Once we are certain about the tones in the key of C Major, we build chords. Chords are created by selecting a root (a tone to build something from), and then selecting Every Other Note (EON). There are 7 tones in a Major scale; therefore, there are 7 triads (each tone becomes a root). Triads are 3 tone chords built by superimposing 3rds.
Note: We are using the terms note & tones interchangeably [EOT - Every Other Tone - not as memorable].
The C triad is made up of C-E-G, the D minor triad is made up of D-F-A, the E minor triad is made of E-G-B, & so on. Often, in chord scale playing, we substitute the V7 for the viio [the 3 tones of the diminished triad are the 3-5-7 of the V7].
We can use the math to see why chords are Major, minor, and diminished [dim or o]. Major triads have 4 half steps between the root and 3rd, & 3 half steps between 3rd and 5th. Minor triads have 3 half steps between the root and 3rd, & 4 half steps between 3rd and 5th [thus why we refer to the 3rd as a flat 3 in parallel thinking - it's one half step closer to the root]. Diminished triads have 3 half steps between the root and 3rd, & 3 half steps between 3rd and 5th [thus why we refer to the 3rd as a flat 3 & the 5th as a flat 5 in parallel thinking - both are one half step closer to the root].
Once we create a Major scale by filtering out 5 tones using the phone number [221-2221], we can then use that set of 7 tones to create chords. The tones in the key of C are C-D-E-F-G-A-B-C [221-2221 applied to C as 1]. C is the only Major scale with only naturals (all of the sharps/flats are skipped).
These 7 tones make up the key of C. In music, a key is a group of tones that point our ear to one of the tones as home. It is the tonal center.
Every tone of a scale can become a root of a chord. Since there are 7 tones in the Major scale, we end up with 7 chords.
To build chords, we select a tone, then select every other note [EON], until we have 3 tones. Three tone chords built in 3rds (EON) are called triads. Triads have a Root, a 3rd, & a 5th. There are 4 types of triads [Major, minor, diminished, augmented. The tones & chords in a key could be called a family & we'll use this term occasionally.
The tones (scale) & chords that are a part of C are called diatonic to it. Diatonic means 'across the tones'. It means what is 'within the key' or 'a part of it'. Diatonic tones are inside.
In a Major key, the I, IV, & V are Major, the ii, iii, & vi are minor, & the viio is diminished. This is consistent in all Major keys.
The process we have applied to the key of C will be the same for all 12 tones. Since the tones are equally spaced [one-half step], & we are using the same filter [221-2221], & the same process for building chords [EON], the relationships are the same for every key.