from the chords C, F and G.
The melody however (the right hand) is allowed to hit any key, so also the black ones.
(If you sing, the melody can even use notes the piano doesn't have).
In spite if the restriction to the key of C, you must try to make acceptable music by variations in tempo, time, measure, rhythm, touch, etc. Play playfully.
Click here to here what I mean (MIDI, time 7:37).

The point is that you have to learn what a key implies. You can hear in the example the musical effect of the restriction to one key: how much I do my very best to make lively music, this restriction hinders the expression. Later on we will change keys during playing, but I can't explain then, how to do that, if you don't even know what the air of a key is. That's why it is important to exercise in the key of C only until you know all the aspects of it.
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